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At least 1,567 records · Page 87

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↗

Smoothing of orbital tracking data: Mission planning, mission analysis and software formulation

The problem created by the presence of wild or outlying data points among orbital tracking data, is addressed. Consideration is given to the effects of such outliers on the orbit determination process, and methods for minimizing or even eliminating these effects are proposed. Some preliminary efforts implementing these new methods are described, and the results thus far obtained are summarized. Based on these ideas and results, recommendations are made for future investigation.

Vedder, J. D.↗

Grid generation using coarse, smooth finite elements

Grid quality solutions of a wide variety of equations can be generated to fit reasonable functional boundary conditions in two dimensions using very coarse rectangular finite elements. Some wavy operators (with no natural variational expression) were tried in order to demonstrate the method's versatility.

Dickson, L. J.↗

A grid spacing control technique for algebraic grid generation methods

A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.

Smith, R. E.↗

A novel partitioning method for block-structured adaptive meshes

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

97 MATHEMATICS AND COMPUTING↗

Visual exploration of high-dimensional data through subspace analysis and dynamic projections

Here, we introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.

97 MATHEMATICS AND COMPUTING↗

TU-F-CAMPUS-J-04: Evaluation of Metal Artifact Reduction Technique for the Radiation Therapy Planning

Purpose: To evaluate the feasibility of using a metal artifact reduction technique in depleting metal artifact and its application in improving dose calculation in External Radiation Therapy Planning. Methods: CIRS electron density phantom was scanned with and without steel drill bits placed in some plug holes. Meta artifact reduction software with Metal Deletion Technique (MDT) was used to remove metal artifacts for scanned image with metal. Hounsfield units of electron density plugs from artifact free reference image and MDT processed images were compared. To test the dose calculation improvement after the MDT processed images, clinically approved head and neck plan with manual dental artifact correction was tested. Patient images were exported and processed with MDT and plan was recalculated with new MDT image without manual correction. Dose profiles near the metal artifacts were compared. Results: The MDT used in this study effectively reduced the metal artifact caused by beam hardening and scatter. The windmill around the metal drill was greatly improved with smooth rounded view. Difference of the mean HU in each density plug between reference and MDT images were less than 10 HU in most of the plugs. Dose difference between original plan and MDT images were minimal. Conclusion: Most metal artifact reduction methods were developed for diagnostic improvement purpose. Hence Hounsfield unit accuracy was not rigorously tested before. In our test, MDT effectively eliminated metal artifacts with good HU reproduciblity. However, it can introduce new mild artifacts so the MDT images should be checked with original images.

60 APPLIED LIFE SCIENCES↗

Improving solve time of aggregation-based adaptive AMG

In this paper, we propose improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.

97 MATHEMATICS AND COMPUTING↗

A special issue on the RCPs

This paper provides an editors' introduction to the special issue of Climatic Change on the RCPs. Scenarios form a crucial element in climate change research. They allow researchers to explore the long-term consequences of decisions today, while taking account of the inertia in both the socio-economic and physical system. Scenarios also form an integrating element among the different research disciplines of those studying climate change, such as economists, technology experts, climate researchers, atmospheric chemists and geologists. In 2007, the IPCC requested the scientific community to develop a new set of scenarios, as the existing scenarios (published in the Special Report on Emissions Scenarios, (Nakicenovic and Swart 2000), and called the 'SRES scenarios') needed to be updated and expanded in scope (see Moss et al. (2010) for a detailed discussion). Researchers from different disciplines worked together to develop a process to craft these new scenarios, as summarized by Moss, et al. (2010). The Integrated Assessment Modeling Consortium (IAMC), founded in response to the IPCC call, played a key role in this process.1 The scenario development process aims to develop a set of new scenarios that facilitate integrated analysis of climate change across the main scientific communities. The process comprises 3 main phases: (1) an initial phase, developing a set of pathways for emissions, concentrations and radiative forcing, (2) a parallel phase, comprising both the development of new socio-economic storylines and climate model projections, and (3) an integration phase, combining the information from the first phases into holistic mitigation, impacts and vulnerability assessments. The pathways developed in the first phase were called 'Representative Concentration Pathways (RCPs)'. They play an important role in providing input for prospective climate model experiments, including both the decadal and long-term projections of climate change. The RCPs also provide an important reference point for new research within the integrated assessment modeling (IAM) community by standardizing on a common set of year-2100 conditions, and exploring alternative pathways and policies that could produce these outcomes. By design, the RCPs, as a set, cover the range of radiative forcing levels examined in the open literature and contain relevant information for climate model runs. This Special Issue documents the main assumptions and characteristics of the RCPs, and, in particular, the various steps that were involved in their development. A number of collaborative activities were initiated and finalized during the last 2-3 years to develop the RCPs. This required the cooperation of researchers from various disciplines involved in climate research, including emission experts, climate modelers, atmospheric chemistry modelers, land use modelers and experts involved in integrated assessment. The four RCPs together reflect the range of year-2100 radiative forcing values found in the literature, i.e. from 2.6 to 8.5 W/m{sup 2}. The papers in this Special Issue describe the individual RCPs, but also the various integrative steps that were necessary within the RCP development process to provide a harmonized set of pathways, that show a smooth transition from the past and extend far into the future for very long-term experiments. Important outcomes of this process included, for instance, the development of new emission inventories, new methods for the harmonization of spatial land use patterns, as well as extensions of the RCP trends beyond 2100. They briefly discuss the content of the individual papers.

54 ENVIRONMENTAL SCIENCES↗

A WELL-POSED KELVIN-HELMHOLTZ INSTABILITY TEST AND COMPARISON

Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability (KHI) in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two-dimensional KHI. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of smoothed particle hydrodynamics (SPH). We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in SPH interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

Improved Blending-Function Algebraic Generation Of Grids

Method of algebraic generation of grids used in computing flows incorporates blending-function techniques to obtain high degree of orthogonality of each grid on its bounding surfaces and to blend grid smoothly, making it conform to all boundaries. Demonstrated in two dimensions, and applied in continuing development of software for real-time interactive generation of three-dimensional grids with color graphical displays. Software used routinely in generating grids for computing flows of practical interest.

Ching-Chung Luh, Raymond↗