非线性介质中的力
Forces in Nonlinear Media
摘要：
我研究了由广义Poisson方程div[mu（abs（grad_phi））grad_phi]=G rho控制的理论中物体上的力的性质，该方程针对由源rho分布产生的势phi。该方程描述了，除其他外，响应系数μ取决于场强的介质，如非线性介质、介电介质或抗磁介质;非线性传输问题，其电导率或扩散系数取决于场强;非线性静电，如Born-Infeld理论;可压缩流体中的某些固定势流，在这种情况下，力作用于流中的源或障碍物。在极低和极高电荷极限下，精确地导出了点电荷所受力的表达式。任意物体在具有渐近常梯度E的外场中所受的力为F=QE，其中Q是物体的总有效电荷。推论Q=0意味着F=0是达恩伯特悖论的推广。我表明，G>0（如在牛顿引力）的两个点电荷的相同（相反）的符号仍然吸引（排斥）对方。对于G<0，情况正好相反。我讨论了推广到扩展机构，并推导维里关系。
英文摘要：
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.
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