Related papers: A three-state cyclic voter model extended with Pot…
We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of…
The one-dimensional long-range voter model, where an agent takes the opinion of another at distance $r$ with probability $\propto r^{-\alpha}$, is studied analytically. The model displays rich and diverse features as $\alpha$ is changed.…
Observing the structure of quantized vortices can provide evidence for the pairing nature of a superfluid or superconductor and pinpoint its order parameter. Spin-triplet superfluid $^3$He supports a variety of vortices, calculated and…
Point vortices take a triangular lattice structure in a rotating system as a minimum energy state. We perform a numerical simulation of point vortex systems using initial conditions indicating that the triangular lattice is randomly…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
We consider a physical model where the total energy is governed by surface tension and attractive screened Coulomb potential on the 3-dimensional space. We obtain different periodic equilibrium patterns i.e. stationary sets for this energy,…
We survey a host of results from discrete geometry that have bearing on the analysis of geometric models of approval voting. Such models view the political spectrum as a geometric space, with geometric constraints on voter preferences.…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
We present a novel model for the effect of echo chambers, filter bubbles, and reinforcement on election results. Our model extends the well known voter model with zealots to include reinforcement. We analyze the behaviour of the model,…
The outcomes of democratic elections rest on individuals' decision-making that is driven by their varying preferences and beliefs. Individuals may prefer consensus to gridlock, or gridlock to consensus, and information may be fractured via…
The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model…
A fundamental task in developmental biology is to identify the mechanisms which drive morphogenesis. In many cases, pattern formation is driven by the positional information determined by both the gradient of maternal factors and hard-wired…
In certain parliamentary democracies, there are two major parties that move in and out of power every few elections, and a third minority party that essentially never governs. We present a simple model to account for this phenomenon, in…
The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of their formation…
Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results…
We demonstrate the effects of geometric perturbation on the Tomonaga-Luttinger liquid (TLL) states in a long, thin, hollow cylinder whose radius varies periodically. The variation in the surface curvature inherent to the system gives rise…
The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model…
We study a coevolving nonlinear voter model on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time…
Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
We study the support (i.e. the set of visited sites) of a t step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties M(t) of the support is considered, including, e.g., the number S(t) of…