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A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
We show that two tight binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that…
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the…
We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a…
Spontaneously crystalline ground states, called quantum crystals, of a trapped Rydberg-dressed Bose-Einstein condensate are numerically investigated. As a result described by a mean-field order parameter, such states simultaneously possess…
We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is nu < 1. Our approach involves the examination of large dots (< 40 electrons) using a partial…
We study the existence and stability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction in dimensions $d\leq 3$. We also study the characterization of finite time blow-up solutions with minimal…
To study crystals that contain heavy atoms, it is important to consider the relativistic effects, as electrons in orbitals close to the atom's nucleus can reach speeds comparable to that of light in a vacuum. In this study, we utilized the…
We study the ground state properties of classical Coulomb charges interacting with a 1/r potential moving on a plane but confined either by a circular hard wall boundary or by a harmonic potential. The charge density in the continuum limit…
Chirality is essential for various amazing phenomena in life and matter. However,chirality and its switching in electronic superlattices, such as charge density wave(CDW) arrays, remain elusive. In this study, we characterize the chirality…
A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range…
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 show that the entangled-plaquette variational ansatz can be adapted to study the two-dimensional $t-J$ model in the presence of two mobile holes. Specifically, we focus on a square lattice comprising up to $N=256$ sites in the parameter…
We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was…
We investigate the crystal structure of classical systems of spherical particles with an embedded point dipole at T=0. The ferroelectric ground state energy is calculated using generalizations of the Ewald summation technique. Due to the…
We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic…
We minimize a discrete version of the fourth-order curvature based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy…
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…
We revisit a model in which the ionization energy of a metal particle is associated with the work done by the image charge force in moving the electron from infinity to a small cut-off distance just outside the surface. We show that this…
Two-dimensional Rydberg atoms are modeled at low temperatures by means of the classical Monte Carlo method. The Coulomb repulsion of charged ions competing with the repulsive van der Waals long-range tail is modeled by a number of…