Contribution to the theory of reaction diffusion kinetics in spatially heterogeneous media

1983 ◽  
Vol 87 (2) ◽  
pp. 347-351 ◽  
Author(s):  
Stephen E. Webber
Keyword(s):  
Heterogeneous Media ◽  
Reaction Diffusion ◽  
Diffusion Kinetics

scholarly journals Non-Arrhenius Reaction-Diffusion Kinetics for Protein Inactivation over a Large Temperature Range

ACS Nano ◽  
2019 ◽  
Vol 13 (8) ◽  
pp. 8669-8679 ◽  
Author(s):  
Daipayan Sarkar ◽  
Peiyuan Kang ◽  
Steven O. Nielsen ◽  
Zhenpeng Qin
Keyword(s):  
Reaction Diffusion ◽  
Large Temperature ◽  
Diffusion Kinetics ◽  
Temperature Range ◽  
Protein Inactivation

scholarly journals Competition and boundary formation in heterogeneous media: Application to neuronal differentiation

2015 ◽  
Vol 25 (13) ◽  
pp. 2477-2502 ◽  
Author(s):  
Benoît Perthame ◽  
Cristóbal Quiñinao ◽  
Jonathan Touboul
Keyword(s):  
Gene Expression ◽  
Heterogeneous Media ◽  
Blow Up ◽  
General Setting ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Developmental Phase ◽  
Inhomogeneous System ◽  
Small Diffusion ◽  
Drive Gene

We analyze an inhomogeneous system of coupled reaction–diffusion equations representing the dynamics of gene expression during differentiation of nerve cells. The outcome of this developmental phase is the formation of distinct functional areas separated by sharp and smooth boundaries. It proceeds through the competition between the expression of two genes whose expression is driven by monotonic gradients of chemicals, and the products of gene expression undergo local diffusion and drive gene expression in neighboring cells. The problem therefore falls in a more general setting of species in competition within a nonhomogeneous medium. We show that in the limit of arbitrarily small diffusion, there exists a unique monotonic stationary solution, which splits the neural tissue into two winner-takes-all parts at a precise boundary point: on both sides of the boundary, different neuronal types are present. In order to further characterize the location of this boundary, we use a blow-up of the system and define a traveling wave problem parametrized by the position within the monotonic gradient: the precise boundary location is given by the unique point in space at which the speed of the wave vanishes.

scholarly journals Multi-functionalization of nanoporous catalytic materials to enhance reaction yield: Statistical mechanical modeling for conversion reactions with restricted diffusive transport

2014 ◽  
Vol 1641 ◽  
Author(s):  
Jing Wang ◽  
Andrés Garcia ◽  
David M. Ackerman ◽  
Mark S. Gordon ◽  
Igor I. Slowing ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Coarse Grained ◽  
Reaction Yield ◽  
Diffusion Kinetics ◽  
Reaction Products ◽  
Dehydration Reactions ◽  
Catalytically Active ◽  
Statistical Mechanical ◽  
And Diffusion ◽  
Reaction Equilibrium

ABSTRACTMulti-functionalization of catalytically-active nanomaterials provides a valuable tool for enhancing reaction yield by shifting reaction equilibrium, and potentially also by adjusting reaction-diffusion kinetics. For example, multi-functionalization of mesoporous silica to make the interior pore surface hydrophobic can enhance yield in dehydration reactions. Detailed molecular-level modeling to describe the pore environment, as well as the reaction and diffusion kinetics is challenging, although we briefly discuss current strategies. Our focus, however, is on coarse-grained stochastic modeling of the overall catalytic process for highly restricted transport within narrow pores (with single-file diffusion), while accounting for a tunable interaction of the pore interior with reaction products. We show that making the pore interior unfavorable to products can significantly enhance yield due to both thermodynamic and kinetics factors.

Loss rate of a plasticizer in a nylon matrix calculated using macroscopic reaction–diffusion kinetics

2003 ◽  
Vol 93 (3) ◽  
pp. 1525-1532
Author(s):  
M. L. Zhang ◽  
N. H. March ◽  
A. Peeters ◽  
C. Van Alsenoy ◽  
I. Howard ◽  
...  
Keyword(s):  
Loss Rate ◽  
Reaction Diffusion ◽  
Diffusion Kinetics

scholarly journals On the Interplay of Geometrical Shapes and the Analysis of a Dispersal Model for Pattern Formations

2019 ◽  
pp. 1-10
Author(s):  
Zakir Hossine ◽  
Md. Kamrujjaman
Keyword(s):  
Reaction Mechanism ◽  
Finite Difference Method ◽  
Reaction Diffusion ◽  
Diffusion Kinetics ◽  
Dispersal Model ◽  
Reaction Diffusion Model ◽  
Chemical Reaction Mechanism ◽  
Geometrical Shapes ◽  
Pattern Formations ◽  
Selection Of

A reaction-diffusion model is put forward which is capable of generating chemical maps whose concentration contours are similar to the patterns seen on the flanks of zebras, leopards and other mammals. Initially, this type of reaction diffusion kinetics model was introduced by Turing and later Murray applied it to animal coat patterns. Among many chemical reaction mechanism, we consider Schnackenberg reaction mechanism in details and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries. Finally the system was solved numerically using finite difference method.

scholarly journals Surface reaction-diffusion kinetics on lattice at the microscopic scale

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Wei-Xiang Chew ◽  
Kazunari Kaizu ◽  
Masaki Watabe ◽  
Sithi V. Muniandy ◽  
Koichi Takahashi ◽  
...  
Keyword(s):  
Surface Reaction ◽  
Reaction Diffusion ◽  
Diffusion Kinetics ◽  
Microscopic Scale
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