Related papers: Crystal Growth Inside an Octant
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
In the current work considering the wave model of the crystal growth control, an influence of heterogeneity of the medium on the forming martensite crystal s profile was examined. The considering of the heterogeneity is provided with the…
The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number $N$. By the analysis of particular examples it is argued that for a hyperbolic knot (link) the absolute value of this…
We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…
In this paper we construct a family of exact strong solutions to the two-dimensional incompressible liquid crystal equations with finite energy. The initial velocity is chosen to be rotationally symmetric and the image of the initial…
There are three types of involutions on a cubic fourfold; two of anti-symplectic type, and one symplectic. Here we show that cubics with involutions exhibit the full range of behaviour in relation to rationality conjectures. Namely, we show…
Liquid crystal elastomers are special cross-linked polymer materials combining the large elastic deformability of elastomers with the orientational orders of liquid crystals. This model exhibits markedly different phenomena than the liquid…
We show, in this report, how a population balance model differential equation describing batch crystal growth from solution can be solved in closed form for the case of diffusion limited growth with and without modeling the effects of…
Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the…
We study the growth of the numbers of critical points in one-dimensional lattice systems by using (real) algebraic geometry and the theory of homoclinic tangency.
We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…
It is a fundamental problem how the universal concept of classical chaos emerges from the microscopic description of quantum mechanics. We here study standard classical chaos in a framework of quantum mechanics. In particular, we design a…
We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…
At the poles of Jupiter, cyclonic vortices are clustered together in patterns made up of equilateral triangles called vortex crystals. Such patterns are seen in laboratory flows but never before in a planetary atmosphere, where the planet's…
In this research paper, the problem of optimization of a quadratic form over the convex hull generated by the corners of hypercube is attempted and solved. It is reasoned that under some conditions, the optimum occurs at the corners of…
Near-equilibrium bottom-up crystallization of fully-ionized neutron star crusts or white dwarf cores is considered. We argue that this process is similar to liquid-phase epitaxial (i.e. preserving order of previous layers) crystal growth or…
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. This parallel is rigorous in one dimension, if the conserved surface current is…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…