Related papers: Gaussian Beam Methods for the Dirac Equation in th…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
We study spectral properties of a one-dimensional Dirac equation with various disorder. We use replicas to calculate the exact density of state and typical localization length of a Dirac particle in several cases. We show that they can be…
A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…
We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
The SEparator for CApture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
Gaussian beams are often used in optical systems. The fundamental Gaussian TEM00 mode is the most common of the Gaussian modes present in various optical devices, systems and equipment. Within an optical system, it is common that this…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
Geometrical interpretation on U(1) gage theory of Dirac monopole, introduced here from the line integral\cite{Brandt} form of vector potentials, shows the gauge representation be multi-valued. In this paper, we construct Euclidean form of…
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic…
Theoretical spin properties of the Kapitza-Dirac effect beyond the plane-wave description are not known in detail. We develop a method for computing electron diffraction of the two-photon Kapitza-Dirac effect in a two-dimensional Gaussian…
The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second-order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts…
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…