596
个编辑
更改
跳到导航
跳到搜索
第82行：
第82行： + + + +
→The force and diffusion terms “force”项与“diff”项
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).
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).
考虑一群以<nowiki><math>f</math></nowiki>分布的粒子。每个粒子均受到外力<nowiki><math>\mathbf{F}</math></nowiki>的作用（不包括粒子间作用力。粒子间的作用见后面对“coll”项的处理)。
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
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
假设在时间 <nowiki><math>t</math></nowiki>，一定数量的粒子都有位置 <nowiki><math>\mathbf{r}</math></nowiki>（于微元 <nowiki><math> d^3\mathbf{r}</math></nowiki> 内），和动量 <nowiki><math>\mathbf{p}</math></nowiki>（于微元 <nowiki><math> d^3\mathbf{p}</math></nowiki> 内）。如果此时有一个力<nowiki><math>\mathbf{F}</math></nowiki>在这一瞬作用在每个颗粒上，那么在时间 <nowiki><math>t + \Delta\,t</math></nowiki>，它们的位置将会是<nowiki><math>\mathbf{r} + \Delta\,\mathbf{r} = \mathbf{r} + \mathbf{p} \Delta\,t/m</math></nowiki>，动量将变成 <nowiki><math>\mathbf{p} + \Delta\,\mathbf{p} = \mathbf{p} + \mathbf{F}\Delta\,t</math></nowiki>。在没有碰撞的情况下，<nowiki><math>f</math></nowiki>必须满足
<math>
<math>