Related papers: Interacting self-avoiding polygons
We consider the evolution of two contact-interacting harmonically-trapped particles following an arbitrary quench in interaction strength. We calculate the post-quench particle separation as a function of time and the total post-quench…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We present a generalized theory for studying phase separation in blends of polymers containing dipoles on their backbone. The theory is used to construct co-existence curves and to study the effects of dipolar interactions on interfacial…
We provide an introductory account of a tricritical phase diagram, in the setting of a mean-field random walk model of a polymer density transition, and clarify the nature of the density transition in this context. We consider a…
Several families of one-point interactions are derived from the system consisting of two and three $\delta$-potentials which are regularized by piecewise constant functions. In physical terms such an approximating system represents two or…
The phase-separation occurring in a system of mutually interacting proteins that can bind on specific sites of a chromatin fiber is here investigated. This is achieved by means of extensive Molecular Dynamics simulations of a simple polymer…
Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft…
Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modeling such systems is realistic description of the steric repulsion between nearby polymers.…
We investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schr\"odinger equation. Numerical simulations reveal distinct collision regimes ranging from…
We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…
Collision avoidance is one of the most challenging tasks people need to consider for developing the self-driving technology. In this paper we propose a new spatiotemporal motion planning algorithm that efficiently solves a constrained…
Self-avoiding walks are a simple and well-known model of long, flexible polymers in a good solvent. Polymers being pulled away from a surface by an external agent can be modelled with self-avoiding walks in a half-space, with a Boltzmann…
Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…
In this paper we present a study of pattern formation in bidimensional systems with competing short-range attractive and long-range repulsive interactions. The interaction parameters are chosen in such a way to analyse two different…
We consider random self-avoiding walks between two points on the boundary of a finite subdomain of Z^d (the probability of a self-avoiding trajectory gamma is proportional to mu^{-length(gamma)}). We show that the random trajectory becomes…
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
We present evidence that the concurrent existence of two populations of particles with different effective diameters is not a prerequisite for the occurrence of anomalous phase behaviors in systems of particles interacting through…
We establish phase transitions for continuum Delaunay multi-type particle systems (continuum Potts or Widom-Rowlinson models) with a repulsive interaction between particles of different types. Our interaction potential depends solely on the…