Content deleted Content added
No edit summary |
Help needed: Maxwellian |
||
Line 10:
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.
A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six dimensional phase space, <math>f(x,y,z;p_x,p_y,p_z)</math> and multiply by the total space volume, to give the momentum distribution i.e. the number of particles in the momentum phase space having approximately the [[momentum]] <math>(p_x,p_y,p_z)</math>.
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]], [[statistical mechanics]] and [[nuclear physics]].
Line 20:
Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the [[exponent]]'s [[numerator]] is <math>m((v_x - u_x)^2 + (v_y - u_y)^2 + (v_z - u_z)^2)</math>; <math>(u_x, u_y, u_z)</math> 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.
Plasma theories such as [[magnetohydrodynamics]] may assume the particles to be in [[thermodynamic equilibrium]]. In this case, the distribution function is ''[[Maxwellian]]{{dn|date=July 2012}}''. 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 [[Plasma (physics)|plasmas]] are rarely in thermal equilibrium.
The mathematical analog of a distribution is a [[measure (mathematics)|measure]]; the time evolution of a measure on a phase space is the topic of study in [[dynamical systems]].
| |||