吸收三重周期极小曲面的平均生存时间
Mean survival times of absorbing triply periodic minimal surfaces
摘要：
通过了解多孔介质的微观结构来了解多孔介质的输运性质是物理、化学和生物科学中一个非常感兴趣的问题。使用首次通过时间方法，我们计算了布朗粒子在广泛一类三周期多孔介质（包括最小表面）的完全吸收陷阱中的平均生存时间$τ$。我们发现，多孔介质的界面是Schwartz P最小的表面最大化的平均生存时间在这一类。这增加了越来越多的证据表明，这种双连续多孔介质的多功能优化。我们推测，平均生存时间（如流体渗透率）是最大化的三重周期性多孔介质的孔隙度$ϕ=1/2$的结构，全局优化的比表面的简单连接的孔隙空间。我们还计算模型微观结构的孔径统计，以确定这些多孔介质的平均生存时间的“通用曲线”的有效性。这是第一个非平凡的统计特征的三重周期极小曲面。
英文摘要：
Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical and biological sciences. Using a first-passage time method, we compute the mean survival time $τ$ of a Brownian particle among perfectly absorbing traps for a wide class of triply-periodic porous media, including minimal surfaces. We find that the porous medium with an interface that is the Schwartz P minimal surface maximizes the mean survival time among this class. This adds to the growing evidence of the multifunctional optimality of this bicontinuous porous medium. We conjecture that the mean survival time (like the fluid permeability) is maximized for triply periodic porous media with a simply connected pore space at porosity $ϕ=1/2$ by the structure that globally optimizes the specific surface. We also compute pore-size statistics of the model microstructures in order to ascertain the validity of a "universal curve" for the mean survival time for these porous media. This represents the first nontrivial statistical characterization of triply periodic minimal surfaces.
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