相关论文: A homogenization result in the gradient theory of …

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where…

This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid-fluid phase transition in…

We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…

Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…

Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquidlike wetting layers adsorbed on flat substrates with an embedded chemical heterogeneity forming a stripe. For a wide range…

We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small spheres distributed in an $\veps$-periodic network. The asymptotic…

We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the…

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…

For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…

Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal…

We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe…

This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…

We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…

We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase…

We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…

We use direct numerical simulations to investigate the interaction between the temperature field of a fluid and the temperature of small particles suspended in the flow, employing both one and two-way thermal coupling, in a statistically…