Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems

Wit, A. De

doi:10.1002/9780470141687.ch5

Cited by 73 publications

(21 citation statements)

References 349 publications

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“…Above this temperature, only wave patterns originating from bulk oscillations occur in this system. It was shown theoretically using the Brusselator 86 and extended Oregonator 87 models that interaction between Turing and Hopf ͑oscilla-tory͒ modes can generate a new type of pattern, an oscillatory Turing pattern. These patterns are stationary in space, but oscillatory in time.…”

Section: E Temperature As a Control Parametermentioning

confidence: 99%

Design and control of patterns in reaction-diffusion systems

Vanag

Epstein

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium isothermal is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a q −4 to a q −2 behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.

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Section: E Temperature As a Control Parametermentioning

confidence: 99%

Design and control of patterns in reaction-diffusion systems

Vanag

Epstein

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The importance of the amplitude formalism lies in its universal character to represent many dynamical systems near the CTHP and its capability for obtaining a Mixed Mode (MM) solution, combining the expected spatial and temporal periodicity. This MM solution was first experimentally verified in chemical systems 3 , and at the same time an important analytic understanding of its existence and stability in small domains was developed 4–6 . With this, the Turing-Hopf amplitude equations were proposed as approximate solutions of a variety of dynamical systems 7–9 .…”

Section: Introductionmentioning

confidence: 87%

“…As it is clear from substituting in Eq. (3), this corresponds to a spatial pattern of constant wavenumber oscillating in time with constant phase 6 . This is the expected solution on very small domains or in systems where no spatial perturbations occur 10 .…”

Section: Antecedentsmentioning

confidence: 99%

Spatio-temporal secondary instabilities near the Turing-Hopf bifurcation

Ledesma-Durán

Aragón

2019

Sci Rep

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In this work, we provide a framework to understand and quantify the spatiotemporal structures near the codimension-two Turing-Hopf point, resulting from secondary instabilities of Mixed Mode solutions of the Turing-Hopf amplitude equations. These instabilities are responsible for solutions such as (1) patterns which change their effective wavenumber while they oscillate as well as (2) phase instability combined with a spatial pattern. The quantification of these instabilities is based on the solution of the fourth order polynomial for the dispersion relation, which is solved using perturbation techniques. With the proposed methodology, we were able to identify and numerically corroborate that these two kinds of solutions are generalizations of the well known Eckhaus and Benjamin-Feir-Newell instabilities, respectively. Numerical simulations of the coupled system of real and complex Ginzburg-Landau equations are presented in space-time maps, showing quantitative and qualitative agreement with the predicted stability of the solutions. The relation with spatiotemporal intermittency and chaos is also illustrated.

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“…Nonlinear dynamical systems possess the capability to exhibit these properties and will be investigated as the medium to create such a system. 13.3.1…”

Section: Intelligent Response and Pattern Formationmentioning

confidence: 99%

“…A good body of theoretical research has been conducted in this field during the past few decades, and several models have been proposed. These are based either on outside-equilibrium thermodynamics, which point to the onset of dissipative structures [9,10], or kinetic models that make use of simplifications and compromises in order to describe and predict the behavior of the nonlinear dynamic system [11][12][13][14][15].…”

Section: Self-organization In Systems Removed From the Equilibrium Statementioning

confidence: 99%