Related papers: Crystal Growth Inside an Octant
We show a strong mesoscopic transverse growth arrest that co-exists with a high-speed longitudinal growth in single-crystalline KDP crystals with large aspect ratios. To explain this unique growth morphology, which cannot be explained by…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
We explore the crystallization in a colloidal monolayer on a structured template starting from a few-particle nucleus. The competition between the substrate structure and that of the growing crystal induces a new crystal growth scenario.…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
Crystal growth behavior of benzoic acid crystals on different surfaces was examined. The performed experiments documented the existence of very strong influence introduced by polar surfaces as glass, gelatin, and polyvinyl alcohol (PVA) on…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the…
We study the motion of tiny heavy inertial particles advected by a two dimensional inviscid fluid flow composed of $N$ identical point vortices regularly placed on a ring, and forming a crystal. In the limit of weak particle inertia, we…
We examine a spatial evolution of lightwaves in a nonlinear photonic crystal with a quadratic nonlinearity when simultaneously a second harmonic and a sum-frequency generation are quasi-phase-matched. We find the conditions of a transition…
We study the long-time behaviour of the focusing cubic NLS on $\R$ in the Sobolev norms $H^s$ for $0 < s < 1$. We obtain polynomial growth-type upper bounds on the $H^s$ norms, and also limit any orbital $H^s$ instability of the ground…
In this work, we study the crystalline nuclei growth in glassy systems focusing primarily on the early stages of the process, at which the size of a growing nucleus is still comparable with the critical size. On the basis of molecular…
We used molecular dynamics simulations to predict the steady state crystal shape of naphthalene grown from ethanol solution. The simulations were performed at constant supersaturation by utilizing a recently proposed algorithm [Perego et…
We consider the rate of volume growth of large Carnot-Carath\'eodory metric balls on a class of unbounded model hypersurfaces in $\mathbb{C}^2$. When the hypersurface has a uniform global structure, we show that a metric ball of radius…
In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational…
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…
For hyperbolic surfaces with geodesic boundary, we study the orthosystole, i.e. the length of a shortest essential arc from the boundary to the boundary. We recover and extend work by Bavard completely characterizing the surfaces maximizing…
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we…
The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic…
It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|{\Delta}S_fus|/R) where {\Delta}S_fus is the entropy of fusion. Here we show that this…
The process of liquid silicon infiltration is investigated for channels with radii from $0.25$ to $0.75$ [mm] drilled in compact carbon preforms. The advantage of this setup is that the study of the phenomenon results to be simplified. For…