Related papers: A Becker-D{\"o}ring model with injection and irrev…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…
We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is…
Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the…
This paper studies rates of decay to equilibrium for the Becker-D\"oring equations with subcritical initial data. In particular, polynomial rates of decay are established when initial perturbations of equilibrium have polynomial moments.…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between…
Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions.These supramolecular polymers have an equilibrium…
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
We study multipartite entanglement measures for a one-dimensional Ising chain that is capable of showing both integrable and nonintegrable behaviour. This model includes the kicked transverse Ising model, which we solve exactly using the…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to generalize well. While minimizers' flatness consistently…
We use machine learning algorithms to detect the crystalline phase in undercooled melts in molecular dynamics simulations. Our classification method is based on local conformation and environmental fingerprints of individual monomers. In…
We study the self-similar behavior of the exchange-driven growth model, which describes a process in which pairs of clusters, consisting of an integer number of monomers, interact through the exchange of a single monomer. The rate of…
Researchers are often interested in predicting outcomes, conducting clustering analysis to detect distinct subgroups of their data, or computing causal treatment effects. Pathological data distributions that exhibit skewness and…
Inspired by recent experiments on chromosomal dynamics, we introduce an exactly solvable model for the interaction between a flexible polymer and a set of motor-like enzymes. The enzymes can bind and unbind to specific sites of the polymer…