Sunday, September 19, 2021

09-19-2021-1447 - Bunsen detected previously unknown new blue spectral emission lines in samples of mineral water from Dürkheim.

Bunsen detected previously unknown new blue spectral emission lines in samples of mineral water from Dürkheim.

https://en.wikipedia.org/wiki/Robert_Bunsen

Cadet's fuming liquid was a red-brown oily liquid prepared in 1760 by the French chemist Louis Claude Cadet de Gassicourt (1731-1799) by the reaction of potassium acetate with arsenic trioxide.^[1] It consisted mostly of dicacodyl (((CH₃)₂As)₂) and cacodyl oxide (((CH₃)₂As)₂O). The reaction for forming the oxide was something like:

4 KCH₃COO + As₂O₃ → ((CH₃)₂As)₂O + 2 K₂CO₃ + 2 CO₂

These were the first organometallic substances prepared; as such, Cadet has been regarded as the father of organometallic chemistry.^[2]

This liquid develops white fumes when exposed to air, resulting in a pale flame producing carbon dioxide, water, and arsenic trioxide. It has a nauseating and very disagreeable garlic-like odor.

Around 1840, Robert Bunsen did much work on characterizing the compounds in the liquid and its derivatives. His research was important in the development of radical theory.

https://en.wikipedia.org/wiki/Cadet%27s_fuming_liquid

Gustav Robert Kirchhoff (German: [ˈkɪʁçhɔf]; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects.^[1]^[2]

He coined the term black-body radiation in 1862. Several different sets of concepts are named "Kirchhoff's laws" after him, concerning such diverse subjects as black-body radiation and spectroscopy, electrical circuits, and thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen.

Gustav Kirchhoff

Born	Gustav Robert Kirchhoff 12 March 1824 Königsberg, Province of East Prussia, Kingdom of Prussia (now Kaliningrad, Russia)
Died	17 October 1887 (aged 63) Berlin, Province of Brandenburg, Kingdom of Prussia, German Empire (now Germany)
Nationality	Prussian (1824–1871) German (1871–1887)
Alma mater	University of Königsberg
Known for	Kirchhoff's circuit laws Kirchhoff's law of thermal radiation Kirchhoff's laws of spectroscopy Kirchhoff's law of thermochemistry
Awards	Rumford medal (1862) Davy Medal (1877) Matteucci Medal (1877) Janssen Medal (1887)
Scientific career
Fields	Physics Chemistry
Institutions	University of Berlin University of Breslau University of Heidelberg
Doctoral advisor	Franz Ernst Neumann^{[citation needed]}
Notable students	Loránd Eötvös Edward Nichols Gabriel Lippmann^{[citation needed]} Dmitri Ivanovich Mendeleev Max Planck Jules Piccard Max Noether Heike Kamerlingh Onnes Ernst Schröder

https://en.wikipedia.org/wiki/Gustav_Kirchhoff

Jonas Ferdinand Gabriel Lippmann^[2] (16 August 1845 – 13 July 1921) was a Franco-Luxembourgish physicist and inventor, and Nobel laureate in physics for his method of reproducing colours photographically based on the phenomenon of interference.^[3]

Gabriel Lippmann

Born	Jonas Ferdinand Gabriel Lippmann 16 August 1845 Bonnevoie/Bouneweg, Luxembourg (since 1921 part of Luxembourg City)
Died	13 July 1921 (aged 75) SS France, Atlantic Ocean
Nationality	France
Alma mater	École Normale Supérieure
Known for	Lippmann colour photography Integral 3-D photography Lippmann electrometer
Awards	Nobel Prize for Physics(1908)
Scientific career
Fields	Physics
Institutions	Sorbonne
Doctoral advisor	Gustav Kirchhoff
Other academic advisors	Hermann von Helmholtz^[1]
Doctoral students	Marie Curie

Career[edit]

Lippmann made several important contributions to various branches of physics over the years.

Lippmann's electrometer (1872)

The capillary electrometer[edit]

One of Lippmann's early discoveries was the relationship between electrical and capillary phenomena which allowed him to develop a sensitive capillary electrometer, subsequently known as the Lippmann electrometer which was used in the first ECG machine. In a paper delivered to the Philosophical Society of Glasgow on 17 January 1883, John G. M'Kendrick described the apparatus as follows:

Lippmann's electrometer consists of a tube of ordinary glass, 1 metre long and 7 millimetres in diameter, open at both ends, and kept in the vertical position by a stout support. The lower end is drawn into a capillary point, until the diameter of the capillary is .005 of a millimetre. The tube is filled with mercury, and the capillary point is immersed in dilute sulphuric acid (1 to 6 of water in volume), and in the bottom of the vessel containing the acid there is a little more mercury. A platinum wire is put into connection with the mercury in each tube, and, finally, arrangements are made by which the capillary point can be seen with a microscope magnifying 250 diameters. Such an instrument is very sensitive; and Lippmann states that it is possible to determine a difference of potential so small as that of one 10,080th of a Daniell. It is thus a very delicate means of observing and (as it can be graduated by a compensation-method) of measuring minute electromotive forces.^[9]^[10]

Lippmann's PhD thesis, presented to the Sorbonne on 24 July 1875, was on electrocapillarity.^[11]

Piezoelectricity[edit]

In 1881, Lippmann predicted the converse piezoelectric effect.^[12]

Colour photography[edit]

A colour photograph made by Lippmann in the 1890s. It contains no pigments or dyes of any kind.

Above all, Lippmann is remembered as the inventor of a method for reproducing colours by photography, based on the interference phenomenon, which earned him the Nobel Prize in Physics for 1908.^[7]

In 1886, Lippmann's interest turned to a method of fixing the colours of the solar spectrum on a photographic plate. On 2 February 1891, he announced to the Academy of Sciences: "I have succeeded in obtaining the image of the spectrum with its colours on a photographic plate whereby the image remains fixed and can remain in daylight without deterioration." By April 1892, he was able to report that he had succeeded in producing colour images of a stained glass window, a group of flags, a bowl of oranges topped by a red poppy and a multicoloured parrot. He presented his theory of colour photography using the interference method in two papers to the Academy, one in 1894, the other in 1906.^[5]

A standing wave. The red dots are the wave nodes.

The interference phenomenon in optics occurs as a result of the wave propagation of light. When light of a given wavelength is reflected back upon itself by a mirror, standing waves are generated, much as the ripples resulting from a stone dropped into still water create standing waves when reflected back by a surface such as the wall of a pool. In the case of ordinary incoherent light, the standing waves are distinct only within a microscopically thin volume of space next to the reflecting surface.

Lippmann made use of this phenomenon by projecting an image onto a special photographic plate capable of recording detail smaller than the wavelengths of visible light. The light passed through the supporting glass sheet into a very thin and nearly transparent photographic emulsion containing sub microscopically small silver halide grains. A temporary mirror of liquid mercury in intimate contact reflected the light back through the emulsion, creating standing waves whose nodes had little effect while their antinodes created a latent image. After development, the result was a structure of laminae, distinct parallel layers composed of submicroscopic metallic silver grains, which was a permanent record of the standing waves. In each part of the image, the spacing of the laminae corresponded to the half-wavelengths of the light photographed.

The finished plate was illuminated from the front at a nearly perpendicular angle, using daylight or another source of white light containing the full range of wavelengths in the visible spectrum. At each point on the plate, light of approximately the same wavelength as the light which had generated the laminae was strongly reflected back toward the viewer. Light of other wavelengths which was not absorbed or scattered by the silver grains simply passed through the emulsion, usually to be absorbed by a black anti-reflection coating applied to the back of the plate after it had been developed. The wavelengths, and therefore the colours, of the light which had formed the original image were thus reconstituted and a full-colour image was seen.^[13]^[14]^[15]

In practice, the Lippmann process was not easy to use. Extremely fine-grained high-resolution photographic emulsions are inherently much less light-sensitive than ordinary emulsions, so long exposure times were required. With a lens of large aperture and a very brightly sunlit subject, a camera exposure of less than one minute was sometimes possible, but exposures measured in minutes were typical. Pure spectral colours reproduced brilliantly, but the ill-defined broad bands of wavelengths reflected by real-world objects could be problematic. The process did not produce colour prints on paper and it proved impossible to make a good duplicate of a Lippmann colour photograph by rephotographing it, so each image was unique. A very shallow-angled prism was usually cemented to the front of the finished plate to deflect unwanted surface reflections, and this made plates of any substantial size impractical. The lighting and viewing arrangement required to see the colours to best effect precluded casual use. Although the special plates and a plate holder with a built-in mercury reservoir were commercially available for a few years circa 1900, even expert users found consistent good results elusive and the process never graduated from being a scientifically elegant laboratory curiosity. It did, however, stimulate interest in the further development of colour photography.^[15]

Lippmann's process foreshadowed laser holography, which is also based on recording standing waves in a photographic medium. Denisyuk reflection holograms, often referred to as Lippmann-Bragg holograms, have similar laminar structures that preferentially reflect certain wavelengths. In the case of actual multiple-wavelength colour holograms of this type, the colour information is recorded and reproduced just as in the Lippmann process, except that the highly coherent laser light passing through the recording medium and reflected back from the subject generates the required distinct standing waves throughout a relatively large volume of space, eliminating the need for reflection to occur immediately adjacent to the recording medium. Unlike Lippmann colour photography, however, the lasers, the subject and the recording medium must all be kept stable to within one quarter of a wavelength during the exposure in order for the standing waves to be recorded adequately or at all.

Integral photography[edit]

In 1908, Lippmann introduced what he called "integral photography", in which a plane array of closely spaced, small, spherical lenses is used to photograph a scene, recording images of the scene as it appears from many slightly different horizontal and vertical locations. When the resulting images are rectified and viewed through a similar array of lenses, a single integrated image, composed of small portions of all the images, is seen by each eye. The position of the eye determines which parts of the small images it sees. The effect is that the visual geometry of the original scene is reconstructed, so that the limits of the array seem to be the edges of a window through which the scene appears life-size and in three dimensions, realistically exhibiting parallax and perspective shift with any change in the position of the observer.^[16] This principle of using numerous lenses or imaging apertures to record what was later termed a light field underlies the evolving technology of light-field cameras and microscopes.

When Lippmann presented the theoretical foundations of his "integral photography" in March 1908, it was impossible to accompany them with concrete results. At the time, the materials necessary for producing a lenticular screen with the proper optical qualities were lacking. In the 1920s, promising trials were made by Eugène Estanave, using glass Stanhope lenses, and by Louis Lumière, using celluloid.^[17] Lippmann's integral photography was the foundation of research on 3D and animated lenticular imagery and also on color lenticular processes.

Measurement of time[edit]

In 1895, Lippmann evolved a method of eliminating the personal equation in measurements of time, using photographic registration, and he studied the eradication of irregularities of pendulum clocks, devising a method of comparing the times of oscillation of two pendulums of nearly equal period.^[4]

The coelostat[edit]

Lippmann also invented the coelostat, an astronomical tool that compensated for the Earth's rotation and allowed a region of the sky to be photographed without apparent movement.^[4]

https://en.wikipedia.org/wiki/Gabriel_Lippmann

Baron Loránd Eötvös de Vásárosnamény (or Loránd Eötvös, pronounced [ˈloraːnd ˈøtvøʃ], Hungarian: vásárosnaményi báró Eötvös Loránd Ágoston; 27 July 1848 – 8 April 1919), also called Baron Roland von Eötvös in English literature,^[2] was a Hungarian physicist. He is remembered today largely for his work on gravitation and surface tension, and the invention of the torsion pendulum.

In addition to Eötvös Loránd University^[3] and the Eötvös Loránd Institute of Geophysics in Hungary, the Eötvös crater on the Moon,^[4] the asteroid 12301 Eötvösand the mineral lorándite also bear his name.

Loránd Eötvös
Eötvös in 1912
Born	27 July 1848 Buda, Kingdom of Hungary
Died	8 April 1919 (aged 70) Budapest, Hungarian Soviet Republic
Nationality	Hungarian
Alma mater	University of Heidelberg
Known for	Eötvös experiment Eötvös rule Eötvös pendulum
Spouse(s)	Gizella Horvát
Children	Jolán Rolanda Ilona
Parent(s)	József Eötvös Agnes Rosty de Barkócz
Scientific career
Fields	Physics
Institutions	University of Budapest
Doctoral advisor	Hermann Helmholtz^[1]

Life[edit]

Born in 1848, the year of the Hungarian revolution, Eötvös was the son of the Baron József Eötvös de Vásárosnamény (1813–1871), a well-known poet, writer, and liberal politician, who was cabinet minister at the time, and played an important part in 19th century Hungarian intellectual and political life. His mother was the Hungarian noble lady Agnes Rosty de Barkócz (1825–1913), member of the illustrious noble family Rosty de Barkócz that originally hailed from the Vas county, and through this, he descended from the ancient medieval Hungarian noble Perneszy family, which died out in the 18th century. Loránd's uncle was Pál Rosty de Barkócz (1830–1874) was a Hungarian nobleman, photographer, explorer, who visited Texas, New Mexico, Mexico, Cuba and Venezuela between 1857 and 1859.

Loránd Eötvös first studied law, but soon switched to physics and went abroad to study in Heidelberg and Königsberg. After earning his doctorate, he became a university professor in Budapest and played a leading part in Hungarian science for almost half a century. He gained international recognition first by his innovative work on capillarity, then by his refined experimental methods and extensive field studies in gravity.

Eötvös is remembered today for his experimental work on gravity, in particular his study of the equivalence of gravitational and inertial mass (the so-called weak equivalence principle) and his study of the gravitational gradient on the Earth's surface. The weak equivalence principle plays a prominent role in relativity theoryand the Eötvös experiment was cited by Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity. Measurements of the gravitational gradient are important in applied geophysics, such as the location of petroleum deposits. The CGS unit for gravitational gradient is named the eotvos in his honor.

From 1886 until his death, Loránd Eötvös researched and taught in the University of Budapest, which in 1950 was renamed after him (Eötvös Loránd University).

Eötvös is buried in the Kerepesi Cemetery in Budapest, Hungary.^[5]

Torsion balance[edit]

A variation of the earlier invention, the torsion balance, the Eötvös pendulum, designed by Hungarian Baron Loránd Eötvös, is a sensitive instrument for measuring the density of underlying rock strata. The device measures not only the direction of force of gravity, but the change in the force of gravity's extent in the horizontal plane. It determines the distribution of masses in the Earth's crust. The Eötvös torsion balance, an important instrument of geodesy and geophysics throughout the whole world, studies the Earth's physical properties. It is used for mine exploration, and also in the search for minerals, such as oil, coal and ores. The Eötvös pendulum was never patented, but after the demonstration of its accuracy and numerous visits to Hungary from abroad, several instruments were exported worldwide, and the richest oilfields in the United States were discovered by using it. The Eötvös pendulum was used to prove the equivalence of the inertial mass and the gravitational mass accurately, as a response to the offer of a prize. This equivalence was used later by Albert Einstein in setting out the theory of general relativity.

This is how Eötvös describes his balance:

It was just a simple, straight stick that I used as instrument, specially loaded at both ends, enclosed into a metal sheath to protect it from the wind and temperature changes. Upon this stick every single mass, be it near or far, exerts a directing force; but the wire upon which it hangs resists, and whilst resisting it twists, with the degree of this twist showing us the exact magnitude of the forces acting upon the stick. This is a Coulomb balance, and that is all there is to it. It is simple, like the flute of Hamlet, you only have to know how to play on it, and just like the musician who can delight you with splendid variations, the physicist can, on this balance, with no less delight determine the finest variations of gravity. This way we can peer into such depth of the crust of the Earth, that neither our eyes, nor our longest drills could reach.^{[citation needed]}

One of Eötvös' assistants who later became a noted scientist was Radó von Kövesligethy.

Honors[edit]

To honor Eötvös, a postage stamp was issued by Hungary on 1 July 1932.^[6] Another stamp was issued on 27 July 1948 to commemorate the centenary of the birth of the physicist.^[7] Hungary issued a postage stamp on 31 January 1991.^[8]

References[edit]

^ Physics Tree – Hermann von Helmholtz Family Tree
^ L. Bod, E. Fishbach, G. Marx, and Maria Náray-Ziegler: One hundred years of the Eötvös experiment, – Acta Physica Hungarica 69/3-4 (1991) 335–355
^ Brief History of ELTE, Eötvös Loránd University, archived from the original on 7 May 2016, retrieved 7 May 2016
^ Pickover, Clifford (2008), Archimedes to Hawking: Laws of Science and the Great Minds Behind Them, Oxford University Press, p. 383, ISBN 9780199792689.
^ See this site for a photograph of his gravesite.
^ colnect.com/en/stamps/stamp/141647-Baron_Loránd_Eötvös_1848-1919_physicist-Personalities-Hungary.
^ colnect.com/en/stamps/stamp/179845-Baron_Lóránd_Eötvös_1848-1919_physicist-Lóránd_Eötvös-Hungary
^ colnect.com/en/stamps/stamp/181792-Lóránd_Eötvös-People-Hungary

eotvos
Unit system	Non-SI metric unit
Unit of	Linear acceleration density
Symbol	E
Named after	Loránd Eötvös
Derivation	10⁻⁹ Gal/cm
Conversions
1 E in ...	... is equal to ...
CGS base units	10⁻⁹ s⁻²
SI base units	10⁻⁹ s⁻²

Ernst Schröder
Ernst Schröder
Born	25 November 1841 Mannheim, Germany
Died	16 June 1902 (aged 60) Karlsruhe, Germany
Nationality	German
Scientific career
Fields	Mathematics

Heike Kamerlingh Onnes

Born	Heike Kamerlingh Onnes 21 September 1853 Groningen, Netherlands
Died	21 February 1926 (aged 72) Leiden, Netherlands
Nationality	Netherlands
Alma mater	Heidelberg University University of Groningen
Known for	Liquid helium Onnes-effect Superconductivity Virial equation of state Coining the term “enthalpy” Kamerlingh Onnes Award
Awards	Matteucci Medal (1910) Rumford Medal (1912) Nobel Prize in Physics (1913) Franklin Medal (1915)
Scientific career
Fields	Physics
Institutions	University of Leiden Delft Polytechnic
Doctoral advisor	Rudolf Adriaan Mees
Other academic advisors	Robert Bunsen Gustav Kirchhoff Johannes Bosscha
Doctoral students	Jacob Clay Wander de Haas Gilles Holst Johannes Kuenen Pieter Zeeman
Influences	Johannes Diderik van der Waals
Influenced	Willem Hendrik Keesom Cryogenics

University of Leiden[edit]

From 1882 to 1923 Kamerlingh Onnes served as professor of experimental physics at the University of Leiden. In 1904 he founded a very large cryogenicslaboratory and invited other researchers to the location, which made him highly regarded in the scientific community. The laboratory is known now as Kamerlingh Onnes Laboratory.^[4] Only one year after his appointment as professor he became member of the Royal Netherlands Academy of Arts and Sciences.^[5]

Liquefaction of helium[edit]

Commemorative plaque in Leiden

On 10 July 1908, he was the first to liquefy helium, using several precooling stages and the Hampson–Linde cycle based on the Joule–Thomson effect. This way he lowered the temperature to the boiling point of helium (−269 °C, 4.2 K). By reducing the pressure of the liquid helium he achieved a temperature near 1.5 K. These were the coldest temperatures achieved on earth at the time. The equipment employed is at the Museum Boerhaave in Leiden.^[4]

Superconductivity[edit]

In 1911 Kamerlingh Onnes measured the electrical conductivity of pure metals (mercury, and later tin and lead) at very low temperatures. Some scientists, such as William Thomson (Lord Kelvin), believed that electrons flowing through a conductor would come to a complete halt or, in other words, metal resistivity would become infinitely large at absolute zero. Others, including Kamerlingh Onnes, felt that a conductor's electrical resistance would steadily decrease and drop to nil. Augustus Matthiessen said that when the temperature decreases, the metal conductivity usually improves or in other words, the electrical resistivity usually decreases with a decrease of temperature.^[6]^[7]

On 8 April 1911, Kamerlingh Onnes found that at 4.2 K the resistance in a solid mercury wire immersed in liquid helium suddenly vanished. He immediately realized the significance of the discovery (as became clear when his notebook was deciphered a century later).^[8] He reported that "Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconductive state". He published more articles about the phenomenon, initially referring to it as "supraconductivity" and, only later adopting the term "superconductivity".

Kamerlingh Onnes received widespread recognition for his work, including the 1913 Nobel Prize in Physics for (in the words of the committee) "his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium".

https://en.wikipedia.org/wiki/Heike_Kamerlingh_Onnes

https://en.wikipedia.org/wiki/Superfluidity

https://en.wikipedia.org/wiki/Superfluid_helium-4

https://en.wikipedia.org/wiki/Hydrogen_fuel

https://en.wikipedia.org/wiki/Vapor-compression_refrigeration

https://en.wikipedia.org/wiki/Lossless_compression

https://en.wikipedia.org/wiki/Infinite_divisibility

https://en.wikipedia.org/wiki/Shear_force

https://en.wikipedia.org/wiki/Compression_(physics)

https://en.wikipedia.org/wiki/Tension_(physics)

https://en.wikipedia.org/wiki/Trapped_ion_quantum_computer

https://en.wikipedia.org/wiki/Quantum_computing

https://en.wikipedia.org/wiki/Coupling_(physics)

https://en.wikipedia.org/wiki/Oscillation

https://en.wikipedia.org/wiki/Hooke%27s_law

https://en.wikipedia.org/wiki/Christiaan_Huygens

https://en.wikipedia.org/wiki/Aromatic_ring_current

https://en.wikipedia.org/wiki/Magnetic_susceptibility

https://en.wikipedia.org/wiki/Ferromagnetism

https://en.wikipedia.org/wiki/scalar

https://en.wikipedia.org/wiki/surface

https://en.wikipedia.org/wiki/tension

https://en.wikipedia.org/wiki/tensor

https://en.wikipedia.org/wiki/dimension

https://en.wikipedia.org/wiki/plane

https://en.wikipedia.org/wiki/vertical

https://en.wikipedia.org/wiki/pressure

https://en.wikipedia.org/wiki/acceleration

https://en.wikipedia.org/wiki/angular

https://en.wikipedia.org/wiki/dihedral_angle

https://en.wikipedia.org/wiki/Ferromagnetic_resonance

https://en.wikipedia.org/wiki/Eddy_current

https://en.wikipedia.org/wiki/Antiferromagnetism#antiferromagnetic_materials

https://en.wikipedia.org/wiki/Geometrical_frustration

https://en.wikipedia.org/wiki/Saturation_(magnetic)

https://en.wikipedia.org/wiki/Coercivity

https://en.wikipedia.org/wiki/Tensor

https://en.wikipedia.org/wiki/Superconductivity

https://en.wikipedia.org/wiki/Gaussian_units

https://en.wikipedia.org/wiki/Electric_susceptibility

https://en.wikipedia.org/wiki/Magnetic_field

https://en.wikipedia.org/wiki/Permeability_(electromagnetism)#Relative_permeability_and_magnetic_susceptibility

https://en.wikipedia.org/wiki/Dimensionless_quantity

https://en.wikipedia.org/wiki/Superconductivity

https://en.wikipedia.org/wiki/Kinetic_theory_of_gases

https://en.wikipedia.org/wiki/Permeability_(electromagnetism)#Relative_permeability_and_magnetic_susceptibility

https://en.wikipedia.org/wiki/Magnetic_susceptibility

https://en.wikipedia.org/wiki/Cyclophane

https://en.wikipedia.org/wiki/Proton_nuclear_magnetic_resonance

https://en.wikipedia.org/wiki/Non-coordinating_anion

https://en.wikipedia.org/wiki/Tetrakis(3,5-bis(trifluoromethyl)phenyl)borate

https://en.wikipedia.org/wiki/Faraday_effect

https://en.wikipedia.org/wiki/Axial_chirality

Karl Johann Freudenberg ForMemRS^[1] (29 January 1886 Weinheim, Baden – 3 April 1983 Weinheim) was a German chemist who did early seminal work on the absolute configurations to carbohydrates, terpenes, and steroids, and on the structure of cellulose (first correct formula published, 1928) and other polysaccharides, and on the nature, structure, and biosynthesis of lignin. The Research Institute for the Chemistry of Wood and Polysaccharides at the University of Heidelberg was created for him in the mid to late 1930s, and he led this until 1969.^[2]

Life[edit]

Freudenberg studied at Bonn University in 1904, and the University of Berlin from 1907 to 1910, where he studied with Emil Fischer. In July 1910, he married Doris Nieden; they had five children.^[3] His grandfather Carl Johann Freudenberg was a tanner and businessman, who in 1849, with Heinrich Christian Heintze, founded Freudenberg Group.

Freudenberg was a professor at University of Freiburg in 1921, at Heidelberg University in 1922, at Karlsruhe University from 1926 to 1956, and director of the Research Institute at the University of Heidelberg, noted above, from 1936 to 1969.^[4]

Works[edit]

Chemie der natürlichen Gerbstoffe (1920) [studies on tannins and their relations to catechins]
Stereochemie (1933)
Tannin, Cellulose, Lignin (1933)

https://en.wikipedia.org/wiki/Karl_Freudenberg

https://en.wikipedia.org/wiki/Christiaan_Huygens

https://en.wikipedia.org/wiki/CRC_Handbook_of_Chemistry_and_Physics

Johannes Diderik van der Waals (Dutch pronunciation: [joːˈɦɑnəz ˈdidərɪk fɑn dər ˈʋaːls] (listen)^{[note 1]}; 23 November 1837 – 8 March 1923) was a Dutch theoretical physicist and thermodynamicist famous for his pioneering work on the equation of state for gases and liquids. Van der Waals started his career as a school teacher. He became the first physics professor of the University of Amsterdam when in 1877 the old Athenaeum was upgraded to Municipal University. Van der Waals won the 1910 Nobel Prize in physics for his work on the equation of state for gases and liquids.^[1]

His name is primarily associated with the Van der Waals equation of state that describes the behavior of gases and their condensation to the liquid phase. His name is also associated with Van der Waals forces (forces between stable molecules),^[2] with Van der Waals molecules (small molecular clusters bound by Van der Waals forces), and with Van der Waals radii (sizes of molecules). As James Clerk Maxwell said, "there can be no doubt that the name of Van der Waals will soon be among the foremost in molecular science."^[3]

In his 1873 thesis, Van der Waals noted the non-ideality of real gases and attributed it to the existence of intermolecular interactions. He introduced the first equation of state derived by the assumption of a finite volume occupied by the constituent molecules.^[4] Spearheaded by Ernst Mach and Wilhelm Ostwald, a strong philosophical current that denied the existence of molecules arose towards the end of the 19th century. The molecular existence was considered unproven and the molecular hypothesis unnecessary. At the time Van der Waals's thesis was written (1873), the molecular structure of fluids had not been accepted by most physicists, and liquid and vapor were often considered as chemically distinct. But Van der Waals's work affirmed the reality of molecules and allowed an assessment of their size and attractive strength. His new formula revolutionized the study of equations of state. By comparing his equation of state with experimental data, Van der Waals was able to obtain estimates for the actual size of molecules and the strength of their mutual attraction.^[5]

The effect of Van der Waals's work on molecular physics in the 20th century was direct and fundamental.^[6] By introducing parameters characterizing molecular size and attraction in constructing his equation of state, Van der Waals set the tone for modern molecular science. That molecular aspects such as size, shape, attraction, and multipolar interactions should form the basis for mathematical formulations of the thermodynamic and transport properties of fluids is presently considered an axiom.^[7] With the help of the Van der Waals's equation of state, the critical-point parameters of gases could be accurately predicted from thermodynamic measurements made at much higher temperatures. Nitrogen, oxygen, hydrogen, and helium subsequently succumbed to liquefaction. Heike Kamerlingh Onnes was significantly influenced by the pioneering work of Van der Waals. In 1908, Onnes became the first to make liquid helium; this led directly to his 1911 discovery of superconductivity.^[8]

https://en.wikipedia.org/wiki/Johannes_Diderik_van_der_Waals

Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century".^[1] He was the father of Emmy Noether.

https://en.wikipedia.org/wiki/Max_Noether

Jules Piccard, also known as Julius Piccard (20 September 1840, in Lausanne – 11 April 1933, in Lausanne) was a Swiss chemist. He was the father of twins Auguste Piccard (1884–1962) and Jean Felix Piccard (1884–1963), both renowned balloonists.

He studied chemistry at the University of Heidelberg as a student of Robert Bunsen, receiving his doctorate in 1862. Shortly afterwards, he obtained his habilitation at the polytechnical institute in Zürich. From 1869 to 1903 he was a professor of chemistry at the University of Basel.^[1]^[2]

He made contributions in the field of food chemistry and in his research of cantharidin, dinitrocresol, chrysin and resorcinol.^[2]^[3] He is also known for his studies involving the atomic weight of rubidium.^[4]

https://en.wikipedia.org/wiki/Jules_Piccard

Justus Freiherr von Liebig^[2] (12 May 1803 – 18 April 1873)^[3] was a German scientist who made major contributions to agricultural and biological chemistry, and is considered one of the principal founders of organic chemistry.^[4] As a professor at the University of Giessen, he devised the modern laboratory-oriented teaching method, and for such innovations, he is regarded as one of the greatest chemistry teachers of all time.^[5] He has been described as the "father of the fertilizerindustry" for his emphasis on nitrogen and trace minerals as essential plant nutrients, and his formulation of the law of the minimum, which described how plant growth relied on the scarcest nutrient resource, rather than the total amount of resources available.^[6] He also developed a manufacturing process for beef extracts,^[7] and with his consent a company, called Liebig Extract of Meat Company, was founded to exploit the concept; it later introduced the Oxo brand beef bouillon cube. He popularized an earlier invention for condensing vapors, which came to be known as the Liebig condenser.^[8]

https://en.wikipedia.org/wiki/Justus_von_Liebig

Eilhard Mitscherlich (German pronunciation: [ˈaɪ̯lhaʁt ˈmɪtʃɐlɪç];^[1]^[2] 7 January 1794 – 28 August 1863) was a German chemist, who is perhaps best remembered today for his discovery of the phenomenon of crystallographic isomorphism in 1819.

https://en.wikipedia.org/wiki/Eilhard_Mitscherlich

Friedlieb Ferdinand Runge (8 February 1794 – 25 March 1867) was a German analytical chemist. Runge identified the mydriatic (pupil dilating) effects of belladonna (deadly nightshade) extract, identified caffeine, and discovered the first coal tar dye (aniline blue).

https://en.wikipedia.org/wiki/Friedlieb_Ferdinand_Runge

Johann Friedrich Ludwig Hausmann (22 February 1782, Hannover – 26 December 1859, Göttingen) was a German mineralogist.^[1]

https://en.wikipedia.org/wiki/Johann_Friedrich_Ludwig_Hausmann

Johann Carl Friedrich Gauss (/ɡaʊs/; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] (listen);^[1]^[2] Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science.^[3] Sometimes referred to as the Princeps mathematicorum^[4] (Latin for '"the foremost of mathematicians"') and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians.^[5]

https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions.

Most fundamentally, planar chirality is a mathematical term, finding use in chemistry, physics and related physical sciences, for example, in astronomy, optics and metamaterials. Recent occurrences in latter two fields are dominated by microwave and terahertz applications as well as micro- and nanostructured planar interfaces for infrared and visible light.

A planar chiral derivative of ferrocene, used for kinetic resolution of some racemic secondary alcohols^[1]

https://en.wikipedia.org/wiki/Planar_chirality#Planar_chirality_in_chemistry

A cyclophane is a hydrocarbon consisting of an aromatic unit (typically a benzene ring) and an aliphatic chain that forms a bridge between two non-adjacent positions of the aromatic ring. More complex derivatives with multiple aromatic units and bridges forming cagelike structures are also known. Cyclophanes are well-studied in organic chemistry because they adopt unusual chemical conformations due to build-up of strain.

Basic cyclophane types are [n]metacyclophanes (I) in scheme 1, [n]paracyclophanes (II) and [n.n']cyclophanes (III). The prefixes meta and paracorrespond to the usual arene substitution patterns and n refers to the number of carbon atoms making up the bridge.

Structure[edit]

Paracyclophanes adopt the boat conformation normally observed in cyclohexanes but are still able to retain aromaticity. The smaller the value of n the larger the deviation from aromatic planarity. In '[6]paracyclophane' which is one of the smallest, yet stable, cyclophanes X-ray crystallography shows that the aromatic bridgehead carbon atom makes an angle of 20.5° with the plane. The benzyl carbons deviate by another 20.2°. The carbon-to-carbon bond length alternation has increased from 0 for benzene to 39 pm.^[1]^[2]

In organic reactions [6]cyclophane tends to react as a diene derivative and not as an arene. With bromine it gives 1,4-addition and with chlorine the 1,2-addition product forms.

Yet the proton NMR spectrum displays the aromatic protons and their usual deshielded positions around 7.2 ppm and the central methylene protons in the aliphatic bridge are even severely shielded to a position of around - 0.5 ppm, that is, even shielded compared to the internal reference tetramethylsilane. With respect to the diamagnetic ring current criterion for aromaticity this cyclophane is still aromatic.

In-cyclophanes, pyridinophanes and superphanes.

One particular research field in cyclophanes involves probing just how close atoms can get above the center of an aromatic nucleus.^[3] In so-called in-cyclophanes with part of the molecule forced to point inwards one of the closest hydrogen to arene distances experimentally determined is just 168 picometers (pm).

A non-bonding nitrogen to arene distance of 244 pm is recorded for a pyridinophane and in the unusual superphane the two benzene rings are separated by a mere 262 pm. Other representative of this group are in-methylcyclophanes,^[4] in-ketocyclophanes^[5] and in,in-Bis(hydrosilane).^[6]

Synthetic methods[edit]

[6]paracyclophane can be synthesized^[7]^[8] in the laboratory by a Bamford-Stevens reaction with spiro ketone 1 in scheme 3 rearranging in a pyrolysis reaction through the carbene intermediate 4. The cyclophane can be photochemically converted to the Dewar benzene 6 and back again by application of heat. A separate route to the Dewar form is by a cationic silver perchlorate induced rearrangement reaction of the bicyclopropenyl compound 7.

Metaparacyclophanes constitute another class of cyclophans like the [14][14]metaparacyclophane^[9] in scheme 4^[10] featuring a in-situ Ramberg-Bäcklund Reaction converting the sulfone 3 to the alkene 4.

Naturally occurring cyclophanes[edit]

Despite carrying strain, the cyclophane motif does exist in nature. One example of a metacyclophane is cavicularin.

Haouamine A is a paracyclophane found in a certain species of tunicate. Because of its potential application as an anticancer drug it is also available from total synthesis via an alkyne - pyrone Diels-Alder reaction in the crucial step with expulsion of carbon dioxide (scheme 5).^[11]

In this compound the deviation from planarity is 13° for the benzene ring and 17° for the bridgehead carbons.^[12] An alternative cyclophane formation strategy in scheme 6^[13] was developed based on aromatization of the ring well after the formation of the bridge.

Two additional types of cyclophanes were discovered in nature when they were isolated from two species of cyanobacteria from the family Nostocacae.^[14] These two classes of cyclophanes are both [7,7] paracyclophanes and were named after the species from which they were extracted: cylindrocyclophanes from Cylindrospermum lichenforme and nostocyclophanes from Nostoc linckia.

[n.n]Paracyclophanes[edit]

A well exploited member of the [n.n]paracyclophane family is [2.2]paracyclophane.^[15]^[16] One method for its preparation is by a 1,6-Hofmann elimination:^[17]

The [2.2]paracyclophane-1,9-diene has been applied in ROMP to a poly(p-phenylene vinylene) with alternating cis-alkene and trans-alkene bonds using Grubbs' second generation catalyst:^[18]

Scheme 8. 2.2-paracyclophane-1,9-diene polymerization

The driving force for ring-opening and polymerization is strain relief. The reaction is believed to be a living polymerization due to the lack of competing reactions.

Because the two benzene rings are in close proximity this cyclophane type also serves as guinea pig for photochemical dimerization reactions as illustrated by this example:^[19]

Formation of Octahedrane by Photochemical Dimerization of Benzene

The product formed has an octahedrane skeleton. When the amine group is replaced by a methylene group no reaction takes place: the dimerization requires through-bond overlap between the aromatic pi electrons and the sigma electrons in the C-N bond in the reactants LUMO.

Cycloparaphenylenes[edit]

[n]Cycloparaphenylenes ([n]CPPs) consist of cyclic all-para-linked phenyl groups.^[20] This compound class is of some interest as potential building block for nanotubes. Members have been reported with 18, 12, 10, 9, 8, 7, 6 and 5 phenylenes. These molecules are unique in that they contain no aliphatic linker group that places strain on the aromatic unit. Instead the entire molecule is a strained aromatic unit.

Phanes[edit]

Generalization of cyclophanes led to the concept of phanes in the IUPAC nomenclature.

The systematic phane nomenclature name for e.g. [14]metacyclophane is 1(1,3)-benzenacyclopentadecaphane;
and [2.2']paracyclophane (or [2.2]paracyclophane) is 1,4(1,4)-dibenzenacyclohexaphane.

References

https://en.wikipedia.org/wiki/Cyclophane

An aromatic ring current is an effect observed in aromatic molecules such as benzene and naphthalene. If a magnetic field is directed perpendicular to the plane of the aromatic system, a ring current is induced in the delocalized π electrons of the aromatic ring.^[1] This is a direct consequence of Ampère's law; since the electrons involved are free to circulate, rather than being localized in bonds as they would be in most non-aromatic molecules, they respond much more strongly to the magnetic field.

The ring current creates its own magnetic field. Outside the ring, this field is in the same direction as the externally applied magnetic field; inside the ring, the field counteracts the externally applied field. As a result, the net magnetic field outside the ring is greater than the externally applied field alone, and is less inside the ring.

Aromatic ring currents are relevant to NMR spectroscopy, as they dramatically influence the chemical shifts of ¹H nuclei in aromatic molecules.^[2] The effect helps distinguish these nuclear environments and is therefore of great use in molecular structure determination. In benzene, the ring protons experience deshieldingbecause the induced magnetic field has the same direction outside the ring as the external field and their chemical shift is 7.3 ppm compared to 5.6 for the vinylicproton in cyclohexene. In contrast any proton inside the aromatic ring experiences shielding because both fields are in opposite direction. This effect can be observed in cyclooctadecanonaene ([18]annulene) with 6 inner protons at −3 ppm.

The situation is reversed in antiaromatic compounds. In the dianion of [18]annulene the inner protons are strongly deshielded at 20.8 ppm and 29.5 ppm with the outer protons significantly shielded (with respect to the reference) at −1.1 ppm. Hence a diamagnetic ring current or diatropic ring current is associated with aromaticity whereas a paratropic ring current signals antiaromaticity.

A similar effect is observed in three-dimensional fullerenes; in this case it is called a sphere current.^[3]

A diagram of an aromatic ring current. B₀is the applied magnetic field, the red arrow indicating its direction. The orange ring shows the direction of the ring current, and the purple rings show the direction of the inducedmagnetic field.

https://en.wikipedia.org/wiki/Aromatic_ring_current

Proton nuclear magnetic resonance (proton NMR, hydrogen-1 NMR, or ¹H NMR) is the application of nuclear magnetic resonancein NMR spectroscopy with respect to hydrogen-1 nuclei within the molecules of a substance, in order to determine the structure of its molecules.^[1] In samples where natural hydrogen (H) is used, practically all the hydrogen consists of the isotope ¹H (hydrogen-1; i.e. having a proton for a nucleus).

Simple NMR spectra are recorded in solution, and solvent protons must not be allowed to interfere. Deuterated (deuterium = ²H, often symbolized as D) solvents especially for use in NMR are preferred, e.g. deuterated water, D₂O, deuterated acetone, (CD₃)₂CO, deuterated methanol, CD₃OD, deuterated dimethyl sulfoxide, (CD₃)₂SO, and deuterated chloroform, CDCl₃. However, a solvent without hydrogen, such as carbon tetrachloride, CCl₄ or carbon disulfide, CS₂, may also be used.

Historically, deuterated solvents were supplied with a small amount (typically 0.1%) of tetramethylsilane (TMS) as an internal standardfor calibrating the chemical shifts of each analyte proton. TMS is a tetrahedral molecule, with all protons being chemically equivalent, giving one single signal, used to define a chemical shift = 0 ppm. ^[2] It is volatile, making sample recovery easy as well. Modern spectrometers are able to reference spectra based on the residual proton in the solvent (e.g. the CHCl₃, 0.01% in 99.99% CDCl₃). Deuterated solvents are now commonly supplied without TMS.

Deuterated solvents permit the use of deuterium frequency-field lock (also known as deuterium lock or field lock) to offset the effect of the natural drift of the NMR's magnetic field $B_{0}$ . In order to provide deuterium lock, the NMR constantly monitors the deuterium signal resonance frequency from the solvent and makes changes to the $B_{0}$ to keep the resonance frequency constant.^[3] Additionally, the deuterium signal may be used to accurately define 0 ppm as the resonant frequency of the lock solvent and the difference between the lock solvent and 0 ppm (TMS) are well known.

Proton NMR spectra of most organic compounds are characterized by chemical shifts in the range +14 to -4 ppm and by spin-spin coupling between protons. The integration curve for each proton reflects the abundance of the individual protons.

Simple molecules have simple spectra. The spectrum of ethyl chloride consists of a triplet at 1.5 ppm and a quartet at 3.5 ppm in a 3:2 ratio. The spectrum of benzene consists of a single peak at 7.2 ppm due to the diamagnetic ring current.

Together with carbon-13 NMR, proton NMR is a powerful tool for molecular structure characterization.

Example ¹H NMR spectrum (1-dimensional) of a mixture of menthol enantiomers plotted as signal intensity (vertical axis) vs. chemical shift (in ppm on is of the horizontal axis). Signals from spectrum have been assigned hydrogen atom groups (a through j) from the structure shown at upper left.

https://en.wikipedia.org/wiki/Proton_nuclear_magnetic_resonance

Pyrones or pyranones are a class of heterocyclic chemical compounds. They contain an unsaturated six-membered ring containing one oxygen atom and a ketone functional group.^[1]There are two isomers denoted as 2-pyrone and 4-pyrone. The 2-pyrone (or α-pyrone) structure is found in nature as part of the coumarin ring system. 4-Pyrone (or γ-pyrone) is found in some natural chemical compounds such as chromone, maltol and kojic acid.

List of nanostructures[edit]

https://en.wikipedia.org/wiki/Nanostructure

Phanes are abstractions of highly complex organic molecules introduced for simplification of the naming of these highly complex molecules.

Systematic nomenclature of organic chemistry consists of building a name for the structure of an organic compound by a collection of names of its composite parts but describing also its relative positions within the structure. Naming information is summarised by IUPAC:^[1]^[2]^[3]

"Phane nomenclature is a new method for building names for organic structures by assembling names that describe component parts of a complex structure. It is based on the idea that a relatively simple skeleton for a parent hydride can be modified by an operation called 'amplification', a process that replaces one or more special atoms (superatoms) of a simplified skeleton by multiatomic structures".

Whilst the cyclophane name describes only a limited number of sub-structures of benzene rings interconnected by individual atoms or chains, 'phane' is a class name which includes others, hence heterocyclic rings as well. Therefore, the various cyclophanes are perfectly good for the general class of phanes as well keeping in mind that the cyclic structures in phanes could have much greater diversity.

References[edit]

^ International Union of Pure and Applied Chemistry - Recommendations on Organic & Biochemical Nomenclature, Symbols & Terminology etc. http://www.chem.qmul.ac.uk/iupac/ World Wide Web material prepared by G. P. Moss, Department of Chemistry, Queen Mary University of London, Mile End Road, London, E1 4NS, UKg.p.moss@qmul.ac.uk
^ International Union of Pure and Applied Chemistry - Organic Chemistry Division - Commission on nomenclature of organic chemistry http://www.chem.qmul.ac.uk/iupac/phane/ Archived 2006-07-03 at the Wayback Machine Phane Nomenclature Part I: Phane Parent Names IUPAC Recommendations 1998 Prepared for publication by W. H. Powell 1436 Havencrest Ct, Columbus, OH 43220-3841, USA
^ Phane Nomenclature Part II: Modification of the Degree of Hydrogenation and Substitution Derivatives of Phane Parent Hydrides

https://en.wikipedia.org/wiki/Phanes_(organic_chemistry)

https://en.wikipedia.org/wiki/Charles_Blagden

https://en.wikipedia.org/wiki/Antoine_Lavoisier

https://en.wikipedia.org/wiki/Category:Independent_scientists

https://en.wikipedia.org/wiki/Category:Executed_scientists

https://en.wikipedia.org/wiki/Rose_Center_for_Earth_and_Space

https://en.wikipedia.org/wiki/Nazis_at_the_Center_of_the_Earth

https://en.wikipedia.org/wiki/Earth%27s_inner_core

https://en.wikipedia.org/wiki/Geographical_centre_of_Earth

https://en.wikipedia.org/wiki/Equirectangular_projection

https://en.wikipedia.org/wiki/Earth

Spontaneous; Center; Symmetry

In geometry, to translate a geometric figure is to move it from one place to another without rotating it. A translation "slides" a thing by a: T_a(p) = p + a.

In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariant under discrete translation.

Analogously an operator A on functions is said to be translationally invariant with respect to a translation operator $T_{\delta }$ if the result after applying A doesn't change if the argument function is translated. More precisely it must hold that

\forall \delta \ Af=A(T_{\delta }f).\,

Laws of physics are translationally invariant under a spatial translation if they do not distinguish different points in space. According to Noether's theorem, space translational symmetry of a physical system is equivalent to the momentum conservation law.

Translational symmetry of an object means that a particular translation does not change the object. For a given object, the translations for which this applies form a group, the symmetry group of the object, or, if the object has more kinds of symmetry, a subgroup of the symmetry group.

https://en.wikipedia.org/wiki/Translational_symmetry

Many powerful theories in physics are described by Lagrangians that are invariant under some symmetry transformation groups.

Gauge theories are important as the successful field theories explaining the dynamics of elementary particles. Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon, three weak bosons and eight gluons.

Gauge theories are also important in explaining gravitation in the theory of general relativity. Its case is somewhat unusual in that the gauge field is a tensor, the Lanczos tensor. Theories of quantum gravity, beginning with gauge gravitation theory, also postulate the existence of a gauge boson known as the graviton. Gauge symmetries can be viewed as analogues of the principle of general covariance of general relativity in which the coordinate system can be chosen freely under arbitrary diffeomorphisms of spacetime. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description of the system. An alternative theory of gravitation, gauge theory gravity, replaces the principle of general covariance with a true gauge principle with new gauge fields.

Historically, these ideas were first stated in the context of classical electromagnetism and later in general relativity. However, the modern importance of gauge symmetries appeared first in the relativistic quantum mechanics of electrons – quantum electrodynamics, elaborated on below. Today, gauge theories are useful in condensed matter, nuclear and high energy physicsamong other subfields.

https://en.wikipedia.org/wiki/Gauge_theory

Standard Model of Particle Physics. The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces. It also depicts the crucial role of the Higgs boson in electroweak symmetry breaking, and shows how the properties of the various particles differ in the (high-energy) symmetric phase (top) and the (low-energy) broken-symmetry phase (bottom).

https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model

https://en.wikipedia.org/wiki/Higgs_mechanism

Gluon radiation

rotation symmetry

electroweak in baryon v. electroweak in exotics v. scale

memory time on chip (signal infinite w/ maintainenance by human)

gravity graviton pressure material surface range tensor step scale friction air intermo intramo force attractiorepulsio channel vaccume space mater void vortex differential gradient

integral net force

slip sppoints topology turbulence (oxygen electron slip point; scale of hydrogen and proton; protonium)

symmetry spontaneous symmetry center spinor

atomic subatomic; baryoinic v. dark matter; tension torque torsion axial plane vertical pressuron preon dust particle syst large expanding particle nuclear

voltage pressure non ideal force v mass and charge hydroelectric thermodynamics

levels time supersymmetry charge mass transitivity

supramolecular chemistry nuclear neutron mirror multilayer particle space division multiplexing hyperfine quantum computing ion scale quantum interace eigenstate

skew asymmetry spiral

molecular gyroscope flyweel maglev linear induction motor rotation energy no activation energy with non covalent bond quantum energy nuclear hydrogen trihydrogencation universe dark matter universe baryonic matter chains hydroelectric nuclear fusion fission transmutation molecular inversion bond rotation energy

phase change water hydrogen microwave matrix glycerine cellulose point particle or particle space division multiplexing cascade change time space quantum ion quantum ion computing oscillation frequency measure hydrogen emission spectra

bunsen Lippmann (physics, 1908)

https://www.nobelprize.org/prizes/physics/1908/summary/

In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist.^[1]Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi-Dirac statistics.^[2]^[3] In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a "selectron" (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. More complex supersymmetry theories have a spontaneously broken symmetry, allowing superpartners to differ in mass.^[4]^[5]^[6]

Supersymmetry has various applications to different areas of physics, such as quantum mechanics, statistical mechanics, quantum field theory, condensed matter physics, nuclear physics, optics, stochastic dynamics, particle physics, astrophysics, quantum gravity, string theory, and cosmology. Supersymmetry has also been applied outside of physics, such as in finance. In particle physics, a supersymmetric extension of the Standard Model is a possible candidate for physics beyond the Standard Model, and in cosmology, supersymmetry could explain the issue of cosmological inflation.

In quantum field theory, supersymmetry is motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric quantum field theory is often much easier to analyze, as many more problems become mathematically tractable. When supersymmetry is imposed as a local symmetry, Einstein's theory of general relativity is included automatically, and the result is said to be a theory of supergravity. Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories with very general assumptions. The Haag–Łopuszański–Sohnius theorem demonstrates that supersymmetry is the only way spacetime and internal symmetries can be combined consistently.^[7]

https://en.wikipedia.org/wiki/Supersymmetry

In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist.[1]Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi-Dirac statistics.[2][3] In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a "selectron" (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. More complex supersymmetry theories have a spontaneously broken symmetry, allowing superpartners to differ in mass.[4][5][6]

In quantum field theory, supersymmetry is motivated by solutions to several theoretical problems, for generally providing many desirable mathematical properties, and for ensuring sensible behavior at high energies. Supersymmetric quantum field theory is often much easier to analyze, as many more problems become mathematically tractable. When supersymmetry is imposed as a local symmetry, Einstein's theory of general relativity is included automatically, and the result is said to be a theory of supergravity. Another theoretically appealing property of supersymmetry is that it offers the only "loophole" to the Coleman–Mandula theorem, which prohibits spacetime and internal symmetries from being combined in any nontrivial way, for quantum field theories with very general assumptions. The Haag–Łopuszański–Sohnius theorem demonstrates that supersymmetry is the only way spacetime and internal symmetries can be combined consistently.[7]

Supersymmetric quantum mechanics[edit]

Main article: Supersymmetric quantum mechanics

Supersymmetric quantum mechanics adds the SUSY superalgebra to quantum mechanics as opposed to quantum field theory. Supersymmetric quantum mechanics often becomes relevant when studying the dynamics of supersymmetric solitons, and due to the simplified nature of having fields which are only functions of time (rather than space-time), a great deal of progress has been made in this subject and it is now studied in its own right.

SUSY quantum mechanics involves pairs of Hamiltonians which share a particular mathematical relationship, which are called partner Hamiltonians. (The potential energy terms which occur in the Hamiltonians are then known as partner potentials.) An introductory theorem shows that for every eigenstate of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy. This fact can be exploited to deduce many properties of the eigenstate spectrum. It is analogous to the original description of SUSY, which referred to bosons and fermions. We can imagine a "bosonic Hamiltonian", whose eigenstates are the various bosons of our theory. The SUSY partner of this Hamiltonian would be "fermionic", and its eigenstates would be the theory's fermions. Each boson would have a fermionic partner of equal energy.

In finance[edit]

In 2021, supersymmetric quantum mechanics was applied to option pricing and the analysis of markets in finance,[19] and to financial networks.[20]

Supersymmetry in condensed matter physics[edit]

SUSY concepts have provided useful extensions to the WKB approximation. Additionally, SUSY has been applied to disorder averaged systems both quantum and non-quantum (through statistical mechanics), the Fokker–Planck equation being an example of a non-quantum theory. The 'supersymmetry' in all these systems arises from the fact that one is modelling one particle and as such the 'statistics' do not matter. The use of the supersymmetry method provides a mathematical rigorous alternative to the replica trick, but only in non-interacting systems, which attempts to address the so-called 'problem of the denominator' under disorder averaging. For more on the applications of supersymmetry in condensed matter physics see Efetov (1997).[21]

In 2021, a group of researchers showed that, in theory, {\displaystyle N=(0,1)} SUSY could be realised at the edge of a Moore-Read quantum Hall state.[22] However, to date, no experiments have been done yet to realise it at an edge of a Moore-Read state.

Supersymmetry in optics[edit]

In 2013, integrated optics was found[23] to provide a fertile ground on which certain ramifications of SUSY can be explored in readily-accessible laboratory settings. Making use of the analogous mathematical structure of the quantum-mechanical Schrödinger equation and the wave equation governing the evolution of light in one-dimensional settings, one may interpret the refractive indexdistribution of a structure as a potential landscape in which optical wave packets propagate. In this manner, a new class of functional optical structures with possible applications in phase matching, mode conversion[24] and space-division multiplexing becomes possible. SUSY transformations have been also proposed as a way to address inverse scattering problems in optics and as a one-dimensional transformation optics.[25]

Supersymmetry in dynamical systems[edit]

Main article: Supersymmetric theory of stochastic dynamics

All stochastic (partial) differential equations, the models for all types of continuous time dynamical systems, possess topological supersymmetry.[26][27] In the operator representation of stochastic evolution, the topological supersymmetry is the exterior derivativewhich is commutative with the stochastic evolution operator defined as the stochastically averaged pullback induced on differential forms by SDE-defined diffeomorphisms of the phase space. The topological sector of the so-emerging supersymmetric theory of stochastic dynamics can be recognized as the Witten-type topological field theory.

The meaning of the topological supersymmetry in dynamical systems is the preservation of the phase space continuity—infinitely close points will remain close during continuous time evolution even in the presence of noise. When the topological supersymmetry is broken spontaneously, this property is violated in the limit of the infinitely long temporal evolution and the model can be said to exhibit (the stochastic generalization of) the butterfly effect. From a more general perspective, spontaneous breakdown of the topological supersymmetry is the theoretical essence of the ubiquitous dynamical phenomenon variously known as chaos, turbulence, self-organized criticality etc. The Goldstone theorem explains the associated emergence of the long-range dynamical behavior that manifests itself as 1/f noise, butterfly effect, and the scale-free statistics of sudden (instantonic) processes, such as earthquakes, neuroavalanches, and solar flares, known as the Zipf's law and the Richter scale.

https://en.wikipedia.org/wiki/Supersymmetry

https://en.wikipedia.org/wiki/Refractive_index

https://en.wikipedia.org/wiki/Topology

https://en.wikipedia.org/wiki/Symmetry

https://en.wikipedia.org/wiki/Equilateral_Triangle

https://en.wikipedia.org/wiki/Perception_Sensation_Cognition

https://en.wikipedia.org/wiki/Goldstone_boson

https://en.wikipedia.org/wiki/Space-division_multiple_access

https://en.wikipedia.org/wiki/Richter_magnitude_scale

https://en.wikipedia.org/wiki/Zipf%27s_law

https://en.wikipedia.org/wiki/Butterfly_effect

https://en.wikipedia.org/wiki/Topological_quantum_field_theory

https://en.wikipedia.org/wiki/Supersymmetric_theory_of_stochastic_dynamics

https://en.wikipedia.org/wiki/Quantum_Hall_effect

https://en.wikipedia.org/wiki/Quantum_state#Pure_states

https://en.wikipedia.org/wiki/WKB_approximation

https://en.wikipedia.org/wiki/Lambda-CDM_model

https://en.wikipedia.org/wiki/Hyperfine_structure

https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Hyperfine_coupling

https://en.wikipedia.org/wiki/Hyperfinite_type_II_factor

https://en.wikipedia.org/wiki/Hypertext_Transfer_Protocol

Friday, September 17, 2021

09-17-2021-0229 - Space-division multiple access (SDMA)



In the 1990s, supramolecular chemistry became even more sophisticated, with researchers such as James Fraser Stoddartdeveloping molecular machinery and highly complex self-assembled structures, and Itamar Willner developing sensors and methods of electronic and biological interfacing. During this period, electrochemical and photochemical motifs became integrated into supramolecular systems in order to increase functionality, research into synthetic self-replicating system began, and work on molecular information processing devices began. The emerging science of nanotechnology also had a strong influence on the subject, with building blocks such as fullerenes, nanoparticles, and dendrimers becoming involved in synthetic systems.
Thermodynamics[edit]Supramolecular chemistry deals with subtle interactions, and consequently control over the processes involved can require great precision. In particular, non-covalent bonds have low energies and often no activation energy for formation. As demonstrated by the Arrhenius equation, this means that, unlike in covalent bond-forming chemistry, the rate of bond formation is not increased at higher temperatures. In fact, chemical equilibrium equations show that the low bond energy results in a shift towards the breaking of supramolecular complexes at higher temperatures.
However, low temperatures can also be problematic to supramolecular processes. Supramolecular chemistry can require molecules to distort into thermodynamically disfavored conformations (e.g. during the "slipping" synthesis of rotaxanes), and may include some covalent chemistry that goes along with the supramolecular. In addition, the dynamic nature of supramolecular chemistry is utilized in many systems (e.g. molecular mechanics), and cooling the system would slow these processes.
https://en.wikipedia.org/wiki/Supramolecular_chemistry

Saturday, August 14, 2021

08-13-2021-2226 - Time Reversal Symmetry

T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,

T:t\mapsto -t.

Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium,^[1] contrary to their classical counterparts, although this has not yet been experimentally confirmed.

Time asymmetries generally are caused by one of three categories:

intrinsic to the dynamic physical law (e.g., for the weak force)
due to the initial conditions of the universe (e.g., for the second law of thermodynamics)
due to measurements (e.g., for the noninvasive measurements)

https://en.wikipedia.org/wiki/T-symmetry

https://en.wikipedia.org/wiki/Molecular_recognition

https://en.wikipedia.org/wiki/Activation_energy

https://en.wikipedia.org/wiki/Micelle

https://en.wikipedia.org/wiki/Cell_membrane

https://en.wikipedia.org/wiki/Mechanically_interlocked_molecular_architectures

https://en.wikipedia.org/wiki/Molecular_sensor

https://en.wikipedia.org/wiki/Molecular_self-assembly

https://en.wikipedia.org/wiki/Catenane

https://en.wikipedia.org/wiki/Dynamic_covalent_chemistry

https://en.wikipedia.org/wiki/Foldamer

https://en.wikipedia.org/wiki/Biomimetics

https://en.wikipedia.org/wiki/Molecular_Borromean_rings

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Molecular_imprinting

https://en.wikipedia.org/wiki/Molecular_machine

Phthalocyanine (H
2Pc) is a large, aromatic, macrocyclic, organic compound with the formula (C
8H
4N
2)
4H
2 and is of theoretical or specialized interest in chemical dyes and photoelectricity.

It is composed of four isoindole units^[a] linked by a ring of nitrogen atoms. (C
8H
4N
2)
4H
2= H
2Pc has a two-dimensional geometry and a ring system consisting of 18 π-electrons. The extensive delocalization of the π-electrons affords the molecule useful properties, lending itself to applications in dyes and pigments. Metal complexesderived from Pc2−
, the conjugate base of H
2Pc, are valuable in catalysis, organic solar cells, and photodynamic therapy.

https://en.wikipedia.org/wiki/Phthalocyanine

https://en.wikipedia.org/wiki/Electrochemistry

https://en.wikipedia.org/wiki/Photochemistry

https://en.wikipedia.org/wiki/Porphyrin

https://en.wikipedia.org/wiki/Ruthenium

https://en.wikipedia.org/wiki/Crown_ether

https://en.wikipedia.org/wiki/Dimer_(chemistry)

https://en.wikipedia.org/wiki/Carboxylic_acid

https://en.wikipedia.org/wiki/Bipyridine

https://en.wikipedia.org/wiki/Pi-Stacking_(chemistry)

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Cucurbituril

https://en.wikipedia.org/wiki/Metallacrown

https://en.wikipedia.org/wiki/Chelate-rings

https://en.wikipedia.org/wiki/Cyclophane

https://en.wikipedia.org/wiki/Cryptand

https://en.wikipedia.org/wiki/Cyclodextrin

https://en.wikipedia.org/wiki/Macrocycle

https://en.wikipedia.org/wiki/Ammonium

https://en.wikipedia.org/wiki/Metal

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Cucurbituril

https://en.wikipedia.org/wiki/Step-growth_polymerization

https://en.wikipedia.org/wiki/Nucleophilic_addition

https://en.wikipedia.org/wiki/Molecular_gyroscope

https://en.wikipedia.org/wiki/Dimethyl_sulfoxide

https://en.wikipedia.org/wiki/Flywheel

https://en.wikipedia.org/wiki/Inclusion_compound

https://en.wikipedia.org/wiki/Oligomer

https://en.wikipedia.org/wiki/Trioxane

https://en.wikipedia.org/wiki/Glyoxal

https://en.wikipedia.org/wiki/Nanorod

https://en.wikipedia.org/wiki/Transition_metal_fullerene_complex

https://en.wikipedia.org/wiki/Dendrimer

https://en.wikipedia.org/wiki/Ether#Polyethers

https://en.wikipedia.org/wiki/Surface_science#Surface_chemistry

https://en.wikipedia.org/wiki/Self-assembled_monolayer

https://en.wikipedia.org/wiki/Multilayer_medium

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Cucurbituril

https://en.wikipedia.org/wiki/Phthalocyanine

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Porphyrin

https://en.wikipedia.org/wiki/Tetrathiafulvalene

https://en.wikipedia.org/wiki/Quinone

https://en.wikipedia.org/wiki/Photoisomerization

https://en.wikipedia.org/wiki/Oxidation_state

https://en.wikipedia.org/wiki/Viologen

https://en.wikipedia.org/wiki/Benzidine

https://en.wikipedia.org/wiki/Fullerene

https://en.wikipedia.org/wiki/Avidin

https://en.wikipedia.org/wiki/Coordination_complex

https://en.wikipedia.org/wiki/Nanoparticle

https://en.wikipedia.org/wiki/Electrode

https://en.wikipedia.org/wiki/Cavitand

https://en.wikipedia.org/wiki/Supramolecular_catalysis

https://en.wikipedia.org/wiki/Catalysis

https://en.wikipedia.org/wiki/Molecular_encapsulation

https://en.wikipedia.org/wiki/Dendrimer

https://en.wikipedia.org/wiki/Protein–protein_interaction

https://en.wikipedia.org/wiki/Electrochromism

https://en.wikipedia.org/wiki/DNA_computing

https://en.wikipedia.org/wiki/Molecular_switch

https://en.wikipedia.org/wiki/Cavitand

https://en.wikipedia.org/wiki/Donald_J._Cram

https://en.wikipedia.org/wiki/Quinoxaline

https://en.wikipedia.org/wiki/Amiloride

https://en.wikipedia.org/wiki/Cavitand

https://en.wikipedia.org/wiki/Calixarene

https://en.wikipedia.org/wiki/Cavitand

https://en.wikipedia.org/wiki/Pillararene

https://en.wikipedia.org/wiki/Cucurbituril

https://en.wikipedia.org/wiki/Resorcinarene

https://en.wikipedia.org/wiki/Pyrogallol

https://en.wikipedia.org/wiki/Resorcinarene

https://en.wikipedia.org/wiki/Condensation_reaction

https://en.wikipedia.org/wiki/Compression

https://en.wikipedia.org/wiki/Trihydroxybenzenes

https://en.wikipedia.org/wiki/Archimedean_solid

https://en.wikipedia.org/wiki/Antiprism

https://en.wikipedia.org/wiki/Convex_polytope

https://en.wikipedia.org/wiki/Platonic_solid

https://en.wikipedia.org/wiki/Elongated_square_gyrobicupola

https://en.wikipedia.org/wiki/Prism_(geometry)

https://en.wikipedia.org/wiki/Mirror_image

https://en.wikipedia.org/wiki/Chirality_(mathematics)

https://en.wikipedia.org/wiki/Hydrogen_bond

https://en.wikipedia.org/wiki/Carcerand

https://en.wikipedia.org/wiki/Prison

https://en.wikipedia.org/wiki/Oligomer

https://en.wikipedia.org/wiki/Grigory_Mairanovsky

https://en.wikipedia.org/wiki/Carceplex

https://en.wikipedia.org/wiki/Hinge

https://en.wikipedia.org/wiki/Cyclobutadiene

https://en.wikipedia.org/wiki/Pendulum

https://en.wikipedia.org/wiki/Wave_theory_of_light?wprov=srpw1_0

https://en.wikipedia.org/wiki/Luminiferous_aether

https://en.wikipedia.org/wiki/Vacuum

https://en.wikipedia.org/wiki/Wave

https://en.wikipedia.org/wiki/Topology

https://en.wikipedia.org/wiki/Mereology

https://en.wikipedia.org/wiki/Methods_of_divination

https://en.wikipedia.org/wiki/Archimedean_solid

https://en.wikipedia.org/wiki/List_of_medical_roots,_suffixes_and_prefixes

https://en.wikipedia.org/wiki/Sarcosine

https://en.wikipedia.org/wiki/Molecular_recognition

https://en.wikipedia.org/wiki/Category:Chelating_agents

https://en.wikipedia.org/wiki/Category:Siderophores

https://en.wikipedia.org/wiki/Supramolecular_chemistry

https://en.wikipedia.org/wiki/Bioorthogonal_chemistry

https://en.wikipedia.org/wiki/Hydrazone

https://en.wikipedia.org/wiki/Hydrazine

https://en.wikipedia.org/wiki/Propellant#Liquid_propellant

The electron transfer is fast because the redox process induces little structural change.

Paraquat is a prominent viologen.

Redox properties[edit]

Viologens, in their dicationic form, typically undergo two one-electron reductions. The first reduction affords the deeply colored radical cation:^[2]

[V]²⁺ + e⁻

{\ce {<=>>}}

[V]⁺

The radical cations are blue for 4,4'-viologens and green for 2,2'-derivatives. The second reduction yields a yellow quinoidcompounds:

[V]⁺ + e⁻

{\ce {<=>>}}

[V]⁰

The electron transfer is fast because the redox process induces little structural change.

Viologen catalysts have been reported to have the potential to oxidize glucose and other carbohydrates catalytically in a mildly alkaline solution, which makes direct carbohydrate fuel cellspossible.^[6]

Modified viologens and related compounds[edit]

Diquat is an isomer of viologens, being derived from 2,2'-bipyridine (instead of the 4,4'-isomer). It also is a potent herbicide that functions by disrupting electron-transfer.

Diquat is related to viologens but is derived from 2,2'bipyridine.

Extended viologens have been developed based on conjugated oligomers such as based on aryl, ethylene, and thiophene units are inserted between the pyridine units.^[7] The bipolaron di-octyl bis(4-pyridyl)biphenyl viologen 2 in scheme 2 can be reduced by sodium amalgam in DMF to the neutral viologen 3.

The resonance structures of the quinoid 3a and the biradical 3b contribute equally to the hybrid structure. The driving force for the contributing 3b is the restoration of aromaticity with the biphenyl unit. It has been established using X-ray crystallography that the molecule is, in effect, coplanar with slight nitrogen pyramidalization, and that the central carbon bonds are longer (144 pm) than what would be expected for a double bond (136 pm). Further research shows that the diradical exists as a mixture of triplets and singlets, although an ESR signal is absent. In this sense, the molecule resembles Tschischibabin's hydrocarbon, discovered during 1907. It also shares with this molecule a blue color in solution, and a metallic-green color as crystals.

Compound 3 is a very strong reducing agent, with a redox potential of −1.48 V.

https://en.wikipedia.org/wiki/Viologen

The quinones are a class of organic compounds that are formally "derived from aromatic compounds [such as benzene or naphthalene] by conversion of an even number of –CH= groups into –C(=O)– groups with any necessary rearrangement of double bonds, resulting in "a fully conjugated cyclic dione structure".^[1]^[2]^[3] The archetypical member of the class is 1,4-benzoquinone or cyclohexadienedione, often called simply "quinone" (thus the name of the class). Other important examples are 1,2-benzoquinone(ortho-quinone), 1,4-naphthoquinone and 9,10-anthraquinone.

https://en.wikipedia.org/wiki/Quinone

https://en.wikipedia.org/wiki/Dimethylformamide

Sodium amalgam, commonly denoted Na(Hg), is an alloy of mercury and sodium. The term amalgam is used for alloys, intermetallic compounds, and solutions (both solid solutions and liquid solutions) involving mercury as a major component. Sodium amalgams are often used in reactions as strong reducing agents with better handling properties compared to solid sodium. They are less dangerously reactive toward water and in fact are often used as an aqueous suspension.

Sodium amalgam was used as a reagent as early as 1862.^[1] A synthesis method was described by J. Alfred Wanklyn in 1866.^[2]

Uses[edit]

Sodium amalgam has been used in organic chemistry as a powerful reducing agent, which is safer to handle than sodium itself. It is used in Emde degradation, and also for reduction of aromatic ketones to hydrols.^[9]

A sodium amalgam is used in the design of the high pressure sodium lamp providing sodium to produce the proper color, and mercury to tailor the electrical characteristics of the lamp.

Mercury cell electrolysis[edit]

Sodium amalgam is a by-product of chlorine manufactured by mercury cell electrolysis. In this cell, brine (concentrated sodium chloride solution) is electrolysed between a liquid mercury cathode and a titanium or graphite anode. Chlorine is formed at the anode, while sodium formed at the cathode dissolves into the mercury, making sodium amalgam. Normally this sodium amalgam is drawn off and reacted with water in a "decomposer cell" to produce hydrogen gas, concentrated sodium hydroxide solution, and mercury to be recycled through the process. In principle, all the mercury should be completely recycled, but inevitably a small portion goes missing. Because of concerns about this mercury escaping into the environment, the mercury cell process is generally being replaced by plants which use a less toxic cathode.

https://en.wikipedia.org/wiki/Sodium_amalgam

https://en.wikipedia.org/wiki/Emde_degradation

https://en.wikipedia.org/wiki/Bipolaron

A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933^[1] and Solomon Pekar in 1946^[2] to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. For comparison of the models proposed in these papers see M. I. Dykman and E. I. Rashba, The roots of polaron theory, Physics Today 68, 10 (2015). This lowers the electron mobility and increases the electron's effective mass.

https://en.wikipedia.org/wiki/Polaron

In organic chemistry, the Menshutkin reaction converts a tertiary amine into a quaternary ammonium salt by reaction with an alkyl halide. Similar reactions occur when tertiary phosphines are treated with alkyl halides.

https://en.wikipedia.org/wiki/Menshutkin_reaction

A coupling reaction in organic chemistry is a general term for a variety of reactions where two fragments are joined together with the aid of a metal catalyst. In one important reaction type, a main group organometallic compound of the type R-M (R = organic fragment, M = main group center) reacts with an organic halide of the type R'-X with formation of a new carbon-carbon bond in the product R-R'. The most common type of coupling reaction is the cross coupling reaction.^[1]^[2]^[3]

Richard F. Heck, Ei-ichi Negishi, and Akira Suzuki were awarded the 2010 Nobel Prize in Chemistry for developing palladium-catalyzed cross coupling reactions.^[4]^[5]

Broadly speaking, two types of coupling reactions are recognized:

Heterocouplings combine two different partners, such as in the Heck reaction of an alkene (RC=CH) and an alkyl halide (R'-X) to give a substituted alkene. Heterocouplings are called cross-couplings.
Homocouplings couple two identical partners, as in the Glaser coupling of two acetylides (RC≡CH) to form a dialkyne (RC≡C-C≡CR).

https://en.wikipedia.org/wiki/Coupling_reaction

Diquat is related to viologens but is derived from 2,2'bipyridine.

Mechanism of action[edit]

Viologens with 2,2'-, 4,4'-, or 2,4'-bipyridylium are highly toxic because these bipyridyl molecules readily form stable free radicals.^[8]The delocalization of charge, which allows for the molecule to stay as a free radical and these structures can be easily stabilized because the nitrogens can be readily hydrogenated. When in the body, these viologens interfere with electron transport chain, often causing cell death.^[8]^[9] These molecules act as redox cycling agents and are able to transfer their electron to molecular oxygen.^[10]^[9] Once the electron has been transferred to the molecular oxygen, it forms a superoxide radical that causes disproportionation, simultaneous reduction and oxidation.

https://en.wikipedia.org/wiki/Viologen

https://en.wikipedia.org/wiki/Thiophene

https://en.wikipedia.org/wiki/Disproportionation

https://en.wikipedia.org/wiki/Superoxide

https://en.wikipedia.org/wiki/Electron_transport_chain

https://en.wikipedia.org/wiki/Delocalized_electron

https://en.wikipedia.org/wiki/Radical_(chemistry)

https://en.wikipedia.org/wiki/Trigonal_planar_molecular_geometry

https://en.wikipedia.org/wiki/Aromaticity

https://en.wikipedia.org/wiki/Coplanarity

https://en.wikipedia.org/wiki/Line_(geometry)

https://en.wikipedia.org/wiki/Skew_lines

https://en.wikipedia.org/wiki/Line–line_intersection

https://en.wikipedia.org/wiki/Parallel_(geometry)

https://en.wikipedia.org/wiki/Distance_geometry

https://en.wikipedia.org/wiki/Empty_set

https://en.wikipedia.org/wiki/Non-Kekulé_molecule

https://en.wikipedia.org/wiki/Resonance_(chemistry)

https://en.wikipedia.org/wiki/Aryl

https://en.wikipedia.org/wiki/Ethylene

https://en.wikipedia.org/wiki/Oligomer

https://en.wikipedia.org/wiki/Conjugated_system

https://en.wikipedia.org/wiki/Pyridine

https://en.wikipedia.org/wiki/Sodium_amalgam

https://en.wikipedia.org/wiki/Viologen

https://en.wikipedia.org/wiki/Reduction_potential

https://en.wikipedia.org/wiki/Reducing_agent

https://en.wikipedia.org/wiki/Aromaticity

These reactive free radicals can cause oxidative stress, which leads to cell death and one example of this is lipid peroxidation. When in a cellular system, the superoxide radicals react with unsaturated lipids, which contain a reactive hydrogen, and produce lipid hydroperoxides.^[10] These lipid hydroperoxides then decompose into lipid free radicals, and causes a chain reaction of lipid peroxidation, damaging the cellular macromolecules and eventually causing cell death. The superoxide radicals have also been found to deplete NADPH, alter other redox reactions that naturally occur in the organism, and interfere with how iron is stored and released in the body.^[9]

IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "viologens". doi:10.1351/goldbook.V06624

https://en.wikipedia.org/wiki/Viologen

https://en.wikipedia.org/wiki/Oxidative_stress

https://en.wikipedia.org/wiki/Lipid_peroxidation

https://en.wikipedia.org/wiki/Sharon_Petersen_subject_sample-group(2020)

https://en.wikipedia.org/wiki/Indium_tin_oxide

https://en.wikipedia.org/wiki/Titanium_dioxide

https://en.wikipedia.org/wiki/Category:Superoxide_generating_substances

https://en.wikipedia.org/wiki/Antimycin_A

https://en.wikipedia.org/wiki/NADPH_oxidase

https://en.wikipedia.org/wiki/Xanthine_oxidase

https://en.wikipedia.org/wiki/Category:Bipyridines

https://en.wikipedia.org/wiki/Phanquinone

https://en.wikipedia.org/wiki/Monomethylhydrazine

https://en.wikipedia.org/wiki/Dinitrogen_tetroxide

https://en.wikipedia.org/wiki/Liquid-propellant_rocket

Electrostatic[edit]

If the acceleration is caused mainly by the Coulomb force (i.e. application of a static electric field in the direction of the acceleration) the device is considered electrostatic. The types of electrostatic drives and their propellants:

Gridded ion thruster – using positive ions as the propellant, accelerated by an electrically charged grid
- NASA Solar Technology Application Readiness (NSTAR) – positive ions accelerated using high-voltage electrodes
- HiPEP – using positive ions as the propellant, created using microwaves
- Radiofrequency ion thruster – generalization of HiPEP
Hall-effect thruster, including its subtypes Stationary Plasma Thruster (SPT) and Thruster with Anode Layer (TAL) – use the Hall effect to orient electrons to create positive ions for propellant
Colloid ion thruster- electrostatic acceleration of droplets of liquid salt as the propellant
Field emission electric propulsion - using electrodes to accelerate ionized liquid metal as a propellant
Nano-particle field extraction thruster - using charged cylindrical carbon nanotubes as propellant

Electrothermal[edit]

These are engines that use electromagnetic fields to generate a plasma which is used as the propellant. They use a nozzle to direct the energized propellant. The nozzle itself may be composed simply of a magnetic field. Low molecular weight gases (e.g. hydrogen, helium, ammonia) are preferred propellants for this kind of system.^[6]

Resistojet - using a usually inert compressed propellant that is energized by simple resistive heating
Arcjet - uses (usually) hydrazine or ammonia as a propellant which is energized with an electrical arc
Microwave - a type of Radiofrequency ion thruster
Variable specific impulse magnetoplasma rocket (VASIMR) - using microwave-generated plasma as the propellant and magnetic field to direct its expulsion

Electromagnetic[edit]

Electromagnetic thrusters use ions as the propellant, which are accelerted by the Lorentz force or by magnetic fields, either of which is generated by electicity:

Electrodeless plasma thruster - a complex system that uses cold plasma as a propellant that is accelerated by ponderomotive force
Magnetoplasmadynamic thruster - propellants include xenon, neon, argon, hydrogen, hydrazine, or lithium; expelled using the Lorentz force
Pulsed inductive thruster - because this reacitve engine uses a radial magnetic field, it acts on both positive and negative particles and so it may use a wide range of gases as a propellant including water, hydrazine, ammonia, argon, xenon and many others
Pulsed plasma thruster - uses a Teflon plasma as a propellant, which is created by an electrical arc and expelled using the Lorantz force
Helicon Double Layer Thruster - a plasma propellant is generated and excited from a gas using a helicon induced by high frequency band radiowaves which form a magnetic nozzle in a cylinder

Nuclear[edit]

Nuclear reactions may be used to produce the energy for the expulsion of the propellants. Many types of nuclear reactors have been used/proposed to produce electricity for electrical propulsion as outlined above. Nuclear pulse propulsion uses a series of nuclear explosions to create large amounts of energy to expel the products of the nuclear reaction as the propellant. Nuclear thermal rocketsuse the heat of a nuclear reaction to heat a propellant. Usually the propellant is hydrogen because the force is a function of the energy irrespective of the mass of the propellant, so the lightest propellant (hydrogen) produces the greatest specific impulse.

Photonic[edit]

A photonic reactive engine uses photons as the propellant and their discrete relativistic energy to produce thrust.

General relativity[edit]

CTCs appear in locally unobjectionable exact solutions to the Einstein field equation of general relativity, including some of the most important solutions. These include:

the Misner space (which is Minkowski space orbifolded by a discrete boost)
the Kerr vacuum (which models a rotating uncharged black hole)
the interior of a rotating BTZ black hole
the van Stockum dust (which models a cylindrically symmetric configuration of dust)
the Gödel lambdadust (which models a dust with a carefully chosen cosmological constant term)
the Tipler cylinder (a cylindrically symmetric metric with CTCs)
Bonnor-Steadman solutions describing laboratory situations such as two spinning balls
J. Richard Gott has proposed a mechanism for creating CTCs using cosmic strings.

Some of these examples are, like the Tipler cylinder, rather artificial, but the exterior part of the Kerr solution is thought to be in some sense generic, so it is rather unnerving to learn that its interior contains CTCs. Most physicists feel that CTCs in such solutions are artifacts.^{[citation needed]}

No CTC can be continuously deformed as a CTC to a point (that is, a CTC and a point are not timelike homotopic), as the manifold would not be causally well behaved at that point. The topological feature which prevents the CTC from being deformed to a point is known as a timelike topological feature.

Contractible versus noncontractible[edit]

There are two classes of CTCs. We have CTCs contractible to a point (if we no longer insist it has to be future-directed timelike everywhere), and we have CTCs which are not contractible. For the latter, we can always go to the universal covering space, and reestablish causality. For the former, such a procedure is not possible. No closed timelike curve is contractible to a point by a timelike homotopy among timelike curves, as that point would not be causally well behaved.^[3]

Cauchy horizon[edit]

The chronology violating set is the set of points through which CTCs pass. The boundary of this set is the Cauchy horizon. The Cauchy horizon is generated by closed null geodesics. Associated with each closed null geodesic is a redshift factor describing the rescaling of the rate of change of the affine parameter around a loop. Because of this redshift factor, the affine parameter terminates at a finite value after infinitely many revolutions because the geometric series converges.

Cone angles of common phosphine ligands
Ligand	Angle (°)
PH₃	87^[1]
PF₃	104^[1]
P(OCH₃)₃	107^[1]
dmpe	107
depe	115
P(CH₃)₃	118^[1]
dppm	121
dppe	125
dppp	127
P(CH₂CH₃)₃	132^[1]
dcpe	142
P(C₆H₅)₃	145^[1]
P(cyclo-C₆H₁₁)₃	179^[1]
P(t-Bu)₃	182^[1]
P(C₆F₅)₃	184^[1]
P(C₆H₄-2-CH₃)₃	194^[1]
P(2,4,6-Me₃C₆H₂)₃	212

Astrophysical applications[edit]

Gravitational lensing[edit]

Main article: Gravitational lensing
Einstein cross: four images of the same astronomical object, produced by a gravitational lens
The deflection of light by gravity is responsible for a new class of astronomical phenomena. If a massive object is situated between the astronomer and a distant target object with appropriate mass and relative distances, the astronomer will see multiple distorted images of the target. Such effects are known as gravitational lensing.^[108]Depending on the configuration, scale, and mass distribution, there can be two or more images, a bright ring known as an Einstein ring, or partial rings called arcs.^[109] The earliest example was discovered in 1979;^[110] since then, more than a hundred gravitational lenses have been observed.^[111] Even if the multiple images are too close to each other to be resolved, the effect can still be measured, e.g., as an overall brightening of the target object; a number of such "microlensing events" have been observed.^[112]
Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matter, provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the Hubble constant. Statistical evaluations of lensing data provide valuable insight into the structural evolution of galaxies.^[113]
https://en.wikipedia.org/wiki/General_relativity#Light_deflection_and_gravitational_time_delay

https://en.wikipedia.org/wiki/Wormhole#Traversable_wormholes
https://en.wikipedia.org/wiki/Tipler_cylinder
https://en.wikipedia.org/wiki/Category:Lorentzian_manifolds
https://en.wikipedia.org/wiki/Supramolecular_chemistry
https://en.wikipedia.org/wiki/Molecular_self-assembly
https://en.wikipedia.org/wiki/Supersymmetry
https://en.wikipedia.org/wiki/Spacetime_symmetries
https://en.wikipedia.org/wiki/Symmetry_(physics)
https://en.wikipedia.org/wiki/Rotation
https://en.wikipedia.org/wiki/Reflection_(physics)
https://en.wikipedia.org/wiki/General_covariance
https://en.wikipedia.org/wiki/Cosmological_principle
https://en.wikipedia.org/wiki/Accretion_(astrophysics)
https://en.wikipedia.org/wiki/Astrophysical_jet#Relativistic_jet
https://en.wikipedia.org/wiki/Physical_cosmology
https://en.wikipedia.org/wiki/Thermal_radiation
https://en.wikipedia.org/wiki/Closed_timelike_curve#Contractible_versus_noncontractible
https://en.wikipedia.org/wiki/Supersymmetry
https://en.wikipedia.org/wiki/Spherically_symmetric_spacetime
https://en.wikipedia.org/wiki/Gravitational_potential
https://en.wikipedia.org/wiki/Gravitational_lens
https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation
https://en.wikipedia.org/wiki/Gravitational_redshift
https://en.wikipedia.org/wiki/Vector_field
https://en.wikipedia.org/wiki/Local_diffeomorphism
https://en.wikipedia.org/wiki/Killing_vector_field
https://en.wikipedia.org/wiki/Homothetic_vector_field
https://en.wikipedia.org/wiki/Affine_vector_field
https://en.wikipedia.org/wiki/Conformal_Killing_vector_field
https://en.wikipedia.org/wiki/Curvature_collineation
https://en.wikipedia.org/wiki/Matter_collineation
https://en.wikipedia.org/wiki/Static_spacetime
https://en.wikipedia.org/wiki/Field_(physics)
https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics
https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking
https://en.wikipedia.org/wiki/Light_cone
https://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)
https://en.wikipedia.org/wiki/Equations_of_motion
https://en.wikipedia.org/wiki/Dimension
The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution). It is also known as the Gödel solution or Gödel universe.
This solution has many unusual properties—in particular, the existence of closed timelike curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial in that the value of the cosmological constant must be carefully chosen to match the density of the dust grains, but this spacetime is an important pedagogical example.
The solution was found in 1949 by Kurt Gödel.^[1]
https://en.wikipedia.org/wiki/Gödel_metric
https://en.wikipedia.org/wiki/Closed_timelike_curve

https://en.wikipedia.org/wiki/Ionic_liquid
https://en.wikipedia.org/wiki/Colloid_thruster
https://en.wikipedia.org/wiki/Field-emission_electric_propulsion
https://en.wikipedia.org/wiki/Carbon_nanotube
https://en.wikipedia.org/wiki/Nano-particle_field_extraction_thruster
https://en.wikipedia.org/wiki/Propellant#Liquid_propellant
https://en.wikipedia.org/wiki/Cucurbituril
https://en.wikipedia.org/wiki/Singularity_(mathematics)
https://en.wikipedia.org/wiki/Henri_Poincaré
https://en.wikipedia.org/wiki/Tensor

https://en.wikipedia.org/wiki/Light_cone
https://en.wikipedia.org/wiki/Topology
https://en.wikipedia.org/wiki/Light
https://en.wikipedia.org/wiki/Pressure
https://en.wikipedia.org/wiki/Magnetic_force
https://en.wikipedia.org/wiki/Plane
https://en.wikipedia.org/wiki/Vertical
https://en.wikipedia.org/wiki/Pressure
https://en.wikipedia.org/wiki/Magnetic_force
https://en.wikipedia.org/wiki/Loop_(topology)
https://en.wikipedia.org/wiki/Free_loop
https://en.wikipedia.org/wiki/Loop_space
https://en.wikipedia.org/wiki/Pendulum
https://en.wikipedia.org/wiki/Spring
https://en.wikipedia.org/wiki/String

https://en.wikipedia.org/wiki/Observable_universe
https://en.wikipedia.org/wiki/Ball_(mathematics)

Saturday, September 18, 2021

09-18-2021-1152 - Gravitational time dilation (two disparities on a plane; two size disparate spheres on a plane; two weight disparate or size disparate on a warped plane)

https://en.wikipedia.org/wiki/Gravitational_time_dilation
https://en.wikipedia.org/wiki/Gravitational_lens

Saturday, September 18, 2021

09-18-2021-1712 - Pressure Measurement (Absolute, gauge and differential pressures — zero reference)

Pressure measurement is the analysis of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure and display pressure in an integral unit are called pressure meters or pressure gauges or vacuum gauges. A manometer is a good example, as it uses the surface area and weight of a column of liquid to both measure and indicate pressure. Likewise the widely used Bourdon gauge is a mechanical device, which both measures and indicates and is probably the best known type of gauge.

A vacuum gauge is a pressure gauge used to measure pressures lower than the ambient atmospheric pressure, which is set as the zero point, in negative values (e.g.: −15 psig or −760 mmHg equals total vacuum). Most gauges measure pressure relative to atmospheric pressure as the zero point, so this form of reading is simply referred to as "gauge pressure". However, anything greater than total vacuum is technically a form of pressure. For very accurate readings, especially at very low pressures, a gauge that uses total vacuum as the zero point may be used, giving pressure readings in an absolute scale.

Other methods of pressure measurement involve sensors that can transmit the pressure reading to a remote indicator or control system (telemetry).

Absolute, gauge and differential pressures — zero reference[edit]

Everyday pressure measurements, such as for vehicle tire pressure, are usually made relative to ambient air pressure. In other cases measurements are made relative to a vacuum or to some other specific reference. When distinguishing between these zero references, the following terms are used:
Absolute pressure is zero-referenced against a perfect vacuum, using an absolute scale, so it is equal to gauge pressure plus atmospheric pressure.
Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted.[citation needed] To distinguish a negative pressure, the value may be appended with the word "vacuum" or the gauge may be labeled a "vacuum gauge". These are further divided into two subcategories: high and low vacuum (and sometimes ultra-high vacuum). The applicable pressure ranges of many of the techniques used to measure vacuums overlap. Hence, by combining several different types of gauge, it is possible to measure system pressure continuously from 10 mbar down to 10−11 mbar.
Differential pressure is the difference in pressure between two points.

The zero reference in use is usually implied by context, and these words are added only when clarification is needed. Tire pressureand blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressuresmust be absolute.

For most working fluids where a fluid exists in a closed system, gauge pressure measurement prevails. Pressure instruments connected to the system will indicate pressures relative to the current atmospheric pressure. The situation changes when extreme vacuum pressures are measured, then absolute pressures are typically used instead.

Differential pressures are commonly used in industrial process systems. Differential pressure gauges have two inlet ports, each connected to one of the volumes whose pressure is to be monitored. In effect, such a gauge performs the mathematical operation of subtraction through mechanical means, obviating the need for an operator or control system to watch two separate gauges and determine the difference in readings.

Moderate vacuum pressure readings can be ambiguous without the proper context, as they may represent absolute pressure or gauge pressure without a negative sign. Thus a vacuum of 26 inHg gauge is equivalent to an absolute pressure of 4 inHg, calculated as 30 inHg (typical atmospheric pressure) − 26 inHg (gauge pressure).

Atmospheric pressure is typically about 100 kPa at sea level, but is variable with altitude and weather. If the absolute pressure of a fluid stays constant, the gauge pressure of the same fluid will vary as atmospheric pressure changes. For example, when a car drives up a mountain, the (gauge) tire pressure goes up because atmospheric pressure goes down. The absolute pressure in the tire is essentially unchanged.

Using atmospheric pressure as reference is usually signified by a "g" for gauge after the pressure unit, e.g. 70 psig, which means that the pressure measured is the total pressure minus atmospheric pressure. There are two types of gauge reference pressure: vented gauge (vg) and sealed gauge (sg).

A vented-gauge pressure transmitter, for example, allows the outside air pressure to be exposed to the negative side of the pressure-sensing diaphragm, through a vented cable or a hole on the side of the device, so that it always measures the pressure referred to ambient barometric pressure. Thus a vented-gauge reference pressure sensor should always read zero pressure when the process pressure connection is held open to the air.

A sealed gauge reference is very similar, except that atmospheric pressure is sealed on the negative side of the diaphragm. This is usually adopted on high pressure ranges, such as hydraulics, where atmospheric pressure changes will have a negligible effect on the accuracy of the reading, so venting is not necessary. This also allows some manufacturers to provide secondary pressure containment as an extra precaution for pressure equipment safety if the burst pressure of the primary pressure sensing diaphragm is exceeded.

There is another way of creating a sealed gauge reference, and this is to seal a high vacuum on the reverse side of the sensing diaphragm. Then the output signal is offset, so the pressure sensor reads close to zero when measuring atmospheric pressure.

A sealed gauge reference pressure transducer will never read exactly zero because atmospheric pressure is always changing and the reference in this case is fixed at 1 bar.

To produce an absolute pressure sensor, the manufacturer seals a high vacuum behind the sensing diaphragm. If the process-pressure connection of an absolute-pressure transmitter is open to the air, it will read the actual barometric pressure.

https://en.wikipedia.org/wiki/Pressure_measurement#Gauge

Saturday, September 18, 2021

09-18-2021-1015 - Linear Stage Translation Stage motion system single axis

A linear stage or translation stage is a component of a precise motion system used to restrict an object to a single axis of motion. The term linear slide is often used interchangeably with "linear stage", though technically "linear slide" refers to a linear motion bearing, which is only a component of a linear stage. All linear stages consist of a platform and a base, joined by some form of guide or linear bearing in such a way that the platform is restricted to linear motion with respect to the base. In common usage, the term linear stage may or may not also include the mechanism by which the position of the platform is controlled relative to the base.
https://en.wikipedia.org/wiki/Linear_stage

External links[edit]

Weisstein, Eric W. "Differentials". MathWorld.
https://en.wikipedia.org/wiki/Differential_(mathematics)

Saturday, September 18, 2021

09-18-2021-1226 - scalar field dark matter

In astrophysics and cosmology scalar field dark matter is a classical, minimally coupled, scalar field postulated to account for the inferred dark matter.^[2]

Background[edit]

The universe may be accelerating, fueled perhaps by a cosmological constant or some other field possessing long range ‘repulsive’ effects. A model must predict the correct form for the large scale clustering spectrum,^[3] account for cosmic microwave background anisotropies on large and intermediate angular scales, and provide agreement with the luminosity distance relation obtained from observations of high redshift supernovae. The modeled evolution of the universe includes a large amount of unknown matter and energy in order to agree with such observations. This energy density has two components: cold dark matter and dark energy. Each contributes to the theory of the origination of galaxies and the expansion of the universe. The universe must have a critical density, a density not explained by baryonic matter (ordinary matter) alone.

Scalar field[edit]

The dark matter can be modeled as a scalar field using two fitted parameters, mass and self-interaction.^[4]^[5] In this picture the dark matter consists of an ultralight particle with a mass of ~10⁻²² eV when there is no self-interaction.^[6]^[7]^[8] If there is a self-interaction a wider mass range is allowed.^[9] The uncertainty in position of a particle is larger than its Compton wavelength (a particle with mass 10⁻²² eV has a Compton wavelength of 1.3 light years), and for some reasonable estimates of particle mass and density of dark matter there is no point talking about the individual particles’ positions and momenta. Ultra-light dark matter would be more like a wave than a particle, and the galactic halos are giant systems of condensed bose liquid, possibly superfluid. The dark matter can be described as a Bose–Einstein condensate of the ultralight quanta of the field^[10] and as boson stars.^[9] The enormous Compton wavelength of these particles prevents structure formation on small, subgalactic scales, which is a major problem in traditional cold dark matter models. The collapse of initial over-densities is studied in the references.^[11]^[12]^[13]^[14]
This dark matter model is also known as BEC dark matter or wave dark matter. Fuzzy dark matter and ultra-light axion are examples of scalar field dark matter.

Saturday, September 18, 2021

09-18-2021-1710 - Degree of Freedom is an Independent Physical Parameter in the Formal Description of the state of a physical system.

In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.
The location of a particle in three-dimensional space requires three position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. If the time evolution of the system is deterministic, where the state at one instant uniquely determines its past and future position and velocity as a function of time, such a system has six degrees of freedom.^{[citation needed]} If the motion of the particle is constrained to a lower number of dimensions – for example, the particle must move along a wire or on a fixed surface – then the system has fewer than six degrees of freedom. On the other hand, a system with an extended object that can rotate or vibrate can have more than six degrees of freedom.
In classical mechanics, the state of a point particle at any given time is often described with position and velocity coordinates in the Lagrangian formalism, or with position and momentum coordinates in the Hamiltonian formalism.
In statistical mechanics, a degree of freedom is a single scalar number describing the microstate of a system.^[1] The specification of all microstates of a system is a point in the system's phase space.
In the 3D ideal chain model in chemistry, two angles are necessary to describe the orientation of each monomer.
It is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the system.
Depending on what one is counting, there are several different ways that degrees of freedom can be defined, each with a different value.^[2]
https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)

Saturday, September 18, 2021

09-18-2021-1708 - alternating current oscillating particle or wave perturbed γ-γ angular correlation heterodyne gyroscope

Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current(DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.^[1]^[2]
The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa. In certain applications, like guitar amplifiers, different waveforms are used, such as triangular waves or square waves. Audio and radiosignals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by modulation of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.
https://en.wikipedia.org/wiki/Alternating_current

The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric fields in crystal structures can be measured. In doing so, electrical field gradients and the Larmor frequency in magnetic fields as well as dynamic effects are determined. With this very sensitive method, which requires only about 10-1000 billion atoms of a radioactive isotope per measurement, material properties in the local structure, phase transitions, magnetism and diffusion can be investigated. The PAC method is related to nuclear magnetic resonance and the Mössbauer effect, but shows no signal attenuation at very high temperatures. Today only the time-differential perturbed angular correlation (TDPAC) is used.
https://en.wikipedia.org/wiki/Perturbed_angular_correlation

rotation translation vibration
https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)

Saturday, September 18, 2021

09-18-2021-1315 - Absolute, gauge and differential pressures — zero reference

Saturday, September 18, 2021

09-18-2021-1243 - mirror nuclei

In physics, mirror nuclei are a pair of isotopes of two different elements where the number of protons of isotope one (Z₁) equals the number of neutrons of isotope two (N₂) and the number of protons of isotope two (Z₂) equals the number of neutrons in isotope one (N₁); in short: Z₁ = N₂ and Z₂ = N₁. This implies that the mass numbers of the isotopes are the same: N₁ + Z₁ = N₂ + Z₂.
Examples of mirror nuclei:
Isotope 1 Z₁ N₁ Isotope 2 Z₂ N₂
³H 1 2 ³He 2 1
¹⁴C 6 8 ¹⁴O 8 6
¹⁵N 7 8 ¹⁵O 8 7
²⁴Na 11 13 ²⁴Al 13 11
Pairs of mirror nuclei have the same spin and parity. If we constrain to odd number of nucleons (A=Z+N) then we find mirror nuclei that differ from one another by exchanging a proton by a neutron. Interesting to observe is their binding energy which is mainly due to the strong interaction and also due to Coulomb interaction. Since the strong interaction is invariant to protons and neutrons one can expect these mirror nuclei to have very similar binding energies.^[1]^[2]
In 2020 Strontium-73 and bromine-73 were found to not behave as expected.^[3]

Isotope 1	Z₁	N₁	Isotope 2	Z₂	N₂
³H	1	2	³He	2	1
¹⁴C	6	8	¹⁴O	8	6
¹⁵N	7	8	¹⁵O	8	7
²⁴Na	11	13	²⁴Al	13	11

References[edit]

^ Cottle, P. D. (2002-04-12). "Excitations in the Mirror Nuclei 32Ar and 32Si". Physical Review Letters. 88 (17): 172502. Bibcode:2002PhRvL..88q2502C. doi:10.1103/PhysRevLett.88.172502. PMID 12005747. Retrieved 2018-01-08.
^ Kamat, Sharmila (2002-04-23). "Focus: Gazing into a Nuclear Mirror". Physics. American Physical Society. Retrieved 2016-04-11.
^ Discovery by UMass Lowell-led team challenges nuclear theory

https://en.wikipedia.org/wiki/Mirror_nuclei

Saturday, September 18, 2021

09-18-2021-0944 - Maxwell stress tensor Poynting vector

The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force law. When the situation becomes more complicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines. It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand.
In the relativistic formulation of electromagnetism, the Maxwell's tensor appears as a part of the electromagnetic stress–energy tensor which is the electromagnetic component of the total stress–energy tensor. The latter describes the density and flux of energy and momentum in spacetime.
https://en.wikipedia.org/wiki/Maxwell_stress_tensor

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m²). It is named after its discoverer John Henry Poynting who first derived it in 1884.^[1]^: 132 Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition.^[2] The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electric and magnetic fields.
https://en.wikipedia.org/wiki/Poynting_vector

Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, or electron, was thus the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually noticed only when at least one of the surfaces has a high resistance to electrical flow, because the charges that transfer are trapped there for a long enough time for their effects to be observed. These charges then remain on the object until they either bleed off to ground, or are quickly neutralized by a discharge. The familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.
https://en.wikipedia.org/wiki/Electrostatics

A gyroscope (from Ancient Greek γῦρος gûros, "circle" and σκοπέω skopéō, "to look") is a device used for measuring or maintaining orientation and angular velocity.^[1]^[2] It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.
Gyroscopes based on other operating principles also exist, such as the microchip-packaged MEMS gyroscopes found in electronic devices (sometimes called gyrometers), solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope.^[3]
Applications of gyroscopes include inertial navigation systems, such as in the Hubble Telescope, or inside the steel hull of a submerged submarine. Due to their precision, gyroscopes are also used in gyrotheodolites to maintain direction in tunnel mining.^[4] Gyroscopes can be used to construct gyrocompasses, which complement or replace magnetic compasses (in ships, aircraft and spacecraft, vehicles in general), to assist in stability (bicycles, motorcycles, and ships) or be used as part of an inertial guidance system.
MEMS gyroscopes are popular in some consumer electronics, such as smartphones.
https://en.wikipedia.org/wiki/Gyroscope

A control moment gyroscope (CMG) is an attitude control device generally used in spacecraft attitude control systems. A CMG consists of a spinning rotor and one or more motorized gimbals that tilt the rotor’s angular momentum. As the rotor tilts, the changing angular momentum causes a gyroscopic torque that rotates the spacecraft.^[1]^[2]
https://en.wikipedia.org/wiki/Control_moment_gyroscope

https://en.wikipedia.org/wiki/Accumulator_(energy)
https://en.wikipedia.org/wiki/Escape_velocity
https://en.wikipedia.org/wiki/Aircraft_catapult#Steam_catapult
https://en.wikipedia.org/wiki/Linear_stage
https://en.wikipedia.org/wiki/Category:Magnetic_propulsion_devices
https://en.wikipedia.org/wiki/Magnetostatics

Aerodynamics, from Greek ἀήρ aero (air) + δυναμική (dynamics), is the study of motion of air, particularly when affected by a solid object, such as an airplane wing. It is a sub-field of fluid dynamics and gas dynamics, and many aspects of aerodynamics theory are common to these fields. The term aerodynamics is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891.^[1] Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational in nature.
https://en.wikipedia.org/wiki/Aerodynamics

Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case).^[1]The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields.

Irregular reflection[edit]

An irregular reflection is much like the case described above, with the caveat that δ is larger than the maximum allowable turning angle. Thus a detached shock is formed and a more complicated reflection occurs.

Supersonic wind tunnels[edit]

Supersonic wind tunnels are used for testing and research in supersonic flows, approximately over the Mach number range of 1.2 to 5. The operating principle behind the wind tunnel is that a large pressure difference is maintained upstream to downstream, driving the flow.
https://en.wikipedia.org/wiki/Compressible_flow

https://en.wikipedia.org/wiki/Eötvös_number
https://en.wikipedia.org/wiki/Thermodynamics
Above. landing baryonic zone
https://en.wikipedia.org/wiki/Graetz_number
https://en.wikipedia.org/wiki/Görtler_vortices
https://en.wikipedia.org/wiki/Dean_number
https://en.wikipedia.org/wiki/Dukhin_number
https://en.wikipedia.org/wiki/Ohnesorge_number
https://en.wikipedia.org/wiki/Archimedes_number
https://en.wikipedia.org/wiki/Cauchy_number
https://en.wikipedia.org/wiki/Péclet_number
https://en.wikipedia.org/wiki/Damköhler_numbers
https://en.wikipedia.org/wiki/Biot_number
https://en.wikipedia.org/wiki/Prandtl_number
https://en.wikipedia.org/wiki/Stanton_number
https://en.wikipedia.org/wiki/Laplace_number
https://en.wikipedia.org/wiki/Ursell_number
https://en.wikipedia.org/wiki/Weissenberg_number

https://en.wikipedia.org/wiki/Viscoelasticity
https://en.wikipedia.org/wiki/Shear_rate
https://en.wikipedia.org/wiki/Category:Continuum_mechanics
https://en.wikipedia.org/wiki/Category:Temporal_rates
https://en.wikipedia.org/wiki/Linear_induction_motor

https://en.wikipedia.org/wiki/Category:Electric_and_magnetic_fields_in_matter
https://en.wikipedia.org/wiki/Demagnetizing_field
https://en.wikipedia.org/wiki/Micromagnetics
https://en.wikipedia.org/wiki/Domain_wall_(magnetism)
https://en.wikipedia.org/wiki/Magnetocrystalline_anisotropy
https://en.wikipedia.org/wiki/Spin–orbit_interaction
https://en.wikipedia.org/wiki/Hyperfine_structure

https://en.wikipedia.org/wiki/Electrostriction
https://en.wikipedia.org/wiki/Tensor
https://en.wikipedia.org/wiki/Relaxor_ferroelectric
https://en.wikipedia.org/wiki/Magnetostriction
https://en.wikipedia.org/wiki/Torque
https://en.wikipedia.org/wiki/Electric_field_gradient
https://en.wikipedia.org/wiki/Magnetization
https://en.wikipedia.org/wiki/Spin_(physics)
https://en.wikipedia.org/wiki/Point_particle

https://en.wikipedia.org/wiki/Rigid_body
https://en.wikipedia.org/wiki/Energy
https://en.wikipedia.org/wiki/Void_(astronomy)
https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)
https://en.wikipedia.org/wiki/Quintessence_(physics)
https://en.wikipedia.org/wiki/Scalar_field
https://en.wikipedia.org/wiki/Symmetric_matrix
https://en.wikipedia.org/wiki/Quadrupole
https://en.wikipedia.org/wiki/Vector_field

Small molecule hyperfine structure[edit]

A typical simple example of the hyperfine structure due to the interactions discussed above is in the rotational transitions of hydrogen cyanide (¹H¹²C¹⁴N) in its ground vibrational state. Here, the electric quadrupole interaction is due to the ¹⁴N-nucleus, the hyperfine nuclear spin-spin splitting is from the magnetic coupling between nitrogen, ¹⁴N (I_N = 1), and hydrogen, ¹H (I_H = 1⁄2), and a hydrogen spin-rotation interaction due to the ¹H-nucleus. These contributing interactions to the hyperfine structure in the molecule are listed here in descending order of influence. Sub-doppler techniques have been used to discern the hyperfine structure in HCN rotational transitions.^[11]
The dipole selection rules for HCN hyperfine structure transitions are $\Delta J=1$ , $\Delta F=\{0,\pm 1\}$ , where $J$ is the rotational quantum number and $F$ is the total rotational quantum number inclusive of nuclear spin ( $F=J+I_{\text{N}}$ ), respectively. The lowest transition ( $J=1\rightarrow 0$ ) splits into a hyperfine triplet. Using the selection rules, the hyperfine pattern of $J=2\rightarrow 1$ transition and higher dipole transitions is in the form of a hyperfine sextet. However, one of these components ( $\Delta F=-1$ ) carries only 0.6% of the rotational transition intensity in the case of $J=2\rightarrow 1$ . This contribution drops for increasing J. So, from $J=2\rightarrow 1$ upwards the hyperfine pattern consists of three very closely spaced stronger hyperfine components ( $\Delta J=1$ , $\Delta F=1$ ) together with two widely spaced components; one on the low frequency side and one on the high frequency side relative to the central hyperfine triplet. Each of these outliers carry ~ ${\tfrac {1}{2}}J^{2}$ ( $J$ is the upper rotational quantum number of the allowed dipole transition) the intensity of the entire transition. For consecutively higher- $J$ transitions, there are small but significant changes in the relative intensities and positions of each individual hyperfine component.^[12]

Measurements[edit]

Hyperfine interactions can be measured, among other ways, in atomic and molecular spectra and in electron paramagnetic resonance spectra of free radicals and transition-metal ions.

Applications[edit]

Astrophysics[edit]

The hyperfine transition as depicted on the Pioneer plaque
As the hyperfine splitting is very small, the transition frequencies are usually not located in the optical, but are in the range of radio- or microwave (also called sub-millimeter) frequencies.
Hyperfine structure gives the 21 cm line observed in H I regions in interstellar medium.
Carl Sagan and Frank Drake considered the hyperfine transition of hydrogen to be a sufficiently universal phenomenon so as to be used as a base unit of time and length on the Pioneer plaque and later Voyager Golden Record.
In submillimeter astronomy, heterodyne receivers are widely used in detecting electromagnetic signals from celestial objects such as star-forming core or young stellar objects. The separations among neighboring components in a hyperfine spectrum of an observed rotational transition are usually small enough to fit within the receiver's IF band. Since the optical depth varies with frequency, strength ratios among the hyperfine components differ from that of their intrinsic (or optically thin) intensities (these are so-called hyperfine anomalies, often observed in the rotational transitions of HCN^[12]). Thus, a more accurate determination of the optical depth is possible. From this we can derive the object's physical parameters.^[13]

Nuclear spectroscopy[edit]

In nuclear spectroscopy methods, the nucleus is used to probe the local structure in materials. The methods mainly base on hyperfine interactions with the surrounding atoms and ions. Important methods are nuclear magnetic resonance, Mössbauer spectroscopy, and perturbed angular correlation.

Nuclear technology[edit]

The atomic vapor laser isotope separation (AVLIS) process uses the hyperfine splitting between optical transitions in uranium-235 and uranium-238 to selectively photo-ionize only the uranium-235 atoms and then separate the ionized particles from the non-ionized ones. Precisely tuned dye lasers are used as the sources of the necessary exact wavelength radiation.

Use in defining the SI second and meter[edit]

The hyperfine structure transition can be used to make a microwave notch filter with very high stability, repeatability and Q factor, which can thus be used as a basis for very precise atomic clocks. The term transition frequency denotes the frequency of radiation corresponding to the transition between the two hyperfine levels of the atom, and is equal to $f = Δ E / h$ , where $Δ E$ is difference in energy between the levels and $h$ is the Planck constant. Typically, the transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks.
Due to the accuracy of hyperfine structure transition-based atomic clocks, they are now used as the basis for the definition of the second. One second is now defined to be exactly 9192631770cycles of the hyperfine structure transition frequency of caesium-133 atoms.
On October 21, 1983, the 17th CGPM defined the metre as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.^[14]^[15]

Precision tests of quantum electrodynamics[edit]

The hyperfine splitting in hydrogen and in muonium have been used to measure the value of the fine structure constant α. Comparison with measurements of α in other physical systems provides a stringent test of QED.

Qubit in ion-trap quantum computing[edit]

The hyperfine states of a trapped ion are commonly used for storing qubits in ion-trap quantum computing. They have the advantage of having very long lifetimes, experimentally exceeding ~10 minutes (compared to ~1 s for metastable electronic levels).
The frequency associated with the states' energy separation is in the microwave region, making it possible to drive hyperfine transitions using microwave radiation. However, at present no emitter is available that can be focused to address a particular ion from a sequence. Instead, a pair of laser pulses can be used to drive the transition, by having their frequency difference (detuning) equal to the required transition's frequency. This is essentially a stimulated Raman transition. In addition, near-field gradients have been exploited to individually address two ions separated by approximately 4.3 micrometers directly with microwave radiation.^[16]

In physics[edit]

In physics, a pseudoscalar denotes a physical quantity analogous to a scalar. Both are physical quantities which assume a single value which is invariant under proper rotations. However, under the parity transformation, pseudoscalars flip their signs while scalars do not. As reflections through a plane are the combination of a rotation with the parity transformation, pseudoscalars also change signs under reflections.

https://en.wikipedia.org/wiki/Pseudoscalar

In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space.^[b] Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation.^[c] However, when a sequence of such small rotations is composed (integrated) to form an overall final rotation, the resulting spinor transformation depends on which sequence of small rotations was used. Unlike vectors and tensors, a spinor transforms to its negative when the space is continuously rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors: spinors can be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential forms).
It is also possible to associate a substantially similar notion of spinor to Minkowski space, in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geometry by Élie Cartan in 1913.^[1]^[d] In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or "spin", of the electron and other subatomic particles.^[e]
Spinors are characterized by the specific way in which they behave under rotations. They change in different ways depending not just on the overall final rotation, but the details of how that rotation was achieved (by a continuous path in the rotation group). There are two topologically distinguishable classes (homotopy classes) of paths through rotations that result in the same overall rotation, as illustrated by the belt trick puzzle. These two inequivalent classes yield spinor transformations of opposite sign. The spin group is the group of all rotations keeping track of the class.^[f] It doubly covers the rotation group, since each rotation can be obtained in two inequivalent ways as the endpoint of a path. The space of spinors by definition is equipped with a (complex) linear representation of the spin group, meaning that elements of the spin group act as linear transformations on the space of spinors, in a way that genuinely depends on the homotopy class.^[g] In mathematical terms, spinors are described by a double-valued projective representation of the rotation group SO(3).
Although spinors can be defined purely as elements of a representation space of the spin group (or its Lie algebra of infinitesimal rotations), they are typically defined as elements of a vector space that carries a linear representation of the Clifford algebra. The Clifford algebra is an associative algebra that can be constructed from Euclidean space and its inner product in a basis-independent way. Both the spin group and its Lie algebra are embedded inside the Clifford algebra in a natural way, and in applications the Clifford algebra is often the easiest to work with.^[h] A Clifford space operates on a spinor space, and the elements of a spinor space are spinors.^[3] After choosing an orthonormal basis of Euclidean space, a representation of the Clifford algebra is generated by gamma matrices, matrices that satisfy a set of canonical anti-commutation relations. The spinors are the column vectors on which these matrices act. In three Euclidean dimensions, for instance, the Pauli spin matrices are a set of gamma matrices,^[i] and the two-component complex column vectors on which these matrices act are spinors. However, the particular matrix representation of the Clifford algebra, hence what precisely constitutes a "column vector" (or spinor), involves the choice of basis and gamma matrices in an essential way. As a representation of the spin group, this realization of spinors as (complex^[j]) column vectors will either be irreducible if the dimension is odd, or it will decompose into a pair of so-called "half-spin" or Weyl representations if the dimension is even.^[k]
https://en.wikipedia.org/wiki/Spinor

In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from the pointed circle S¹ to X, equipped with the compact-open topology. Two loops can be multiplied by concatenation. With this operation, the loop space is an A_∞-space. That is, the multiplication is homotopy-coherently associative.
The set of path components of ΩX, i.e. the set of based-homotopy equivalence classes of based loops in X, is a group, the fundamental group π₁(X).
The iterated loop spaces of X are formed by applying Ω a number of times.
There is an analogous construction for topological spaces without basepoint. The free loop space of a topological space X is the space of maps from the circle S¹ to X with the compact-open topology. The free loop space of X is often denoted by ${\mathcal {L}}X$ .
As a functor, the free loop space construction is right adjoint to cartesian product with the circle, while the loop space construction is right adjoint to the reduced suspension. This adjunction accounts for much of the importance of loop spaces in stable homotopy theory. (A related phenomenon in computer science is currying, where the cartesian product is adjoint to the hom functor.) Informally this is referred to as Eckmann–Hilton duality.
https://en.wikipedia.org/wiki/Loop_space
https://en.wikipedia.org/wiki/Hom_functor
https://en.wikipedia.org/wiki/Suspension_(topology)#Reduced_suspension

In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.
Light cone in 2D space plus a time dimension.
https://en.wikipedia.org/wiki/Light_cone
https://en.wikipedia.org/wiki/Hypercone

https://en.wikipedia.org/wiki/Hermann_Minkowski

Plane horizontal
verticle pressuron
preon point particle
JND threshold excission
light cone
not detectable not obs comp

Riddle
https://en.wikipedia.org/wiki/Supersymmetry

https://en.wikipedia.org/wiki/Refractive_index
https://en.wikipedia.org/wiki/Topology
https://en.wikipedia.org/wiki/Symmetry
https://en.wikipedia.org/wiki/Equilateral_Triangle
https://en.wikipedia.org/wiki/Perception_Sensation_Cognition

https://en.wikipedia.org/wiki/Light_cone
https://en.wikipedia.org/wiki/White_dwarf
https://en.wikipedia.org/wiki/Nuclear_fusion
https://en.wikipedia.org/wiki/Nuclear_transmutation

https://en.wikipedia.org/wiki/Hydrogen
https://en.wikipedia.org/wiki/Helium-4
https://en.wikipedia.org/wiki/Helium_dimer
https://en.wikipedia.org/wiki/Helium–neon_laser
https://en.wikipedia.org/wiki/Infrared
https://en.wikipedia.org/wiki/Microwave
https://en.wikipedia.org/wiki/Terahertz_radiation
https://en.wikipedia.org/wiki/Fusor_(astronomy)
https://en.wikipedia.org/wiki/Fusor
https://en.wikipedia.org/wiki/Hydrogen_maser

https://en.wikipedia.org/wiki/Stellar_core
https://en.wikipedia.org/wiki/Isotopes_of_hydrogen
https://en.wikipedia.org/wiki/F-type_main-sequence_star
https://en.wikipedia.org/wiki/Red-giant_branch
https://en.wikipedia.org/wiki/Schönberg–Chandrasekhar_limit
https://en.wikipedia.org/wiki/Tritium
https://en.wikipedia.org/wiki/Neutron_source
https://en.wikipedia.org/wiki/TRAPPIST-1f
https://en.wikipedia.org/wiki/Suspension_(topology)#Reduced_suspension
https://en.wikipedia.org/wiki/Pointed_space#Category_of_pointed_spaces

https://en.wikipedia.org/wiki/Baryon#Baryonic_matter
https://en.wikipedia.org/wiki/Symmetry_breaking
https://en.wikipedia.org/wiki/X_and_Y_bosons
https://en.wikipedia.org/wiki/Mirror
https://en.wikipedia.org/wiki/Preon
https://en.wikipedia.org/wiki/Pressuron
https://en.wikipedia.org/wiki/Vertical_pressure_variation
https://en.wikipedia.org/wiki/Pressure-gradient_force
https://en.wikipedia.org/wiki/Pressure_cooker
https://en.wikipedia.org/wiki/Hydrostatic_equilibrium
https://en.wikipedia.org/wiki/List_of_gravitationally_rounded_objects_of_the_Solar_System
https://en.wikipedia.org/wiki/Galactic_Center
https://en.wikipedia.org/wiki/Barycenter

https://en.wikipedia.org/wiki/Plane_axial_one_dimension

https://en.wikipedia.org/wiki/Two-body_problem
https://en.wikipedia.org/wiki/Point_particle

https://en.wikipedia.org/wiki/Acid–base_reaction
https://en.wikipedia.org/wiki/Metal
https://en.wikipedia.org/wiki/Hydrogen
https://en.wikipedia.org/wiki/Oxygen
https://en.wikipedia.org/wiki/Hydrogenation
https://en.wikipedia.org/wiki/Hantzsch_pyridine_synthesis
https://en.wikipedia.org/wiki/Water_gas
https://en.wikipedia.org/wiki/Hydrothermal_synthesis
https://en.wikipedia.org/wiki/Strecker_amino_acid_synthesis
https://en.wikipedia.org/wiki/Dehydration_reaction
https://en.wikipedia.org/wiki/Kiliani–Fischer_synthesis
https://en.wikipedia.org/wiki/Polyester

https://en.wikipedia.org/wiki/Liquid-crystal_polymer
https://en.wikipedia.org/wiki/Ultimate_tensile_strength
https://en.wikipedia.org/wiki/Yield_(engineering)

https://en.wikipedia.org/wiki/Sensory_threshold
https://en.wikipedia.org/wiki/Threshold
https://en.wikipedia.org/wiki/Absolute_threshold
https://en.wikipedia.org/wiki/Reference_range#cutoff
https://en.wikipedia.org/wiki/Transparency_(data_compression)
https://en.wikipedia.org/wiki/Threshold_energy
https://en.wikipedia.org/wiki/Threshold_voltage
https://en.wikipedia.org/wiki/Comparator_applications
https://en.wikipedia.org/wiki/Threshold_cryptosystem
https://en.wikipedia.org/wiki/Percolation_threshold
https://en.wikipedia.org/wiki/Threshold_graph
https://en.wikipedia.org/wiki/Polygyny_threshold_model
https://en.wikipedia.org/wiki/Threshold_model
https://en.wikipedia.org/wiki/Critical_value
https://en.wikipedia.org/wiki/Displaced_threshold
https://en.wikipedia.org/wiki/Electoral_threshold
https://en.wikipedia.org/wiki/Poverty_thresholds_(United_States_Census_Bureau)
https://en.wikipedia.org/wiki/Poverty_in_the_United_States#Poverty_income_guidelines
https://en.wikipedia.org/wiki/Prison
https://en.wikipedia.org/wiki/State_(polity)
https://en.wikipedia.org/wiki/Hydrogen_bond
https://en.wikipedia.org/wiki/Carcerand
https://en.wikipedia.org/wiki/Prison
https://en.wikipedia.org/wiki/Oligomer

https://en.wikipedia.org/wiki/Grigory_Mairanovsky

https://en.wikipedia.org/wiki/Antoine_Lavoisier

https://en.wikipedia.org/wiki/Divine_right_of_kings

In stereochemistry, a torsion angle is defined as a particular example of a dihedral angle, describing the geometric relation of two parts of a molecule joined by a chemical bond.^[5]^[6] Every set of three not-colinear atoms of a molecule defines a half-plane. As explained above, when two such half-planes intersect (i.e., a set of four consecutively-bonded atoms), the angle between them is a dihedral angle. Dihedral angles are used to specify the molecular conformation.^[7] Stereochemical arrangements corresponding to angles between 0° and ±90° are called syn (s), those corresponding to angles between ±90° and 180° anti (a). Similarly, arrangements corresponding to angles between 30° and 150° or between −30° and −150° are called clinal (c) and those between 0° and ±30° or ±150° and 180° are called periplanar (p).
The two types of terms can be combined so as to define four ranges of angle; 0° to ±30° synperiplanar (sp); 30° to 90° and −30° to −90° synclinal (sc); 90° to 150° and −90° to −150° anticlinal (ac); ±150° to 180° antiperiplanar (ap). The synperiplanar conformation is also known as the syn- or cis-conformation; antiperiplanar as anti or trans; and synclinal as gauche or skew.
For example, with n-butane two planes can be specified in terms of the two central carbon atoms and either of the methyl carbon atoms. The syn-conformation shown above, with a dihedral angle of 60° is less stable than the anti-conformation with a dihedral angle of 180°.
For macromolecular usage the symbols T, C, G⁺, G⁻, A⁺ and A⁻ are recommended (ap, sp, +sc, −sc, +ac and −ac respectively).
https://en.wikipedia.org/wiki/Dihedral_angle#In_stereochemistry

Saturday, September 18, 2021

09-18-2021-1248 - Rotation as possible energy source

Rotation as possible energy source [edit]

Because of the enormous amount of energy needed to launch a relativistic jet, some jets are possibly powered by spinning black holes. However, the frequency of high-energy astrophysical sources with jets suggest combinations of different mechanisms indirectly identified with the energy within the associated accretion disk and X-ray emissions from the generating source. Two early theories have been used to explain how energy can be transferred from a black hole into an astrophysical jet:

Blandford–Znajek process.[14] This theory explains the extraction of energy from magnetic fields around an accretion disk, which are dragged and twisted by the spin of the black hole. Relativistic material is then feasibly launched by the tightening of the field lines.

Penrose mechanism.[15] Here energy is extracted from a rotating black hole by frame dragging, which was later theoretically proven to be able to extract relativistic particle energy and momentum,[16] and subsequently shown to be a possible mechanism for jet formation.[17] This effect may also be explained in terms of gravitoelectromagnetism.

https://en.wikipedia.org/wiki/Astrophysical_jet#Relativistic_jet

Saturday, September 18, 2021

09-18-2021-0909 - In a single-sided version, the magnetic field can create repulsion forces that push the conductor away from the stator, levitating it and carrying it along the direction of the moving magnetic field.

The history of linear electric motors can be traced back at least as far as the 1840s to the work of Charles Wheatstone at King's College in London,^[3] but Wheatstone's model was too inefficient to be practical. A feasible linear induction motor is described in US patent 782312 (1905; inventor Alfred Zehden of Frankfurt-am-Main), and is for driving trains or lifts. German engineer Hermann Kemper built a working model in 1935.^[4] In the late 1940s, professor Eric Laithwaite of Imperial College in London developed the first full-size working model.
FEMM simulation of a Cross-section of Magnetic River, coloured by electric current density
In a single-sided version, the magnetic field can create repulsion forces that push the conductor away from the stator, levitating it and carrying it along the direction of the moving magnetic field. Laithwaite called the later versions a magnetic river. These versions of the linear induction motor use a principle called transverse flux where two opposite poles are placed side by side. This permits very long poles to be used, and thus permits high speed and efficiency.^[5]
https://en.wikipedia.org/wiki/Linear_induction_motor

Qubit in ion-trap quantum computing[edit]

The hyperfine states of a trapped ion are commonly used for storing qubits in ion-trap quantum computing. They have the advantage of having very long lifetimes, experimentally exceeding ~10 minutes (compared to ~1 s for metastable electronic levels).
The frequency associated with the states' energy separation is in the microwave region, making it possible to drive hyperfine transitions using microwave radiation. However, at present no emitter is available that can be focused to address a particular ion from a sequence. Instead, a pair of laser pulses can be used to drive the transition, by having their frequency difference (detuning) equal to the required transition's frequency. This is essentially a stimulated Raman transition. In addition, near-field gradients have been exploited to individually address two ions separated by approximately 4.3 micrometers directly with microwave radiation.^[16]

Saturday, September 18, 2021

09-18-2021-1708 - alternating current oscillating particle or wave perturbed γ-γ angular correlation heterodyne gyroscope

Saturday, September 18, 2021

09-18-2021-1315 - Absolute, gauge and differential pressures — zero reference

Saturday, September 18, 2021

09-18-2021-0944 - Maxwell stress tensor Poynting vector

Sunday, September 19, 2021

09-19-2021-0918 - Oxy-fuel welding (commonly called oxyacetylene welding, oxy welding, or gas welding in the United States) and oxy-fuel cutting

https://en.wikipedia.org/wiki/Henry_Grey,_1st_Duke_of_Kent 1702
https://en.wikipedia.org/wiki/Henry_Cavendish 1731
https://en.wikipedia.org/wiki/Torbern_Bergman 1735
https://en.wikipedia.org/wiki/Antoine_Lavoisier 1743
https://en.wikipedia.org/wiki/Thomas_Charles_Hope 1766
https://en.wikipedia.org/wiki/Hydrogen_fuel

https://en.wikipedia.org/wiki/Pierre-Simon_Laplace - French 1749
https://en.wikipedia.org/wiki/Alessandro_Volta - Italy 1745
https://en.wikipedia.org/wiki/William_Herschel - German 1738

https://en.wikipedia.org/wiki/Isaac_Newton 1643

https://en.wikipedia.org/wiki/Pendulum
https://en.wikipedia.org/wiki/Harmonic_oscillator
https://en.wikipedia.org/wiki/Christiaan_Huygens 1629

https://en.wikipedia.org/wiki/Hooke%27s_law
https://en.wikipedia.org/wiki/Robert_Hooke 1635

A point particle (ideal particle^[1] or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.^[2] Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space.^[3] A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. A point particle can also be referred in the case of a moving body in terms of physics.
In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge.^[4]
Sometimes, due to specific combinations of properties, extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in 3-dimensional space whose interactions are described by the inverse square law behave in such a way as if all their matter were concentrated in their centers of mass.^{[citation needed]} In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.^[5]^[6]
In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. For example, the atomic orbit of an electron in the hydrogen atom occupies a volume of ~10⁻³⁰ m³. There is nevertheless a distinction between elementary particles such as electronsor quarks, which have no known internal structure, versus composite particles such as protons, which do have internal structure: A proton is made of three quarks.
Elementary particles are sometimes called "point particles", but this is in a different sense than discussed above.

1Property concentrated at a single point
2Physical point mass
2.1Application
3Probability point mass
4Point charge
5In quantum mechanics
6See also
7Notes and references
7.1Notes
7.2Bibliography
8Further reading

Property concentrated at a single point[edit]

When a point particle has an additive property, such as mass or charge, concentrated at a single point in space, this can be represented by a Dirac delta function.

Physical point mass[edit]

An example of a point mass graphed on a grid. The grey mass can be simplified to a point mass (the black circle). It becomes practical to represent point mass as small circle, or dot, as an actual point is invisible.
Point mass (pointlike mass) is the concept, for example in classical physics, of a physical object (typically matter) that has nonzero mass, and yet explicitly and specifically is (or is being thought of or modeled as) infinitesimal (infinitely small) in its volume or linear dimensions.

Application[edit]

A common use for point mass lies in the analysis of the gravitational fields. When analyzing the gravitational forces in a system, it becomes impossible to account for every unit of massindividually. However, a spherically symmetric body affects external objects gravitationally as if all of its mass were concentrated at its center.

Probability point mass[edit]

A point mass in probability and statistics does not refer to mass in the sense of physics, but rather refers to a finite nonzero probability that is concentrated at a point in the probability mass distribution, where there is a discontinuous segment in a probability density function. To calculate such a point mass, an integration is carried out over the entire range of the random variable, on the probability density of the continuous part. After equating this integral to 1, the point mass can be found by further calculation.

Point charge[edit]

Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right.
A point charge is an idealized model of a particle which has an electric charge. A point charge is an electric charge at a mathematical point with no dimensions.
The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges. The electric field associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero making energy (thus mass) of point charge infinite.
Earnshaw's theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges.

In quantum mechanics[edit]

A proton is a combination of two up quarks and one down quark, held together by gluons.
Main article: Elementary particle
In quantum mechanics, there is a distinction between an elementary particle (also called "point particle") and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no known internal structure. Whereas a composite particle, such as a proton or neutron, has an internal structure (see figure). However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle. The particle wavepacketalways occupies a nonzero volume. For example, see atomic orbital: The electron is an elementary particle, but its quantum states form three-dimensional patterns.
Nevertheless, there is good reason that an elementary particle is often called a point particle. Even if an elementary particle has a delocalized wavepacket, the wavepacket can be represented as a quantum superposition of quantum states wherein the particle is exactly localized. Moreover, the interactions of the particle can be represented as a superposition of interactions of individual states which are localized. This is not true for a composite particle, which can never be represented as a superposition of exactly-localized quantum states. It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero.
For example, for the electron, experimental evidence shows that the size of an electron is less than 10⁻¹⁸ m.^[7] This is consistent with the expected value of exactly zero. (This should not be confused with the classical electron radius, which, despite the name, is unrelated to the actual size of an electron.)

Notes and references

https://en.wikipedia.org/wiki/Point_particle
https://en.wikipedia.org/wiki/Two-body_problem
https://en.wikipedia.org/wiki/Warped_plane
https://en.wikipedia.org/wiki/N-body_problem
https://en.wikipedia.org/wiki/Mass_ratio

https://en.wikipedia.org/wiki/Mass_ratio
https://en.wikipedia.org/wiki/Escape_velocity
https://en.wikipedia.org/wiki/Vis-viva_equation
https://en.wikipedia.org/wiki/Perturbation_(astronomy)
https://en.wikipedia.org/wiki/Mass_ratio
https://en.wikipedia.org/wiki/Lyapunov_stability
https://en.wikipedia.org/wiki/Propellant_mass_fraction
https://en.wikipedia.org/wiki/Oberth_effect
https://en.wikipedia.org/wiki/Category:Astrodynamics
https://en.wikipedia.org/wiki/Propellant

https://en.wikipedia.org/wiki/Line_segment
https://en.wikipedia.org/wiki/String
https://en.wikipedia.org/wiki/Chord_(geometry)
https://en.wikipedia.org/wiki/Loop
https://en.wikipedia.org/wiki/Spring
https://en.wikipedia.org/wiki/Spiral
https://en.wikipedia.org/wiki/Angular_acceleration
https://en.wikipedia.org/wiki/Period
https://en.wikipedia.org/wiki/Pendulum
https://en.wikipedia.org/wiki/Linear_energy_transfer
https://en.wikipedia.org/wiki/Longest_path_problem
https://en.wikipedia.org/wiki/Linear_motor
https://en.wikipedia.org/wiki/Bipartite_graph
https://en.wikipedia.org/wiki/Eulerian_path
https://en.wikipedia.org/wiki/Phonograph
https://en.wikipedia.org/wiki/Linear_induction_motor
https://en.wikipedia.org/wiki/Electrostatics

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09-19-2021-1444 - Diethylzinc (C2H5)2Zn, or DEZ
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09-19-2021-1438 - Organotin stannanes
09-19-2021-1438 - Intramolecular
09-19-2021-1435 - Neutron Cross Section Phosphorus...
09-19-2021-1434 - dihedral angle
09-19-2021-1432 - Atropisomers
09-19-2021-1429 - conformational isomerism
09-19-2021-1427 - molecular configuration
09-19-2021-1346 - 3475/6-7,8
09-19-2021-1308 - electromotive force (emf)
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09-19-2021-1230 - Strontium oxide or strontia, SrO
09-19-2021-1227 - hydrogen fuel
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09-19-2021-1154 - Joseph Black 1728 1799
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09-19-2021-1137 - Drafting hydroelectricity hydrop...
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09-19-2021-1033 - The Gobelins Manufactory (Paris,...
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09-19-2021-1029 - Radical Theory phlogiston theory
09-19-2021-1027 - Antoine-Laurent de Lavoisier 174...
09-19-2021-1024 - Encyclopédie méthodique par ord...
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Kurzgesagt – In a Nutshell -

The Last Light Before Eternal Darkness – White Dwarfs & Black Dwarfs

Saturday, September 18, 202109-18-2021-1253 - scalars (scalar quantities ; physics ; physical quantity)

Blog Archive

Sunday, September 19, 2021

09-19-2021-1447 - Bunsen detected previously unknown new blue spectral emission lines in samples of mineral water from Dürkheim.

Career[edit]

The capillary electrometer[edit]

Piezoelectricity[edit]

Colour photography[edit]

Integral photography[edit]

Measurement of time[edit]

The coelostat[edit]

Life[edit]

Torsion balance[edit]

Honors[edit]

See also[edit]

References[edit]

Further reading[edit]

University of Leiden[edit]

Liquefaction of helium[edit]

Superconductivity[edit]

Life[edit]

Works[edit]

Structure[edit]

Synthetic methods[edit]

Naturally occurring cyclophanes[edit]

[n.n]Paracyclophanes[edit]

Cycloparaphenylenes[edit]

Phanes[edit]

References

See also[edit]

List of nanostructures[edit]

See also[edit]

References[edit]

Friday, September 17, 2021

09-17-2021-0229 - Space-division multiple access (SDMA)

Thermodynamics[edit]

Saturday, August 14, 2021

08-13-2021-2226 - Time Reversal Symmetry

Redox properties[edit]

Modified viologens and related compounds[edit]

Uses[edit]

Mercury cell electrolysis[edit]

Mechanism of action[edit]

Electrostatic[edit]

Electrothermal[edit]

Electromagnetic[edit]

Nuclear[edit]

Photonic[edit]

See also[edit]

General relativity[edit]

Contractible versus noncontractible[edit]

Cauchy horizon[edit]

See also[edit]

Time[edit]

Saturday, September 18, 2021

09-18-2021-0818 - Ligand Cone Angle Tolman Cone Angle ligand cone angle Tolman cone angle tolman cone angle

Asymmetric cases[edit]

Variations[edit]

Application[edit]

See also[edit]

Time dilation caused by a relative velocity[edit]

Astrophysical applications[edit]

Gravitational lensing[edit]

Saturday, September 18, 2021

09-18-2021-1152 - Gravitational time dilation (two disparities on a plane; two size disparate spheres on a plane; two weight disparate or size disparate on a warped plane)

https://en.wikipedia.org/wiki/Gravitational_time_dilationhttps://en.wikipedia.org/wiki/Gravitational_lens

Saturday, September 18, 2021

09-18-2021-1712 - Pressure Measurement (Absolute, gauge and differential pressures — zero reference)

Saturday, September 18, 2021

09-18-2021-1015 - Linear Stage Translation Stage motion system single axis

External links[edit]

Weisstein, Eric W. "Differentials". MathWorld.https://en.wikipedia.org/wiki/Differential_(mathematics)

Saturday, September 18, 2021

09-18-2021-1226 - scalar field dark matter

In astrophysics and cosmology scalar field dark matter is a classical, minimally coupled, scalar field postulated to account for the inferred dark matter.[2]

Background[edit]

Scalar field[edit]

See also[edit]

Saturday, September 18, 2021

09-18-2021-1710 - Degree of Freedom is an Independent Physical Parameter in the Formal Description of the state of a physical system.

Saturday, September 18, 2021

https://en.wikipedia.org/wiki/Gravitational_time_dilation
https://en.wikipedia.org/wiki/Gravitational_lens

Weisstein, Eric W. "Differentials". MathWorld.
https://en.wikipedia.org/wiki/Differential_(mathematics)

In astrophysics and cosmology scalar field dark matter is a classical, minimally coupled, scalar field postulated to account for the inferred dark matter.^[2]

Dynamic nuclear polarisation
Electron paramagnetic resonance
https://en.wikipedia.org/wiki/Hyperfine_structure

1Property concentrated at a single point
2Physical point mass
2.1Application
3Probability point mass
4Point charge
5In quantum mechanics
6See also
7Notes and references
7.1Notes
7.2Bibliography
8Further reading