Distribution function (physics): Difference between revisions

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The [[Maxwell-Boltzmann distribution|basic distribution function]] uses the [[Boltzmann constant]] <math>k</math> and temperature <math>T</math> with the number density to modify the [[normal distribution]]:

:<math> f = \frac{n}{\sqrt{(2 \pi RTkT)^3}} \exp\left({-\frac{m(v_x^2 + v_y^2 + v_z^2)}{2kT}}\right) </math>

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.