Related papers: A proof of finite crystallization via stratificati…
Pairing of valence electrons can lead to energy minimization of a crystal. It can be proved by use of representation of the valence electrons as plane waves in periodic potential of the crystal.
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
Using an extension of Pirogov-Sinai theory we prove phase transitions, corresponding to sublattice orderings, for a general class of hard core lattice particle systems with a finite number of close packed configurations. These include many…
We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e. its Wulff crystal is a…
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…
We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization…
We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms…
We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the bending energy and the tangent-point functional. Based on…
Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity''…
In this paper, we use quadratic forms diagonalization methods applied to the function thermodynamic energy to analyze the stability of physical systems. Taylor's expansion was useful to write a quadratic expression for the energy function.…
We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also…
A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites).…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-body contributions. Our main focus is on characterizing those…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
We study $\phi^4$ lattice field theory at finite chemical potential $\mu$ in two and four dimensions, using a worldline representation that overcomes the complex action problem. We compute the particle number at very low temperature as a…
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…