Related papers: Dendrites with corners
A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand…
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it…
We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The thermal compatibility condition, as well as a positive entropy-production property, is derived analytically and…
We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After re-scaling by the characteristic size, the interface becomes progressively more…
We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field…
We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the…
By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in…
The growth of snow crystals is dependent on the temperature and saturation of the environment. In the case of dendrites, Reiter's local two-dimensional model provides a realistic approach to the study of dendrite growth. In this paper we…
In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
In this work, we consider the three-dimensional solid-state dewetting with strongly anisotropic surface energy, assuming an axisymmetric morphology of the thin film. However, when surface energy exhibits strong anisotropy, certain…
Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the…
Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and…
The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin…
We study the expansion of a dilute ultracold sample of fermions initially trapped in a anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In…
We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…