一般多孔介质中具有非均匀部分吸收边界的扩散松弛动力学问题
Aspects of diffusive-relaxation dynamics with a non-uniform, partially absorbing boundary in general porous media
摘要：
我们认为Helmholtz问题的背景下，在一般多孔介质的物理属性的均匀初始分布的演化受到部分吸收边界条件。它的光谱特性作为边界几何形状的反映已经被广泛利用，例如在生物和地球物理应用中。我们考虑的情况下，关键的假设，使这些应用程序打破。具体而言，不均匀吸收强度的后果是什么？通过微扰理论，精确的理论结果，和随机球包的数值模拟，我们确定的区域参数空间中，这种不均匀性是重要的，在这些区域中，它不是。我们的研究结果揭示了限制扩散/弛豫谱和底层边界几何之间的映射的问题。
英文摘要：
We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down. Specifically, what are the consequences of an inhomogeneous absorption strength? By means of perturbation theory, exact theoretical results, and numerical simulations on random sphere packs, we identify the regions of parameter space in which such inhomogeneity is important and those in which it is not. Our findings shed light on the issue that limits the mapping between the diffusion/relaxation spectrum and the underlying boundary geometry.
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