Related papers: Polymers with spatial or topological constraints: …
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings,…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by…
We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this…
The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and…
Packing under confinement could generate rich ordered structures through entropic effects, which is a fundamental problem in condensed matter, biophysics and material science. The influence of confinement to the anisotropic hard…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
Motivated by recent nanofluidics experiments, we use Brownian dynamics and Monte Carlo simulations to study the conformation, organization and dynamics of two polymer chains confined to a single box-like cavity. The polymers are modeled as…
Investigating the geometric effects resulting from the detailed behaviors of the confining potential, we consider square and circular confinements to constrain a particle to a space curve. We find a torsion-induced geometric potential and a…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
This study focuses on comparing the individual polymer chain dynamics in an entangled polymeric liquid under different shear and extension rates. Polymer chains under various shear rates and extension rates were simulated using a…
Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations…
The interplay of topological constraints and persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three dimensional lattice model. We ask if the results are consistent with…
We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed…
Entropic repulsion between DNA ring polymers under confinement is the key mechanism governing the spatial segregation of bacterial chromosomes, although it remains incompletely understood how proteins aid the process of entropic…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…