非均匀部分吸收和边界形状对一般多孔介质中扩散分子布居演化的影响
Effects of inhomogeneous partial absorption and the geometry of the boundary on the population evolution of molecules diffusing in general porous media
摘要：
我们认为方面的人口动态，在一个有界域，扩散剂携带的属性，这是随机破坏后，与边界接触。部分吸收，但统一的边界条件下的相关亥姆霍兹方程的正常模式分析提供了一个起始框架，在理解详细的演化动态的属性在时域中。特别是，边界局部耗尽已被广泛应用于实际应用中，取决于各种多孔介质的几何形状，如岩石，水泥，骨头，奶酪。虽然孔隙几何形状和扩散-弛豫谱之间的直接关系形成了这种应用的基础，并已被广泛研究，相对较少的注意已经支付给边界条件的空间变化。在这项工作中，我们专注于孔隙几何形状和边界的不均匀耗尽强度变得交织在一起，从而模糊了光谱和几何形状之间的直接关系。通常不可能用实验来测量这种干涉发生的程度。我们填补了这一空白，通过扰动纳入类空间变化的边界条件，并得出其后果是通过数值模拟或控制实验玻璃珠包和人工制造的多孔介质观察。我们确定的频谱是最敏感的不均匀性的功能，并应用该方法的球形孔与一个简单的半球形的二元分布的耗尽强度和获得的最慢的弛豫模式的诱导变化的界限。
英文摘要：
We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation under the partially absorbing, but uniform, boundary condition provides a starting framework in understanding detailed evolution dynamics of the attribute in the time domain. In particular, the boundary-localized depletion has been widely employed in practical applications that depend on geometry of various porous media such as rocks, cement, bones, and cheese. While direct relationship between the pore geometry and the diffusion-relaxation spectrum forms the basis for such applications and has been extensively studied, relatively less attention has been paid to the spatial variation of the boundary condition. In this work, we focus on the way the pore geometry and the inhomogeneous depletion strength of the boundary become intertwined and thus obscure the direct relationship between the spectrum and the geometry. It is often impossible to gauge experimentally the degree to which such interference occur. We fill this gap by perturbatively incorporating classes of spatially-varying boundary conditions and derive their consequences that are observable through numerical simulations or controlled experiments on glass bead packs and artificially fabricated porous media. We identify features of the spectrum that are most sensitive to the inhomogeneity and apply the method to the spherical pore with a simple hemi-spherical binary distribution of the depletion strength and obtain bounds for the induced change in the slowest relaxation mode.
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