Related papers: Face-centered cubic crystallization of atomistic c…
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…
Recent advances in spin-dependent optical lattices [Meng et al., Nature \textbf{615}, 231 (2023)] have enabled the experimental implementation of two superimposed three-dimensional lattices, presenting new opportunities to investigate…
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring local square-lattice arrangements. An additional interaction…
Targeting specific technological applications requires the control of nanoparticle properties, especially the crystalline polymorph. Freezing a nanodroplet deposited on a solid substrate leads to the formation of crystalline structures. We…
A brief description of the novel approach towards solving few-body scattering problems in a finite-dimensional functional space of the $L_2$-type is presented. The method is based on the complete few-body continuum discretization in the…
We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
The focusing of high energy charged particles by a bent crystal is considered. The limits and constraints of focusing imposed by dynamics of particles are pointed out. The crystalline geometry provided the maximum magnification and minimum…
Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which…
In this paper, we study minimization problems among Bravais lattices for finite energy per point. We prove that if a function is completely monotonic, then the triangular lattice minimizes energy per particle among Bravais lattices with…
We examine nanoparticles (NPs) forming polyhedral sections of the ideal cubic lattice, simple (sc), body centered (bcc), and face centered (fcc) cubic, which are confined by facets characterized by densest and second densest {h k l}…
There is a very natural map from the configuration space of n distinct points in Euclidean 3-space into the flag manifold U(n)/U(1)^n, which is compatible with the action of the symmetric group. The map is well-defined for all…
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this…
We study the local optimality of Simple Cubic, Body-Centred-Cubic and Face-Centred-Cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola [Math. Proc. Cambridge, 60:855--875,…
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…
We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the…
To clarify the relation of energy shifts to scattering phase shifts in one-body and many-body problems, we examine their relation in a number of different situations. We derive, for a particle in a container of arbitrary shape with a…
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…
We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \cite{Radin_soft}. We give an alternative proof that relies on the geometric decomposition of the energy…
We examine the structure of compact metal nanoparticles (NPs) forming polyhedral sections of face centered (fcc) and body centered (bcc) cubic lattices, which are confined by facets characterized by highly dense {100}, {110}, and {111}…