Related papers: Facet shapes in a Wulff crystal
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on…
Experimental determination of absolute surface energies remains a challenge. We propose a simple method based on two independent measurements on 3D and 2D equilibrium shapes completed by the analysis of the thermal fluctuation of an…
We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface…
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…
In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with…
A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones being empty. Allowed atom configurations are such that they…
Quantitative stability for crystalline anisotropic perimeters, with control on the oscillation of the boundary with respect to the corresponding Wulff shape, is proven for $n\geq 3$. This extends a result of [Neu16] in $n=2$.
Due to the potential application of regulating droplet shape by external fields in microfluidic technology and micro devices, it becomes increasingly important to understand the shape formation of a droplet in the presence of an electric…
We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under…
The shape of nanocrystals is crucial in determining their surface area, reactivity, optical properties, mechanical strength, and self-assembly behavior. Traditionally, shape control has been achieved through empirical methods, highlighting…
Crystallization of dense matter in neutron star crusts and white dwarf cores may be similar to epitaxial crystal growth in terrestrial laboratories. However in stellar crystals, the spacing between horizontal planes has to gradually…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding…
In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an…
While measurements of the polar dependence of the surface free energy are easily available, measurements of the whole polar dependence of the surface stress of a crystal do not exist. In this paper is presented a new procedure that allows,…
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…
We study a crystal growth Markov model proposed by Gates and Westcott (\cite{Kinetics1}, \cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model…