Related papers: Spanning trees for the geometry and dynamics of co…
We give new general formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay (1983) for regular graphs. The general answer involves a quantity for infinite graphs that we call…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
Constitutive equations are derived for the viscoelastic response of rubbery polymers at finite strains. A polymer is thought of as a network of long chains connected to temporary junctions. At a random time, a chain detaches from a…
We present an analytical approach to the out of equilibrium dynamics of a class of kinetic lattice gases under gravity. The location of the jamming transition, the critical exponents, and the scaling functions characterizing the relaxation…
The meander problem is a combinatorial problem which provides a toy model of the compact folding of polymer chains. In this paper we study various questions relating to the enumeration of meander diagrams, using diagrammatical methods. By…
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results.…
We present an extremely simplified model of multiple-domains polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the…
Slow relaxation and aging of the conductance are experimental features of a range of materials, which are collectively known as electron glasses. We report dynamic Monte Carlo simulations of the standard electron glass lattice model. In a…
Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…
Using a simple three-dimensional lattice copolymer model and Monte Carlo dynamics, we study the collapse and folding of protein-like heteropolymers. The polymers are 27 monomers long and consist of two monomer types. Although these chains…
Folding mechanisms are zero elastic energy motions essential to the deployment of origami, linkages, reconfigurable metamaterials and robotic structures. In this paper, we determine the fate of folding mechanisms when such structures are…
We examine the structural relaxation of glassy materials at finite temperatures, considering the effect of activated rearrangements and long-range elastic interactions. Our three-dimensional mesoscopic relaxation model shows how the…
We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The…
We develop Monte Carlo simulations for uniformly charged polymers and machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments.…
We explore the transport features of a single flexible polymer chain that walks on a periodic ratchet potential coupled with spatially varying temperature. At steady state the polymer exhibits a fast unidirectional motion where the…
The quadratic minimum spanning tree problem (QMSTP) is the problem of finding a spanning tree of a graph such that the total interaction cost between pairs of edges in the tree is minimized. We first show that most of the bounding…
In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against…
Analogous to a model that predicts the linear scaling of the binding energy of a nucleus from the number of nucleons, a simple model was developed to account for the observed linear variation of the quantum-chemically computed total…
The unfolding of a polymer below the $\theta$ point when pulled by an external force is studied both in d=2 on the lattice and in $d=3$ off lattice. A ground state analysis of finite length chains shows that the globule unfolds via multiple…
We use molecular dynamics simulations to study the dynamics of an ensemble of interacting self-propelled semi-flexible polymers in contact with a thermal bath. Our intention is to model complex systems of biological interest. We find that…