Related papers: Exact Solution of the Discrete Wormlike Chain Mode…
Taking into account the nonequivalence of fixed-force and fixed-length ensembles in the weak-force regime, equations of state are derived that describe the equilibrium extension or compression of an ideal Gaussian polymer chain in response…
The present paper investigates the extension behavior of a wormlike chain with varied persistence length under the confinement of a cylindrical tube. Based on Odijk theory of a confined polymer chain, we have developed a theory which can…
The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
A narrow Gaussian excluded volume potential, which tends to a delta-function repulsive potential in the limit of a width parameter d* going to zero, has been used to examine the universal consequences of excluded volume interactions on the…
The freely rotating chain is one of the classic discrete models of a polymer in dilute solution. It consists of a broken line of N straight segments of fixed length such that the angle between adjacent segments is constant and the N-1…
We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via…
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…
The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact…
We present a lattice formulation of a dynamic self-consistent field (DSCF) theory that is capable of resolving interfacial structure, dynamics and rheology in inhomogeneous, compressible melts and blends of unentangled homopolymer chains.…
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…
The number of allowed configurations of a polymer is reduced by the presence of a repulsive surface resulting in an entropic force between them. We develop a method to calculate the entropic force, and detailed pressure distribution, for…
We present analytic results for a special dimer model on the {\em non-bipartite} and {\em non-planar} checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We {\em exactly} calculate the number of closed…
A quantitative theory of the buckling of a worm like chain based on a semi-classical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows to go beyond the…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
The thermodynamics of a long self-repulsive chain is studied. In $D<4$ dimensions it shows two distinctly different regimes, corresponding to weak and strong correlations in the system. A simple microscopic analytical model is presented…
We study a heteropolymer model with random contact interactions introduced some time ago as a simplified model for proteins. The model consists of self-avoiding walks on the simple cubic lattice, with contact interactions between nearest…