Related papers: Self-consistent rate theory for submonolayer surfa…
The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady…
Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates…
Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept, called subroughness, meaning that there exist two…
A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability…
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…
The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the…
A mean field rate theory description of the homo- and co-polymerization of $f$-functional molecules is developed, which contains the formation of short cyclic structures inside the network. The predictions of this model are compared with…
Stochastic growth of binary alloys on a weakly interacting substrate is studied by kinetic Monte Carlo simulation. The underlying lattice model relates to fcc alloys, and the kinetics are based on deposition, atomic migration with…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time.…
In the framework of the second-quantization representation of the master equation governing the irreversible epitaxial growth, exact equations describing the evolution of the island densities has been obtained. Their decoupling within a…
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 rate of second layer nucleation -- the formation of a stable nucleus on top of a two-dimensional island -- determines both the conditions for layer-by-layer growth, and the size of the top terrace of multilayer mounds in…
Formation of monodispersed colloidal particles is a complex process: nuclei, produced rapidly in a supersaturated solution, grow to nanosize primary particles, which then aggregate (coagulate) to form much larger final colloids. This paper…
Monodispersed spherical cadmium sulfide particles were used as a model system in order to explain the size selection in the formation of colloids by aggregation of nanosize subunits. Several procedures of mixing the reactants were employed…
A cell dynamics method for domain separation of diblock copolymers (DBCPs) interacting with nanoparticles (NPs) whose diffusion coefficients depend on chain configuration is proposed for self-assembly of DBCP/NP composites. Increasing NP…
We examine the island size distribution function and spatial correlation function of a model for island growth in the submonolayer regime in both 1 and 2 dimensions. In our model the islands do not grow in shape, and a fixed number of…
We consider the micellization of block copolymers in solution, employing self consistent field theory with an additional constraint that permits the examination of intermediate structures. From the information for an isolated micelle…