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We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on the square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases…
We propose an algorithm based on local growth rules for kinetically generating self avoiding walk configurations at any given temperature. This algorithm, called the Interacting Growth Walk (IGW) algorithm, does not suffer from attrition on…
Motility-induced phase separation, MIPS, is arguably the most well-studied collective phenomenon occurring in active matter without alignment interactions (scalar active matter). Its basic origin is simple: since self-propelled particles…
We consider Activated Random Walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the non-reversibility of the dynamics and the lack of knowledge on the stationary distribution,…
The self-avoid random walk algorithm has been extensively used in the study of polymers. In this work we study the basic properties of the trajectories generated with this algorithm when two interactions are added to it: contact and folding…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
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,…
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…
We consider a model of semi-flexible interacting self-avoiding trails (sISAT's) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting…
We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the…
We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the…
How long does a self-avoiding walk on a discrete $d$-dimensional torus have to be before it begins to behave differently from a self-avoiding walk on $\mathbb{Z}^d$? We consider a version of this question for weakly self-avoiding walk on a…
A phase diagram for a surface-interacting long flexible polymer chain in a two-dimensional poor solvent where the possibility of collapse exists is determined using exact enumeration method. A model of a self-attracting self avoiding walk…
We introduce a method for determining the functional form of the stochastic and dissipative interactions in a dissipative particle dynamics (DPD) model from projected phase space trajectories. The DPD model is viewed as a coarse graining of…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
Self-avoiding walk (SAW) represents linear polymer chain on a large scale, neglecting its chemical details and emphasizing the role of its conformational statistics. The role of the latter is important in formation of agglomerates and…
This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give…
This article is concerned with self-avoiding walks (SAW) on $\mathbb{Z}^{d}$ that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary…
Active particles may undergo phase separation when interactions oppose self-propulsion, in the absence of any cohesive forces. The corresponding Motility-Induced Phase Separation (MIPS) is arguably the simplest non-trivial collective…
Self-avoiding random walks on graphs can be seen as walkers interacting with their own past history. This letter considers a complementary class of dynamics: Mutual future avoiding random walks (MFARWs), where stochastically driven walkers…