Related papers: Minimizing Lattice Energy and Hexagonal Crystalliz…

We study a harmonic triangular lattice, which relaxes in the presence of a weak, short-wavelength periodic potential. Monte Carlo simulations reveal that the elastic lattice has only short-ranged positional correlations, despite the absence…

Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr\"{o}dinger equation of the reflection-asymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic…

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential,…

Let $\delta_0(P,k)$ denote the degree $k$ dilation of a point set $P$ in the domain of plane geometric spanners. If $\Lambda$ is the infinite square lattice, it is shown that $1+\sqrt{2} \leq \delta_0(\Lambda,3) \leq (3+2\sqrt2) \, 5^{-1/2}…

Isospin-1/2 $D\pi$ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately $(3.6\; \mathrm{fm})^3$ and with a light quark mass corresponding to $m_\pi\approx239$ MeV. The spectrum of the elastic…

Minimum total energy calculations, which account for both electron--lattice and electron--electron interactions in conjugated polymers are performed for chains with up to eight carbon atoms. These calculations are motivated in part by…

In a recent paper S. Friedland and the author presented a formal expression for lambda_d(p) of the monomer-dimer problem on a d-dimensional rectangular lattice, which involved a power series in p. Herein, we find simlar expressions for…

We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…

We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.

Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to explain patterns produced by biological and physical systems. In…

We consider the 3D smectic energy $$\mathcal{E}_{\epsilon }\left( u\right) =\frac{1}{2}\int_{\Omega }\frac{1}{\varepsilon } \left( u_z-\frac{( u_x)^{2}+( u_y)^{2}}{2}\right) ^{2}+\varepsilon \left( u_{xx}+u_{yy}\right)^{2}\,dx\,dy\,dz. $$…

In this paper a Blaschke-Santal\'o diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of set $$\mathcal{E}:=\left\{(x,y)\in \R^2, x=\frac{4\pi…

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…

It was recently proved that the elastic energy $E(\gamma)=\tfrac{1}{2}\int_\gamma\kappa^2 ds$ of a closed curve $\gamma$ with curvature $\kappa$ has a minimizer among all plane, simple, regular and closed curves of given enclosed area…

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…

Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice $\mathbb{z}$ is a minimizer for the so-called renormalized energy which they…

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…

Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine…

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole…

We consider a lattice of spin-1 particles with a general pairwise interaction $ [ {\rm cos} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1}) \ + {\rm sin} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1})^2 \ ]$. We show that, for a large class of lattices…