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Zakharov System
In mathematics, the Zakharov system is a system of non-linear partial differential equations, introduced by Vladimir Zakharov in 1972 to describe the propagation of Langmuir waves in an ionized plasma. The system consists of a complex field ''u'' and a real field ''n'' satisfying the equations :i \partial_t^ u + \nabla^2 u = un :\Box n = -\nabla^2 (, u, ^2_) See also * Resonant interaction In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met ...; the Zakharov equation describes non-linear resonant interactions. References * Zakharov, V. E. (1968). ''Stability of periodic waves of finite amplitude on the surface of a deep fluid.'' Journal of Applied Mechanics and Technical Physics, 9(2), 190-194. *. Partial differential equations Waves in plasmas Plasma physics Gravity waves { ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir E
Vladimir may refer to: Names * Vladimir (name) for the Bulgarian, Croatian, Czech, Macedonian, Romanian, Russian, Serbian, Slovak and Slovenian spellings of a Slavic name * Uladzimir for the Belarusian version of the name * Volodymyr for the Ukrainian version of the name * Włodzimierz (given name) for the Polish version of the name * Valdemar for the Germanic version of the name * Wladimir for an alternative spelling of the name Places * Vladimir, Russia, a city in Russia * Vladimir Oblast, a federal subject of Russia * Vladimir-Suzdal, a medieval principality * Vladimir, Ulcinj, a village in Ulcinj Municipality, Montenegro * Vladimir, Gorj, a commune in Gorj County, Romania * Vladimir, a village in Goiești Commune, Dolj County, Romania * Vladimir (river), a tributary of the Gilort in Gorj County, Romania * Volodymyr (city), a city in Ukraine Religious leaders * Metropolitan Vladimir (other), multiple * Jovan Vladimir (d. 1016), ruler of Doclea and a saint of the S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langmuir Wave
Langmuir may refer to: * Langmuir (crater), an impact crater on the Moon's far side * ''Langmuir'' (journal), an academic journal on colloids, surfaces and interfaces, published by the American Chemical Society * Langmuir (unit), a unit of exposure of an adsorbate/gas to a substrate used in surface science to study adsorption * Langmuir Cove, a cove in the north end of Arrowsmith Peninsula, Graham Land, Antarctica * Langmuir monolayer, a one-molecule thick layer of an insoluble organic material spread onto an aqueous subphase in a Langmuir-Blodgett trough People * Alexander Langmuir Alexander Duncan Langmuir (12 September 1910 – 22 November 1993) was an American epidemiologist. He is renowned for creating the Epidemic Intelligence Service. Biography Alexander D. Langmuir was born in Santa Monica, California. He received h ... (1910–1993), American epidemiologist * Gavin I. Langmuir (1924–2005), Canadian veteran of World War II, historian of anti-Semitism and medieva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ionized
Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected. Uses Everyday examples of gas ionization are such as within a fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Müller counter or the ionization chamber. The ionizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma (physics)
Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are ''anisotropic'', meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the plasma high conductivity, the electric field associated with a plasma moving with velocity \mathbf in the magnetic field \mathbf is given by the usual Lorentz force, Lorentz formula \mathbf = -\mathbf\times\mathbf, and is not affected by Debye shielding. Mathematical descriptions To completely describe the state of a plasma, all of the particle locations and velocities that describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonant Interaction
In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; instabilities offer insight into high-dimensional chaos and turbulence. Discussion The underlying concept is that when the sum total of the energy and momentum of several vib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Journal Of Experimental And Theoretical Physics
The ''Journal of Experimental and Theoretical Physics'' (''JETP'') [russian: Журнал Экспериментальной и Теоретической Физики, italic=yes (''ЖЭТФ''), or ''Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki'' (''ZhÉTF'')] is a peer-reviewed Russian bilingual scientific journal covering all areas of experimental and theoretical physics. For example, coverage includes solid state physics, elementary particles, and cosmology. The journal is published simultaneously in both Russian and English languages. The editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... is Alexander F. Andreev. In addition, this journal is a continuation of ''Soviet physics, JETP'' (1931–1992), which began English translation in 1955. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waves In Plasmas
In plasma physics, waves in plasmas are an interconnected set of particles and fields which propagate in a periodically repeating fashion. A Plasma (physics), plasma is a Plasma (physics)#Plasma_potential, quasineutral, electrical conductivity, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its electrical conductivity, a plasma couples to electric field, electric and magnetic fields. This complex of particles and fields supports a wide variety of wave phenomena. The electromagnetic fields in a plasma are assumed to have two parts, one static/equilibrium part and one oscillating/perturbation part. Waves in plasmas can be classified as electromagnetic or electrostatic according to whether or not there is an oscillating magnetic field. Applying Faraday's law of induction to plane waves, we find \mathbf\times\ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma Physics
Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the . It contains a significant portion of charged particles – s and/or s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of |
