Related papers: Localization of polymers in a finite medium with f…
We calculate the free energy and the pressure of a weakly slip-linked Gaussian polymer chains. We show that the equilibrium statistics of a slip-linked system is different from one of the corresponding ideal chain system without any…
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary…
We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using…
We introduce $\infty$-dimensional versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the…
A Gaussian variational approximation is often used to study interfaces in random media. By considering the 1+1 dimensional directed polymer in a random medium, it is shown here that the variational Ansatz typically leads to a negative…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
We consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate,…
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…
We use an off - lattice bead - spring model of a self - avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass mean-squared…
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…
Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in…
We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops…
We present a computer simulation of entangled polymer solutions at equilibrium. The chains repel each other via a soft Gaussian potential, appropriate for semi-dilute solutions at the scale of a correlation blob. The key innovation to…
We analyze the equlibrium statistics of a long linear homo-polymer chain confined in between two flat geometrical constraints under good solvent condition. The chain is ocupying two dimensional space and geometrical constraints are two…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
The effect of ambient disorders and sequence heterogeneities on the reptation of a long polymer is studied with the aid of a disordered tube model. The dynamics of a random heteropolymer is found to be much slower than that of a homopolymer…