Escape rate and diffusion of a Stochastically Driven particle

Piscitelli, Antonio; Ciamarra, Massimo Pica

doi:10.1038/srep41442

Cited by 3 publications

(14 citation statements)

References 24 publications

(29 reference statements)

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“…Subsequent works [47,48] solved the IK dynamics for a free particle and for a particle confined in a harmonic potential, following a path integral approach, showing remarkable deviations from the Brownian Motion in the case m = M . We have recently investigated the diffusive properties of the IK model [42] in a periodic potential, introducing a novel physically motivated approach that allows to obtain exact results without solving Eq. 3.…”

Section: Modelsmentioning

confidence: 99%

“…This distribution represents the invariant distribution of the dynamics and is preserved along the piecewise deterministic trajectory. In the underdamped regime, these simulations are speed-up through the use of analytical results [42] for the time needed by a particle moving deterministically to traverse a well, or to perform one oscillation inside a well.…”

Section: Modelsmentioning

confidence: 99%

“…We have recently investigated [42] the diffusion coefficient of the IK model, and compared it to that of the BM, in both the overdamped and the underdamped limit. The main result is that the diffusivities of the two models coincide in the overdamped regime, while they are qualita-tively different in the underdamped regime.…”

Section: A Overviewmentioning

confidence: 99%

“…From dimensional arguments it can be argued that P d should be proportional to ω b t c , and from the simulations the constant turns out to be 2. This value of the constant makes the escape rate of the IK model equal to that of the BM, in the low temperature limit [39,42].…”

Section: Correlation Between Barrier Crossing Flights P Dmentioning

confidence: 99%

“…Specifically, a number of different systems exhibit a long transient during which the displacement distribution is not Gaussian, but the dynamics is Fickian with the mean square displacement growing linearly in time [13], a feature termed as Brownian non-Gaussian dynamics. Indeed, a Brownian non-Gaussian dynamics is observed, for * AntPs@ntu.edu.sg † massimo@ntu.edu.sg instance, in dense colloidal suspensions [5,[14][15][16], granular materials [17][18][19][20][21][22], supercooled liquids and structural glasses [7,21,23,24], gels [25], plasmas [26], biological cells [27][28][29][30][31][32][33], networks or active suspensions [32,34,35], turbulent flow [36] and finance [37].…”

Section: Introductionmentioning

confidence: 99%

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Unifying description of the damping regimes of a stochastic particle in a periodic potential

Piscitelli

Ciamarra

2017

SciPost Phys.

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We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Il'in and Khasminskii model, with a novel semianalytical approach. Our approach gives access to the transient and the asymptotic dynamics in all damping regimes, which are difficult to investigate in the usual Brownian model. We show that the crossover from the overdamped to the underdamped regime is associated with the loss of a typical time scale and of a typical length scale, as signaled by the divergence of the probability distribution of a certain dynamical event. In the underdamped regime, normal diffusion coexists with a non-Gaussian displacement probability distribution for a long transient, as recently observed in a variety of different systems. We rationalize the microscopic physical processes leading to the non-Gaussian behavior, as well as the timescale to recover the Gaussian statistics. The theoretical results are supported by numerical calculations, and are compared to those obtained for the Brownian model.

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Section: Modelsmentioning

confidence: 99%

Section: Modelsmentioning

confidence: 99%

Section: A Overviewmentioning

confidence: 99%

Section: Correlation Between Barrier Crossing Flights P Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unifying description of the damping regimes of a stochastic particle in a periodic potential

Piscitelli

Ciamarra

2017

SciPost Phys.

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Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

Faran

Bisker

2023

J. Phys. Chem. B

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Many biological systems rely on the ability to self-assemble target structures from different molecular building blocks using nonequilibrium drives, stemming, for example, from chemical potential gradients. The complex interactions between the different components give rise to a rugged energy landscape with a plethora of local minima on the dynamic pathway to the target assembly. Exploring a toy physical model of multicomponents nonequilibrium self-assembly, we demonstrate that a segmented description of the system dynamics can be used to provide predictions of the first assembly times. We show that for a wide range of values of the nonequilibrium drive, a log-normal distribution emerges for the first assembly time statistics. Based on data segmentation by a Bayesian estimator of abrupt changes (BEAST), we further present a general data-based algorithmic scheme, namely, the stochastic landscape method (SLM), for assembly time predictions. We demonstrate that this scheme can be implemented for the first assembly time forecast during a nonequilibrium self-assembly process, with improved prediction power compared to a naïve guess based on the mean remaining time to the first assembly. Our results can be used to establish a general quantitative framework for nonequilibrium systems and to improve control protocols of nonequilibrium self-assembly processes.

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Liquid to supercooled-liquid crossover from a Boltzmann transport approach to escape and diffusion

Piscitelli¹,

Ciamarra²

2020

J. Phys.: Condens. Matter

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We develop a model describing the motion of a non-Brownian particle in a periodic potential, which we then use to predict the temperature dependence of the diffusivity of a glass-former. In the model, the velocity of the particle is drawn for the equilibrium distribution at rate 1/t c, where t c is the intercollision time in the relaxation time approximation. Solutions within a Boltzmann transport approach show that the diffusivity crossovers from a low-t c regime in which the particle at most crosses a single barrier in between two successive collisions, to a high-t c regime in which the particle may cross several barriers. We then use our model to predict the temperature dependence of the diffusion coefficient of a system of harmonic-spheres, whose energy landscape has features resembling those of the potential considered in our model. We successfully recover a crossover in the temperature dependence of the diffusion coefficient observed through numerical dynamics simulations, as well as the relationship of the diffusivity on the temperature in the high-temperature limit.

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Escape rate and diffusion of a Stochastically Driven particle

Cited by 3 publications

References 24 publications

Unifying description of the damping regimes of a stochastic particle in a periodic potential

Unifying description of the damping regimes of a stochastic particle in a periodic potential

Nonequilibrium Self-Assembly Time Forecasting by the Stochastic Landscape Method

Liquid to supercooled-liquid crossover from a Boltzmann transport approach to escape and diffusion

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