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→The force and diffusion terms “force”项与“diff”项
==The force and diffusion terms “force”项与“diff”项==
==The force and diffusion terms “force”项与“diff”项==
Consider particles described by ''f'', each experiencing an ''external'' force '''F''' not due to other particles (see the collision term for the latter treatment).
Consider particles described by ''f'', each experiencing an ''external'' force '''F''' not due to other particles (see the collision term for the latter treatment).
Suppose at time ''t'' some number of particles all have position '''r''' within element <math> d^3\bf{r}</math> and momentum '''p''' within <math> d^3\bf{p}</math>. If a force '''F''' instantly acts on each particle, then at time ''t'' + Δ''t'' their position will be '''r''' + Δ'''r''' = '''r''' + '''p'''Δ''t''/''m'' and momentum '''p''' + Δ'''p''' = '''p''' + '''F'''Δ''t''. Then, in the absence of collisions, ''f'' must satisfy
Suppose at time ''t'' some number of particles all have position '''r''' within element <math> d^3\bf{r}</math> and momentum '''p''' within <math> d^3\bf{p}</math>. If a force '''F''' instantly acts on each particle, then at time ''t'' + Δ''t'' their position will be '''r''' + Δ'''r''' = '''r''' + '''p'''Δ''t''/''m'' and momentum '''p''' + Δ'''p''' = '''p''' + '''F'''Δ''t''. Then, in the absence of collisions, ''f'' must satisfy
A rangle = frac 1n int a f，d ^ 3p
A rangle = frac 1n int a f，d ^ 3p
== 通用方程（对于混合物） ==
== 通用方程（对于混合物） ==
For a mixture of chemical species labelled by indices i = 1, 2, 3, ..., n the equation for species i is
== 应用与推广 ==
== 应用与推广 ==
守恒方程
For a fluid consisting of only one kind of particle, the number density n is given by
<math>n = \int f \,d^3p.</math>
The average value of any function A is
任何函数 a 的平均值都是
<math>\langle A \rangle = \frac 1 n \int A f \,d^3p.</math>
== 方程求解 ==
== 方程求解 ==