Related papers: Hybrid Basis Scheme for computing Electrostatic fi…
Most non-relativistic interacting quantum many-body systems, such as atomic and molecular ensembles or materials, are naturally described in terms of continuous-space Hamiltonians. The simulation of their ground-state properties on digital…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
The implementation of quantum entangling gates between qubits is essential to achieve scalable quantum computation. Here, we propose a robust scheme to realize an entangling gate for distant solid-state spins via a mechanical oscillator in…
The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$…
We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes…
Multi-stage cathodes are promising candidates for field emission due to the multiplicative effect in local field predicted by the Schottky conjecture and its recent corrected counterpart [J. Vac. Sci. Technol. B 38, 023208 (2020)]. Due to…
Hybrid-VPIC is an extension of the open-source high-performance particle-in-cell (PIC) code VPIC incorporating hybrid kinetic ion/fluid electron solvers. This paper describes the models that are available in the code and gives an overview…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface…
Many high power electronic devices operate in a regime where the current they draw is limited by the self-fields of the particles. This space-charge-limited current poses particular challenges for numerical modeling where common techniques…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
We study isotropic Gaussian random fields on the high-dimensional sphere with an added deterministic linear term, also known as mixed p-spin Hamiltonians with external field. We prove that if the external field is sufficiently strong, then…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
We present two methods for solving the electrostatics of point charges and multipoles on the surface of a sphere, \textit{i.e.} in the space $\mathcal{S}_{2}$, with applications to numerical simulations of two-dimensional polar fluids. In…
We analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface. In order to accommodate the homogeneous essential boundary condition along the surface boundary, scaled radial basis functions…
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…