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We develop a mean-field model to examine the stability of a `quasi-2D suspension' of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by…
We study the stability of the ordered phase of compressible polar flocks against the nucleation of counter-propagating droplets, using a combination of analytical theory, microscopic and hydrodynamic simulations. For discrete-symmetry…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
We propose a simple dissipative system with purely cubic defocusing nonlinearity and nonuniform linear gain that can support stable localized dissipative vortex solitons with high topological charges without the utilization of competing…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
In this study, we investigate the stability and solid fraction of columns comprised of highly non-convex particles. These particles are constructed by extruding arms onto the faces of Platonic solids, a configuration we term \emph{Platonic…
We use a recently developed lattice model to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long semiflexible chain. We study the effects of the…
Using Monte Carlo simulations and a mean-field theory, we study domain growth in a driven lattice gas. Mediated by a single vacancy, two species of particles (``charges'') unmix, so that a disordered initial configuration develops…
When a colloidal suspension is dried, capillary pressure may overwhelm repulsive electrostatic forces, assembling aggregates that are out of thermal equilibrium. This poorly understood process confers cohesive strength to many geological…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
We study a continuous time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as…
We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying…
Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law.…