Anomalous Diffusion On Archimedean Spiral Structure With Cattaneo Flux Model

In this paper, we study the properties of anomalous diffusion on a specific Archimedean spiral backbone with radial fingers. The partial differential equation with Cattaneo flux model is derived using spiral transformation and solved numerically. The influence of relaxation time and geometrical parameter on partide distribution and MSD is discussed graphically. Our results show that there is a transition between two types of diffusions. The super- diffusion (MSD similar to t(alpha): alpha > 1) starts for a short time then changes to sub-diffusion (MSD similar to t(alpha) : 0 < alpha < 1) for a long time. This phenomenon is due to the length variation of radial fingers with the spiral geometrical structure. Our model can be used to study a class of specific anomalous diffusion, such as the search of DNA-binding proteins for their binding sites. (C) 2020 Elsevier B.V. All rights reserved.