Related papers: Minimizing lattice structures for Morse potential …
We prove that the hexagonal lattice is a local minimizer, among all point configurations, of the interaction energy per unit volume for pair potentials that are completely monotonic functions of the square distance. This includes Gaussian…
Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301…
By introducing appropriate lattice parameters for a bi-lattice smoothly connecting the hexagonal close-packed (hcp) with the cuboidal structures, namely the body-centered (bcc) and the face centered cubic (fcc) lattices, we were able to map…
We present our latest study of Lambda-Nucleon (LN) interaction by using lattice QCD, following up on our report at LATTICE 2008. We have calculated not only the scattering lengths but also the central and tensor potentials, which are…
We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application,we study the hard-core lattice gas on the triangular lattice with the first- and the second-neighbor exclusions. The data are analyzed by…
In this work we investigate the interatomic correlation moments in two-dimensional model of a weakly anharmonic crystal (i.e., not very high temperatures) with hexagonal lattice, using the Correlative Method of Unsymmetrized Self-Consistent…
Three-parametric Lenard-Jones and Morse interatomic potentials are the simplest ones, which that can be used to obtain thermophysical properties of the liquid and solid substances. Upon adjusting the model parameters to real substance…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely monotone functions among lattices is located…
In this study, a variational method for the inverse problem of self-assembly, i.e., a reconstruction of the interparticle interaction potential of a given structure, is applied to three-dimensional crystals. According to the method, the…
We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the…
The diffusionless Burgers-Bain phase transition from a hcp arrangement to a cuboidal lattice (fcc and bcc) is analysed in great detail for Lennard-Jones solids. From the lattice vectors of an underlying bi-lattice smoothly connecting these…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
Analytical formulae are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Gr\"{u}neisen parameter within the Einstein model for the cubic lattices (sc, bcc and fcc) and for the…
To reproduce the diamond structure of silicon, double lattice (DL) potential constructed from two interatomic potentials for face centered cubic (fcc) lattice, is proposed for molecular dynamics (MD) simulations. For the validity test of MD…
We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional…
We study the two dimensional Lennard-Jones energy per particle of lattices and we prove that the minimizer among Bravais lattices with sufficiently large density is triangular and that is not the case for sufficiently small density. We give…
In the current work we revisit the pair-potential recently proposed by Wang et al. (Phys. Chem. Chem. Phys. 10624, 22, 2020) as a well defined finite-range alternative to the widely used Lennard-Jones interaction model. The advantage of…
We study a system of particles in two dimensions interacting via a dipolar long-range potential $D/r^3$ and subject to a square-lattice substrate potential $V({\bf r})$ with amplitude $V$ and lattice constant $b$. The isotropic interaction…
We investigate the isoperimetric problem for the Voronoi cells of three-dimensional lattices. Using Selling parameters, we derive an explicit closed formula for the scale-invariant isoperimetric quotient $F$ in terms of six non-negative…