|
Elsasser Number
The Elsasser number, Λ, is a dimensionless number in magnetohydrodynamics that represents the ratio of magnetic forces to the Coriolis force. \Lambda = \frac where σ is the conductivity of the fluid, ''B'' is the magnetic field, ρ is the density of the fluid, and Ω is the rate of rotation of the body. Applications This number is useful when studying the linear stability In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the for ... of an accretion disc to the magnetorotational instability. Notes References * {{Fluiddynamics-stub Dimensionless numbers of fluid mechanics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetohydrodynamics
In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single Continuum mechanics, continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in Plasma (physics), plasmas and liquid metals and has applications in multiple fields including space physics, geophysics, astrophysics, and engineering. 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. History The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature (journal), ''Nature'' titled "Existence of Electromagnetic–Hydrodynamic Waves" which outlined his discovery ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Conductivity
Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek alphabet, Greek letter (Rho (letter), rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the Electrical resistance, 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 (letter), sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function (mathematics), function assigning a Euclidean vector, vector to each point of space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Stability
In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form dr/dt = A r, where ''r'' is the perturbation to the steady state, ''A'' is a linear operator whose spectrum contains eigenvalues with ''positive'' real part. If all the eigenvalues have ''negative'' real part, then the solution is called linearly stable. Other names for linear stability include exponential stability or stability in terms of first approximation. If there exists an eigenvalue with ''zero'' real part then the question about stability cannot be solved on the basis of the first approximation and we approach the so-called "centre and focus problem". Examples Ordinary differential equation The differential equation \frac = x - x^2 has two stationary (time-independent) solutions: ''x'' = 0 and ''x'' = 1. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
