Related papers: Metastability of diffusion processes in narrow tub…
The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the…
The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
The electron transport in current-biased superconducting nano-bridges is determined by the motion of the quantum vortex confined in the internal disorder landscape. Here we consider a simple case of a single or two neighbouring linear…
Using novel micro-printing techniques, we develop a versatile experimental setup that allows us to study how lateral confinement tames the active flows and defect properties of the microtubule/kinesin active nematic system. We demonstrate…
The assisted tunneling of a metastable state between barriers is investigated analytically by means of a simplified one dimensional model. A time dependent perturbation changes the pole spectrum of the wave function introducing a larger…
In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between…
It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials,…
We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…
The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism that allows us to evaluate the…
In this paper we consider Markov chains with transition rates that depend on a small parameter $\varepsilon$. Under a mild assumption on the asymptotics of these transition rates, we describe the behavior of the chain at various…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics. Molecular dynamics simulations with a time dependent mapping…
In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…
This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…
The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from…