Related papers: KPP transition fronts in a one-dimensional two-pat…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
A phenomenological model for the unbinding transition of multi-component fluid membranes is proposed, where the unbinding transition is described using a theory analogous to Flory-Huggins theory for polymers. The coupling between the…
The present work concerns a version of the Fisher-KPP equation where the nonlinear term is replaced by a saturation mechanism, yielding a free boundary problem with mixed conditions. Following an idea proposed in [BrunetDerrida.2015], we…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the…
We assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition recently discovered in trapped dipolar quantum gases. We find that one-row supersolids can have already two types of phase…
Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or…
We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…
Steadily moving transition (switching) fronts, bringing local transformation, symmetry breaking or collapse, are among the most important dynamic coherent structures. The nonlinear mechanical waves of this type play a major role in many…
We propose a model describing the liquid-vapour phase transition according to a phase-field approach. The model takes up a setting proposed by the second author, where a phase field is introduced whose equilibrium values 0 and 1 are…
In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of…
The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…
Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of…
We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several…
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds…