Active width at a slanted active boundary in directed percolation

Cc, Chen; H, Park; M, den Nijs

doi:10.1103/physreve.60.2496

Cited by 10 publications

(14 citation statements)

References 15 publications

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“…Of course (11) could simply be obtained by adding the advective velocity r ′ to the usual Fisher wave velocity in the absence of advection, (4αD) 1/2 . In the subcritical phase, the modified wave described by (7) has a velocity given by a distinct expression. Here, for large x, (7) becomeṡ…”

Section: Mean-field Theorymentioning

confidence: 99%

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Discontinuous transition in a boundary driven contact process

Costa¹,

Blythe²,

Evans³

2010

J. Stat. Mech.

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The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an active wall. This model exhibits waves of activity emanating from the active wall and, when the system is supercritical, propagating indefinitely as travelling (Fisher) waves. In the subcritical phase the activity is localised near the wall. We study the phase transition numerically and show that certain properties of the system, notably the wave velocity, are discontinuous across the transition. Using a modified Fisher equation to model the system we elucidate the mechanism by which the the discontinuity arises. Furthermore we establish relations between properties of the travelling wave and DP critical exponents.

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Section: Mean-field Theorymentioning

confidence: 99%

“…In the subcritical phase, the modified wave described by (7) has a velocity given by a distinct expression. Here, for large x, (7) becomeṡ…”

Section: Mean-field Theorymentioning

confidence: 99%

Discontinuous transition in a boundary driven contact process

Costa¹,

Blythe²,

Evans³

2010

J. Stat. Mech.

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“…16,17,18,19,20,21,22,23,24,25,26,27,28 We will describe the boundary critical behavior of DP and BARW by using a variety of methods, including mean field theory, scaling theory, field theory, exact calculations, Monte-Carlo simulations, and series expansions. The rest of this review is organized as follows: In Section 2 we introduce percolation and reaction-diffusion models for DP and BARW for bulk systems (without boundaries).…”

Section: Introductionmentioning

confidence: 99%

“…(iii) active, but slanted, walls in DP, which give rise to a "curtain" of activity whose width is given by an angle-dependent correction to bulk DP; 25 and, finally, (iv) Monte-Carlo simulation studies of rigidity percolation with and without walls, which have shown the model to belong to the DP universality class. 23 …”

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confidence: 99%

Directed Percolation and Other Systems With Absorbing States: Impact of Boundaries

Fröjdh

Howard

Lauritsen

2001

Int. J. Mod. Phys. B

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We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of these models, we devote the main part of this review to analyzing the impact of walls on their critical behavior. We discuss the possible boundary universality classes for the DP and BARW models, which can be described by a general scaling theory which allows for two independent surface exponents in addition to the bulk critical exponents. Above the upper critical dimension dc, we review the use of mean field theories, whereas in the regime d < dc, where fluctuations are important, we examine the application of field theoretic methods. Of particular interest is the situation in d = 1, which has been extensively investigated using numerical simulations and series expansions. Although DP and BARW fit into the same scaling theory, they can still show very different surface behavior: for DP some exponents are degenerate, a property not shared with the BARW model. Moreover, a "hidden" duality symmetry of BARW in d = 1 is broken by the boundary and this relates exponents and boundary conditions in an intricate way.

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“…In particular DP with absorbing walls at positions x(t) = ±C · t 1/z shows spreading exponents that continuously depend on C [21,22]. Analogous results with a moving active wall are presented in [23]. Moreover, one dimensional models with soft or hard walls conditions can be studied analytically in the case of Compact DP.…”

Section: Discussion and Related Modelsmentioning

confidence: 99%

Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities

Landes¹,

Rosso²,

Jagla³

2012

Phys. Rev. E

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We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value p(c). Criticality is lost as soon as the probability to activate sites at the first attempt, p(1), is changed. We show here that criticality can be restored by "compensating" the change in p(1) by an appropriate change of the second time activation probability p(2) in the opposite direction. At compensation, we observe that the bulk exponents of the process coincide with those of the normal directed percolation process. However, the spreading exponents are changed and take values that depend continuously on the pair (p(1),p(2)). We interpret this situation by acknowledging that the model with modified initial probabilities has an infinite number of absorbing states.

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Active width at a slanted active boundary in directed percolation

Cited by 10 publications

References 15 publications

Discontinuous transition in a boundary driven contact process

Discontinuous transition in a boundary driven contact process

Directed Percolation and Other Systems With Absorbing States: Impact of Boundaries

Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities

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