Related papers: Fractionation of polydisperse systems: multi-phase…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
Colloid-polymer mixtures may undergo either fluid-fluid phase separation or gelation. This depends on the depth of the quench (polymer concentration) and polymer-colloid size ratio. We present a real-space study of dynamics in phase…
Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the…
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…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the…
Phase separation of two phase separating solutes in a common solvent can result in mesoscale (micron-sized) droplets with complex topologies of the domains of each solute within each droplet. Such topologies have been observed in-vitro in…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
We calculate for the first time the full phase-diagram of an asymmetric non-additive hard-sphere mixture. The non-additivity strongly affects the crystallization and the fluid-fluid phase-separation. The global topology of the phase-diagram…
In this paper, some equations are derived to describe the out-of-equilibrium thermodynamics of colloidal suspensions. These results are obtained assuming that the properties of the colloids essentially come from their surfaces which are…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase…
The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is…
We consider a dense assembly of repulsive particles whose fluctuating sizes are subject to an energetic landscape that defines three species: two distinct states of particles with a finite size, and point particles as an intermediate state…
Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
Microphase separation in random multiblock copolymers is studied with mean-field theory assuming that long blocks of a copolymer are strongly segregated, whereas short blocks are able to penetrate into "alien" domains and exchange between…