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Induction Equation
The induction equation, one of the magnetohydrodynamic equations, is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo theory. Mathematical statement Maxwell's equations describing the Faraday's and Ampere's laws read: \vec \times \vec= -, and \vec\times\vec = \mu_0\vec, where: *\vec is the electric field. *\vec is the magnetic field. *\vec is the electric current. The displacement current can be neglected in a plasma as it is negligible compared to the current carried by the free charges. The only exception to this is for exceptionally high frequency phenomena: for example, for a plasma with a typical electrical conductivity of \sigma = 10^7 \mathrm , the displacement current is smaller than the free current by a factor of 10^3 for frequencies below 2.10^ \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamic
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word ''magnetohydrodynamics'' is derived from ' meaning magnetic field, ' meaning water, and ' meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. The fundamental concept behind MHD is that magnetic fields can induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the Navier–Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetism. These differential equations must be solved simultaneously, either analytically or numerically. History The first recorde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Field
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfvén's Theorem
In magnetohydrodynamics, Alfvén's theorem, or the frozen-in flux theorem, "states that in a fluid with infinite electric conductivity, the magnetic field is frozen into the fluid and has to move along with it." Hannes Alfvén put the idea forward for the first time in 1942. In his own words: "In view of the infinite conductivity, every motion (perpendicular to the field) of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. Thus the matter of the liquid is “fastened” to the lines of force...." In later life, Alfvén changed his mind and advised against use of his own theorem. However, Alfvén's theorem is much used today because of a second mechanism, magnetic reconnection. This is a breakdown of Alfvén's theorem in thin current sheets and is important as it can untangle field lines that would become increasingly tangled by plasma velocity shears and vortices in regions of low plasma beta if Alfvén's theorem applied every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfvén's Theorem
In magnetohydrodynamics, Alfvén's theorem, or the frozen-in flux theorem, "states that in a fluid with infinite electric conductivity, the magnetic field is frozen into the fluid and has to move along with it." Hannes Alfvén put the idea forward for the first time in 1942. In his own words: "In view of the infinite conductivity, every motion (perpendicular to the field) of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. Thus the matter of the liquid is “fastened” to the lines of force...." In later life, Alfvén changed his mind and advised against use of his own theorem. However, Alfvén's theorem is much used today because of a second mechanism, magnetic reconnection. This is a breakdown of Alfvén's theorem in thin current sheets and is important as it can untangle field lines that would become increasingly tangled by plasma velocity shears and vortices in regions of low plasma beta if Alfvén's theorem applied every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accretion Disc
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward towards the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology. Manifestations Accretion disks are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These disks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxies
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. Galaxies, averaging an estimated 100 million stars, range in size from dwarfs with less than a hundred million stars, to the largest galaxies known – supergiants with one hundred trillion stars, each orbiting its galaxy's center of mass. Most of the mass in a typical galaxy is in the form of dark matter, with only a few percent of that mass visible in the form of stars and nebulae. Supermassive black holes are a common feature at the centres of galaxies. Galaxies are categorized according to their visual morphology as elliptical, spiral, or irregular. Many are thought to have supermassive black holes at their centers. The Milky Way's central black hole, known as Sagittarius A*, has a mass four million times greater than the S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sky, night, but their immense distances from Earth make them appear as fixed stars, fixed points of light. The most prominent stars have been categorised into constellations and asterism (astronomy), asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated to stars. Only about 4,000 of these stars are visible to the naked eye, all within the Milky Way galaxy. A star's life star formation, begins with the gravitational collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. Its stellar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Reynolds Number
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by: : \mathrm_\mathrm = \frac ~~ \sim \frac where * U is a typical velocity scale of the flow, * L is a typical length scale of the flow, * \eta is the magnetic diffusivity. The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory. When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case focus instead often rests on the influence of the magnetic field on the flow. Derivation In the theory of magnetohydrodynamics, the magnetic Reynolds number can be derived from the induction equation: : \frac = \nabla \times (\mathbf \times \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter (sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can be both fluid and solid. Viscoelastic fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers any liquid constituent of the body (body fluid), whereas "liquid" is not used in this sense. Sometimes liquids given for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter (sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Current Density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Definition Assume that ''A'' (SI unit: m2) is a small surface centred at a given point ''M'' and orthogonal to the motion of the charges at ''M''. If ''I'' (SI unit: A) is the electric current flowing through ''A'', then electric current density ''j'' at ''M'' is given by the limit: :j = \lim_ \frac = \left.\frac \_, with surface ''A'' remaining centered at ''M'' and orthogonal to the motion of the charges during the limit process. The current density vector j is the vector whose magnitude is the electric current density, and whose dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
