Related papers: A Soluble Phase Field Model
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time integration of temperature, and the order…
Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable…
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be…
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…
The dynamics of typical phase transitions is studied out of equilibrium in weakly coupled inflaton-type scalar field theories in Minkowski space. The shortcomings of the effective potential and equilibrium descriptions are pointed out. A…
We explore the stability properties of multi-field solutions of assisted inflation type, where several fields collectively evolve to the same configuration. In the case of noninteracting fields, we show that the condition for such solutions…
We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
We analyze the early phase of brine entrapment in sea ice, using a phase field model. This model for a first-order phase transition couples non-conserved order parameter kinetics to salt diffusion. The evolution equations are derived from a…
The phase-field model for the description of the solidification processes with the glass-crystal competition is suggested. The model combines the first-order phase transition model in the phase-field formalism and gauge-field theory of…
Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…
Computer simulations of contact melting and associated interfacial phenomena in binary eutectic systems were performed on the basis of the standard phase-field model with miscibility gap in solid state. It is shown that the model predicts…
A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a…
We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes…
We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze…
Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…
We consider the nonequilibrium dynamics of a a real scalar field in a degenerate double-well potential. The system is prepared in the lowest free energy state in one of the wells and the dynamics is driven by the coupling of the field to a…