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On solutions of spatial pattern formation in nonlinear reaction-diffusion systems

Research Project

Project/Area Number 06640339
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionDoshisha University

Principal Investigator

KAWASAKI Kohkichi  Doshisha University, Faculty of Engineering, Professor, 工学部, 教授 (10150799)

Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1995: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1994: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsReaction-diffusion equation / Nonlinear equation / traveling wave / Spatial pattern / Chemotaxis / Dense-braching morphology
Research Abstract

Many organisms display chemotactic aggregation in response to the concentration gradient of attractant molecules to form variety of spatial patterns. As typically seen in bacterial colonies, cellular slim molds and swarming insects, it has been known that bacterial colonies could show very complex spatial pattern depending on various culture conditions such as nutrient concentration and the solidity of agar plate. In this study I have attemped to elucidate the mechanism of such pattern formation in bacterial colony by means of mathematical modeling. The chemotactic movement of bacteria were formulated by a nonlinear partial differential equation. Its numerical solution reproduces concentric spotty patterns, whose front advances outward with time. Furthermore, by employing a diffusion reaction equation with a nonlinear diffusion coefficient, I could also obtain a more complex dense branched morphology. This branching morphology was found to be emphasized if the effect of random fluctuation in bacterial density are taken into consideration.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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