Related papers: An asymptotic result for Brownian polymers
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…
The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H_t denotes the set of…
In dimensions 3 or larger, it is a classical fact that the directed polymer model has two phases: Brownian behavior at high temperature, and non-Brownian behavior at low temperature. We consider the response of the polymer to an external…
Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. However, physically detailed modeling of highly entangled polymers can prove challenging, especially as one considers…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
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 study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian and non-Gaussian processes. More precisely we study the asymptotic behaviour for large $T$, of the probability…
The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight…
The drag of turbulent flows can be drastically decreased by addition of small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the…
Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motor-like enzymes. The enzymes can bind and unbind to specific sites of the polymer…
We prove a conjecture of Broadurst (arXiv:1004.0519v1) on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient of its own occupation time measure…
The role of polymers additives on the turbulent convective flow of a Rayleigh--Taylor system is investigated by means of direct numerical simulations (DNS) of Oldroyd-B viscoelastic model. The dynamics of polymers elongation follow…
Polymer-induced drag reduction is bounded by an asymptotic limit of maximum drag reduction (MDR). For decades, researchers have presumed that MDR reflects the convergence to an ultimate flow state that is not further changed by polymers.…
Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions.These supramolecular polymers have an equilibrium…
Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is…
In this paper we study asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells. This tumor model was proposed by Pettet et al in…
A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…