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Landau–Lifshitz Equation (continuous Spin Field)
In physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a name used for several different differential equations *For the Landau–Lifshitz aeroacoustic equation see aeroacoustics. *For the Landau–Lifshitz equation describing the precessional motion of magnetization M in a solid with an effective magnetic field H and with damping, see Landau–Lifshitz–Gilbert equation. *For the Landau–Lifshitz equation describing a magnetic field in dimensions see Landau–Lifshitz model In solid-state physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a partial differential equation describing time evolution of magnetism in solids, depending on 1 time variable and 1, 2, or 3 space variable .... *For the Landau-Lifshitz equation approximating the Abraham-Lorentz force. {{mathematical disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Landau
Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet- Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's equations for ''S'' matrix singularities. He received the 1962 Nobel Prize in Physics for his development of a mathematical theory of superfluidity that accounts for the properties of liquid helium II at a temperature below (). Life Early years Landau was born ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evgeny Lifshitz
Evgeny Mikhailovich Lifshitz (russian: Евге́ний Миха́йлович Ли́фшиц; February 21, 1915, Kharkiv, Russian Empire – October 29, 1985, Moscow, Russian SFSR) was a leading Soviet physicist and brother of the physicist Ilya Lifshitz. Work Born into a Ukrainian Jewish family in Kharkov, Kharkov Governorate, Russian Empire (now Kharkiv, Ukraine). Lifshitz is well known in the field of general relativity for coauthoring the BKL conjecture concerning the nature of a ''generic curvature singularity''. , this is widely regarded as one of the most important open problems in the subject of classical gravitation. With Lev Landau, Lifshitz co-authored ''Course of Theoretical Physics'', an ambitious series of physics textbooks, in which the two aimed to provide a graduate-level introduction to the entire field of physics. These books are still considered invaluable and continue to be widely used. Lifshitz was the second of only 43 people ever to pass Landau's " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aeroacoustics
Aeroacoustics is a branch of acoustics that studies noise generation via either turbulent fluid motion or aerodynamic forces interacting with surfaces. Noise generation can also be associated with periodically varying flows. A notable example of this phenomenon is the Aeolian tones produced by wind blowing over fixed objects. Although no complete scientific theory of the generation of noise by aerodynamic flows has been established, most practical aeroacoustic analysis relies upon the so-called ''aeroacoustic analogy'', proposed by Sir James Lighthill in the 1950s while at the University of Manchester. whereby the governing equations of motion of the fluid are coerced into a form reminiscent of the wave equation of "classical" (i.e. linear) acoustics in the left-hand side with the remaining terms as sources in the right-hand side. History The modern discipline of aeroacoustics can be said to have originated with the first publication of Lighthill in the early 1950s, when noise ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called ''nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, ''precession'' refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes. Torque-free Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, but the angular velocit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Diametric. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field. Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed. Ferromagnetic and ferrimagnetic materials have strong magnetization in a magnetic field, and can be ''magnetized'' to have magnetization in the absence of an external field, becoming a permanent magnet. Magnetization is not necessarily uniform within a material, but may vary between different points. Magnetizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Magnetic Field
A magnetic field is a vector 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, and are created by electric currents such as those used in electromagnets, and by 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 assigning a vector to each point of space, calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Damping
Magnetic damping is a form of damping that occurs when a magnetic field (i.e. a magnet) travels some distance through or past an electrical conductor (or vice versa). Definition When a magnetic field moves through a conductor the movement induces an eddy current in the conductor. The flow of electrons in the conductor immediately creates an opposing magnetic field which results in damping of the magnet and produces heat inside the conductor similar to heat buildup inside of a power cord during use. The amount of energy transferred to the conductor in the form of heat is equal to the change in kinetic energy lost by the magnet – the greater the loss of kinetic energy of a magnet (a product of its mass and speed), the greater the heat buildup in the conductor and the more forceful the damping effect. Eddy currents induced in conductors are much stronger as temperatures approach cryogenic levels. This allows for critical damping for cryogenic applications and testing in the aerospac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau–Lifshitz–Gilbert Equation
In physics, the Landau–Lifshitz–Gilbert equation, named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the precession, precessional motion of magnetization in a Solid-state physics, solid. It is a modification by Gilbert of the original equation of Landau and Lifshitz. The various forms of the equation are commonly used in micromagnetics to model the effects of a magnetic field on ferromagnetic materials. In particular it can be used to model the time domain behavior of magnetic elements due to a magnetic field. An additional term was added to the equation to describe the effect of spin polarized current on magnets. Landau–Lifshitz equation In a ferromagnet, the magnetization can vary internally but at each point its magnitude is equal to the saturation magnetization . The Landau–Lifshitz–Gilbert equation predicts the rotation of the magnetization in response to torques. An earlier, but equivalent, equation (t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau–Lifshitz Model
In solid-state physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a partial differential equation describing time evolution of magnetism in solids, depending on 1 time variable and 1, 2, or 3 space variables. Landau–Lifshitz equation The LLE describes an anisotropic magnet. The equation is described in as follows: It is an equation for a vector field S, in other words a function on R1+''n'' taking values in R3. The equation depends on a fixed symmetric 3 by 3 matrix ''J'', usually assumed to be diagonal; that is, J=\operatorname(J_, J_, J_). It is given by Hamilton's equation of motion for the Hamiltonian :H=\frac\int \left sum_i\left(\frac\right)^-J(\mathbf)\right, dx\qquad (1) (where ''J''(S) is the quadratic form of ''J'' applied to the vector S) which is : \frac = \mathbf\wedge \sum_i\frac + \mathbf\wedge J\mathbf.\qquad (2) In 1+1 dimensions this equation is : \frac = \mathbf\wedge \frac + \mathbf\wedge J\mathbf.\qquad (3) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
