Diffusion Equation and Stochastic Processes

Diffusion Equation and Stochastic Processes.

Stochastic Simulation of Coupled Reaction–Diffusion Processes

actants is used to compute the time evolution of reactant concentrations. The stochastic algorithm is rigorous in the The stochastic time evolution method has been used previously to study non-linear chemical reaction processes in well-stirred hosense that it provides an exact solution to the correspondmogeneous systems. We present the first treatment of diffusion, in ing master equation for ch...

Stochastic diffusion processes on Cartesian meshes

Diffusion of molecules is simulated stochastically by letting them jump between voxels in a Cartesian mesh. The jump coefficients are first derived using finite difference, finite element, and finite volume approximations of the Laplacian on the mesh. An alternative is to let the first exit time for a molecule in random walk in a voxel define the jump coefficient. Such coefficients have the adv...

Stochastic analysis of reaction-diffusion processes.

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartm...

Stochastic Simulation of Reaction-Diffusion Processes

Hellander, S. 2013. Stochastic Simulation of Reaction-Diffusion Processes. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1042. 46 pp. Uppsala. ISBN 978-91-554-8667-9. Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with hi...