Author : Richard D. Tatum
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (855 download)
Book Synopsis Analysis of a Reaction-diffusion System with Local and Nonlocal Diffusion Terms by : Richard D. Tatum
Download or read book Analysis of a Reaction-diffusion System with Local and Nonlocal Diffusion Terms written by Richard D. Tatum and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reaction-diffusion describes the process in which multiple participating chemicals or agents react with each other, while simultaneously diffusing or spreading through a liquid or gaseous medium. Typically, these processes are studied for their ability to produce nontrivial patterns that evolve over time. These patterns, often referred to as Turing structures or Turing patterns, are diffusion driven. In the presence of diffusion, the Turing patterns are observable, but are not present in the absence of diffusion. It is important for reactiondiffusion models to replicate the behavior that is experimentally observed. That is to say that the models must be able to produce solutions with traits, such as pattern type, that are similar to experimentally observed traits. Mathematically, we seek to explain certain aspects of the models such as pattern selection in the hope of broadening our understanding of the underlying process for which the model represents. I analyze a mixed reaction-diffusion system containing an instability that results in nontrivial Turing structures. This system uses a homotopy parameter [beta] to vary the effect of both local ([beta] = 1) and nonlocal ([beta] = 0) diffusion. Furthermore, I consider [element-of symbol]-scaled kernels J such that [th]J is -independent for [th] [element-of symbol] R. For [th]