Exact solution of a reaction-diffusion model with particle-number conservation

Jafarpour, Farhad H.; Masharian, S. R.

doi:10.1103/physreve.70.056121

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…Recently, shocks in one-dimensional reaction-diffusion models have absorbed much interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. There are some exact results on shocks in one-dimensional reaction-diffusion models as well as simulations, numeric results [6] and also mean field results [2].…”

Section: Introductionmentioning

confidence: 99%

Multi-shocks in reaction-diffusion models

Arabsalmani

Aghamohammadi

2007

Eur. Phys. J. B

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It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbor interaction, there are only four independent models possessing double-shocks. Evolution of the width of the doubleshocks in different models is investigated. Double-shocks may vanish, and the final state is a state with no shock. There is a model for which at large times the average width of double-shocks will become smaller. Although there may exist stationary single-shocks in nearest neighbor reaction diffusion models, it is seen that in none of these models, there exist any stationary double-shocks. Models admitting multi-shocks are classified, and the large time behavior of multi-shock solutions is also investigated.

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Section: Introductionmentioning

confidence: 99%

Multi-shocks in reaction-diffusion models

Arabsalmani

Aghamohammadi

2007

Eur. Phys. J. B

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“…Shocks in one-dimensional reaction-diffusion models have been absorbed many interest recently [2][3][4][5][6][7][8][9][10][11][12]. There are some exact results about shocks in one-dimensional reaction-diffusion models together with simulations, numeric results [7] and also mean field results [3].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in systems possessing shock solutions

Arabsalmani

Aghamohammadi

2006

Phys. Rev. E

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Recently it has been shown that there are three families of stochastic one-dimensional nonequilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states and dynamics of single-shocks on a one-dimensional lattice are studied. This is done for both an infinite lattice and a finite lattice with boundaries. It is seen that these models possess both static and dynamical phase transitions. The static phase transition is the well-known low-high density phase transition for the asymmetric simple exclusion process. The branching-coalescing random walk and asymmetric Kawasaki-Glauber process models also show the same phase transition. Double-shocks on a one-dimensional lattice are also investigated. It is shown that at the stationary state the contribution of double-shocks with higher width becomes small, and the main contribution comes from thin double-shocks.

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Repelling random walkers in a diffusion-coalescence system

Jafarpour

Masharian

2008

Phys. Rev. E

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We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double-shock structures which perform biased random walks on the lattice while repelling each other. The shocks can enter into the system and leave it from the boundaries. Depending on the microscopic reaction rates, the system is known to have two different phases. We have found that the mean distance between the shock positions is of order L in one phase while it is of order 1 in the other phase.

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Exact solution of a reaction-diffusion model with particle-number conservation

Cited by 3 publications

References 27 publications

Multi-shocks in reaction-diffusion models

Multi-shocks in reaction-diffusion models

Phase transitions in systems possessing shock solutions

Repelling random walkers in a diffusion-coalescence system

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