scholarly journals Reaction rates for reaction-diffusion kinetics on unstructured meshes

2017 ◽  
Vol 146 (6) ◽  
pp. 064101 ◽  
Author(s):  
Stefan Hellander ◽  
Linda Petzold
Keyword(s):  
Reaction Diffusion ◽  
Reaction Rates ◽  
Unstructured Meshes ◽  
Diffusion Kinetics

scholarly journals Reaction rates for mesoscopic reaction-diffusion kinetics

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
Stefan Hellander ◽  
Andreas Hellander ◽  
Linda Petzold
Keyword(s):  
Reaction Diffusion ◽  
Reaction Rates ◽  
Diffusion Kinetics

Enhancement of solid-state reaction rates by non-hydrostatic stress effects on polycrystalline diffusion kinetics

2010 ◽  
Vol 95 (10) ◽  
pp. 1399-1407 ◽  
Author(s):  
L. M. Keller ◽  
L. C. Gotze ◽  
E. Rybacki ◽  
G. Dresen ◽  
R. Abart
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Hydrostatic Stress ◽  
Reaction Rates ◽  
Diffusion Kinetics ◽  
Stress Effects

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

Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200003 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Autonomous Systems ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Dependent Model ◽  
Spatio Temporal

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

scholarly journals A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates

2003 ◽  
Vol 13 (06) ◽  
pp. 1529-1543 ◽  
Author(s):  
Juncheng Wei ◽  
Matthias Winter
Keyword(s):  
Eigenvalue Problem ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
The Stability ◽  
Nonlocal Eigenvalue Problem ◽  
Fractional Reaction

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction–diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray–Scott system, the hypercycle of Eigen and Schuster, angiogenesis, and the generalized Gierer–Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters.

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.

Evaluation of Lattice Boltzmann Method for Reaction-Diffusion Process in a Porous SOFC Anode Microstructure

2012 ◽  
Author(s):  
Hedvig Paradis ◽  
Bengt Sundén
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Transport Processes ◽  
Microscopic Level ◽  
Reaction Diffusion Equation ◽  
Interaction Sites ◽  
Boltzmann Method

In the microscale structure of a porous electrode, the transport processes are among the least understood areas of SOFC. The purpose of this study is to evaluate the Lattice Boltzmann Method (LBM) for a porous microscopic media and investigate mass transfer processes with electrochemical reactions by LBM at a mesoscopic and microscopic level. Part of the anode structure of an SOFC for two components is evaluated qualitatively for two different geometry configurations of the porous media. The reaction-diffusion equation has been implemented in the particle distribution function used in LBM. The LBM code in this study is written in the programs MATLAB and Palabos. It has here been shown that LBM can be effectively used at a mesoscopic level ranging down to a microscopic level and proven to effectively take care of the interaction between the particles and the walls of the porous media. LBM can also handle the implementation of reaction rates where these can be locally specified or as a general source term. It is concluded that LBM can be valuable for evaluating the risk of local harming spots within the porous structure to reduce these interaction sites. In future studies, the information gained from the microscale modeling can be coupled to a macroscale CFD model and help in development of a smooth structure for interaction of the reforming reaction and the electrochemical reaction rates. This can in turn improve the cell performance.

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