Continuum mechanics, stresses, currents and electrodynamics
Continuum mechanics, stresses, currents and electrodynamics
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连续介质力学、应力、电流和电动力学
DOI：
10.1098/rsta.2015.0174
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Segev
中科院分区：
文献类型：
--
作者：
R. Segev
连续介质力学的欧拉方法不使用物体流形。相反，所有考虑的场都定义在空间或时空流形上。某些向量丛的截面表示广义速度，它不需要与物质点的运动相联系。利用德拉姆流理论和向量丛的广义截面，我们建立了一个由向量值流表示的力和应力的弱理论。考虑到广义速度表示的微分形式和解释这样的形式作为一个广义的势场，我们提出了一个弱的制定pre-metric，p-形式电动力学作为一个自然的例子，上述理论。最后，它表明，导致p-形式电动力学的假设可能会被替换的条件，力的功能是连续的平面拓扑结构的形式。
The Eulerian approach to continuum mechanics does not make use of a body manifold. Rather, all fields considered are defined on the space, or the space–time, manifolds. Sections of some vector bundle represent generalized velocities which need not be associated with the motion of material points. Using the theories of de Rham currents and generalized sections of vector bundles, we formulate a weak theory of forces and stresses represented by vector-valued currents. Considering generalized velocities represented by differential forms and interpreting such a form as a generalized potential field, we present a weak formulation of pre-metric, p-form electrodynamics as a natural example of the foregoing theory. Finally, it is shown that the assumptions leading to p-form electrodynamics may be replaced by the condition that the force functional is continuous with respect to the flat topology of forms.