scholarly journals Numerical solution of a class of advection-reaction-diffusion system

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1503-1511
Author(s):  
Li Cao ◽  
Zhanxin Ma
Keyword(s):  
Numerical Experiment ◽  
Numerical Solution ◽  
Collocation Method ◽  
High Precision ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Collocation Methods ◽  
Barycentric Interpolation ◽  
Precision Method

In this article, the barycentric interpolation collocation methods is proposed for solving a class of non-linear advection-reaction-diffusion system. Compared with other methods, the numerical experiment shows the barycentric interpolation collocation method is a high precision method to solve the advection- reaction-diffusion system.

scholarly journals Numerical solution of a coupled reaction-diffusion model using barycentric interpolation collocation method

2020 ◽  
Vol 24 (4) ◽  
pp. 2561-2567
Author(s):  
Yu Zhang ◽  
Wei Zhang ◽  
Chenhui Zhao ◽  
Yulan Wang
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Collocation Method ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Barycentric Interpolation ◽  
Reaction Diffusion Model ◽  
Linear Reaction ◽  
Coupled Reaction

In thermal science, chemical and mechanics, the non-linear reaction-diffusion model is very important, and an approximate solution with high precision is always needed. In this article, the barycentric interpolation collocation method is proposed for this purpose. Numerical experiments show that the proposed approach is highly reliable.

A geometrical approach to wave-type solutions of excitable reaction-diffusion systems

1991 ◽  
Vol 433 (1887) ◽  
pp. 151-164 ◽  
Keyword(s):  
Numerical Solution ◽  
Wave Front ◽  
Eikonal Equation ◽  
Reaction Diffusion ◽  
Stationary Wave ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Wave Boundary

We formulate the eikonal equation approximation for travelling waves in excitable reaction-diffusion systems, which have been proposed as models for a large number of biomedical situations. This formulation is particularly suited, in a natural way, to numerical solution by finite difference methods. We show how this solution is independent of the parametric variable used for expressing the eikonal equation, and how a reduction of dimensionality implies a major saving over the time taken to solve the original reaction-diffusion system. Neumann boundary conditions on reactants in the original system translate into a geometric constraint on the wave boundary itself. We show how this leads to geometrically stable stationary wave boundaries in appropriately shaped non-convex domains. This analytical prediction is verified by numerical solution of the eikonal equation on a domain which supports geometrically stable stationary wave boundary configurations. We show how the concepts of geometrical stability and wave-front stability relate to a problem where a bi-stable reaction-diffusion system has a stable stationary wave-front configuration.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals The human EDAR 370V/A polymorphism affects tooth root morphology potentially through the modification of a reaction–diffusion system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  
Keyword(s):  
Molecular Mechanisms ◽  
Computational Study ◽  
Reaction Diffusion ◽  
Human Migration ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Tooth Root ◽  
Computed Tomography Images ◽  
Diffusion Dynamics ◽  
Root Morphogenesis

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.

Geographic tongue as a reaction–diffusion system

2021 ◽  
Vol 31 (3) ◽  
pp. 033118
Author(s):  
Margaret K. McGuire ◽  
Chase A. Fuller ◽  
John F. Lindner ◽  
Niklas Manz
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Characterization
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