Related papers: Geometry Equilibration of Crystalline Defects in Q…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural, phonon stability assumption we quantify the decay of the long-range elastic fields…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
We develop and analyze a framework for consistent QM/MM (quantum/classic) hybrid models of crystalline defects, which admits general atomistic interactions including traditional off-the-shell interatomic potentials as well as state of art…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. N\'emeth and M. Challacombe, J. Chem. Phys. {\bf 121}, 2877, (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid…
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
Point defects are ubiquitous in two dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite length grain boundaries (scars) are…
The analysis of defects and defect dynamics in crystalline materials is important for fundamental science and for a wide range of applied engineering. With increasing system size the analysis of molecular-dynamics simulation data becomes…
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical import. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…