# A simple mathematical approach to optimize the structure of reaction-diffusion physicochemical systems

@article{Chehab2013ASM, title={A simple mathematical approach to optimize the structure of reaction-diffusion physicochemical systems}, author={Jean-Paul Chehab and Alejandro A. Franco and Youcef Mammeri}, journal={arXiv: Chemical Physics}, year={2013} }

The calculation of optimal structures in reaction-diffusion models is of great importance in many physicochemical systems. We propose here a simple method to monitor the number of interphases for long times by using a boundary flux condition as a control. We consider as an illustration a 1-D Allen-Cahn equation with Neumann boundary conditions. Numerical examples are given and perspectives for the application of this approach to electrochemical systems are discussed.

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SHOWING 1-10 OF 15 REFERENCES

### A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening

- Materials Science
- 1979

### Carbon-Based Electrodes for Lithium Air Batteries: Scientific and Technological Challenges from a Modeling Perspective

- Materials Science
- 2013

The carbon-based positive electrode of Lithium Air Batteries (LABs) is the component where the major competitive mechanisms occur, such as the electrochemical reactions leading to the formation and…

### Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

- Mathematics
- 2010

Stability analyses and error estimates are carried out for a number of commonly used
numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that
all the schemes we considered…

### Modern Thermodynamics: From Heat Engines to Dissipative Structures

- PhysicsEntropy
- 1999

For readers interested in the Prigogine school of thermodynamics, this book is the first choice because it is a textbook.[...]

### Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws

- MathematicsMath. Comput.
- 2015

It is proved that, at the numerical level, the large time dynamics depends on the amount of numerical viscosity introduced by the scheme: while Engquist-Osher and Godunov yield the same N-wave asymptotic behavior, the Lax-Friedrichs scheme leads to viscous self-similar profiles, corresponding to the asymPTotic behavior of the solutions of the continuous viscous Burgers equation.

### Bromination Reactions Important in the Mechanism of the Belousov−Zhabotinsky System

- Chemistry
- 1999

We investigate the kinetics of bromination of malonic acid, bromomalonic acid, tartronic acid, and ethanetetracarboxylic acid in 1 M sulfuric acid with bromine and hypobromous acid as brominating…

### Self organization in catalyst layers of PEM Fuel Cells

- J. Phys. Chem. C, 111 (36),
- 2007

### Matlab's optimization toolbox

### Multiscale modeling and numerical simulation of rechargeable lithium ion batteries: concepts, methods and challenges

- 2013