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Studying Arctic ice formation stays in the focus of research groups over the past decades in the context of ice cover changes, thermal budget and climate agenda in general. Nevertheless, the phenomenon's underlying mechanisms are still not completely understood and described. The main reason for the lack in understanding is the limited experimental access to the field data when it comes to the processes that occur below the ice floe. Thus, there is a need to build competent analogies between the natural (ocean water–ice) and laboratory (here: binary alloy) conditions of the experiment as a step of data preparation for the verification of the mathematical model. In the current paper, the existing qualitative models describing the process of melting and crystallization were expanded and the experimental method was developed copying the layering of the natural ocean water–ice mixture. The experimental set‐up for studying the solidification within the intermediate zone was designed for Al–Cu alloys being the system with appropriate solidus line for creating a sufficient concentration gradient and by that temperature dependent phase fraction under isothermal conditions. The gained experimental data were used for validating a binary phase‐field model for solidification considering moving boundaries. The model includes the description of the free energy of both phases and their respective diffusion coefficients. It allows modeling a binary system at a mesoscopic spatial level by including the concentration‐driven phase transition and resolidification in the two‐phase region. The novel results will help the quantitative understanding of solidification phenomena and are highly‐evaluated from interdisciplinary point of view, including glaciology and geosciences, being ultimately significant for the understanding the global climate change landscape. [ABSTRACT FROM AUTHOR]

The issue is devoted to theoretical, computational, and experimental studies of phase and structural transitions and non-equilibrium phenomena (phase transformations, heat generation, rheology, and relaxation phenomena) in disordered systems, e.g., composite and metastable materials, biological tissues and systems; polymer and other soft materials; amorphous and glass-forming systems, as well as multicomponent melts. Special attention is paid to the detailed microscopical study of various phenomena in the aforementioned systems. [ABSTRACT FROM AUTHOR]

Motivated by a wide range of applications in various fields of physics and materials science, we consider a generalized approach to the evolution of a polydisperse ensemble of spherical particles in metastable media. An integrodifferential system of governing equations, consisting of a kinetic equation for the particle-size distribution function (Fokker–Planck type equation) and a balance equation for the temperature (concentration) of a metastable medium, is formulated. The kinetic equation takes into account fluctuations in the growth/reduction rates of individual particles, the velocity of particles in a spatial direction, the withdrawal of particles of a given size from the metastable medium, and their source/sink term. The heat (mass) balance equation takes into account the growth/reduction of particles in a metastable system as well as heat (mass) exchange with the environment. A generalized system of equations describes various physical and chemical processes of phase transformations, such as the growth and dissolution of crystals, the evaporation of droplets, the boiling of liquids and the combustion of a polydisperse fuel. The ways of analytical solution of the formulated integrodifferential system of equations based on the saddle-point technique and the separation of variables method are considered. The theory can be applied when describing the evolution of an ensemble of particles at the initial and intermediate stages of phase transformation when the distances between the particles are large enough, and interactions between them can be neglected. [ABSTRACT FROM AUTHOR]

The phase-field crystal (PFC) method is known as a relatively new continuum approach for describing the microstructural dynamics of materials during structural and phase transitions. In contrast to molecular dynamics (MD) or density functional theory (DFT) methods, PFC allows description processes on diffusion time scales while maintaining an atomistic spatial resolution which explains its attraction to scientists over the last 20 years. After certain development, PFC serves today as a solution of a wide variety of new and increasingly complex problems. As a result, dozens of various modifications of the original PFC model are already helping to study special features in material science. New possibilities and challenges arise when extended spatio-temporal correlations are introduced in PFC model. The current paper briefly systematizes and characterizes PFC model's applications mainly focused on spatio-temporal correlations, systems with memory and models suitable for the description of non-equilibrium phase transformations. [ABSTRACT FROM AUTHOR]

When looking for solutions to nonstationary problems in the field of binary melts or solutions, the scientific community regularly faces the need to transform the classical Stefan‐type approach in order to obtain both new analytical results and explicit solutions. Within the framework of the current paper, we present the analysis of the problem of directional crystallization of binary solutions or melts in the presence of a mushy layer, based on the consideration of field data under the prism of a modified formulation, which made it possible to obtain such characteristics of the behavior of the mushy zone as the thickness and growth rate of the solid phase, temperature distribution, and also to determine heat‐conducting and latent heat flows. The simulation results are presented, including in the form of illustrative material; a good agreement was noted between the predicted values of the growth rates and temperature profiles of the mushy zone and the area of solid matter with the existing observations of young sea ice dynamics. [ABSTRACT FROM AUTHOR]

In order to get a deeper physical insight into the problem of directional solidification, which is a common feature both for the materials processing and crystal growth, the analytical description of the non-linear model was provided for the case of the binary solutions with a mushy layer. Both convective and conductive conditions of the liquid phase were considered, the Stefan-type model was adjusted for the nonstationary case, the validation of the models prediction was given through the comparison of analytical data and field experiment for the behavior of phase transition interfaces between the pure ice and mushy layer and the liquid phase and mushy layer. [ABSTRACT FROM AUTHOR]

A phase field model of rapid multi–grain growth is developed. Using a multi–phase model for polycrystalline growth in multi–component alloying systems and the model of fast phase transformations, the Gibbs free energy change on crystallization is formulated as a driving force for polycrystalline growth. The model of fast phase transitions, which introduces not only classical slow variables (concentration, chemical potential and phase field), but also the fast ones (diffusion flux and gradient flow), was used to capture short periods of times usually occurring in the rapid solidification and in the fast solid-state transformations. The evolution equations for the fast crystallization are written using multi–phase interpolation functions among growing polycrystallites. [ABSTRACT FROM AUTHOR]

Contributions devoted to real applications of nonlinear dynamics of phase transitions in physical, physicochemical, and biophysical processes and natural phenomena are included as well. This special issue "Nonlinear dynamics of phase transitions" is devoted to recent trends in the mathematical description of phase transitions, which arise in many research problems ranging from physical and chemical processes to biophysics and life science. [Extracted from the article]