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We analyze the non-equilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria--membrane collisions, we experimentally observe a significant increase in the magnitude of membrane…
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state.…
We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights $z_h, z_v$ of the dimer model and arbitrary dimensions of the lattice $m, n$.…
We reconsider the problem of even-visiting random walks in one dimension. This problem is mapped onto a non-Hermitian Anderson model with binary disorder. We develop very efficient numerical tools to enumerate and characterize even-visiting…
We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…
We discuss a novel approach that allows to obtain effective potentials from ab initio trajectories. Our method consists in fitting the weighted radial distribution functions obtained from the ab initio data with the ones obtained from…
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant $\Gamma=2$ and that the number $n$ of particles is large. We find that the correlation…
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we have a complete understanding on the part of these…
The interaction of vortical structures with boundaries has been extensively studied in Newtonian fluids, where conditions such as no slip walls, free surfaces, or contaminated surfaces dictate whether vortices rebound, dissipate, or…
For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact…
This study investigates the role of wall wettability, characterized by the wall contact angle (WCA), in controlling cavitation dynamics and stability around a Clark Y hydrofoil. High-fidelity Large Eddy Simulations (LES) coupled with a…
In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is at variance with respect to the simple symmetric random walk…
The Casimir-Polder interaction between an atom and a metal wall is investigated under the influence of real conditions including the dynamic polarizability of the atom, finite conductivity of the wall metal and nonzero temperature of the…
We consider a non-linear integro-differential model describing $z$, the position of the cell center on the real line presented in [Grec et al., J. Theo. Bio. 2018]. We introduce a new $\varepsilon$-scaling and we prove rigorously the…
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
The one-dimensional Brownian motion starting from the origin at time $t=0$, conditioned to return to the origin at time $t=1$ and to stay positive during time interval $0 < t < 1$, is called the Bessel bridge with duration 1. We consider…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
We study quantum walks of many non-interacting particles on a beam splitter array, as a paradigmatic testing ground for the competition of single- and many-particle interference in a multi-mode system. We derive a general expression for…