Campos Daniel, Méndez Vicenç, Fort Joaquim
Departmento de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterrra, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 1):031115. doi: 10.1103/PhysRevE.69.031115. Epub 2004 Mar 31.
The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived.
为了对这些动态过程有一个总体的认识，我们回顾了分形上扩散的已知性质。在此之后，我们提出了一种在分形的内在度量背景下发展起来的描述，这使我们得到了一个能够描述渐近区域中实分形上扩散的微分方程。我们表明，我们的方法比该领域以前的工作有更强的物理依据。我们给出的最重要的结果是引入了分形中电导率对时间和空间的依赖性，这是通过标度论证推导出来的，并得到了计算机模拟的支持。最后，利用扩散方程引入了分形上反应扩散过程的可能性并分析了它们的性质。具体来说，推导了相应行波前沿速度的解析表达式，这对于应用目的可能非常有意义。
