Related papers: Direct numerical simulation of homogeneous nucleat…
A continuum growth equation in 1+1 dimensions is obtained by considering the contributions to the underlying current from kinetics of adatoms on the surface. These considerations reproduce the slope dependent term that represents a stable…
The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal…
We investigate with computer simulations the effect of applying an electric field on the water-to-ice transition. We use a combination of state-of-the-art simulation techniques to obtain phase boundaries and crystal growth rates (direct…
Consecutive stochastic 90{\deg} polarization switching events, clearly resolved in recent experiments, are described by a new nucleation and growth multi-step model. It extends the classical Kolmogorov-Avrami-Ishibashi approach and includes…
The thermodynamic properties of nuclei are studied in a mean field model using a Skryme interaction. Properties of two component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
The performance of organic solar cells strongly depends on the bulk heterojunction (BHJ) morphology of the photoactive layer. This BHJ forms during the drying of the wet-deposited solution, because of physical processes such as…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
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…
A quantum molecular model for fermions is investigated which works with antisymmetrized many-body states composed of localized single-particle wave packets. The application to the description of atomic nuclei and collisions between them…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
Molecular dynamics simulations were carried out to test the thermodynamic theory of weakly excited, two-dimensional granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78, 2764 (1997)], where granular materials are viewed as a collection…
We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on…
We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained…
A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…