Related papers: Crystal Growth Inside an Octant
We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication…
We present a tutorial on the principles of crystal growth of intermetallic and oxide compounds from molten solutions, with an emphasis on the fundamental principles governing the underlying phase equilibria and phase diagrams of…
We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for…
We consider two spherical, roughened crystals with approximately isotropic surface free energy which are brought into contact and begin to sinter. We argue that the geometry immediately post-contact is two dimensional and Cartesian and can…
It is shown that the dynamics of the growth of a two dimensional surface in a Laplacian field can be mapped onto Hamiltonian dynamics. The mapping is carried out in two stages: first the surface is conformally mapped onto the unit circle,…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
Given a smooth convex cone in the Euclidean $(n+1)$-space ($n\geq2$), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If…
Crystal growth has been widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface have been understood as forms of tangential crystal growth mediated by…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
We study entanglement growth in a harmonic oscillator chain subjected to the weak measurement of observables which have been smeared-out over a length scale $R$. We find that entanglement grows diffusively ($S \sim t^{1/2}$) for a large…
Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along…
We consider the two-dimensional Euler equations in non-smooth domains with corners. It is shown that if the angle of the corner $\theta$ is strictly less than $\pi/2$, the Lipschitz estimate of the vorticity at the corner is at most single…
We report a study on the kinetics of drying of a droplet of aqueous gelatin containing sodium chloride. The process of drying recorded on video, clearly shows different regimes of growth leading to a variety of crystalline patterns. Large…
Understanding the nature of entanglement growth in many-body systems is one of the fundamental questions in quantum physics. Here, we study this problem by characterizing the entanglement fluctuations and distribution of $(d+1)$ qubit…
Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the…
We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…
We show that the metric entropy of a $C^1$ diffeomorphism with a dominated splitting and the dominating bundle uniformly expanding is bounded from above by the integrated volume growth of the dominating (expanding) bundle plus the maximal…
Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the…
Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with non-equilibrium problems, however, the distinction in…
This application note describes how to model diffusion-limited crystal growth from vapor using QuickField - a commercial finite-element analysis code. The crystal growth problem is cast into the format of a steady-state heat diffusion…