scholarly journals Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials

2009 ◽  
Vol 80 (6) ◽  
Author(s):  
Samuel A. Isaacson ◽  
David Isaacson
Keyword(s):  
Master Equation ◽  
Reaction Diffusion ◽  
Singular Potentials ◽  
Diffusion Limited

scholarly journals Integrodifference master equation describing actively growing blood vessels in angiogenesis

2020 ◽  
Vol 21 (7-8) ◽  
pp. 705-713 ◽  
Author(s):  
Luis L. Bonilla ◽  
Manuel Carretero ◽  
Filippo Terragni
Keyword(s):  
Master Equation ◽  
Blood Vessels ◽  
Transition Probabilities ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Birth Process ◽  
Sink Term ◽  
System Of Particles ◽  
Vessel Network ◽  
Tip Cells

AbstractWe study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.

scholarly journals Hierarchical algorithm for the reaction-diffusion master equation

2020 ◽  
Vol 152 (3) ◽  
pp. 034104
Author(s):  
Stefan Hellander ◽  
Andreas Hellander
Keyword(s):  
Master Equation ◽  
Reaction Diffusion ◽  
Hierarchical Algorithm

Experimental Study of An A+B→C Reaction-Diffusion System in a Capillary: Crossovers from Reaction to Diffusion-Limited Regimes

1992 ◽  
Vol 290 ◽  
Author(s):  
Yong-Eun Koo ◽  
Raoul Kopelman ◽  
Andrew Yen ◽  
Anna Lin
Keyword(s):  
Experimental Study ◽  
Reaction Zone ◽  
Reaction Front ◽  
Reaction Rate ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Theoretical Studies ◽  
Boundary Motion ◽  
Diffusion Limited ◽  
Front Dynamics

AbstractContinuing work on elementary A+B→C reactions in capillaries, we study the reaction front dynamics of xylanol orange with Cr3+ in an effectively one-dimentional system with initially separated reactants. This reaction, in contrast to previously studied systems, is not strictly in the diffusion limited regime. i.e. the probability of reaction between species is not unity. Anamalous behavior not seen in the diffusion-limited case has been observed experimentally for the reaction rate, boundary motion, reaction zone width, and local reaction rate. The observed behavior is consistent with recent theoretical studies.

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