Single-file dynamics with different diffusion constants

Ambjörnsson, Tobias; Lizana, Ludvig; Lomholt, Michael A.; Silbey, R.

doi:10.1063/1.3009853

Cited by 32 publications

(64 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerically, the SFD and fBm systems were simulated stochastically with the Gillespie-type algorithm presented in Ref. [21], and spectral approach [61], respectively.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…(2) Move a random particle according to the algorithm in [21] and update the time t. (3) repeat step (2) until either t ≥ t stop (some designated stop time) or the tracer particle position becomes ≥ x c , and record the corresponding first-passage time; see Fig. 1 for a diagrammatic explanation.…”

Section: Simulationsmentioning

confidence: 99%

“…Of interest for the present study is the recent increasing amount of research into complex population types or heterogeneous SFD systems [18,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

First passage times for a tracer particle in single file diffusion and fractional Brownian motion

Sanders

Ambjörnsson

2012

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e. all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavytailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBmdefined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result.SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

show abstract

“…Numerically, the SFD and fBm systems were simulated stochastically with the Gillespie-type algorithm presented in Ref. [21], and spectral approach [61], respectively.…”

Section: Summary and Discussionmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

See 1 more Smart Citation

First passage times for a tracer particle in single file diffusion and fractional Brownian motion

Sanders

Ambjörnsson

2012

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Steps (iii) to (vi) is a description of the trial-and-error -method, outlined in Ref. [29] (except that we here use a fixed time step between attempted jumps, see…”

Section: Simulations Using the Gillespie Algorithmmentioning

confidence: 99%

Tracer particle diffusion in a system with hardcore interacting particles

et al. 2017

Self Cite

View full text Add to dashboard Cite

Abstract. In this study, inspired by the work of K. Nakazato and K. Kitahara [Prog. Theor. Phys. 64, 2261(1980], we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on regular Bravais lattices we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.

show abstract

“…Previous studies have also investigated related models governed by stochastic dynamics, including one-dimensional systems with continuous coordinates (17)(18)(19)(20)(21), quasi-one-dimensional fluids in narrow pores (22)(23)(24), and singleoccupancy lattice gases in higher dimensions (12,13,(25)(26)(27)(28). Additionally, this work focuses on two-point correlation functions that describe the dynamics of the system of interest.…”

mentioning

confidence: 99%

Kinetic theories of dynamics and persistent caging in a one-dimensional lattice gas

Abel

Tse

Andersenb

2009

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

The one-dimensional, single-occupancy lattice gas exhibits highly cooperative particle motion and provides an interesting challenge for theoretical methods designed to describe caging in liquids. We employ this model in an effort to gain insight into caging phenomena in more realistic models of liquids, using a diagrammatic kinetic theory of density fluctuations to develop a series of approximations to the kinetic equations for the van Hove selfcorrelation function. The approximations are formulated in terms of the irreducible memory function, and we assess their efficacy by comparing their solutions with computer simulation results and the well-known subdiffusive behavior of a tagged particle at long times. The first approximation, a mode coupling theory, factorizes the 4-point propagators that contribute to the irreducible memory function into products of independent single-particle propagators. This approximation fails to capture the subdiffusive behavior of a tagged particle at long times. Analysis of the mode coupling approximation in terms of the diagrammatic kinetic theory leads to the development of two additional approximations that can be viewed as diagrammatic extensions or modifications of mode coupling theory. The first, denoted MC1, captures the long-time subdiffusive behavior of a tagged particle. The second, denoted MC2, captures the subdiffusive behavior of a tagged particle and also yields the correct amplitude of its mean square displacement at long times. Numerical and asymptotic solutions of the approximate kinetic equations share many qualitative and quantitative features with simulation results at all timescales.liquids | mode coupling D ense liquids exhibit highly correlated motions of constituent particles. Understanding the dynamics of particle motion can give deep insight into both microscopic and macroscopic properties of liquids, including the diffusive properties of labeled particles and macroscopic transport coefficients (1). In many dense liquids, correlated particle motion is closely related to the phenomenon of caging, in which the motion of each particle is severely constrained by the presence of other nearby particles. Each particle is said to be surrounded by a "cage" of neighboring particles, and in order for a particle to move an appreciable distance, a collective rearrangement of its caging particles must occur.Characterizing the breakdown of a cage is of paramount importance in understanding the properties of many liquids, including atomic, polymeric, and colloidal fluids. For example, caging is thought to dominate the dynamics of liquids near the glass transition, and it plays an important role in polymer physics, where entanglement effects at the microscopic level affect macroscopic properties such as viscosity and elasticity.This article examines the development of approximate kinetic theories for a one-dimensional, single-occupancy lattice gas in which particles undergo symmetric, continuous-time random walks subject to the constraint that they cannot pass through eac...

show abstract

Single-file dynamics with different diffusion constants

Cited by 32 publications

References 43 publications

First passage times for a tracer particle in single file diffusion and fractional Brownian motion

First passage times for a tracer particle in single file diffusion and fractional Brownian motion

Tracer particle diffusion in a system with hardcore interacting particles

Kinetic theories of dynamics and persistent caging in a one-dimensional lattice gas

Contact Info

Product

Resources

About