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At least 163 records · Page 9

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Edge Based Viscous Method for Node-Centered Formulations

This paper presents a novel, efficient, conservative, edge-based method for evaluation of mean flow viscous fluxes and turbulence-model diffusion terms of the Reynolds-averaged Navier-Stokes equations on tetrahedral grids. The new method is implemented in a practical, node-centered, finite-volume computational fluid dynamics solver. The baseline finite-volume scheme that is equivalent to a second-order accurate finite-element Galerkin approximation of viscous stresses is reformulated. The order of operations to compute the cell-based Green-Gauss gradients is changed to combine the operations by edge, which leads to an equivalent formulation on tetrahedral grids, improves efficiency, and preserves the compact discretization stencil based on the nearest neighbors. The computational results presented in this paper verify the implementation of this edge-based method by comparing its accuracy and iterative convergence with those of the well verified and validated baseline formulation. Efficiency gains for residual and Jacobian evaluations result in significant reduction of time to solution. This novel edge-based formulation on tetrahedra can be seamlessly combined with the baseline formulation on cells of other types for computing solutions on mixed-element grids.

Edge Based↗

Using Near-Infrared-Enabled Digital Repeat Photography to Track Structural and Physiological Phenology in Mediterranean Tree–Grass Ecosystems

Tree–grass ecosystems are widely distributed. However, their phenology has not yet been fully characterized. The technique of repeated digital photographs for plant phenology monitoring (hereafter referred as PhenoCam) provide opportunities for long-term monitoring of plant phenology, and extracting phenological transition dates (PTDs, e.g., start of the growing season). Here, we aim to evaluate the utility of near-infrared-enabled PhenoCam for monitoring the phenology of structure (i.e., greenness) and physiology (i.e., gross primary productivity—GPP) at four tree–grass Mediterranean sites. We computed four vegetation indexes (VIs) from PhenoCams: (1) green chromatic coordinates (GCC), (2) normalized difference vegetation index (CamNDVI), (3) near-infrared reflectance of vegetation index (CamNIRv), and (4) ratio vegetation index (CamRVI). GPP is derived from eddy covariance flux tower measurement. Then, we extracted PTDs and their uncertainty from different VIs and GPP. The consistency between structural (VIs) and physiological (GPP) phenology was then evaluated. CamNIRv is best at representing the PTDs of GPP during the Green-up period, while CamNDVI is best during the Dry-down period. Moreover, CamNIRv outperforms the other VIs in tracking growing season length of GPP. In summary, the results show it is promising to track structural and physiology phenology of seasonally dry Mediterranean ecosystem using near-infrared-enabled PhenoCam. We suggest using multiple VIs to better represent the variation of GPP.

47 OTHER INSTRUMENTATION↗

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

An Infinite Domain 3D Poisson Solver Based on the Barnes-Hut Algorithm

We present a domain decomposition method for the solution of the 3D Poisson equation with infinite domain boundary conditions. The method is based on an application of the Barnes-Hut tree particle scheme adapted to gridded data. Long range interactions are computed using the first two terms in the Cartesian multipole expansion of Green’s function convoluted with the charge while short range computations are performed using Hockney’s domain doubling algorithm. A standard domain decomposition strategy requires O(N 2 ) applications of Hockney’s algorithm, where N is the number of subdomains that intersect that charge support, while in the present approach only O(Nlog 2 N) such computations suffice. The discretization scheme employed is a sixth order Mehrstellen approximation of the 3D Laplace opera tor. The method exhibits satisfactory accuracy at a substantially reduced computational cost compared to the full domain decomposition Hockney’s algorithm.

97 MATHEMATICS AND COMPUTING↗

Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods

A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.

DeBonis, James R.↗

Defects go green: using defects in nanomaterials for renewable energy and environmental sustainability

Induction of point defects in nanomaterials can bestow upon them entirely new physics or augment their pre-existing physical properties, thereby expanding their potential use in green energy technology. Predicting structure-property relationships for defects a priori is challenging, and developing methods for precise control of defect type, density, or structural distribution during synthesis is an even more formidable task. Hence, tuning the defect structure to tailor nanomaterials for enhanced device performance remains an underutilized tool in materials design. We review here the state of nanomaterial design through the lens of computational prediction of defect properties for green energy technology, and synthesis methods to control defect formation for optimal performance. We illustrate the efficacy of defect-focused approaches for refining nanomaterial physics by describing several specific applications where these techniques hold potential. Most notably, we focus on quantum dots for reabsorption-free solar windows and net-zero emission buildings, oxide cathodes for high energy density lithium-ion batteries and electric vehicles, and transition metal dichalcogenides for electrocatalytic green hydrogen production and carbon-free fuels.

14 SOLAR ENERGY↗

Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

In this work we develop EPOCH (equilibrium propagator by orthogonal polynomial chain), a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of superconductors, to capture the time evolution in large inhomogeneous systems. The EPOCH method generalizes the Chebyshev wave-packet propagation method from quantum chemistry and efficiently incorporates the Fermi-Dirac statistics that is needed for equilibrium quantum condensed matter systems. The computational cost of EPOCH scales only linearly in the system degrees of freedom, generating an extremely efficient algorithm also for very large systems. We demonstrate the power of the EPOCH method by calculating the time evolution of an excitation near a superconductor–normal metal interface in two and three dimensions, capturing transmission as well as normal and Andreev reflections.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Imaging pyrometry for most color cameras using a triple pass filter

A simple combination of the Planck blackbody emission law, optical filters, and digital image processing is demonstrated to enable most commercial color cameras (still and video) to be used as an imaging pyrometer for flames and explosions. The hardware and data processing described take advantage of the color filter array (CFA) that is deposited on the surface of the light sensor array present in most digital color cameras. In this work, a triple-pass optical filter incorporated into the camera lens allows light in three 10-nm wide bandpass regions to reach the CFA/light sensor array. These bandpass regions are centered over the maxima in the blue, green, and red transmission regions of the CFA, minimizing the spectral overlap of these regions normally present. A computer algorithm is used to retrieve the blue, green, and red image matrices from camera memory and correct for remaining spectral overlap. A second algorithm calibrates the corrected intensities to a gray body emitter of known temperature, producing a color intensity correction factor for the camera/filter system. The Wien approximation to the Planck blackbody emission law is used to construct temperature images from the three color (blue, green, red) matrices. A short pass filter set eliminates light of wavelengths longer than 750 nm, providing reasonable accuracy (±10%) for temperatures between 1200 and 6000 K. The effectiveness of this system is demonstrated by measuring the temperature of several systems for which the temperature is known.

47 OTHER INSTRUMENTATION↗

Contribution of National near Real Time MODIS Forest Maximum Percentage NDVI Change Products to the U.S. ForWarn System

This presentation reviews the development, integration, and testing of Near Real Time (NRT) MODIS forest % maximum NDVI change products resident to the USDA Forest Service (USFS) ForWarn System. ForWarn is an Early Warning System (EWS) tool for detection and tracking of regionally evident forest change, which includes the U.S. Forest Change Assessment Viewer (FCAV) (a publically available on-line geospatial data viewer for visualizing and assessing the context of this apparent forest change). NASA Stennis Space Center (SSC) is working collaboratively with the USFS, ORNL, and USGS to contribute MODIS forest change products to ForWarn. These change products compare current NDVI derived from expedited eMODIS data, to historical NDVI products derived from MODIS MOD13 data. A new suite of forest change products are computed every 8 days and posted to the ForWarn system; this includes three different forest change products computed using three different historical baselines: 1) previous year; 2) previous three years; and 3) all previous years in the MODIS record going back to 2000. The change product inputs are maximum value NDVI that are composited across a 24 day interval and refreshed every 8 days so that resulting images for the conterminous U.S. are predominantly cloud-free yet still retain temporally relevant fresh information on changes in forest canopy greenness. These forest change products are computed at the native nominal resolution of the input reflectance bands at 231.66 meters, which equates to approx 5.4 hectares or 13.3 acres per pixel. The Time Series Product Tool, a MATLAB-based software package developed at NASA SSC, is used to temporally process, fuse, reduce noise, interpolate data voids, and re-aggregate the historical NDVI into 24 day composites, and then custom MATLAB scripts are used to temporally process the eMODIS NDVIs so that they are in synch with the historical NDVI products. Prior to posting, an in-house snow mask classification product is computed for the current compositing period and integrated into the change images to account for snow related NDVI drops. The supplemental snow classification product was needed because other available QA cloud/snow mask typically underestimates snow cover. MODIS true and false color composites were also computed from eMODIS reflectance data and the true color RGBs are also posted on ForWarn?s FCAV; this data is used for assessing apparent occasional quality issues on the change products due to residual unmasked cloud cover. New forest change products are posted with typical latencies of 1-2 days after the last input eMODIS data collection date for a given 24 day compositing period.

Spruce, Joseph P.↗

Scattering from dielectric structures above impedance surfaces and resistive sheets

Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods.

Sarabandi, Kamal↗

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗

MONTE CARLO SIMULATION OF METASTABLE OXYGEN PHOTOCHEMISTRY IN COMETARY ATMOSPHERES

Cometary atmospheres are produced by the outgassing of material, mainly H{sub 2}O, CO, and CO{sub 2} from the nucleus of the comet under the energy input from the Sun. Subsequent photochemical processes lead to the production of other species generally absent from the nucleus, such as OH. Although all comets are different, they all have a highly rarefied atmosphere, which is an ideal environment for nonthermal photochemical processes to take place and influence the detailed state of the atmosphere. We develop a Monte Carlo model of the coma photochemistry. We compute the energy distribution functions (EDF) of the metastable O({sup 1}D) and O({sup 1}S) species and obtain the red (630 nm) and green (557.7 nm) spectral line shapes of the full coma, consistent with the computed EDFs and the expansion velocity. We show that both species have a severely non-Maxwellian EDF, that results in broad spectral lines and the suprathermal broadening dominates due to the expansion motion. We apply our model to the atmosphere of comet C/1996 B2 (Hyakutake) and 103P/Hartley 2. The computed width of the green line, expressed in terms of speed, is lower than that of the red line. This result is comparable to previous theoretical analyses, but in disagreement with observations. We explain that the spectral line shape does not only depend on the exothermicity of the photochemical production mechanisms, but also on thermalization, due to elastic collisions, reducing the width of the emission line coming from the O({sup 1}D) level, which has a longer lifetime.

79 ASTRONOMY AND ASTROPHYSICS↗

Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico

We construct a climatology of Lagrangian coherent structures (LCSs)—the concealed skeleton that shapes transport—with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy–Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. The cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, showing that a climatological velocity can preserve meaningful transport information. The quasi-steady transport patterns revealed by the cLCSs agree well with aspects of the GoM circulation described in several previous observational and numerical studies. For example, the cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact are regions of maximal attraction. We also show that cLCSs are remarkably accurate at identifying transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus it is shown that computing cLCSs is an efficient and meaningful way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.

54 ENVIRONMENTAL SCIENCES↗