Experimental Study of a Reaction-Diffusion System in a Capillary: Complex Behavior of a Seemingly Simple System

1994 ◽  
Vol 366 ◽  
Author(s):  
Anna Lin ◽  
Andrew Yen ◽  
Yong-Eun Koo ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Capillary Tube ◽  
Xylenol Orange ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Product Concentration ◽  
Global Rate ◽  
Global Reaction

ABSTRACTWe study a reaction-diffusion system within the confines of a thin capillary tube. Xylenol orange and Cr 3+ are introduced into a capillary tube from opposite ends and meet in the middle forming a reaction front. Unequal initial concentrations of the reactants causes the center of the reaction front to move in time. Characteristics of the front such as the width of the reaction zone, w, the position of the center of the front, xf, the global reaction rate, R, and the local reaction rate, r(xf,t) are determined by continuously monitoring the product concentration in space vs. time. We observe crossover of the global rate from classical to non-classical behavior and a splitting of the reaction front.

Study of an A+2B--->C Reaction-Diffusion System with Initially Separated Components

1994 ◽  
Vol 366 ◽  
Author(s):  
Andrew Yen ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Biological Processes ◽  
Local Production ◽  
Kinetic Behavior ◽  
Acetate Trihydrate ◽  
Physical Chemical ◽  
Global Reaction ◽  
Front Dynamics

ABSTRACTThe presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. A chemical reaction exhibits a front (spatially localized region where concentration of product is non zero), provided the diffusing reactants are separated in space. We study the reaction front dynamics of a termolecular A+2B--->C reaction with initially separated components in a capillary. The reaction tetra+2Ni2+--->1:2 complex is used, where ‘tetra’ is disodium ethyl bis(5-tetrazolylazo) acetate trihydrate. We measure and compare with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xf,t). The non-classical nature of this dynamical system is confirmed.

Reaction Dynamics and Chemical Pattern Formation in Capillary Tubes Resulting from the Competition Between Two Elementary Complex Formation Reactions

1996 ◽  
Vol 464 ◽  
Author(s):  
Anna L. Lin ◽  
Andrew Yen ◽  
Yong-Eun Lee Koo ◽  
Baruch Vilensky ◽  
Haim Taitelbaum ◽  
...  
Keyword(s):  
Reaction Rate ◽  
Capillary Tube ◽  
Xylenol Orange ◽  
Early Time ◽  
Temporal Patterns ◽  
Competing Species ◽  
Elementary Reactions ◽  
Reaction Diffusion Model ◽  
Global Rate ◽  
Spatio Temporal

AbstractA system of competing elementary reactions is investigated experimentally usingthe reaction of xylenol orange with Cr3+ in aqueous solution. The two reagents areinitially separated in a long, thin capillary tube and meet in the center, forming a reactionfront (s). The geometry of the reactor and the initial separation of the reagents makes the system effectively one-dimensional. Aqueous Cr3+ solution has a very rich chemistryand provides two different chemical Cr3+ reactants which compete to react with xylenolorange. Rich spatio-temporal patterns are observed experimentally and are explained by a reaction-diffusion model. Results from exact enumeration simulations predict that when the concentrations of the competing species are very different and the microscopic rate constants of the competing species are such that the majority species reaction rate is much faster than the reaction rate of the minority species, the reaction front splits into two distinct regions. The spatio-temporal patterns generated by theory and experiment agree quantitatively. Also in agreement with the theory are the experimental early time and asymptotic time global rate behaviors, which exhibit multiple crossovers.

Study of A+B-4C and A+2B–C Reaction-Diffusion System with Initially Separated Components

1995 ◽  
Vol 407 ◽  
Author(s):  
Andrew Yen ◽  
Raoul Kopelman
Keyword(s):  
Dynamical System ◽  
Reaction Front ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Biological Processes ◽  
Local Production ◽  
Kinetic Behavior ◽  
Physical Chemical ◽  
Global Reaction ◽  
Front Dynamics

ABSTRACTThe presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. The reaction exhibits a front, provided that the diffusing reactants are separated in space. We study the reaction front dynamics of both A+B→C bimolecular and A+2B→C termolecular reactions with initially separated components in a capillary. We measure and compare with theory and simulations the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xft). The non-classical nature of this dynamical system is confirmed.

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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