Related papers: Theoretical study of the competition between foldi…
A self-avoiding walk with small attractive interactions is described here. The existence of the connective constant is established, and the diffusive behavior is proved using the method of the lace expansion.
Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of…
We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope $m_c$ of the critical line at the origin. In mathematical terms,…
Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
In this thesis we study in detail the self-intersection properties of Random Walks. Although notoriously hard to tackle, these properties are crucially related to the excluded-volume effect and other central features of real polymers. Our…
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
We present a dynamic nonlocal hybrid Monte Carlo algorithm consisting of pivot and ``cut-and-permute'' moves. The algorithm is suitable for the study of polymers in semiconfined geometries at the ordinary transition, where the pivot…
Contacts between particles in dense, sheared suspensions are believed to underpin much of their rheology. Roughness and adhesion are known to constrain the relative motion of particles, and thus globally affect the shear response, but an…
In this work we derive certain topological theories of transverse vector fields whose amplitudes reproduce topological invariants involving the interactions among the trajectories of three and four random walks. This result is applied to…
The effect of adding nonadsorbing polymer to a lamellar phase of surfactant bilayers is studied theoretically. We find that the polymer produces coexistence between two lamellar phases of different layer spacings. The coexistence region is…
An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…
We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve translocation probability. At the same time, it also increases…
We consider the response of an adsorbed polymer that is pulled by an AFM within a simple geometric framework. We separately consider the cases of i) fixed polymer-surface contact point, ii) sticky case where the polymer is peeled off from…
The two-dimensional contact process (CP) with a competitive dynamics proposed by Martins {\it et al.} [Phys. Rev. E {\bf 84}, 011125(2011)] leads to the appearance of an unusual active asymmetric phase, in which the system sublattices are…
A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. As the piston approaches the wall the…
The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (\emph{e.g.} colloids, droplets, microrobots) and understanding their collective dynamics. The…
I consider the possibility that Gaussian random walk statistics are sufficient to trap nanoscopic additives at either a polymer interface or surface. When an additive particle goes to the free surface, two portions of the polymer surface…
This study deals with polymer looping, an important process in many chemical and biological systems. We investigate basic questions on the looping dynamics of a polymer under tension using the freely-jointed chain (FJC) model. Previous…
Self-avoidance is a common mechanism to improve the efficiency of a random walker for covering a spatial domain. However, how this efficiency decreases when self-avoidance is impaired or limited by other processes has remained largely…