Related papers: Influence of spatial correlation for directed poly…
Talk presented at the International Conference on Mathematical Physics (Brisbane 1997). This is an introduction to recent work on the scaling and intermittency in forced Burgers turbulence. The mapping between Burgers' equation and the…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do…
In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us…
Following a recent work by Yoshino, we study the aging dynamics of a directed polymer in random media, in 1+1 dimensions. Through temperature quench, and temperature cycling numerical experiments similar to the experiments on real spin…
Half-space directed polymers in random environments are models of interface growth in the presence of an attractive hard wall. They arise naturally in the study of wetting and entropic repulsion phenomena. In 1985, Kardar predicted a…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be…
We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
We consider the long time behavior of solutions to a nonlocal reaction diffusion equation that arises in the study of directed polymers. The model is characterized by convolution with a kernel $R$ and an $L^2$ inner product. In one spatial…
The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding…
We consider a stochastic model of N evolving particles studied by Brunet and Derrida. This model can be seen as a directed polymer in random medium with N sites in the transverse direction. Cook and Derrida, use heuristic arguments to…
We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the…
Using Langevin dynamics simulations, we study a system of transversely propelling filament and passive Brownian particles. We consider a polymer whose monomers experience a constant propulsion force perpendicular to the local tangent in the…
The non-equilibrium structural and dynamical properties of a flexible polymer tethered to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as…
The non-thermal nature of self-propelling colloids offers new insights into non-equilibrium physics. The central mathematical model to describe their trajectories is active Brownian motion, where a particle moves with a constant speed,…
We present a study of diffusion enhancement of underdamped Brownian particles in 1D symmetric space-periodic potential due to external symmetric time-periodic forcing with zero mean. We show that the diffusivity can be enhanced by many…
A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale…
We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by Leibler- Rubinstein-Colby theory. Although a…