Related papers: Lectures on random polymers
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
We propose a novel characterization method of randomly branched polymers based on the geometrical property of such objects in confined spaces. The central idea is that randomly branched polymers exhibit passing/clogging transition across…
These lecture notes aim to provide a self-contained, pedagogical introduction to the physics of local constraints, fractionalisation and topological liquids organised around the Rokhsar-Kivelson quantum dimer model. Topics and phenomena…
The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…
Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized…
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically…
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
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…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
We revisit the classical problem of the behavior of an isolated linear polymer chain in confined spaces, introducing the distinction between two different confinement regimes (the {\it weak} and the {\it strong} confinement regimes,…
Through extensive molecular simulations we determine a phase diagram of attractive, flexible polymer chains in two and three dimensions. A surprisingly rich collection of distinct crystal morphologies appear, which can be finely tuned…
We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the…
From understanding the sand on the beach to the foam on your beer, soft sphere simulations have been crucial to the study of the amorphous world around us. However, many of the materials we interact with on a daily basis aren't comprised of…
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…
Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in…
We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic…