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==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 <math> f</math> , each experiencing an ''external'' force '''<math> F</math>''' 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 <math> t+\Delta t</math> their position will be <math> \mathbf{r}+\Delta \mathbf{r}= \textbf{r}+\frac{\textbf{p}}{m}\Delta t</math> and momentum <math> \mathbf{p}+\Delta \mathbf{p}= \mathbf{p}+\mathbf{F}\Delta t</math>. Then, in the absence of collisions, <math> f</math>must satisfy

Suppose at time <math> t</math> some number of particles all have position '''<math> r</math>''' within element <math> d^3\bf{r}</math> and momentum '''<math> p</math>''' within <math> d^3\bf{p}</math>. If a force '''<math> F</math>''' instantly acts on each particle, then at time <math> t+\Delta t</math> their position will be <math> \mathbf{r}+\Delta \mathbf{r}= \textbf{r}+\frac{\textbf{p}}{m}\Delta t</math> and momentum <math> \mathbf{p}+\Delta \mathbf{p}= \mathbf{p}+\mathbf{F}\Delta t</math>. Then, in the absence of collisions, <math> f</math> must satisfy

<math>

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