Related papers: Lectures on random polymers
We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
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…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
This is a set of introductory lectures on the behaviour of a directed polymer in a random medium. Both the intuitive picture that helps in developing an understanding and systematic approaches for quantitative studies are discussed.
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…
A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by…
Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are…
These lectures deal with: (1) a brief review of the theory of flexible random manifolds (with fixed intrinsic metric), connected to the physics of polymerized membranes, and of the effect of extrinsic curvature (crumpling transitions); (2)…
Molecular dynamics simulation methods are used to study the folding of polymer chains into packed cubic states. The polymer model, based on a chain of linked sites moving in the continuum, includes both excluded volume and torsional…
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…
This article provides a comprehensive understanding of the interactions that can occur at the interface between liquids and materials. It describes the phenomena of sorption (adsorption and absorption), permeation and leaching from a…
In this chapter we review the rich behavior of polymer chains embedded in a quenched random environment. We first consider the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derive the…
The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The…
This paper is extended and broadly generalized version of earlier published rapid communication, Phys.Rev.E, Vol.58, R 5213 (1998). It also elaborates on some problems which were left unsolved or just mentioned in Physics Reports Vol.298,…
Using molecular dynamics simulations we examine the dynamics of a family of model polymers with varying chain length and torsional potential barriers. We focus on features of the dynamics of polymers that are seen experimentally but absent…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization…