Related papers: Formation of an interface by competitive erosion
Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we…
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…
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…
We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…
The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled the instantaneous conformation of the…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
We study the dynamics of weakly deformed interfaces separating two stable phases, starting from the fluctuating hydrodynamics of the phase-separating fields. Using a well-chosen definition for the interface and the dynamical-action…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
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…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the variant in which red particles die and describe the phase diagram…
A graph $H$ is common if the limit as $n\to\infty$ of the minimum density of monochromatic labelled copies of $H$ in an edge colouring of $K_n$ with red and blue is attained by a sequence of quasirandom colourings. We apply an…
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell…
Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, the phylogenetic tree represents the…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…
The construction of a network of cell-to-cell contacts makes it possible to characterize the patterns and spatial organisation of tissues. Such networks are highly dynamic, depending on the changes of the tissue architecture caused by cell…
We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their…