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where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the [[diffusion]] of particles, and "coll" is the [[collision]] term – accounting for the forces acting between particles in collisions. Expressions for each term on the right side are provided below.<ref name="McGrawHill" />
where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the [[diffusion]] of particles, and "coll" is the [[collision]] term – accounting for the forces acting between particles in collisions. Expressions for each term on the right side are provided below.<ref name="McGrawHill" />
Note that some authors use the particle velocity '''v''' instead of momentum '''p'''; they are related in the definition of momentum by '''p''' = ''m'''''v'''.
Note that some authors use the particle velocity '''v''' instead of momentum '''p'''; they are related in the definition of momentum by '''p''' = ''m'''''v'''.
is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.
is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.
Category:Statistical mechanics
Category:Statistical mechanics
=== Simplifications to the collision term ===
=== Simplifications to the collision term ===
where <math>\nu</math> is the molecular collision frequency, and <math>f_0</math> is the local Maxwellian distribution function given the gas temperature at this point in space.
其中“ nu”是分子碰撞频率，而“ math”是给定空间此点气体温度的局部马克斯韦尔分布函数。
Since much of the challenge in solving the Boltzmann equation originates with the complex collision term, attempts have been made to "model" and simplify the collision term. The best known model equation is due to Bhatnagar, Gross and Krook.<ref>{{Cite journal|title = A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems|journal = Physical Review|date = 1954-05-01|pages = 511–525|volume = 94|issue = 3|doi = 10.1103/PhysRev.94.511|first1 = P. L.|last1 = Bhatnagar|first2 = E. P.|last2 = Gross|first3 = M.|last3 = Krook|bibcode = 1954PhRv...94..511B }}</ref> The assumption in the BGK approximation is that the effect of molecular collisions is to force a non-equilibrium distribution function at a point in physical space back to a Maxwellian equilibrium distribution function and that the rate at which this occurs is proportional to the molecular collision frequency. The Boltzmann equation is therefore modified to the BGK form:
Since much of the challenge in solving the Boltzmann equation originates with the complex collision term, attempts have been made to "model" and simplify the collision term. The best known model equation is due to Bhatnagar, Gross and Krook.<ref>{{Cite journal|title = A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems|journal = Physical Review|date = 1954-05-01|pages = 511–525|volume = 94|issue = 3|doi = 10.1103/PhysRev.94.511|first1 = P. L.|last1 = Bhatnagar|first2 = E. P.|last2 = Gross|first3 = M.|last3 = Krook|bibcode = 1954PhRv...94..511B }}</ref> The assumption in the BGK approximation is that the effect of molecular collisions is to force a non-equilibrium distribution function at a point in physical space back to a Maxwellian equilibrium distribution function and that the rate at which this occurs is proportional to the molecular collision frequency. The Boltzmann equation is therefore modified to the BGK form:
Equation
Equation
:<math>\frac{\partial f}{\partial t} + \frac{\mathbf{p}}{m}\cdot\nabla f + \mathbf{F} \cdot \frac{\partial f}{\partial \mathbf{p}} = \nu (f_0 - f),</math>
:<math>\frac{\partial f}{\partial t} + \frac{\mathbf{p}}{m}\cdot\nabla f + \mathbf{F} \cdot \frac{\partial f}{\partial \mathbf{p}} = \nu (f_0 - f),</math>
<noinclude>
<small>This page was moved from [[wikipedia:en:Boltzmann equation]]. Its edit history can be viewed at [[玻尔兹曼方程/edithistory]]</small></noinclude>
== 通用方程（对于混合物） ==
== 应用与推广 ==
== 方程求解 ==
== 另见 ==
== 注释 ==
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== 参考文献 ==
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