Related papers: Universality in diffusion-controlled nucleation an…
Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial…
Using a self-similar approach a general nonsteady theory is elaborated for the case of the diffusion growth of a gas bubble in a supersaturated solution of gas in liquid. Due to the fact that the solution and the bubble in it are physically…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
Dissipation in granular media leads to interesting phenomena as there are cluster formation and crystallization in non-equilibrium dynamical states. The freely cooling system is examined concerning the energy decay and the cluster evolution…
We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium phase transition known to occur in…
We present modeling approaches to explain mechanisms of control of uniformity (narrow distribution) of sizes and shapes in synthesis of nanosize crystals and micron-size colloids. We consider those situations when the nanocrystals are…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…
This paper is devoted to the study of the regularity of solutions to some systems of reaction--diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without…
It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
Full nucleation control for deposited functional molecules on pre-patterned surfaces is of major technological relevance. To understand the nucleation behavior we combine the numerical solution for the evolution of the adatom concentration…
The global energy fluctuations of a low density gas granular gas in the homogeneous cooling state near its clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown…
The growth by condensation of small water droplets in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are…
An analytical description of nucleation stage in a supersaturated vapor with instantly created supersaturation is given with taking into account the vapor concentration inhomogeneities arising as a result of depletion due to non-stationary…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
Diffusion coefficients for crystallized Coulomb plasmas are essential microphysics input for modeling white dwarf cores and neutron star crusts but are poorly understood. In this work we present a model for diffusion in Coulomb crystals. We…