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Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z^d for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
A significant fraction of Milky Way (MW) satellites exhibit phase-space properties consistent with a coherent orbital plane. Using tailored N--body simulations of a spherical MW halo that recently captured a massive (1.8$\times…
Arrangement of interacting particles on a sphere is historically a well known problem, however, ordering of particles with anisotropic interaction, such as the dipole-dipole interaction, has remained unexplored. We solve the orientational…
In this note, we prove the existence of a limiting distribution of the free path lengths on flat surfaces with circular obstacles as the radius of the obstacles goes to zero. Moreover, we relate this distribution to the distribution of the…
This paper presents $N$-body and stochastic models that describe the motion of tracer particles in a potential that contains a large population of extended substructures. Fluctuations of the gravitational field induce a random walk of…
Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it sends the order ideal x to the order ideal generated by the minimal elements not in x. It can also be computed in "slow motion" as a sequence of…
Robots with very limited capabilities are placed on the vertices of a graph and are required to move toward a single, common vertex, where they remain stationary once they arrive. This task is referred to as the GATHERING problem. Most of…
We present an algorithm to simulate random sequential adsorption (random "parking") of discs on constant-curvature surfaces: the plane, sphere, hyperboloid, and projective plane, all embedded in three-dimensional space. We simulate complete…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely…
Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of…
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work we consider the limit of large random skew plane partitions where the inner boundary…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported, of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the…
Ensembles of elongated magnetic droplets in a rotating field are studied experimentally. In a given range of field strength and frequency the droplets form rotating structures with a triangular order - rotating crystals. A model is…
We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form…