Related papers: Interface growth in the channel geometry and tripo…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw…
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…
Natural evolution has produced a tremendous diversity of functional organisms. Many believe an essential component of this process was the evolution of evolvability, whereby evolution speeds up its ability to innovate by generating a more…
We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by…
We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field…
Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at…
A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…
We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
In this work, we develop a cutting method for solving problems with moving and growing interfaces in 3D. This new method is able to resolve large displacement or deformation of immersed objects by combining the Arbitrary Lagrangian-Eulerian…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can…
We consider global geometric properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow of diffeomorphisms. In particular, we obtain expressions describing the…