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We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…
Certain point defects in solids can efficiently be used as qubits for applications in quantum technology. They have spin states that are initializable, readable, robust, and can be manipulated optically. New theoretical methods are needed…
Classical effective potentials are indispensable for any large-scale atomistic simulations, and the relevance of simulation results crucially depends on the quality of the potentials used. For complex alloys like quasicrystals, however,…
Optimal elemental configuration search in crystal is a crucial task to discovering industrially important materials such as lithium-ion battery cathodes. In this paper we present application of quantum approximate optimization algorithm,…
Much work has gone into the construction of quasicontinuum energies that reduce the coupling error along the interface between atomistic and continuum regions. The largest consistency errors are typically pointwise $O(\frac{1}{\eps})$…
In this paper we construct energy based numerical methods free of ghost forces in three dimensional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
The present review includes the description of theoretical methods for the investigations of the spectra of hydrogen-like systems. Various versions of the quasipotential approach and the method of the effective Dirac equation are…
The quasi-nonlocal quasicontinuum method (QNL) is a consistent hybrid coupling method for atomistic and continuum models. Embedded atom models are empirical many-body potentials that are widely used for FCC metals such as copper and…
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…
In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…
In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under…
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…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations…
Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modelling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here we extend the theoretical framework of…
Ab initio methods based on the second-order and higher connected moments, or cumulants, of a reference function have seen limited use in the determination of correlation energies of chemical systems throughout the years. Moment-based…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
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…
Valence excitation spectra are computed for all deep-center silicon-vacancy defect types in 3C, 4H, and 6H silicon carbide (SiC) and comparisons are made with literature photoluminescence measurements. Nuclear geometries surrounding the…