Some "moving boundaries paradoxes" in electrodynamics
Some "moving boundaries paradoxes" in electrodynamics
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DOI：
10.1070/pu1975v018n06abeh001967
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发表时间：
1975-06
期刊：
影响因子：
2.7
通讯作者：
L. A. Ostrovskiĭ
中科院分区：
文献类型：
--
作者：
L. A. Ostrovskiĭ
讨论了在获得和利用沿两种介质运动表面的边界条件时，与电动力学材料方程的特性有关的几个非平凡问题。值得注意的是，边界条件本身可以取决于边界厚度和介质中粒子运动的适当次数之间的关系(甚至简单地取决于边界的速度)。考虑到介质的惯性性质，所有的电动量在其参数在时间上的理想急剧不连续时保持连续(连续定律)。一个例外是边界以速度c运动的情况，以及冻结在介质中的不连续面。对于变化更平缓(虽然与场的外部变化尺度相比变化很大)的边界层，可以忽略介质的惯性特性(色散)；在这种情况下，场和极化经历了“不连续”。然而，在这种情况下，当边界的速度一边高于光速，一边低于光速时，就会出现另一种困难(特别是，小扰动与激波的相互作用属于这种情况)；这些情况需要单独调查。以弹性振子介质中的电磁波为例，说明了介质的惯性性质对边界条件的影响。
Several nontrivial questions are discussed which arise in obtaining and utilizing boundary conditions along moving surfaces separating two media and which are associated with characteristics features of electrodynamic material equations. It is noted that the boundary conditions themselves can depend on the relationship between the thickness of the boundary and the proper times of the motion of the particles of the medium (and even simply on the velocity of the boundary). In view of the inertial properties of the medium all the electrodynamic quantities remain continuous (the law of continuity) at an ideally sharp discontinuity of its parameters in time. An exception is presented by the case of the motion of the boundary with velocity c, and also by discontinuities "frozen into" the medium. For a more smoothly varying (although sharply varying compared to the external scale of variation of the field) boundary layer one can neglect the inertial properties (dispersion) of the medium; in this case the field and the polarization undergo a "discontinuity." However, in this case difficulties of another kind arise when the velocity of the boundary is "above light velocity" on one side and "below light velocity" on the other side (in particular, the interaction of small perturbations with shock waves belongs to such a case); these cases require a separate investigation. The effect of the inertial properties of the medium on the boundary conditions is illustrated on the example of electromagnetic waves in a dielectric with elastic oscillators.