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The DFT/vdW-QHO-WF method, recently developed to include the van der Waals (vdW) interactions in approximated Density Functional Theory (DFT) by combining the Quantum Harmonic Oscillator model with the Maximally Localized Wannier Function…
Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend a choice of unitary transform known as a gauge…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of…
The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…
Localized Wannier functions provide an efficient and intuitive framework to compute electric polarization from first-principles. They can also be used to represent the electronic systems at fixed electric field and to determine dielectric…
We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green's function for the scalar wave equation). With $M$ points in the spatial discretization and $N_t$…
In this note we prove the estimate $M^{\sharp}_{0,s}(Tf)(x) \le c\,M_\gamma f(x)$ for general fractional type operators $T$, where $M^{\sharp}_{0,s}$ is the local sharp maximal function and $M_\gamma$ the fractional maximal function, as…
Localized solutions are known to arise in a variety of singularly perturbed reaction-diffusion systems. The Gierer-Meinhardt (GM) system is one such example and has been the focus of numerous rigorous and formal studies. A more recent focus…
Pulay terms arise in the Hellman-Feynman forces in electronic structure calculations when one employs a basis set made of localized orbitals that move with their host atoms. If the total energy of the system depends on a subspace population…
The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different…
A new implementation is proposed for including van der Waals interactions in Density Functional Theory using the Maximally-Localized Wannier functions. With respect to the previous DFT/vdW-WF method, the present DFT/vdW-WF2 approach, which…
Maximally localized Wannier functions are widely used in electronic structure theory for analyses of bonding, electric polarization, orbital magnetization, and for interpolation. The state of the art method for their construction is based…
Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…
Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for partial differential equations (PDEs) work in general geometries, and can have exponential convergence properties for smooth solution…
The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…
We propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector's Positive-Operator-Value-Measure (POVM) elements. This method extends the works of S. Wallentowitz and Vogel [Phys. Rev.…