Related papers: Polymers with Randomness: Phases and Phase Transit…
This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges…
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 study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
In this paper we prove a scaling limit phase transition for a class of two-dimensional random polymers.
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 investigate theoretically the transfer of excitation along a one dimensional chain of monomers for a situation in which initially the excitation is shared coherently by two monomers. We show that depending on the relative phase between…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
We study the dynamics of the phase behavior of a polymer blend in the presence of shear flow. By adopting a two fluid picture and using a generalization of the concept of material derivative, we construct kinetic equations that describe the…
We analyze a (1+1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in…
It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved…
We present an approach to studying directed polymers in interaction with a defect line and subject to a force, which pulls them away from the line. We consider in particular the case of inhomogeneous interactions. We first give a formula…
In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the…
Liquids with quasi - chemical bonding between molecules are described in terms of vertex model. It is shown that this bonding results in liquid - liquid phase transition, which occurs between phases with different mean density of…
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one…
The effect of ambient disorders and sequence heterogeneities on the reptation of a long polymer is studied with the aid of a disordered tube model. The dynamics of a random heteropolymer is found to be much slower than that of a homopolymer…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
We study the Directed Polymer model subject to a particular form of disorder, $\eta(x,t)=\eta_X(x) \eta_T(t)$, recently proposed in biological applications. We find that two new universality classes arise, depending on the the lattice…