Related papers: Moving boundary problems for quasi-steady conducti…
We study the influence of quenched disorder on the two-dimensional melting behavior by using both video-microscopy of superparamagnetic colloidal particles and computer simulations of repulsive parallel dipoles. Quenched disorder is…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid-liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes…
The statistical theory of flow stress, including yield strength, for polycrystalline materials under quasi-static plastic deformation suggested in [arxiv:1803.08247[cond-mat.mtr-sci], arxiv:1805.08623[cond-mat.mtr-sci]] is developed in the…
Inorganic scintillating crystals can be modelled as continua with microstructure. For rigid and isothermal crystals the evolution of charge carriers becomes in this way described by a reaction-diffusion-drift equation coupled with the…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing…
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of…
Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The full non-axisymmetric morphology of the steady-state dendrite tip and $\sigma^*$ are determined as a…
For flow-enhanced crystallization in fiber spinning, the viscoelastic two-phase fiber models by Doufas et al. (J. Non-Newton. Fluid Mech., 2000) and Shrikhande et al. (J. Appl. Polym. Sci., 2006) are state of the art. However, the boundary…
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…
Classical density-functional theory is employed to study finite-temperature trends in the relative stabilities of one-component quasicrystals interacting via effective metallic pair potentials derived from pseudopotential theory. Comparing…
We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a…
At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline…
In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…
We study the thermodynamics of a crystalline solid by applying intermediate statistics obtained by deforming known solid state models using the mathematics of $q$-analogs. We apply the resulting $q$-deformation to both the Einstein and…
We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical…
This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of…
The structure and evolution of grain boundaries underlies the nature of polycrystalline materials. Here we describe an experimental apparatus and light reflection technique for measuring disorder at grain boundaries in optically clear…