标题： 梳状结构沿主链的有效扩散与有限跨度的一维和二维指状结构 显示英文标题

标题： Effective diffusion along the backbone of combs with finite-span 1D and 2D fingers

摘要： 扩散在诸如生物组织或多孔材料等复杂的异质介质中通常涉及在曲折结构和{\em 粘性}环境中的受限位移。 因此，扩散粒子会同时经历熵（排除体积）力以及复杂能量景观的存在。 在这种情况下，可以通过一个有效的扩散系数来描述传输过程。 在本文中，我们研究了具有有限长度的一维和有限面积的二维指状结构，它们作为纯粹的扩散陷阱起作用。 我们发现，存在一个临界宽度的二维指状结构，超过该宽度时，沿着主干的有效扩散速度比等效的一维指状结构更快。 此外，我们表明，只要正确识别了作为结构参数函数的缩放变量，该有效扩散系数对于一维和二维指状结构都可以用一个通用的解析形式来描述。 有趣的是，这个公式对应于一种众所周知的扩散情况，即在具有快速可逆吸附的介质中扩散。 最后，我们表明，同样的公式也适用于稀释势能陷阱的存在下的扩散，例如通过方形势阱的景观。 虽然扩散最终总是微观相互作用的结果（与流体中的粒子、其他溶质和环境相互作用），但有效表示通常在实践中非常有用。 本文报告的结果有助于澄清复杂介质中扩散的全局综合描述的微观起源和适用性。 显示英文摘要

摘要： Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both entropic (excluded-volume) forces and the presence of complex energy landscapes. In this situation, one may describe transport through an effective diffusion coefficient. In this paper, we examine comb structures with finite-length 1D and finite-area 2D fingers, which act as purely diffusive traps. We find that there exists a critical width of 2D fingers above which the effective diffusion along the backbone is faster than for an equivalent arrangement of 1D fingers. Moreover, we show that the effective diffusion coefficient is described by a general analytical form for both 1D and 2D fingers, provided the correct scaling variable is identified as a function of the structural parameters. Interestingly, this formula corresponds to the well-known general situation of diffusion in a medium with fast reversible adsorption. Finally, we show that the same formula describes diffusion in the presence of dilute potential energy traps, e.g. through a landscape of square wells. While diffusion is ultimately always the results of microscopic interactions (with particles in the fluid, other solutes and the environment), effective representations are often of great practical use. The results reported in this paper help clarify the microscopic origins and the applicability of global, integrated descriptions of diffusion in complex media.