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At least 1,549 records · Page 86

All-quad meshing without cleanup

Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.

97 MATHEMATICS AND COMPUTING↗

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

Fractional Operators Applied to Geophysical Electromagnetics

A growing body of applied mathematics literature in recent years has focused on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is presumed attributable to long–range correlations of material properties within an inherently complex, and in some cases self-similar, conducting medium. Rather than considering an exquisitely discretized (and computationally intractable) representation of the medium, the complex and spatially correlated heterogeneity is represented through reformulation of the governing equation for the relevant transport physics such that its coefficients are, instead, smooth but paired with fractional–order space derivatives. Here we apply these concepts to the scalar Helmholtz equation and its use in electromagnetic interrogation of Earth’s interior through the magnetotelluric method. We outline a practical algorithm for solving the Helmholtz equation using spectral methods coupled with finite element discretizations. Execution of this algorithm for the magnetotelluric problem reveals several interesting features observable in field data: long–range correlation of the predicted electromagnetic fields; a power–law relationship between the squared impedance amplitude and squared wavenumber whose slope is a function of the fractional exponent within the governing Helmholtz equation; and, a non–constant apparent resistivity spectrum whose variability arises solely from the fractional exponent. In geologic settings characterized by self–similarity (e.g. fracture systems; thick and richly–textured sedimentary sequences, etc.) we posit that these diagnostics are useful for geologic characterization of features far below the typical resolution limit of electromagnetic methods in geophysics.

58 GEOSCIENCES↗

Hierarchical Model-Free Transactive Control of Building Loads to Support Grid Services

Residential buildings consume 4.4 quads of electricity annually, approximately 37% of the total electricity consumption in the United States. This represents a vast resource that can be used for demand management and other ancillary services. This project aims to develop a robust, scalable hierarchical transactional control mechanism incorporating elements of model-free control (MFC) and game theory to harness buildings to provide ancillary services to the grid. This approach is being taken to address the challenges of incorporating traditional transactional control schemes into existing buildings. The challenges include small individual building sizes requiring aggregation of many buildings, unpredictable energy usage that makes model identification difficult, and satisfying the sensitive occupant comfort constraints. In the proposed approach, by separating the control mechanism into two layers above and below the load aggregator, MFC can be used below the aggregator to modulate flexible building loads in response to pricing signals with guaranteed performance. This allows the burden of identifying an accurate model of the system to be shifted to the above-aggregator layer, where fluctuations in individual building usage have less impact on predicted building system behavior. Game theory concepts can then be used to determine pricing curves and control signals among regional aggregators. Managing this control in a game-theoretic approach will allow us to build in financial incentives that increase customer engagement. Additionally, the usage of MFC necessitates less burdensome computational and communication requirements, thus, it is easily deployable on small, embedded devices. In a broader sense, developing a strategy capable of effectively incorporating residential and small commercial buildings will allow greater throughput of existing and emerging grid services in addition to future transactive energy grid management methods. Using MFC within a hierarchical control architecture will allow the shifting of existing forecasting challenges to an aggregate level, where dynamics are slower and more predictable. This will enable a smooth interface between the grid services requests of utilities and the reliable control required by participating buildings. MFC, which supports distributed control architecture, permits a scalable solution that can be deployed to neighborhood-size systems as well as individual buildings. This project focuses on three objectives: (1) developing the mathematical framework, algorithm toolkit, and software toolset of the two-layer transactive control testbed; (2) developing a scalable solution for application over many residential and small-size commercial buildings with sparse distributed communication; and (3) field testing and implementation on hardware of the control strategies developed in the previous two objectives. The research and development activities are focused and designed to be impactful within the relevant 2025 targets timeframe. An open-source control framework for exploiting variability and dispatchability of building loads will be delivered as the outcome of the project. This capability enables greater participation of loads in electricity markets and ancillary services that are both useful for the utility and financially beneficial for building owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Computerized processing of data from Interkosmos-7 and Interkosmos-8 satellite experiments

Computerized data processing problems are analyzed using telemetry data received from Intercosmos-7 and Intercosmos-8 satellites. Problems related to the restoration of measurement data in the form of piecewise continuous and smooth calibrated functions of time and problems encountered in the scientific interpretation of the experimental results are considered. Curve smoothing is discussed in the case of distinct assignments of calibration levels, synchronization, and synchronization checks over time. A proposal is presented for checking a piecewise linear function providing a simple method for the elimination of isolated values due to channel failures and the separation of individual intervals.

Pfau, H.↗

Analysis of general-aviation accidents using ATC radar records

It is pointed out that general aviation aircraft usually do not carry flight recorders, and in accident investigations the only available data may come from the Air Traffic Control (ATC) records. A description is presented of a technique for deriving time-histories of aircraft motions from ATC radar records. The employed procedure involves a smoothing of the raw radar data. The smoothed results, in combination with other available information (meteorological data and aircraft aerodynamic data) are used to derive the expanded set of motion time-histories. Applications of the considered analytical methods are related to different types of aircraft, such as light piston-props, executive jets, and commuter turboprops, as well as different accident situations, such as takeoff, climb-out, icing, and deep stall.

Wingrove, R. C.↗

Completely monotone regression estimates of software failure rates

A method for estimating the present failure rate of a program is presented. A crude nonparameter estimate of the failure rate function is obtained from past failure times. This estimate is then smoothed by fitting a completely monotonic function, which is the solution of a quadratic programming problem. The value of the smoothed function at present time is used as the estimate of present failure rate. Results of a Monte Carlo study of performance are given.

Miller, D. R.↗

Sectioning Coated Specimens Without Edge Rounding

New method devised for preparation of cross sections of coated specimens for scanning electron microscopy or energy-dispersive analysis without rounding edges of coatings. After cutting and polishing, specimen section remains smooth and flat so it can be examined under high magnification out to edge of coating. Sectioned blade first electroplated with hard nickel 0.003 in., then encapsulated in two layers of material: soft conductive material at bottom and 0.25 in. of hard diallyl phthalate at top. Nickel plate provides electrical path from surface of section to conductive material below.

Mckechnie, Timothy N.↗

Analysis of flight-measured boundary-layer stability and transition data

The paper concentrates on the computational analysis of both the Tollmien-Schlichting and crossflow-type instabilities using the results of a boundary-layer transition flight experiment on a smooth swept test surface. In addition, the effect of nonadiabatic wall conditions is analyzed using the measured surface temperature distribution on the boundary-layer development and stability growth. The computational methods utilized in analyzing the boundary-layer stability characteristics are discussed: one approach analyzes the Tollmien-Schlichting and crossflow instabilities independently with maximum Tollmien-Schlichting n-factors near nine and maximum crossflow n-factors near six at transition onset for separate cases, while the second approach analyzes the instabilities for maximum growth regardless of the type. As much as a 27-percent increase in n-factor is found at transition onset due to an increased Tollmien-Schlichting instability.

Obara, Clifford J.↗

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Day, Brad A.↗

Improving the reconstruction of the velocity potential and primordial density fluctuations by choice of smoothing windows

Recently considerable attention has been focused on improving algorithms for restoring primordial density fluctuations in the universe or investigating large-scale velocity fields by going to higher order approximations relating nonlinear states to their initial conditions. An alternative approach is to investigate the use of alternative smoothing windows within the context of first-order approximations. I present evidence that the universally used Gaussian smoothing window is far from optimal. A sharp truncation P(k) = 0 for k greater than k(c) leads to a much more direct connection to initial conditions for either 'Gaussianization' methods or use of the Zel'dovich approximation, as discussed in the text.

Melott, Adrian L.↗

Registration of video sequences from multiple sensors

In this paper, we describe an approach for registration of video sequences from a suite of multiple sensors including television, infrared and radar. Video sequences generated by these sensors may contain abrupt changes in local contrast and inconsistent image features, which pose additional difficulties for registration. Our approach to registration addresses the difficulties caused by using multiple sensors. We use a representation for registration that is invariant to local contrast changes, followed by smoothing of the resulting error measure used for registration, for robust estimation of registration parameters. We use an iterative procedure to reduce the effect of inconsistent features. Finally, we describe a method that uses same-sensor registration to aide in performing registration of sequences of video frames across multiple sensors.

Sharma, Ravi K.↗

Effective Area of the AXAF High Resolution Camera (HRC)

The AXAF High-Resolution Camera (HRC) was calibrated at NASA MSFC's X-Ray Calibration Facility (XRCF) during 1997 March and April. We have undertaken an analysis of the HRC effective area using all data presently available from the XRCF. We discuss our spectral fitting of the beam-normalization detectors (BNDs), our method of removing higher order contamination lines present in the spectra, and corrections for beam non-uniformities. We apply a model of photon absorption depth in order to fit a smooth curve to the quantum efficiency of the detector. This is then combined with the most recent model of the AXAF High-Resolution Mirror Assembly (HRMA) to determine the ensemble effective area versus energy for the HRC. We also address future goals and concerns.

Patnaude, Daniel↗

SPHERICAL HARMONIC ANALYSES OF INTENSITY MAPPING POWER SPECTRA

Intensity mapping is a promising technique for surveying the large-scale structure of our universe from z = 0 to z ∼ 150, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of our cosmic timeline. Examples of targeted lines include the 21 cm hyperfine transition of neutral hydrogen, rotational lines of carbon monoxide, and fine-structure lines of singly ionized carbon. Recent efforts have focused on detections of the power spectrum of spatial fluctuations, but have been hindered by systematics such as foreground contamination. This has motivated the decomposition of data into Fourier modes perpendicular and parallel to the line of sight, which has been shown to be a particularly powerful way to diagnose systematics. However, such a method is well-defined only in the limit of a narrow-field, flat-sky approximation. This limits the sensitivity of intensity mapping experiments, as it means that wide surveys must be separately analyzed as a patchwork of smaller fields. In this paper, we develop a framework for analyzing intensity mapping data in a spherical Fourier–Bessel basis, which incorporates curved sky effects without difficulty. We use our framework to generalize a number of techniques in intensity mapping data analysis from the flat sky to the curved sky. These include visibility-based estimators for the power spectrum, treatments of interloper lines, and the “foreground wedge” signature of spectrally smooth foregrounds.

79 ASTRONOMY AND ASTROPHYSICS↗

Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems

The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable. The analysis makes use of a nonlocal vector calculus that allows one to define a variational formulation of the nonlocal problem. In a manner analogous to the local partial differential equations counterpart, we demonstrate, for certain kernel functions, the existence of at least one optimal solution in the space of admissible parameters. We introduce a Galerkin finite element discretization of the optimal control problem and derive a priori error estimates for the approximate state and control variables. Using one-dimensional numerical experiments, we illustrate the theoretical results and show that by using nonlocal models it is possible to estimate non-smooth and discontinuous diffusion parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗

Collective neutrino oscillations in turbulent backgrounds

Using a Kolmogorov turbulence model, we investigate the effects of fluctuations in matter and neutrino density in the region near a supernova core on the flavor oscillations of neutrinos emitted in the core collapse in a single-angle, two-flavor approximation. Deviation from a smooth background neutrino density causes significant alterations in the final flavor state of the neutrino ensemble after 400 km, but even very large fluctuations in the matter density do not strongly affect the state of the neutrinos after the collective phase. In both cases, there is a strong effect on the neutrino flavor evolution at intermediate radii, with the flavor evolution becoming much more chaotic. The effect of fluctuations also depends strongly on the initial neutrino spectra. We conclude that the true neutrino fluxes arriving at Earth from core-collapse supernova could differ considerably from predictions of neutrino fluxes based on approximate models with smoothly decreasing matter and neutrino densities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗