Related papers: Lectures on random polymers
We propose a two-body spherically symmetric (isotropic) potential such that particles interacting by the potential self assemble into linear semiflexible polymeric chains without branching. By suitable control of the potential parameters we…
The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…
We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model…
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…
We analyze the localized phase of a general model of a directed polymer in the proximity of an interface that separates two solvents. Each monomer unit carries a charge, $\omega_n$, that determines the type (attractive or repulsive) and the…
We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian…
These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.
Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. A two--state model provides a consistent and robust way to study…
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 ground states of a hybrid system consisting of a polymer and an attractive nanowire by means of computer simulations. Depending on structural and energetic properties of the substrate, we find different adsorbed polymer…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal…
We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We have performed multicanonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations…
We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…