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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Function space requirements for the single-electron functions within the multiparticle Schroedinger equation

Our previously described method to approximate the many-electron wavefunction in the multiparticle Schroedinger equation reduces this problem to operations on many single-electron functions. In this work, we analyze these operations to determine which function spaces are appropriate for various intermediate functions in order to bound the output. This knowledge then allows us to choose the function spaces in which to control the error of a numerical method for single-electron functions. We find that an efficient choice is to maintain the single-electron functions in L{sup 2} Intersection L{sup 4}, the product of these functions in L{sup 1} Intersection L{sup 2}, the Poisson kernel applied to the product in L{sup 4}, a function times the Poisson kernel applied to the product in L{sup 2}, and the nuclear potential times a function in L{sup 4/3}. Due to the integral operator formulation, we do not require differentiability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Lie–Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie–Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie–Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie–Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Data-based modeling↗
DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗
NASA NTRS1986

Confidence limits for small numbers of events in astrophysical data

The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations. Convenient tables and approximate formulae are here presented for confidence limits which are based on such Poisson and binomial statistics. The limits in the tables are given for all confidence levels commonly used in astrophysics.

Gehrels, N.↗
DOE OSTI2018

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals

We demonstrate the efficacy of wave-interference-based light trapping and carrier transport in parabolic-pore photonic-crystal, thin-crystalline silicon (c -Si) solar cells to achieve above 29% power conversion efficiencies. Using a rigorous solution of Maxwell’s equations through a standard finite-difference time domain scheme, we optimize the design of the vertical-parabolic-pore photonic crystal (PhC) on a 10 μm -thick (c -Si) solar cell to obtain a maximum achievable photocurrent density (MAPD) of 40.6 mA/cm 2 beyond the ray-optical, Lambertian light-trapping limit. For a slanted-parabolic-pore PhC that breaks x-y symmetry, improved light trapping occurs due to better coupling into parallel-to-interface refraction modes. We achieve the optimum MAPD of 41.6 mA/cm 2 for a tilt angle of 10° with respect to the vertical axis of the pores. This MAPD is further improved to 41.72 mA/cm 2 by introducing a 75-nm SiO 2 antireflective coating on top of the solar cell. We use this MAPD and the associated charge-carrier generation profile as input for a numerical solution of Poisson’s equation coupled with semiconductor drift-diffusion equations using a Shockley-Read-Hall and Auger recombination model. Using experimentally achieved surface recombination velocities of 10 cm/s, we identify semiconductor doping profiles that yield power conversion efficiencies over 29%. Practical considerations of additional upper-contact losses suggest efficiencies close to 28%. This improvement beyond the current world record is largely due to an open-circuit voltage approaching 0.8 V enabled by reduced bulk recombination in our thin silicon architecture while maintaining a high short-circuit current through wave-interference-based light trapping.

14 SOLAR ENERGY↗
DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗
DOE OSTI2021

Beyond Schrödinger-Poisson: nonrelativistic effective field theory for scalar dark matter

Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schrödinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out ‘fast modes’ and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Kernel-Correlated Levy Field Driven Forward Rate and Application to Derivative Pricing

We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Compound Poisson Law for Hitting Times to Periodic Orbits in Two-Dimensional Hyperbolic Systems

We show that a compound Poisson distribution holds for scaled exceedances of observables ϕ uniquely maximized at a periodic point ζ in a variety of two-dimensional hyperbolic dynamical systems with singularities (M,T,μ), including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form ϕ(z)=−ln d(z,ζ) where d is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index θ. We calculate θ in terms of the derivative of the map T. Furthermore if we define M{sub n}=max{ϕ,…,ϕ∘T"n} and u{sub n}(τ) by lim{sub n→∞}nμ(ϕ>u{sub n}(τ))=τ the maximal process satisfies an extreme value law of form μ(M{sub n}≤u{sub n})=e{sup −θτ}. These results generalize to a broader class of functions maximized at ζ, though the formulas regarding the parameters in the distribution need to be modified.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On the Magnetic Shield for a Vlasov–Poisson Plasma

We study the screening of a bounded body Γ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of Γ. The charged wind is modeled by a Vlasov–Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of Γ. We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Modeling of Dual Gate Material Hetero-dielectric Strained PNPN TFET for Improved ON Current

The tunnel field effect transistor (TFET) is considered to be a promising alternative device for future low-power VLSI circuits due to its steep subthreshold slope, low leakage current and its efficient performance at low supply voltage. However, the main challenging issue associated with realizing TFET for wide scale applications is its low ON current. To overcome this, a dual gate material with the concept of dielectric engineering has been incorporated into conventional TFET structure to tune the tunneling width at source–channel interface allowing significant flow of carriers. In addition to this, N+ pocket is implanted at source–channel junction of the proposed structure and the effect of strain is added for exploring the performance of the model in nanoscale regime. All these added features upgrade the device characteristics leading to higher ON current, low leakage and low threshold voltage. The present work derives the surface potential, electric field expression and drain current by solving 2D Poisson’s equation at different boundary conditions. A comparative analysis of proposed model with conventional TFET has been done to establish the superiority of the proposed structure. All analytical results have been compared with the results obtained in SILVACO ATLAS device simulator to establish the accuracy of the derived analytical model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Analytical Modeling of Triple-Metal Hetero-Dielectric DG SON TFET

In this paper, a 2-D analytical model of triple-metal hetero-dielectric DG TFET is presented by combining the concepts of triple material gate engineering and hetero-dielectric engineering. Three metals with different work functions are used as both front- and back gate electrodes to modulate the barrier at source/channel and channel/drain interface. In addition to this, front gate dielectric consists of high-K HfO{sub 2} at source end and low-K SiO{sub 2} at drain side, whereas back gate dielectric is replaced by air to further improve the ON current of the device. Surface potential and electric field of the proposed device are formulated solving 2-D Poisson’s equation and Young’s approximation. Based on this electric field expression, tunneling current is obtained by using Kane’s model. Several device parameters are varied to examine the behavior of the proposed device. The analytical model is validated with TCAD simulation results for proving the accuracy of our proposed model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Exploring the Short-Channel Characteristics of Asymmetric Junctionless Double-Gate Silicon-on-Nothing MOSFET

This paper presents an analytical model of an asymmetric junctionless double-gate (asymmetric DGJL) silicon-on-nothing metal-oxide-semiconductor field-effect transistor (MOSFET). Solving the 2-D Poisson’s equation, the expressions for center potential and threshold voltage are calculated. In addition, the response of the device toward the various short-channel effects like hot carrier effect, drain-induced barrier lowering and threshold voltage roll-off has also been examined along with subthreshold swing and drain current characteristics. Performance analysis of the present model is also demonstrated by comparing its short-channel behavior with conventional DGJL MOSFET. The effect of variation of the device features due to the variation of device parameters is also studied. The simulated results obtained using 2D device simulator, namely ATLAS, are in good agreement with the analytical results, hence validating our derived model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

In this study, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as , where is the number of grid points. The cost of the 3D spectral solver scales as , where is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Computer Science↗
DOE OSTI2016

A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids

A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell-centered, conservative, finite-volume method, it is applicable to any flow model in which one can isolate a pressure equation. Herein, we only discuss single and two-phase incompressible models. Compressible flow, e.g., as modeled by the black-oil equations, is discussed in a separate paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

An electrostatic Particle-In-Cell code on multi-block structured meshes

We present an electrostatic Particle-In-Cell (PIC) code on multi-block, locally structured, curvilinear meshes called Curvilinear PIC (CPIC). Multi-block meshes are essential to capture complex geometries accurately and with good mesh quality, something that would not be possible with single-block structured meshes that are often used in PIC and for which CPIC was initially developed. In spite of the structured nature of the individual blocks, multi-block meshes resemble unstructured meshes in a global sense and introduce several new challenges, such as the presence of discontinuities in the mesh properties and coordinate orientation changes across adjacent blocks, and polyjunction points where an arbitrary number of blocks meet. In CPIC, these challenges have been met by an approach that features: (1) a curvilinear formulation of the PIC method: each mesh block is mapped from the physical space, where the mesh is curvilinear and arbitrarily distorted, to the logical space, where the mesh is uniform and Cartesian on the unit cube; (2) a mimetic discretization of Poisson's equation suitable for multi-block meshes; and (3) a hybrid (logical-space position/physical-space velocity), asynchronous particle mover that mitigates the performance degradation created by the necessity to track particles as they move across blocks. The numerical accuracy of CPIC was verified using two standard plasma–material interaction tests, which demonstrate good agreement with the corresponding analytic solutions. And compared to PIC codes on unstructured meshes, which have also been used for their flexibility in handling complex geometries but whose performance suffers from issues associated with data locality and indirect data access patterns, PIC codes on multi-block structured meshes may offer the best compromise for capturing complex geometries while also maintaining solution accuracy and computational efficiency.

36 MATERIALS SCIENCE↗