Momentum Effects in Reaction-Diffusion Systems

Vilensky, Baruch; Havlin, Shlomo; Taitelbaum, Haim; Weiss, George H.

doi:10.1021/j100081a015

Cited by 11 publications

(5 citation statements)

References 5 publications

(4 reference statements)

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“…1993, 1997, Schenkel et al 1993, Lee and Cardy 1994, 1995, Vilensky et al 1994, Araujo 1995, Howard and Cardy 1995, Hoyuelos et al 1995, Krapivsky 1995, Barkema et al 1996, Koza 1996, 1997, Taitelbaum et al 1996a,b, Koza and Taitelbaum 1997, Malyutin et al 1997, Richardson and Evans 1997, Rodriguez and Wio 1997. …”

Section: $2 Methods and Resultsmentioning

confidence: 99%

Anomalous kinetics of reaction diffusion fronts

Taitelbaum

Koza

1998

Philosophical Magazine B

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Section: $2 Methods and Resultsmentioning

confidence: 99%

Anomalous kinetics of reaction diffusion fronts

Taitelbaum

Koza

1998

Philosophical Magazine B

Self Cite

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“…In many cases the predictions of the mean-field PDE agree well with simulation averages, especially at low densities of agents, but the quality of agreement degrades when inter-agent interactions have a significant attractive component [16], or when agents reproduce at random as well as moving at random. In many scenarios including modelling of vehicle movement [17], chemical reaction kinetics [18], cell motility [6] and animal movement [19], it is clear that agents do not move completely at random but exhibit short-term persistence in the direction of motion, thus giving rise to the notion of a persistent random walk (PRW) [3,19,20]. The case of non-interacting walkers has received substantial attention [3,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Persistent exclusion processes: Inertia, drift, mixing, and correlation

2019

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In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple walkers with motion persistence and spatial exclusion in one and two dimensions, and use a mean-field approximation to investigate relevant populationlevel partial differential equations in the continuum limit. We show that this model of a persistent exclusion process is in general well described by a nonlinear diffusion equation. With reference to results presented in the current literature, our results reveal that the nonlinearity arises from the combination of motion persistence and volume exclusion, with linearity in terms of the canonical diffusion or heat equation being recovered in either the case of persistence without spatial exclusion, or spatial exclusion without persistence. We generalise our results to include systems of multiple species of interacting, motion-persistent walkers, as well as to incorporate a global drift in addition to persistence. These models are shown to be governed approximately by systems of nonlinear advection-diffusion equations. By comparing the prediction of the mean-field approximation to stochastic simulation results, we assess the performance of our results. Finally, we also address the problem of inferring the presence of persistence from simulation results, with a view to application to experimental cell-imaging data.

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“…products. The conditions for these front patterns are significant differences in the microscopic reaction constants and in the initial densities of the competing species.[S0031-9007(96)00897-6] 05.40.+j In a series of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], it has been shown that elementary reaction-diffusion systems with initially separated components have very unusual dynamical properties. For the elementary reaction A 1 B !…”

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Competing Reactions with Initially Separated Components

et al. 1996

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The first theoretical and experimental study of a competitive reaction with initially separated components is presented. Rich spatiotemporal reaction front patterns are produced by a simple theoretical reaction-diffusion model. Such patterns are observed experimentally for the reaction Cr 31 1 xylenol orange ͑XO͒ ! products. The conditions for these front patterns are significant differences in the microscopic reaction constants and in the initial densities of the competing species.[S0031-9007(96)00897-6] 05.40.+j In a series of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], it has been shown that elementary reaction-diffusion systems with initially separated components have very unusual dynamical properties. For the elementary reaction A 1 B ! C, the initial separation of reactants leads to the formation of a dynamic reaction front. The presence of such a reaction interface is characteristic of many processes in nature [17][18][19][20][21][22]. Interesting properties of the front are the global reaction rate R͑t͒, the location of the center of the reaction front x f ͑t͒, the width of the front w͑t͒, and the local reaction rate at the center of the front R͑x f , t͒. These reaction rate and front properties have been shown to follow a nonclassical behavior, with anomalous time exponents [1,5,6].The first level of complexity in chemical reaction kinetics is competing elementary reactions, which occur in many chemical systems [23]. These reactions also provide the simplest case for the formation of a complex reaction front pattern. In this Letter we show how such a pattern can be simply accounted for by two competing elementary reactions; two similar species, A 1 and A 2 , on one side of the initially separated system, compete to react with the species on the other side of the system, B, according to the schemeThese two processes are taking place simultaneously, each with a different microscopic reaction constant, k 1 and k 2 . In the simplest model of the A 1 B ! C initially separated system, the following set of mean-field reactiondiffusion equations for the local concentrations r a , r b has been assumed to describe the system [1]:≠r a ≠t D a = 2 r a 2 kr a r b ,where D a , D b are the diffusion constants, and k is the microscopic reaction constant. These equations are subject to the initial separation condition along the x axis, r a ͑x, 0͒ a 0 ͓1 2 H͑x͔͒,where a 0 , b 0 are the initial densities and H͑x͒ is the Heaviside step function, so that the A's are initially uniformly distributed on the left side ͑x , 0͒, and the B's on the right side ͑x . 0͒ of the initial boundary.In the mean-field description, which is valid [7] above d 2, the local production rate of C, is defined by the term R͑x, t͒ kr a ͑x, t͒r b ͑x, t͒, which is the basis for defining all other quantities of interest [1]. In our model (1), which allows for the existence of more than a single species on one side of the initially separated system, the products C 1 and C 2 are assumed to be either identical or experimentall...

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Momentum Effects in Reaction-Diffusion Systems

Cited by 11 publications

References 5 publications

Anomalous kinetics of reaction diffusion fronts

Anomalous kinetics of reaction diffusion fronts

Persistent exclusion processes: Inertia, drift, mixing, and correlation

Competing Reactions with Initially Separated Components

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