Mean escape time for randomly switching narrow gates in a cellular flow

Hui Wang; Jinqiao Duan; Xianguo Geng; Ying Chao

Home/Archive/arXiv

arXiv · 1812.00800

Mean escape time for randomly switching narrow gates in a cellular flow

Hui Wang·Jinqiao Duan·Xianguo Geng·Ying Chao

View original source ↗Read source document ↗Export metadata ↓

Abstract

The escape of particles through a narrow absorbing gate in confined domains is a abundant phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a cellular flow when the two gates randomly switch between different states with a switching rate k between the two gates. After briefly deriving the coupled partial differential equations for the escape time through two gates, we compute the mean escape time for particles escaping from the gates with different initial states. By numerical simulation under nonuniform boundary conditions, we quantify how narrow escape time is affected by the switching rate k between the two gates, arc length s between two gates, angular velocity w of the cellular flow and diffusion coefficient D. We reveal that the mean escape time decreases with the switching rate k between the two gates, angular velocity w and diffusion coefficient D for fixed arc length, but takes the minimum when the two gates are evenly separated on the boundary for any given switching rate k between the two gates. In particular, we find that when the arc length size {\epsilon} for the gates is sufficiently small, the average narrow escape time is approximately independent of the gate arc length size. We further indicate combinations of system parameters (regions located in the parameter space) such that the mean escape time is the longest or shortest. Our findings provide mathematical understanding for phenomena such as how ions select ion channels and how chemicals leak in annulus ring containers, when drift vector fields are present.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

BibTeX RIS

Hui Wang, Jinqiao Duan, Xianguo Geng, Ying Chao. 2018-11-30. Mean escape time for randomly switching narrow gates in a cellular flow. https://arxiv.org/abs/1812.00800

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗