Related papers: Directed polymer in a random medium - an introduct…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational…
The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this…
The coupled dynamics of entangled polymers which span a broad time and length scales govern the unique viscoelastic properties of polymers. To follow chain mobility by numerical simulations from the intermediate Rouse and reptation regimes…
We study the semi-discrete directed random polymer model introduced by O'Connell and Yor. We obtain a representation for the moment generating function of the polymer partition function in terms of a determinantal measure. This measure is…
We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
With the rapid development of computer technology, computer music has begun to appear in the laboratory. Many potential utility of computer music is gradually increasing. The purpose of this paper is attempted to analyze the possibility of…
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…
Dimensional analysis is a simple qualitative method for determining essential connections between physical quantities. It is applicable to a multitude of physics problems, many of which canbe introduced early on in a university physics…
For a Brownian directed polymer in a Gaussian random environment, with $q(t,\cdot)$ denoting the quenched endpoint density and \[ Q_n(t,x_1,\ldots,x_n)=\mathbf{E}[q(t,x_1)\ldots q(t,x_n)], \] we derive a hierarchical PDE system satisfied by…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
The irreversible adsorption of polymers to a two-dimensional solid surface is studied. An operator formalism is introduced for chemisorption from a polydisperse solution of polymers which transforms the analysis of the adsorption process to…
In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The…
The dynamics of polymer decompression, i.e., a process from compressed, compact state to the relaxed swoll en conformation, can be formally described as a {\it nonlinear diffusion}. We discuss here two basic examples: (i) the expansion, or…
In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…
A method is given for calculation of a distribution of small particles, embedded in a medium, so that the resulting medium would have a desired radiation pattern for the plane wave scattering by this medium.
These introductory lectures present a broad overview of the physics of high parton densities in QCD and its application to our understanding of the early time dynamics in heavy ion collisions.
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…