Antiresonance and Stabilization in Spatio‐Temporal Dynamics of a Periodically Driven Gray‐Scott Reaction‐Diffusion System

This review summarizes recent studies on the catalytic CO oxidation on Iridium(111) surfaces. This was investigated experimentally under ultrahigh vacuum (UHV) conditions using mass spectroscopy to detect gaseous products and photoelectron emission microscopy (PEEM) to visualize surface species. The underlying reaction–diffusion system based on the Langmuir–Hinshelwood mechanism was analyzed numerically.The existence of bistability for this surface reaction was shown in experiment. For the first time the effect of noise on a bistable surface reaction was examined. In a surface science experiment the effects on product formation and the development of spatio-temporal patterns on the surface were explored.Steady state CO2rates were measured under constant flux of the CO + O mixture as a function of sample temperature (360 K < T < 700 K) and gas composition, characterized by the molar fraction of CO in the feed gas (0 ≤ Y ≤ 1). The reaction reveals bistability in a limited region of Y and T. A rate hysteresis with two steady state rates was observed for cycling Y up and down, one of high reactivity (upper rate, oxygen covered surface) and one of low reactivity (lower rate, CO covered surface). The position of the hysteresis loop shifts to higher Y values and decreases in width with increasing temperature. For small CO content in the feed gas the CO2rate is proportional to Y3/2. At 500 K extremely slow Y cycling measurements (about 100 hours per direction) were done and showed that bistability still exists and no slowly changing transients were observed. The requirements for the speed with which experiments can be executed without producing experimental artifacts were explored. Since over-sampling alters the measured hysteresis loop, a maximum rate for changing the gas composition in Y cycling experiments was determined.The influence of noise on the reaction rates and the formation of spatio-temporal patterns on the surface was explored by superposing noise of Gaussian white type on Y and on T. Noisy Y (deviation Δ Y) represents multiplicative and additive noise, noisy T (deviation Δ T) multiplicative noise only. Noisy T enters the reaction via the rate-determining step, the observed CO2rates become noisy for low temperatures (around 420 K) when the surface is dominantly oxygen covered ( CO + O reaction step is rate-limiting) and for higher temperatures (around 500 K) when the surface is dominantly CO covered ( CO desorption step is rate-limiting).The effect of noisy Y was examined for a sample temperature of 500 K and is dependent on the selected average gas composition. In the regions with one steady state CO2rate (outside the hysteresis) the recorded rates were noisy. The probability distribution of the rates is Gaussian shaped for the upper rate (below hysteresis) and asymmetric for the lower rate (above hysteresis). For large noise strength bursts, short-time excursions to and above the upper rate, were observed.Inside the hysteresis small noise made the steady state rates noisy, but above a Y-dependent Δ Y transients from the locally stable to the globally stable rate branch were observed. These transients take up to several ten thousand seconds and become faster with increasing noise. For larger Y noise strength bursts and switching between both steady state rates were detected.Photoelectron emission microscopy (PEEM) was done to visualize spatio-temporal adsorbate patterns on the surface as expected from the observations in the CO2rate measurements. CO - and oxygen-covered regions on the Ir (111) surface are visible in PEEM images as gray and black areas as a consequence of their work function contrast. Islands of the adsorbate, corresponding to the globally stable branch, are formed in a background of the other one. The long transient times are the result of the extremely slow domain wall motion of these islands (around 0.05 μm s-1). In the hysteresis region CO oxidation on Iridium(111) surfaces is dominated by domain formation and wall motion for small to moderate noise strength. The island density increases with noise, but the wall velocity is independent of applied Δ Y. For larger noise amplitudes, fast switching between oxygen- and CO -dominated surfaces is observed as well as nucleation and growth of the minority phase in the majority phase.In the numerically analyzed reaction–diffusion system all parameters were taken from the experiment. Modeling the reaction–diffusion system shows qualitative up to quantitative agreement with the experimental observations. The length scale for the modeling grid is determined from wall velocity seen in the experiments.

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Traveling wavefronts in a bistable reaction diffusion system with spatio-temporal delay

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2011.02.017 ◽

2011 ◽

Vol 16 (11) ◽

pp. 4276-4283

Author(s):

Hai-Qin Zhao

Keyword(s):

Reaction Diffusion ◽

Reaction Diffusion System ◽

Diffusion System ◽

Temporal Delay ◽

Spatio Temporal

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SPATIO-TEMPORAL CHAOS IN A DISCRETE TURING MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410028008 ◽

2010 ◽

Vol 20 (11) ◽

pp. 3741-3752

Author(s):

HUNSEOK KANG

Keyword(s):

Numerical Computation ◽

Reaction Diffusion ◽

Reaction Diffusion System ◽

Diffusion System ◽

Discrete Version ◽

Lattice Systems ◽

Spatio Temporal ◽

Turing Model

In this paper, we present a study of a discrete version of a reaction–diffusion system which corresponds to the Turing model of morphogenesis. We present a review on spatio-temporal chaos in lattice systems, and then show that the discrete version possesses a hyperbolic property displaying spatio-temporal chaos. Finally, some numerical computation will be performed to observe the hyperbolic properties of the system.

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Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19980761 ◽

1998 ◽

Vol 63 (6) ◽

pp. 761-769 ◽

Cited By ~ 1

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.

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

Scientific Reports ◽

10.1038/s41598-021-84653-4 ◽

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.

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Geographic tongue as a reaction–diffusion system

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0020906 ◽

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

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