Related papers: Homogenization and phase separation with space dep…
We consider a thin heterogeneous layer consisted of the thin beams (of radius $r$) and we study the limit behaviour of this problem as the periodicity $\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to zero. The…
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools…
We study the ground state of a large bosonic system trapped in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of particles. In this context, one should expect an…
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…
We present a minimal model to study liquid phase separation in a fixed pH ensemble. The model describes a mixture composed of macromolecules that exist in three different charge states and have a tendency to phase separate. We introduce the…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
This paper continues the study of the asymptotic development of order 2 by $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions initiated in [8]. While in the first paper, the Dirichlet data are assumed…
The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total…
We present a new class of quantum phase transitions that refer neither to local order parameter and critical fluctuations nor to continuous symmetry breaking but are assigned by the step-wise change in topology of the multi-particle system…
The thermodynamics of phase transitions of binary solutions into spatially inhomogeneous one-dimensional states is studied theoretically with taking into account nonlinear effects. It is shown that below the spinodal decomposition…
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have…
We study the limit behavior of Cahn--Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the…
We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…
Phases with distinct thermodynamic properties must differ in their underlying distributions of microscopic structures. While ordered phases are readily distinguished by unit cells and space groups, the local structural basis differentiating…
We show that a liquid mixture in the thermodynamically stable homogeneous phase can undergo a phase-separation transition when rotated at sufficiently high frequency $\omega$. This phase-transition is different from the usual case where two…
Real crystals almost unavoidably contain a finite density of dislocations. We show that this generic type of long--range correlated disorder leads to a breakdown of the conventional scenario of critical behavior and standard renormalization…
We study the $\Gamma$-convergence of sequences of free-discontinuity functionals depending on vector-valued functions $u$ which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of…
It is found experimentally that the coexistence region of a vapor-liquid system or a binary mixture is substantially narrowed when the fluid is confined in a aerogel with a high degree of porosity (e.g. of the order of 95% to 99%). A…