In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is (ṁ, pronounced "m-dot"), although sometimes μ (Greek lowercase mu) is used.
Sometimes, mass flow rate is termed mass flux or mass current, see for example Schaum's Outline of Fluid Mechanics.[1] In this article, the (more intuitive) definition is used.
Mass flow rate is defined by the limit:[2][3]
i.e. the flow of mass m through a surface per unit time t.
The overdot on the m is Newton's notation for a time derivative. Since mass is a scalar quantity, the mass flow rate (the time derivative of mass) is also a scalar quantity. The change in mass is the amount that flows after crossing the boundary for some time duration, not the initial amount of mass at the boundary minus the final amount at the boundary, since the change in mass flowing through the area would be zero for steady flow.
https://en.wikipedia.org/wiki/Mass_flow_rate
In general relativity, a gravitational plane wave is a special class of a vacuum pp-wave spacetime, and may be defined in terms of Brinkmann coordinates by
![ds^2=[a(u)(x^2-y^2)+2b(u)xy]du^2+2dudv+dx^2+dy^2](https://wikimedia.org/api/rest_v1/media/math/render/svg/a222a809d795f518ad1e13bf32f91d33d907e699)
Here, can be any smooth functions; they control the waveform of the two possible polarization modes of gravitational radiation. In this context, these two modes are usually called the plus mode and cross mode, respectively.
Gravitational waves exist and travel at the speed of light. Every form of matter and energy with which we are familiar has the same gravitational effect positive attraction. Gravitational waves are very weak. Consider two neutron stars of one solar mass (MNS =M) and radius rNS = 6 km orbiting each other essentially in contact. (This is for example, clearly tidal forces will have a very disruptive effect on the two neutron stars.)
The characteristic acceleration at the neutron stars is
https://en.wikipedia.org/wiki/Gravitational_plane_wave
A topological soliton or "toron" occurs when two adjoining structures or spaces are in some way "out of phase" with each other in ways that make a seamless transition between them impossible. One of the simplest and most commonplace examples of a topological soliton occurs in old-fashioned coiled telephone handset cords, which are usually coiled clockwise. Years of picking up the handset can end up coiling parts of the cord in the opposite counterclockwse direction, and when this happens there will be a distinctive larger loop that separates the two directions of coiling. This odd looking transition loop, which is neither clockwise nor counterclockwise, is an excellent example of a topological soliton. No matter how complex the context, anything that qualifies as a topological soliton must at some level exhibit this same simple issue of reconciliation seen in the twisted phone cord example.
Topological solitons arise with ease when creating the crystalline semiconductors used in modern electronics, and in that context their effects are almost always deleterious. For this reason such crystal transitions are called topological defects. However, this mostly solid-state terminology distracts from the rich and intriguing mathematical properties of such boundary regions. Thus for most non-solid-state contexts the more positive and mathematically rich phrase "topological soliton" is preferable.
A more detailed discussion of topological solitons and related topics is provided below.
In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution.
https://en.wikipedia.org/wiki/Topological_defect
n physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, rate of fluid flow, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol Q (sometimes V̇). The SI unit is cubic metres per second (m3/s). Another unit used is standard cubic centimetres per minute (SCCM). In hydrometry, it is known as discharge.
In US customary units and imperial units, volumetric flow rate is often expressed as cubic feet per second (ft3/s) or gallons per minute (either US or imperial definitions).
Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m3/(m2·s), that is, m·s−1. The integration of a flux over an area gives the volumetric flow rate.
https://en.wikipedia.org/wiki/Volumetric_flow_rate
A current in a fluid is the magnitude and direction of flow within that fluid. An air current presents the same properties specifically for a gaseousmedium.
Types of fluid currents include
- Boundary current
- Current (stream), a current in a river or stream
- Longshore current
- Ocean current
- Rip current
- Rip tide
- Subsurface currents
- Turbidity current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume.[1]: 2 [2]: 622 The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons.[3]
The SI unit of electric current is the ampere, or amp, which is the flow of electric charge across a surface at the rate of one coulomb per second. The ampere (symbol: A) is an SI base unit[4]: 15 Electric current is measured using a device called an ammeter.[2]: 788
Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers. In ordinary conductors, they cause Joule heating, which creates light in incandescent light bulbs. Time-varying currents emit electromagnetic waves, which are used in telecommunications to broadcast information.
https://en.wikipedia.org/wiki/Electric_current
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two values differ only by a constant and the units of measurement.[1][2] The principle is described by the physicist Albert Einstein's famous formula: .[3]
Massless particles such as photons have zero invariant mass, but massless free particleshave both momentum and energy. The equivalence principle implies that when energy is lost in chemical reactions, nuclear reactions, and other energy transformations, the system will also lose a corresponding amount of mass. The energy, and mass, can be released to the environment as radiant energy, such as light, or as thermal energy. The principle is fundamental to many fields of physics, including nuclear and particle physics.
https://en.wikipedia.org/wiki/Mass–energy_equivalence
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