1998 Fiscal Year Final Research Report Summary
On solutions of spatio-temporal patterns in nonlinear reaction-diffusion systems
| Project/Area Number |
09640301
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Doshisha University |
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Principal Investigator |
KAWASAKI Kohkichi Doshisha University, Faculty of Engineering, Professor, 工学部, 教授 (10150799)
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| Project Period (FY) |
1997 – 1998
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| Keywords | reaction-diffusion equation / pattern formation / bacterial colony / chemotaxis / Dense-braching morphology |
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| 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. For instance, the colony pattern shows DLA (diffusion limited aggregation) patterns or DBM (dense branching morphology) patterns, In this study I have attempted 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. The reproduction of the spotty patterns depends on the degree of chemotactic coefficient. Furthermore, by employing a diffusion reaction equation with a nonlinear diffusion coefficient, I could also obtain a more complex dense branched morphology, which depends on initial concentration of nutrient and diffusion coefficient of bacteria. The rate of expansion of colony pattern parabolically increases, as initial concentration of nutrient increases. Expansion rate obtained by numerical simulations mostly agrees with one given by theoretical calculations, when the inticial concentration of nutrient is high.
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