Single-file diffusion in an interval: First passage properties

Ryabov, Artem

doi:10.1063/1.4801326

Cited by 11 publications

(4 citation statements)

References 41 publications

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“…The exponents of the subdiffusive behavior in regions c and e are approximately 0.33 and 0.5, respectively. The slope of 0.5 indicates possible single-file diffusive behavior [42,43]. In future studies, we will investigate systems with increasing numbers of particles at fixed topology to test the robustness of the subdiffusive behavior, and identify rare microstates that give rise to structural relaxation from the caged regions b and d. These preliminary results indicate that there is nontrivial dynamics in Q1D systems even far from kinetic arrest.…”

Section: Discussionmentioning

confidence: 92%

Quasi-One Dimensional Models for Glassy Dynamics

Pal,

Blawzdziewicz,

O'Hern

2014

Preprint

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We describe numerical simulations and analyses of a quasi-one-dimensional (Q1D) model of glassy dynamics. In this model, hard rods undergo Brownian dynamics through a series of narrow channels connected by J intersections. We do not allow the rods to turn at the intersections, and thus there is a single, continuous route through the system. This Q1D model displays caging behavior, collective particle rearrangements, and rapid growth of the structural relaxation time, which are also found in supercooled liquids and glasses. The mean-square displacement Σ(t) for this Q1D model displays several dynamical regimes: 1) short-time diffusion Σ(t) ∼ t, 2) a plateau in the mean-square displacement caused by caging behavior, 3) single-file diffusion characterized by anomalous scaling Σ(t) ∼ t 0.5 at intermediate times, and 4) a crossover to long-time diffusion Σ(t) ∼ t for times t that grow with the complexity of the circuit. We develop a general procedure for determining the structural relaxation time tD, beyond which the system undergoes long-time diffusion, as a function of the packing fraction φ and system topology. This procedure involves several steps: 1) define a set of distinct microstates in configuration space of the system, 2) construct a directed network of microstates and transitions between them, 3) identify minimal, closed loops in the network that give rise to structural relaxation, 4) determine the frequencies of 'bottleneck' microstates that control the slow dynamics and time required to transition out of them, and 5) use the microstate frequencies and lifetimes to deduce tD(φ). We find that tD obeys power-law scaling, tD ∼ (φ * − φ) −α , where both φ * (signaling complete kinetic arrest) and α > 0 depend on the system topology.

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Section: Discussionmentioning

confidence: 92%

Quasi-One Dimensional Models for Glassy Dynamics

Pal,

Blawzdziewicz,

O'Hern

2014

Preprint

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“…Furthermore, numerous other aspects of individual or tagged particle dynamics is contingent on the presence of exclusion; for instance on very large domains with uniform initial distributions of excluding walkers, the mean square displacement of a walker scales with t 1/2 , where t is time [8,20]. This is sub-diffusive and fundamentally different from the linear t scaling of the mean square displacement for random walkers which can pass each other, emphasizing that exclusion can produce fundamentally different statistics for an individual particle, and by extension, correlations of particles too, while similar remarks apply for particle escape times, as illustrated by long time off-lattice studies [21].…”

Section: Introductionmentioning

confidence: 99%

Fock-space methods for diffusion: Capturing volume exclusion via fermionic statistics

2020

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Volume exclusion and single file diffusion play an important role at very small scales, such as those associated with molecular machines, ion channels and transport in zeolites, while introducing fundamental differences compared to Brownian motion, such as changes to the power law relation between the mean square displacement and time. In this work, we map the chemical master equation for excluded diffusion onto a Schrödinger equation via annihilation and creation ladder operators with Fermionic statistics, together with linear and symbolic algebra with the resulting Fock space representation to describe the effect of volume exclusion processes in finite one-dimensional chains. We contrast the dynamics with the non-exclusive (Bosonic) diffusion for crowded, intermediate and dilute particle populations. Motivated by shuttling in molecular machines we proceed to investigate differences in exit time distributions introduced by volume exclusion, incorporating the presence of transport bias. More generally, this study demonstrates how one can analyze volume excluded transport for small stochastic systems, without the need for stochastic simulation and ensemble averaging, simply by considering anti-commutation relations and Fermionic statistics in a Fock space representation of the stochastic dynamics.

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“…Further direct observation was possible in colloidal experiments by optical imaging [16]. The aspect of subdiffusion was further elaborated in connection with general theories of anomalous transport [17], including descriptions in terms of fractional Brownian motion [18], effects of initial and boundary conditions [19,20], external force fields [21], time-varying potentials [22], first-passage time distributions [23][24][25], and partial overtaking of particles [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

2019

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Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand basic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. In this BASEP, hard rods are driven by a constant drag force through a periodic potential with an amplitude much larger than the thermal energy. Here we derive general properties of the collective dynamics in the BASEP, discuss its connection to single-file transport by traveling wave potentials, and give a complete description of currents in steady states for all particle densities and diameters. For the open BASEP coupled to particle reservoirs, the nonequilibrium phases predicted by extremal current principles are verified by Brownian dynamics simulations. * dlips@uos.de †

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Single-file diffusion in an interval: First passage properties

Cited by 11 publications

References 41 publications

Quasi-One Dimensional Models for Glassy Dynamics

Quasi-One Dimensional Models for Glassy Dynamics

Fock-space methods for diffusion: Capturing volume exclusion via fermionic statistics

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

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