标题： 非线性介质中的力 显示英文标题

标题： Forces in Nonlinear Media

摘要： 我研究了在由广义泊松方程div[mu(abs(grad_phi))grad_phi]=G rho描述的理论中，物体所受力的性质，该方程描述了由源分布rho产生的势phi。 该方程描述了诸如非线性、电介质或抗磁性介质中响应系数mu依赖于场强的情况；场强依赖的电导率或扩散系数的非线性传输问题；如Born-Infeld理论中的非线性静电学；以及可压缩流体中的某些定常势流，在这种情况下，力作用于流中的源或障碍物。 对于非常低和非常高的电荷极限，推导出了点电荷所受力的精确表达式。 显示在渐近常梯度外部场E中的任意物体所受的力为F=QE，其中Q是物体的总有效电荷。 推论Q=0意味着F=0是对达朗贝尔悖论的推广。 我表明对于G>0（如牛顿引力），相同（相反）符号的两个点电荷仍然相互吸引（排斥）。 对于G<0则相反。 我讨论了将其推广到扩展物体的情况，并推导了维里关系。 显示英文摘要

摘要： I investigate the properties of forces on bodies in theories governed by the generalized Poisson equation div[mu(abs(grad_phi))grad_phi]=G rho, for the potential phi produced by a distribution of sources rho. This equation describes, inter alia, media with a response coefficient, mu, that depends on the field strength, such as in nonlinear, dielectric, or diamagnetic, media; nonlinear transport problems with field-strength dependent conductivity or diffusion coefficient; nonlinear electrostatics, as in the Born-Infeld theory; certain stationary potential flows in compressible fluids, in which case the forces act on sources or obstacles in the flow. The expressions for the force on a point charge is derived exactly for the limits of very low and very high charge. The force on an arbitrary body in an external field of asymptotically constant gradient, E, is shown to be F=QE, where Q is the total effective charge of the body. The corollary Q=0 implies F=0 is a generalization of d'Aembert's paradox. I show that for G>0 (as in Newtonian gravity) two point charges of the same (opposite) sign still attract (repel) each other. The opposite is true for G<0. I discuss the generalization of this to extended bodies, and derive virial relations.