Nonlinear Brownian motion - mean square displacement

Ébeling, W.

doi:10.5488/cmp.7.3.539

Cited by 23 publications

(17 citation statements)

References 17 publications

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“…For each condition, we calculated the mean square displacement (MSD) of the proton during simulations of 40-50 ps [23]. The MSD can be calculated from a single trajectory by only performing a time average.…”

Section: Resultsmentioning

confidence: 99%

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

Fronzi

Tateyama

Marzari

et al. 2016

Mater Renew Sustain Energy

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First-principles molecular dynamics simulations have been employed to analyse the proton diffusion in cubic BaZrO 3 perovskite at 1300 K. A non-linear effect on the proton diffusion coefficient arising from an applied isometric strain up to 2 % of the lattice parameter, and an evident enhancement of proton diffusion under compressive conditions have been observed. The structural and electronic properties of BaZrO 3 are analysed from Density Functional Theory calculations, and after an analysis of the electronic structure, we provide a possible explanation for an enhanced ionic conductivity of this bulk structure that can be caused by the formation of a preferential path for proton diffusion under compressive strain conditions. By means of Nudged Elastic Band calculations, diffusion barriers were also computed with results supporting our conclusions.

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Section: Resultsmentioning

confidence: 99%

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

Fronzi

Tateyama

Marzari

et al. 2016

Mater Renew Sustain Energy

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“…According to the Langevin picture of Brownian motion, the stochastic dynamics of the Brownian particle due to the interaction with the bath, and in the presence of a conservative external force field, F (t, x) can be described by the differential equations [25,41,42,46,48,49,77,112,423] …”

Section: Langevin Equations and Discretization Rulesmentioning

confidence: 99%

Relativistic Brownian motion

2009

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a b s t r a c tOver the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuationdissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions must necessarily be non-Markovian. We compare different proposals that were made in the literature and discuss their respective benefits and drawbacks. The review concludes with a summary of open questions, which may serve as a starting point for future investigations and extensions of the theory.

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“…(1) and its obvious generalizations to two and three spatial dimensions, to the inclusion of force fields, and to different kinds of coupling of such active particles have been studied extensively in the literature [4][5][6][7][8][9][10]. So far, mostly two different friction functions were considered.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

Diffusion in different models of active Brownian motion

Lindner

Nicola

2008

Eur. Phys. J. Spec. Top.

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Abstract. Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and RayleighHelmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

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Nonlinear Brownian motion - mean square displacement

Cited by 23 publications

References 17 publications

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

First-principles molecular dynamics simulations of proton diffusion in cubic BaZrO $$_3$$ 3 perovskite under strain conditions

Relativistic Brownian motion

Diffusion in different models of active Brownian motion

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