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Encyclopedia > Distribution function

In physics, a particle's distribution function is a function of seven variables, f(x,y,z,t;vx,vy,vz), which gives the number of particles per unit volume in phase space. It is the number of particles having approximately the velocity(vx,vy,vz) near the place (x,y,z) and time (t). The usual normalization of the distribution function is Wikibooks Wikiversity has more about this subject: School of Physics sci. ... A phase diagram or phase space is a useful construct used in mathematics and physics to demonstrate and visualise the changes in a given system. ... This article is about velocity in physics. ...

Here, N is the total number of particles and n is the number density of particles - the number of particles per unit volume, or the density divided by the mass of individual particles. Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. ...

Particle distribution functions are often used in plasma physics to describe wave-particle interactions and velocity-space instabilities. Distribution functions are also used in fluid mechanics and statistical mechanics. This article is about plasma in the sense of an ionized gas. ... Fluid mechanics or fluid dynamics is the study of the macroscopic physical behaviour of fluids . ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

The basic distribution function uses the Boltzmann constant k and temperature T with the number density to modify the normal distribution: The Maxwell-Boltzmann distribution is a probability distribution with applications in physics and chemistry. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields, especially in physics and engineering. ...

Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is (m(vxux)2 + (vxux)2 + (vxux)2); (ux,uy,uz) is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature. In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ... In algebra, a vulgar fraction consists of one integer divided by a non-zero integer. ...

Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is Maxwellian. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used since plasmas are rarely in thermal equilibrium. MHD Simulation of Solar Wind Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics), is the academic discipline which studies the dynamics of electrically conducting fluids. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ... The word plasma has a Greek root which means to be formed or molded (the word plastic shares this root). ...

Results from FactBites:

 Distribution functions for identical particles (249 words) The distribution function f(E) is the probability that a particle is in energy state E. The distribution function is a generalization of the ideas of discrete probability to the case where energy can be treated as a continuous variable. The term A in the denominator of each distribution is a normalization term which may change with temperature. The Maxwell-Boltzmann distribution is the classical distribution function for distribution of an amount of energy between identical but distinguishable particles.
 Cumulative distribution function - Wikipedia, the free encyclopedia (556 words) It is conventional to use a capital F for a cumulative distribution function, in contrast to the lower-case f used for probability density functions and probability mass functions. Continuity of the distribution implies that P(X = a) = P(X = b) = 0, so the difference between "<" and "≤" ceases to be important in this context.) The function f is equal to the derivative of F almost everywhere, and it is called the probability density function of the distribution of X. The Kolmogorov-Smirnov test is based on cumulative distribution functions and can be used to test to see whether two empirical distributions are different or whether an empirical distribution is different from an ideal distribution.
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