第77行: |
第77行: |
| | | |
| ==The force and diffusion terms “force”项与“diff”项== | | ==The force and diffusion terms “force”项与“diff”项== |
− |
| |
− | For a mixture of chemical species labelled by indices i = 1, 2, 3, ..., n the equation for species i is For a fluid consisting of only one kind of particle, the number density n is given by
| |
− |
| |
− | 对于以指数 i = 1,2,3,... ,n 标记的化学物种混合物,物种 i 的方程是: 对于只包含一种粒子的流体,数密度 n 由
| |
− |
| |
− | <math>n = \int f \,d^3p.</math>
| |
− |
| |
− | [ math ] n = int f,d ^ 3p
| |
| | | |
| 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). |
− |
| |
− |
| |
− |
| |
− | The average value of any function A is
| |
− |
| |
− | 任何函数 a 的平均值都是
| |
| | | |
| 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 |
| | | |
− | <math>\langle A \rangle = \frac 1 n \int A f \,d^3p.</math> | + | |
| | | |
| A rangle = frac 1n int a f,d ^ 3p | | A rangle = frac 1n int a f,d ^ 3p |
第360行: |
第346行: |
| | | |
| == 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 == |