Pinning by directed percolation

Tang, Lei-Han; Leschhorn, Heiko

doi:10.1103/physreva.45.r8309

Cited by 218 publications

(299 citation statements)

References 20 publications

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“…Scaling arguments in 1 + 1 dimensions give a velocity exponent θ = ν − ν ⊥ ≈ 0.637 and a roughness exponent α G = ν ⊥ /ν ≈ 0.633 at criticality [7,8]. These relations are supported by numerical estimates of the exponents θ and α G of the DPD and related models [7,8,41].…”

Section: Growing Interfaces In Disordered Mediasupporting

confidence: 58%

“…However, some recently developed methods were applied to analyze theoretical and experimental data and showed that fluid flow in random media formed by packed glass beads were indeed in the RFIM class [45]. Now we will discuss the anisotropic class of depinning transitions, whose main representatives are the DPD model of Buldyrev et al [7] and a related model by Tang and Leschhorn [8]. The DPD model was introduced to describe results of experiments on paper wetting.…”

Section: Growing Interfaces In Disordered Mediamentioning

confidence: 99%

“…The first group is that of isotropic growth models, whose main representative is the problem of domain wall motion in the random-field Ising model [6,35,36] (RFIM), and the second one includes models of directed percolation depinning (DPD) [7,8]. The common ingredient of these models is the presence of quenched disorder, which eventually form spanning clusters that block an interface growth.…”

Section: Growing Interfaces In Disordered Mediamentioning

confidence: 99%

“…III). We will be mainly interested in the problems of domain wall motion in the RFIM and directed percolation depinning, introduced in the works by Ji and Robbins [6], Tang and Leschhorn [8] and Buldyrev et al [7]. In those systems, the interface becomes pinned when the concentration of impurities is high enough to generate a blocking cluster running perpendicular to the growth direction.…”

Section: Introductionmentioning

confidence: 99%

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Depinning transitions in interface growth models

Reis

2003

Braz. J. Phys.

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Pinning-depinning transitions are roughening transitions separating a growing phase and pinned (or blocked) one, and are frequently connected to transitions into absorbing states. In this review, we discuss lattice growth models exhibiting this type of dynamic transition. Driven growth in media with impurities, the competition between deposition and desorption and deposition of poisoning species are some of the physical mechanisms responsible for the transitions, leading to different types of stochastic growth rules. The growth models are classified according to the those mechanisms and possible applications are shown, which include suggestions of experimental realizations of directed percolation transitions. I IntroductionThe study of surface and interface growth processes attracts much interest from the technological point of view mainly because it helps to understand the growth mechanisms of nanostructures and, consequently, their physical properties [1]. From the theoretical point of view, they motivated significant advances in non-equilibrium Statistical Mechanics and related fields [2,3]. Theoretical modeling is usually based on stochastic differential equations or on discrete atomistic models. In various models, changing one parameter leads to a roughening transition between a rough and a smooth phase. Two well known examples are the transition in the Kardar-Parisi-Zhang equation in dimensions d ≥ 3, separating regimes with linear (smooth) and nonlinear growth, and temperature-induced roughening transitions in equilibrium conditions [2]. On the other hand, in the so-called depinning transitions, the interface propagates only in the rough phase, being pinned in the smooth phase. Several mechanisms may be responsible for this type of transition, such as the presence of impurities in the growth media, competition between deposition and evaporation or formation of poisoning species at the growing surface. One of the interesting features of depinning transitions is that they frequently can be mapped onto transitions into absorbing states, whose most prominent example is directed percolation (DP). Different connections of depinning transitions to DP are found in discrete and continuous growth models, as well as connections with other classes of transitions to absorbing states [4] and, eventually, with statistical equilibrium transitions. Besides the fundamental interest of these systems, the large variety of interface growth phenomena observed in nature suggests them as strong candidates to experimental realizations of models of dynamic transitions, such as DP (see e. g. Ref.[5]).The aim of the present work is to review the basic features of lattice growth models exhibiting depinning transitions. Before introducing these systems, we will briefly summarize the theory and phenomenology concerning interface growth and phase transitions into absorbing states (Sec. II). Then we will discuss the problem of growing interfaces in disordered media with quenched disorder, in which transitions in the DP class or in the cl...

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Section: Growing Interfaces In Disordered Mediasupporting

confidence: 58%

Section: Growing Interfaces In Disordered Mediamentioning

confidence: 99%

Section: Growing Interfaces In Disordered Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Depinning transitions in interface growth models

Reis

2003

Braz. J. Phys.

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“…According to a conjecture by Janssen and Grassberger [9,10], all absorbing state transitions with a scalar order parameter, short-range interactions, and no extra symmetries or conservation laws belong to this class. Examples include the transitions in the contact process [11], catalytic reactions [12], interface growth [13], or Pomeau's conjecture regarding turbulence [14]. In the presence of conservation laws or additional symmetries, other universality classes such as the parity conserving class or the Z 2 -symmetric directed percolation (DP2) class can occur (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Infinite-randomness critical point in the two-dimensional disordered contact process

2009

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We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to 10 10 and system sizes up to 8000 × 8000 sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.

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Collective Transport and Depinning

Tang¹

2009

Encyclopedia of Complexity and Systems Science

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Pinning by directed percolation

Cited by 218 publications

References 20 publications

Depinning transitions in interface growth models

Depinning transitions in interface growth models

Infinite-randomness critical point in the two-dimensional disordered contact process

Collective Transport and Depinning

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