Related papers: A Convergence result for a Stefan problem with pha…
The asymptotics of the strongly stratified Boussinesq system when the Froude number goes to zero have been previously investigated, but the resulting limit system surprisingly did not depend on the thermal diffusivity $\nu$ ' . In this…
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based on a novel Markovian gluing principle. In contrast, we then…
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed…
We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables.…
In this paper we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative…
We analyse the theory of consistent approximations given by Polak and we use it in an impulsive optimal control problem. We reparametrize the original system and build consistent approximations for this new reparametrized problem. So, we…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
We study the long-time behavior of solutions of the one-phase Stefan problem in inhomogeneous media in dimensions $n \geq 2$. Using the technique of rescaling which is consistent with the evolution of the free boundary, we are able to show…
This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…
In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], where the pointwise internal…
This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the…
We present an experimental study on the non-equilibrium tunnel dynamics of two coupled one-dimensional Bose-Einstein quasi-condensates deep in the Josephson regime. Josephson oscillations are initiated by splitting a single one-dimensional…
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
Convergence is proved for solutions of Dirichlet problems in regions with many small excluded sets (holes), as the holes become smaller and more numerous. The problem is formulated in the context of Markov processes associated with general…
Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…
In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…
For a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…