相关论文: A homogenization result in the gradient theory of …
On the basis of a lattice gas model and the convolution formula with cell construction scheme, we demonstrate that intermittency in the rapidity-space with respect to the scaled moments comes from a phase transition between ordered phase…
The Rayleigh-Taylor instability develops when fluids are accelerated counter to their density gradients; intense interfacial fluid mixing ensues with time. The Rayleigh-Taylor mixing controls a broad range of processes in fluids, plasmas,…
Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the…
The development of microfluidic devices has recently revived the interest in "old" problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids…
In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one…
We consider turbulence in the Gross-Pitaevsky model and study the creation of a coherent condensate via an inverse cascade originated at small scales. The growth of the condensate leads to a spontaneous breakdown of symmetries of…
The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena,…
We study the effects of confinement between two parallel walls on a two dimensional fluid with competing interactions which lead to the formation of particle micro-domains at the thermodynamic equilibrium (microphases or microseparation).…
Liquids with quasi - chemical bonding between molecules are described in terms of vertex model. It is shown that this bonding results in liquid - liquid phase transition, which occurs between phases with different mean density of…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
We develop an analogy between fluids and black holes to study phase transitions in the latter. The entropy-temperature graph shows the onset of a phase transition without any latent heat. The nature of this continuous (higher order) phase…
We perform the periodic homogenization (i.e. $\eps\to 0$) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where $\eps$ is a suitable scale parameter. The objective is to investigate the influence of…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
A quantum phase transition that was recently observed in a high-mobility silicon MOSFET is analyzed in terms of a scaling theory. The most striking characteristic of the transition is a divergence of the thermopower, according to an inverse…
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, could be treated as periodic bi-domain structures, which…
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
In this work we give a characterisation of first order phase transitions as equilibrium processes on the thermodynamic phase space for which the Legendre symmetry is broken. Furthermore, we consider generalised theories of thermodynamics,…
A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings…
We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase…
In this work we develop a homogenisation methodology to upscale mathematical descriptions of microcirculatory blood flow from the microscale (where individual vessels are resolved) to the macroscopic (or tissue) scale. Due to the assumed…