Related papers: Front Velocity and Directed Polymers in Random Med…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We consider the continuum directed random polymer (CDRP) model that arises as a scaling limit from $1+1$ dimensional directed polymers in the intermediate disorder regime. We show that for a point-to-point polymer of length $t$ and any…
Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than…
In nanoscale space and pico- to nanoseconds enormous physical, chemical and biological processes take place, while the motions of involved particles/molecules under thermal fluctuations are usually analyzed using the conventional theory of…
Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles…
We present results about large deviations and laws of large numbers for various polymer related quantities. In a completely general setting and strictly positive temperature, we present results about large deviations for directed polymers…
We study the question of how the competition between $\textit{bulk disorder}$ and a $\textit{localized microscopic defect}$ affects the macroscopic behavior of a system in the directed polymer context at the free energy level. We consider…
Novel kinetic models for both Dumbbell-like and rigid-rod like polymers are derived, based on the probability distribution function $f(t, x, n, \dot n)$ for a polymer molecule positioned at $x$ to be oriented along direction $n$ while…
We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable through…
We prove existence of a solution for a polymer crystal growth model describing the movement of a front $(\Gamma(t))$ evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with…
The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…
We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$…
Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the…
We consider the drift of a polymer chain in a disordered medium, which is caused by a constant force applied to the one end of the polymer, under neglecting the thermal fluctuations. In the lowest order of the perturbation theory we have…
Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between…
We prove new velocity averaging lemmas for multi-dimensional hyperbolic-parabolic partial differential equations. These theorems may be applied to establish several compactness results for both deterministic and stochastic…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…