First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Groß, Markus

doi:10.1088/1742-5468/aaa792

Cited by 11 publications

(17 citation statements)

References 103 publications

(295 reference statements)

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“…We remark that the solution of WNT for Dirichlet no-flux boundary conditions [Eqs.( 1.7) and (1.8)] is technically involved since it requires the consideration of an adjoint eigenproblem [see Appendix B 1 a]. Predictions of WNT will be compared to Langevin simulations in an accompanying paper [47].The first-passage problem for the MH equation discussed here and in Ref.[47] is relevant, inter alia, for the rupture of liquid wetting films. In contrast to previous studies [9, 48-61], we focus here on the case where disjoining pressure is negligible and film rupture is solely driven by noise.…”

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confidence: 99%

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First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

Groß

2018

J. Stat. Mech.

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We consider a one-dimensional fluctuating interfacial profile governed by the Edwards-Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path of an interfacial fluctuation conditioned to reach a given maximum height M at a finite (first-passage) time T is calculated within the weak-noise approximation. Dynamic and static scaling functions for the profile shape are obtained in the transient and the equilibrium regime, i.e., for first-passage times T smaller or lager than the characteristic relaxation time, respectively. In both regimes, the profile approaches the maximum height M with a universal algebraic time dependence characterized solely by the dynamic exponent of the model. It is shown that, in the equilibrium regime, the spatial shape of the profile depends sensitively on boundary conditions and conservation laws, but it is essentially independent of them in the transient the dependence of the relaxation time τ of a typical fluctuation governed by Eq. (1.1) or (1.2) on the system size L via τ ∝ L z , with z = 2 (EW equation), z = 4 (MH equation).(1.12)Large deviations of stochastic processes are formally described by Freidlin-Wentzel theory [35][36][37], which is equivalent to a Martin-Siggia-Rose/Janssen/de Dominicis path-integral formulation [38][39][40][41] in the limit of weak noise [42][43][44]. This approach provides an action functional, the minimization of which yields the most probable ("optimal") path connecting two states [e.g., Eqs. (1.5) and (1.4)]. For an explicit derivation of the corresponding weak-noise theory (WNT) for the EW and MH equation see, e.g., Refs. [30,45]. A related large deviation formalism in the context of lattice gases is reviewed in Ref. [46].An important predecessor to the present work is Ref. [30], where the WNT of Eq. (1.2) with periodic boundary conditions has been solved. Here, we extend that study by discussing further aspects of the first-passage dynamics, focusing, in particular, on the effect of boundary conditions. Within the WNT of Eqs. (1.1) and (1.2), we obtain minimum-action paths describing extremal fluctuations of the profile fulfilling Eqs. (1.4) and (1.5), without conditioning on the first-passage. We remark that the solution of WNT for Dirichlet no-flux boundary conditions [Eqs.( 1.7) and (1.8)] is technically involved since it requires the consideration of an adjoint eigenproblem [see Appendix B 1 a]. Predictions of WNT will be compared to Langevin simulations in an accompanying paper [47].The first-passage problem for the MH equation discussed here and in Ref.[47] is relevant, inter alia, for the rupture of liquid wetting films. In contrast to previous studies [9, 48-61], we focus here on the case where disjoining pressure is negligible and film rupture is solely driven by noise. A related WNT describing the noise-induced breakup of a liquid thread has been analyzed in Ref. [62]. Rare-event trajectories of the kind considered here are furthermore relevant fo...

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“…( 1.7) and (1.8)] is technically involved since it requires the consideration of an adjoint eigenproblem [see Appendix B 1 a]. Predictions of WNT will be compared to Langevin simulations in an accompanying paper [47].…”

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confidence: 99%

First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

Groß

2018

J. Stat. Mech.

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“…[80]), which is distinct from the fully conservative model B [39] (denoted as "model B B " in this context). A modification of Dirichlet BCs in order to implement the no-flux condition is possible but leads to transcendental eigenvalues [81,82] and is left for future investigations.…”

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Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

2019

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Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameterconserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter. * gross@is.mpg.de arXiv:1905.00269v2 [cond-mat.stat-mech]

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“…(2.8)] is given by χ = 1 (unless we consider temperatures T R /T φ = 1). We remark that, due to technical reasons, conserved dynamics is applied only to OP fields subject to Neumann BCs [73]. Data is recorded after an initial transient period (of approximate duration (L/π) 2+2a ) required to equilibrate the OP field.…”

Section: A Simulationsmentioning

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Dynamics and steady states of a tracer particle in a confined critical fluid

Gross

2021

Preprint

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The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying dissipative or conservative equilibrium dynamics and (non-)symmetrybreaking boundary conditions. The tracer, which represents, e.g., a colloidal particle, interacts with the fluid by locally modifying its chemical potential or its correlation length. The coupling between tracer and fluid gives rise to a nonlinear and non-Markovian tracer dynamics, which is investigated here analytically and via numerical simulations for a one-dimensional system. From the coupled Langevin equations for the tracer-fluid system we derive an effective Fokker-Planck equation for the tracer by means of adiabatic elimination as well as perturbation theory within a weak-coupling approximation. The effective tracer dynamics is found to be governed by a fluctuation-induced (Casimir) potential, a spatially dependent mobility, and a spatially dependent (multiplicative) noise, the characteristics of which depend on the interaction and the boundary conditions. The steadystate distribution of the tracer is typically inhomogeneous.

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First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Cited by 11 publications

References 103 publications

First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

Dynamics and steady states of a tracer particle in a confined critical fluid

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