Related papers: Competitive Erosion is Conformally Invariant
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this…
Consider a graph $G=(V,E)$ and an initial random coloring where each vertex $v \in V$ is blue with probability $P_b$ and red otherwise, independently from all other vertices. In each round, all vertices simultaneously switch their color to…
We propose a dynamical model of price formation on a spatial market where sellers and buyers are placed on the nodes of a graph, and the distribution of the buyers depends on the positions and prices of the sellers. We find that, depending…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…
We study the dynamics of visco-elastic materials coupled by a common cohesive interface (or, equivalently, {two single domains separated by} a prescribed cohesive crack) in the anti-plane setting. We consider a general class of…
Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated…
We investigate the problem of speciation and coexistence in simple ecosystems when the competition among individuals is included in the Eigen model for quasi-species. By suggesting an analogy between the competition among strains and the…
We study horizontal differentiation when the set of feasible products is a structured subset of the Lancasterian characteristics space. Modeling this set as a compact Riemannian manifold, we show that intrinsic geometry governs…
The interaction between two chemically identical charge-regulated surfaces is studied using the classical density functional theory. In contrast to common expectations and assumptions, under certain realistic conditions we find a…
We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of…
A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal…
We consider a model in which positive and negative particles with equal densities diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent…
We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix…
We present a coherent approach to the competition between thermodynamic states in spatially inhomogeneous systems, such as the Edwards-Anderson spin glass with a fixed coupling realization. This approach explains and relates chaotic size…
The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background…