Related papers: Higher-order singular perturbation models for phas…
In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a…
We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises…
Models with higher order derivative terms in the kinetic energy appear not only as effective theories, they can be considered as elementary, renormalizable models in their own right. The extension of Higgs mechanism is discussed for…
We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close---but not too close---to -1. We are particularly interested in a quantitative…
Measurements of energy separations in highly charged ions can in many cases nowadays be performed with very high accuracy, an accuracy that sometimes cannot be matched by the corresponding theoretical calcula- tions. Furthermore, it has…
In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced…
We introduce a new method for calculating density perturbations in hybrid inflation which avoids treating the fluctuations of the "waterfall" field as if they were small perturbations about a classical trajectory. We quantize only the…
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a…
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…
We investigate a singular perturbation for Hamilton-Jacobi equations in an open subset of two dimensional Euclidean space, where the set is determined through a Hamiltonian function and the Hamilton-Jacobi equations are the dynamic…
In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…
Renormalisation group flows of the bosonic nonlinear \sigma-model are governed, perturbatively, at different orders of \alpha', by the perturbatively evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the flow equations…
Phase transitions and critical behaviour of a class of MV-SDEs, whose concomitant non-local Fokker-Planck equation includes the Granular Media equation with quadratic interaction potential as a special case, is studied. By careful analysis…
We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove…
The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless…
Within the framework of spatially covariant theories, we propose a general model for dark energy (DE) in which the cosmological background and perturbations are independently controlled by different sets of coefficients, and the equation of…
Models for branched networks are often expressed as the minimization of an energy $M^\alpha$ over vector measures concentrated on $1$-dimensional rectifiable sets with a divergence constraint. We study a Modica-Mortola type approximation…
The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range…
This paper addresses the asymptotic development of order 2 by Gamma convergence of the Cahn-Hillard functional with Dirichlet boundary conditions, where the potential has subquadratic growth near the wells.
The following is a thermodynamic analysis of a III order (and some aspects of a IV order) phase transition. Such a transition can occur in a superconductor if the normal state is a diamagnet. The equation for a phase boundary in an H-T (H…