Thermally activated escape far from equilibrium: A unified path-integral approach

Getfert, Sebastian; Reimann, Peter

doi:10.1016/j.chemphys.2010.04.028

Cited by 7 publications

(4 citation statements)

References 95 publications

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“…The case of ac actuation force is much more complex. In fact, no simple expression for the escape rate has been derived in the presence of ac fields [33][34][35]. As a consequence, a simple relation for the friction force reduction is also missing.…”

Section: A Scaling Behaviormentioning

confidence: 99%

Out-of-plane and in-plane actuation effects on atomic-scale friction

2014

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The influence of out-of-plane and in-plane contact vibrations and temperature on the friction force acting on a sharp tip elastically pulled on a crystal surface is studied using a generalized Prandtl-Tomlinson model. The average friction force is significantly lowered in a frequency range determined by the "washboard" frequency of the stick-slip motion and the viscous damping accompanying the tip motion. An approximately linear relationship between the actuation amplitude and the effective corrugation of the surface potential is derived in the case of in-plane actuation, extending a similar conclusion for out-of-plane actuation. Temperature causes an additional friction reduction with a scaling relation in formal agreement with the predictions of reaction rate theory in the absence of contact vibrations. In this case the actuation effects can be described by the effective energy or, more accurately, by introducing an effective temperature.

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Section: A Scaling Behaviormentioning

confidence: 99%

Out-of-plane and in-plane actuation effects on atomic-scale friction

2014

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“…Yet more, equation (54) allows to reach an approximation of the nucleation rate via equation (41). Now this result can be extended as a first-order approximation for time-varying conditions, as shown by Getfert and Reimann 53 for slowly time-dependent Kramers-Moyal coefficients. Thus, under the assumption of the semiadiabatic limit, and following the notation introduced by Getfert and Reimann 53 , the instantaneous MFPT can be estimated as follows, τ (α; t) ∼ 1 2 χ(t) I(α, κ(t)) f (X * , κ(t)) −α e βW (X * ,κ(t)) .…”

Section: Estimation Of Induction Times and Nucleation Ratesmentioning

confidence: 80%

Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation

Durán-Olivencia

Lutsko

2015

Phys. Rev. E

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Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of firstorder phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J.F. Lutsko and M.A. Durán-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer.

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“…This phenomenon has been discovered by Martin Day, who called it cycling [20,21,22,24]. See also [49,11,36,37] for related work. The intuitive explanation of cycling is as follows.…”

Section: The Origin Of Oscillationsmentioning

confidence: 93%

Noise-induced phase slips, log-periodic oscillations, and the Gumbel distribution

Berglund

2014

Preprint

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When two synchronised phase oscillators are perturbed by weak noise, they display occasional losses of synchrony, called phase slips. The slips can be characterised by their location in phase space and their duration. We show that when properly normalised, their location converges, in the vanishing noise limit, to the sum of an asymptotically geometric random variable and a Gumbel random variable. The duration also converges to a Gumbel variable with different parameters. We relate these results to recent works on the phenomenon of log-periodic oscillations and on links between transition path theory and extreme-value theory.

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Thermally activated escape far from equilibrium: A unified path-integral approach

Cited by 7 publications

References 95 publications

Out-of-plane and in-plane actuation effects on atomic-scale friction

Out-of-plane and in-plane actuation effects on atomic-scale friction

Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation

Noise-induced phase slips, log-periodic oscillations, and the Gumbel distribution

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