Formal Validation of Asynchronous Interaction-Agents Algorithms for Reaction-Diffusion Problems

  • Authors:
  • Pascal Redou;Sebastien Kerdelo;Gireg Desmeulles;Jean-Francois Abgrall;Vincent Rodin;Jacques Tisseau

  • Affiliations:
  • Brest University Hospital, France;Brest University Hospital, France;Brest University Hospital, France;Brest University Hospital, France;Brest University Hospital, France;Brest University Hospital, France

  • Venue:
  • Proceedings of the 21st International Workshop on Principles of Advanced and Distributed Simulation
  • Year:
  • 2007

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Abstract

In the context of biological complex systems multi-agent simulation, we present an interaction-agentmodel for reaction-diffusion problems that enables interaction with the simulation during the execution, and we establish a mathematical validation for our model. We use two types of interaction-agents: on one hand, in a chemical reactor with no spatial dimension -e.g. a cell-, a reaction-agent represents an autonomous chemical reaction between several reactants, and modifies the concentration of reaction products. On the other hand, we use interface-agents in order to take into account the spatial dimension that appears with diffusion : interface-agents achieve the matching transfer of reactants between cells. This approach, where the simulation engine makes agents intervene in a chaotic and asynchronous way, is an alternative to the classical model - which is not relevant when the limits conditions are frequently modified- based on partial derivative equations. We enounciate convergence results for our interaction-agent methods, and illustrate our model with an example about coagulation inside a blood vessel.