相关论文: A Note on Homogenization Effects on Phase Transiti…
We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with…
We study phase behaviour of a model fluid confined between two unlike parallel walls in the presence of long range (dispersion) forces. Predictions obtained from macroscopic (geometric) and mesoscopic arguments are compared with numerical…
We consider periodic homogenization of boundary value problems for second-order semilinear elliptic systems in 2D of the type $$ \partial_{x_i}\left(a_{ij}^{\alpha…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
The thermodynamics of phase transitions between phases that are size-mismatched but coherent differs from conventional stress-free thermodynamics. Most notably, in open systems such phase transitions are always associated with hysteresis.…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
We analyze a model problem based on highly disparate elastic constants that we propose in order to understand corners and cusps that form on the boundary between the nematic and isotropic phases in a liquid crystal. For a bounded planar…
The flow equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a…
In this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the…
The phase transition of a fluid adsorbed in a heterogeneous system is studied with two simple lattice gas models within the framework of a mean-field theory. Despite the different origin of the heterogeneity (spatial variation of binding…
We compute the complete one-loop finite temperature effective potential for electroweak symmetry breaking in the Standard Model with a Higgs potential supplemented by higher dimensional operators as generated for instance in composite Higgs…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
We consider a model fluid with long-ranged, dispersion interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence while the other is solvophobic and…
Perturbation theory at finite temperature suffers from well-known infrared problems. In the standard model, as a result, one cannot calculate the effective potential for arbitrarily small values of $\phi$, the Higgs expectation value.…
In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of $M$ for which the pressure…
This article characterizes phase transitions in temperature within a specific space of H\"older continuous potentials, distinguished by their regularity and asymptotic behavior at zero. We also characterize the phase transitions in…
In this paper, we study the prototypical model of liquid-liquid phase separation, the Cahn-Hilliard functional, in a highly irregular setting. Specifically, we analyze potentials with low regularity vanishing on space-dependent wells. Under…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory (MCT) at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement…