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We consider the initial value problem for the generalized Allen-Cahn equation, \[\partial_t \Phi = \Delta \Phi-\varepsilon^{-2} \Phi (\Phi^t \Phi - I), \qquad x \in \Omega, \ t\geq 0,\] where $\Phi$ is an $n\times n$ real matrix-valued…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
We develop a novel method for building a gravitational analog model for a flowing Bose-Einstein condensate. The analogue metric is obtained using effective field theory methods, integrating out the heavy radial fluctuations. In this way, we…
This paper discusses a relation between the re-initialization equation of the level-set functions derived by Wac{\l}awczyk [J.Comp.Phys., 299, (2015)] and the condition for the phase equilibrium provided by the stationary solution to the…
The Allen-Cahn action functional is related to the probability of rare events in the stochastically perturbed Allen-Cahn equation. Formal calculations suggest a reduced action functional in the sharp interface limit. We prove in two and…
In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be…
The numerical approximation of non-isothermal liquid-vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface…
In this article we study the second variation of the energy functional associated to the Allen-Cahn equation on closed manifolds. Extending well known analogies between the gradient theory of phase transitions and the theory of minimal…
The dynamics of compressible liquid-vapor flow depends sensitively on the microscale behavior at the phase boundary. We consider a sharp-interface approach, and propose a multiscale model to describe liquid-vapor flow accurately, without…
We prove the convergence of a Wasserstein gradient flow of a free energy in inhomogeneous media. Both the energy and media can depend on the spatial variable in a fast oscillatory manner. In particular, we show that the gradient-flow…
The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We…
This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and…
We are interested in the averaged behavior of interfaces moving in stationary ergodic environments, with oscillatory normal velocity which changes sign. This problem can be reformulated, using level sets, as the homogenization of a…
Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and…
We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
We consider a class of condensed matter theories in a Newtonian framework with a Lagrange formalism related in a natural way with the classical conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i…
We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An essential feature of this model is the use of Butler-Volmer kinetics for lithium-ion…