Related papers: Competitive Erosion is Conformally Invariant
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys…
Two laboratory scale experiments of dry and under-water avalanches of non-cohesive granular materials are investigated. We trigger solitary waves and study the conditions under which the front is transversally stable. We show the existence…
Consider a system of homogeneous interacting diffusive particles labeled by the nodes of a unimodular Galton-Watson (UGW) tree, where the state of each node evolves like a d-dimensional diffusion whose drift coefficient depends on (the…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of…
We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an…
We consider systems with two competing species whose actions are completely symmetric, with same mobility, reproduction and competition rates. Numerical implementations of the model in two and three-dimensional space show that regions of…
Recent works have shown that in contrast to classical linear elastic fracture mechanics, endowing crack fronts in a brittle Green-elastic solid with Steigmann-Ogden surface elasticity yields a model that predicts bounded stresses and…
We discuss the steady state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers,…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
In this work we address graph based semi-supervised learning using the theory of the spatial segregation of competitive systems. First, we define a discrete counterpart over connected graphs by using direct analogue of the corresponding…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…
We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on…