A continuum approximation for the excitations of the interface in the quantum Heisenberg model.
A Discrete Model For Pattern Formation In Volatile Thin Films
We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a discrete analog of the continuous dynamics of evaporation of thin liquid films. Within mean field approximation the dynamics of this model, averaged over many realizations of the growing cluster, reduces to that of the idealized evaporation model in which surface tension is neglected. However fluctuations beyond the mean field level play an important role, and...
A simple fluctuation lower bound for a disordered massless random continuous spin model in .
Confinement of the two dimensional discrete Gaussian free field between two hard walls.
Convergence results and sharp estimates for the voter model interfaces.
Corrector results for a parabolic problem with a memory effect
The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl.54 (2009) 189–222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux...
Decay of covariances, uniqueness of ergodic component and scaling limit for a class of systems with non-convex potential
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.
Dichotomy in a scaling limit under Wiener measure with density.
Fluctuations of the front in a stochastic combustion model
Green's function method approach to electron configuration of superlattices.
Integral Quadratic Forms, Kac-Moody Algebras, and Fractional Quantum Hall Effect. An ADE- Classification
Internal diffusion-limited aggregation on non-amenable graphs.
Localization and delocalization of random interfaces.
Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models
Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...
Quantum interfaces
We review recent results on interface states in quantum statistical mechanics.
Scaling limits of anisotropic Hastings–Levitov clusters
We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...
The periodic unfolding method for a class of parabolic problems with imperfect interfaces
In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with ε-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative via a function of order εγ with γ ≤ −1. We give the homogenization results which include those obtained by Jose in [Rev. Roum. Math. Pures Appl. 54 (2009) 189–222]. We also get the...
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
Variational characterization of interior interfaces in phase transition models on convex plane domains.