Ferrari Leonardo
Dipartimento di Fisica, Università di Parma, and Istituto Nazionale per la Fisica della Materia, Unità di Parma, Parco Area delle Scienze, 7/A, I-43100 Parma, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021103. doi: 10.1103/PhysRevE.68.021103. Epub 2003 Aug 11.
The evolution equation for a generic average quantity relevant to a swarm of particles homogeneously dispersed in a uniform gas, is obtained directly from the Newton's law, without having recourse to the (intermediary) Boltzmann equation. The procedure makes use of appropriate averages of the term resulting from the impulsive force (due to collisions) in the Newton's law. When the background gas is assumed to be in thermal equilibrium, the obtained evolution equation is shown to agree with the corresponding one following from the Boltzmann equation. But the new procedure also allows to treat physical situations in which the Boltzmann equation is not valid, as it happens when some correlation exists (or is assumed) between the velocities of swarm and gas particles.
对于均匀分散在均匀气体中的一群粒子相关的一般平均量的演化方程，可直接从牛顿定律得出，而无需借助（中间的）玻尔兹曼方程。该过程利用了牛顿定律中由（碰撞引起的）冲力产生的项的适当平均值。当假设背景气体处于热平衡时，所得到的演化方程被证明与从玻尔兹曼方程导出的相应方程一致。但新方法也允许处理玻尔兹曼方程不适用的物理情形，例如当群粒子和气体粒子的速度之间存在（或假设存在）某种相关性时。
