相关论文: The one-dimensional equilibrium shape of a crystal
In this paper we completely settle the Almgren problem in $\mathbb R^3$ under some generic conditions on the potential and tension functions. The problem, among other things, appears in classical thermodynamics when one is to understand if…
A solution is given to a long-standing open problem posed by Almgren.
In the nonlocal Almgren problem, the goal is to investigate the convexity of a minimizer under a mass constraint via a nonlocal free energy generated with some nonlocal perimeter and convex potential. In the paper, the main result is a…
The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical import. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in…
The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
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…
We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration at fixed density -- also called crystallization -- is shown in…
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
The equilibrium properties of particles adsorption is investigated theoretically. The model relies on a free energy formulation which allows to generalize the Maxwell-Boltzmann description to solutions for which the bulk volume fraction of…
Surface energies for different GaAs surface orientations have been calculated as a function of the chemical potential. We use an energy density formalism within the first-principles pseudopotential density-functional approach. The…
We prove the sharp quantitative stability in the radial isotropic Almgren problem. In addition, we develop a theory for estimating the sharp modulus in the context of minimal assumptions on the surface tension and the potential and obtain…
Starting from the assumption that general relativity might be an emergent phenomenon showing up at low-energies from an underlying microscopic structure, we re-analyze the stability of a static closed Universe filled with radiation. In this…
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an…
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied,…
We present a uniform construction of level 1 perfect crystals $\mathcal B$ for all affine Lie algebras. We also introduce the notion of a crystal algebra and give an explicit description of its multiplication. This allows us to determine…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…