Persistence and survival in equilibrium step fluctuations

Constantin, Magdalena; Dasgupta, Chandan; Sarma, S. Das; Dougherty, Daniel B.; Williams, Ellen D.

doi:10.1088/1742-5468/2007/07/p07011

Cited by 11 publications

(13 citation statements)

References 75 publications

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“…A reasonable conjecture is that one has to a priori distinguish between a macroscopic behavior of the interface under study, reflected by the growth exponent, and a microscopic behavior of the particular elements of the interface. While the kinetic roughening has to do with the collective behavior of the advancing interface, and allows for estimation of the lateral correlation length [7,8], the persistence measure is much more sensitive [14]. Hence we suggest that the behavior of our reactive-wetting system is dichotomic.…”

Section: Summary and Discussionmentioning

confidence: 90%

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Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Efraim

Taitelbaum

2009

Open Physics

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Abstract:The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a small (∼ 150 µm) Hg droplet that spreads on a thin (∼ 4000 Å) Ag substrate. We calculated the kinetic roughening exponents (growth and roughness), as well as the persistence exponent of points on the advancing interface.In this paper we address the question whether there exists a well-defined model to describe the interface dynamics of this system, by performing two sets of numerical simulations. The first one is a simulation of an interface propagating according to the QKPZ equation, and the second one is a landscape of an Ising chain with ferromagnetic interactions in zero temperature. We show that none of these models gives a full description of the dynamics of the experimental reactivewetting system, but each one of them has certain common growth properties with it. We conjecture that this results from a microscopic behavior different from the macroscopic one. The microscopic mechanism, reflected by the persistence exponent, resembles the Ising behavior, while in the macroscopic scale, exemplified by the growth exponent, the dynamics looks more like the QKPZ dynamics.

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Section: Summary and Discussionmentioning

confidence: 90%

“…The persistence measure gives more detailed information as it takes into account local, microscopic fluctuations [14].…”

Section: Introductionmentioning

confidence: 99%

Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Efraim

Taitelbaum

2009

Open Physics

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“…For a nice review of the theoretical and experimental results of persistence and first-passage properties of interfaces, particularly in connection to step edges on crystals, see Ref. [271]. Apart from step edges on crystals, persistence of fluctuating interfaces have also been measured in a variety of other experimental systems, such as in combustion fronts in paper [39], for interfaces between phase-separated coloid-polymer mixtures [272], advancing interfaces or fronts in reactive-wetting systems such as mercury on silver [41] and growing droplets of turbulent phase in nematic liquid crystals [42].…”

Section: Persistence Of Fluctuating Interfacesmentioning

confidence: 99%

“…Another interesting first-passage quantity is called the survival probability S(t 0 , t) defined as the probability that height field h(0, t) does not return to its average value, namely, to 0 in the time interval [t 0 , t 0 + t] [271,281]. This is different from the temporal persistence Q(t 0 , t) where one is concerned with the event of not returning to the initial value.…”

Section: • Molecular Beam Epitaxy (Mbe) Equation: This Is a 4-th Ordementioning

confidence: 99%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

530

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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“…In recent years, there has been significant interest in studies of the first-passage properties of dynamical fluctuations [2], quantified in terms of persistence probability. The persistence probability P (t) is the probability that a stochastic variable will never cross some reference level within time interval t. The persistence probability was calculated and measured for several theoretical, numerical, and experimental systems [3][4][5][6][7] and was shown to decrease with time as a power law,…”

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confidence: 99%

Persistence in reactive-wetting interfaces

Efraim

Taitelbaum

2011

Phys. Rev. E

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In this paper, we report on persistence results of reactive-wetting advancing interfaces performed with mercury on silver at room temperature. Earlier kinetic roughening studies of reactive-wetting systems at room temperature as well as at high temperatures revealed some limited information on the spatiotemporal behavior of these systems. However, by calculating the persistence exponent, we were able to identify two distinct kinetic time regimes in this process. In the first one, while the interface is moving but its width is not yet growing, the persistence exponent is θ=0.55±0.05, which is typical for a random, noisy behavior. In the second regime, there is an effective growth of the interface width with a growth exponent β=0.67±0.06 followed by saturation, according to the Family-Vicsek description of interface growth. The persistence exponent in this regime is θ=0.37±0.05, which indicates that the relation θ=1-β seems to hold even for this nonlinear experimental system.

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Persistence and survival in equilibrium step fluctuations

Cited by 11 publications

References 75 publications

Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

Persistence and first-passage properties in nonequilibrium systems

Persistence in reactive-wetting interfaces

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