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A new type of boundary dynamics is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is…
We consider first-order phase transitions of the Universe in the radiation-dominated era. We argue that in general the velocity of interfaces is non-relativistic due to the interaction with the plasma and the release of latent heat. We…
This article covers thermodynamic, dynamic, and kinetic models that are suitable for the analysis of wetting, adsorption, and related interfacial phenomena in colloidal and multiphase systems. Particular emphasis is made on describing…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…
A clear understanding and proper control of interfacial thermal transport is important in nanoscale device. In this review, we first discuss the theoretical methods to handle the interfacial thermal transport problem, such as the…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
Colloidal particles are often seen as big atoms that can be directly observed in real space. They are therefore playing an increasingly important role as model systems to study processes of interest in condensed matter physics such as…
When a stable ordered phase and a metastable disordered phase are separated by a flat interface, the metastable state changes to the stable state through the propagation of the interface. For cases in which latent heat is generated, the…
Hypothesis Roughening transitions at solid-liquid interfaces govern crystal morphology in diverse systems. In ice crystallization, these transitions control interfacial faceting and surface kinetics. Faceted morphologies are often…
In alloy solidification, the transport processes of heat and solute result in morphological instability of the interface, forming different patterns of solidification structure and determining the mechanical properties of components. As the…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
We revisit the two-dimensional quantum Ising model by computing renormalization group flows close to its quantum critical point. The low but finite temperature regime in the vicinity of the quantum critical point is squashed between two…
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the Oseen-Frank model), free interfaces and topological defects…
Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction. However, presently often a fundamental…
We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We argue that the relative thermal conductance between interfaces with different morphologies is controlled by crystal structure through $M_{min}/M_c > 1$, the ratio between the {\it minimum mode} count on either side $M_{min}$, and the…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the…
The glass transition refers to the non-equilibrium process by which an equilibrium liquid is transformed to a non-equilibrium disordered solid, or vice versa. Associated response functions, such as heat capacities, are markedly different on…