Related papers: Action minimization and macroscopic interface moti…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
Many intelligent user interfaces employ application and user models to determine the user's preferences, goals and likely future actions. Such models require application analysis, adaptation and expansion. Building and maintaining such…
We address optimal placement of vehicles with simple motion to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy…
The variational problem of the least uncomfortable journey between two locations on a straight line is simplified by a choice of the dependent variable. It is shown that taking the position, instead of the velocity, as the optimal function…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We develop a computational method for simulating the nonlinear dynamics of an elastic tumor-host interface. This work is motivated by the recent linear stability analysis of a two-phase tumor model with an elastic membrane interface in 2D.…
We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete ``forest fire'' lattice models through Monte Carlo simulations in two and…
We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field. The field has a profile with a fixed shape designed to stabilize a flat interface, and is…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
For a model of a driven interface in an elastic medium with random obstacles we prove existence of a stationary positive supersolution at non-vanishing driving force. This shows the emergence of a rate independent hysteresis through the…
We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and…
A one-dimensional flocking model using active Ising spins is studied, where the system evolves through the reinforcement learning approach \textit{via} defining state, action, and cost function for each spin. The orientation of spin with…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole…
An interface preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving $(d-1)$-dimensional manifold directly within the $d$-dimensional mesh, which means that the interface is represented by a subset of…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical…
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…