FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Fast radiative transfer models for retrieval of cloud properties in the back-scattering region: application to DSCOVR-EPIC sensor

NASA Astrophysics Data System (ADS)

Molina Garcia, Victor; Sasi, Sruthy; Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego

2017-04-01

In this work, the requirements for the retrieval of cloud properties in the back-scattering region are described, and their application to the measurements taken by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) is shown. Various radiative transfer models and their linearizations are implemented, and their advantages and issues are analyzed. As radiative transfer calculations in the back-scattering region are computationally time-consuming, several acceleration techniques are also studied. The radiative transfer models analyzed include the exact Discrete Ordinate method with Matrix Exponential (DOME), the Matrix Operator method with Matrix Exponential (MOME), and the approximate asymptotic and equivalent Lambertian cloud models. To reduce the computational cost of the line-by-line (LBL) calculations, the k-distribution method, the Principal Component Analysis (PCA) and a combination of the k-distribution method plus PCA are used. The linearized radiative transfer models for retrieval of cloud properties include the Linearized Discrete Ordinate method with Matrix Exponential (LDOME), the Linearized Matrix Operator method with Matrix Exponential (LMOME) and the Forward-Adjoint Discrete Ordinate method with Matrix Exponential (FADOME). These models were applied to the EPIC oxygen-A band absorption channel at 764 nm. It is shown that the approximate asymptotic and equivalent Lambertian cloud models give inaccurate results, so an offline processor for the retrieval of cloud properties in the back-scattering region requires the use of exact models such as DOME and MOME, which behave similarly. The combination of the k-distribution method plus PCA presents similar accuracy to the LBL calculations, but it is up to 360 times faster, and the relative errors for the computed radiances are less than 1.5% compared to the results when the exact phase function is used. Finally, the linearized models studied show similar behavior, with relative errors less than 1% for the radiance derivatives, but FADOME is 2 times faster than LDOME and 2.5 times faster than LMOME.

Discrete ordinates-Monte Carlo coupling: A comparison of techniques in NERVA radiation analysis

NASA Technical Reports Server (NTRS)

Lindstrom, D. G.; Normand, E.; Wilcox, A. D.

1972-01-01

In the radiation analysis of the NERVA nuclear rocket system, two-dimensional discrete ordinates calculations are sufficient to provide detail in the pressure vessel and reactor assembly. Other parts of the system, however, require three-dimensional Monte Carlo analyses. To use these two methods in a single analysis, a means of coupling was developed whereby the results of a discrete ordinates calculation can be used to produce source data for a Monte Carlo calculation. Several techniques for producing source detail were investigated. Results of calculations on the NERVA system are compared and limitations and advantages of the coupling techniques discussed.

Introduction to the Theory of Atmospheric Radiative Transfer

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1986-01-01

The fundamental physical and mathematical principles governing the transmission of radiation through the atmosphere are presented, with emphasis on the scattering of visible and near-IR radiation. The classical two-stream, thin-atmosphere, and Eddington approximations, along with some of their offspring, are developed in detail, along with the discrete ordinates method of Chandrasekhar. The adding and doubling methods are discussed from basic principles, and references for further reading are suggested.

Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system.

PubMed

Hestenes, Kjersti; Nielsen, Kristian P; Zhao, Lu; Stamnes, Jakob J; Stamnes, Knut

2007-04-20

We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air-tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650 nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey-Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.

Comparison of discrete ordinate and Monte Carlo simulations of polarized radiative transfer in two coupled slabs with different refractive indices.

PubMed

Cohen, D; Stamnes, S; Tanikawa, T; Sommersten, E R; Stamnes, J J; Lotsberg, J K; Stamnes, K

2013-04-22

A comparison is presented of two different methods for polarized radiative transfer in coupled media consisting of two adjacent slabs with different refractive indices, each slab being a stratified medium with no change in optical properties except in the direction of stratification. One of the methods is based on solving the integro-differential radiative transfer equation for the two coupled slabs using the discrete ordinate approximation. The other method is based on probabilistic and statistical concepts and simulates the propagation of polarized light using the Monte Carlo approach. The emphasis is on non-Rayleigh scattering for particles in the Mie regime. Comparisons with benchmark results available for a slab with constant refractive index show that both methods reproduce these benchmark results when the refractive index is set to be the same in the two slabs. Computed results for test cases with coupling (different refractive indices in the two slabs) show that the two methods produce essentially identical results for identical input in terms of absorption and scattering coefficients and scattering phase matrices.

Analytic approach to photoelectron transport.

NASA Technical Reports Server (NTRS)

Stolarski, R. S.

1972-01-01

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

Shielding analyses: the rabbit vs the turtle?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Broadhead, B.L.

1996-12-31

This paper compares solutions using Monte Carlo and discrete- ordinates methods applied to two actual shielding situations in order to make some general observations concerning the efficiency and advantages/disadvantages of the two approaches. The discrete- ordinates solutions are performed using two-dimensional geometries, while the Monte Carlo approaches utilize three-dimensional geometries with both multigroup and point cross-section data.

Modeling Personalized Email Prioritization: Classification-based and Regression-based Approaches

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo S.; Yang, Y.; Carbonell, J.

2011-10-24

Email overload, even after spam filtering, presents a serious productivity challenge for busy professionals and executives. One solution is automated prioritization of incoming emails to ensure the most important are read and processed quickly, while others are processed later as/if time permits in declining priority levels. This paper presents a study of machine learning approaches to email prioritization into discrete levels, comparing ordinal regression versus classier cascades. Given the ordinal nature of discrete email priority levels, SVM ordinal regression would be expected to perform well, but surprisingly a cascade of SVM classifiers significantly outperforms ordinal regression for email prioritization. Inmore » contrast, SVM regression performs well -- better than classifiers -- on selected UCI data sets. This unexpected performance inversion is analyzed and results are presented, providing core functionality for email prioritization systems.« less

Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Norris, Edward T.; Liu, Xin, E-mail: xinliu@mst.edu; Hsieh, Jiang

Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. Themore » CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer. Conclusions: The simulation results showed that the deterministic method can be effectively used to estimate the absorbed dose in a CTDI phantom. The accuracy of the discrete ordinates method was close to that of a Monte Carlo simulation, and the primary benefit of the discrete ordinates method lies in its rapid computation speed. It is expected that further optimization of this method in routine clinical CT dose estimation will improve its accuracy and speed.« less

Flow of rarefied gases over two-dimensional bodies

NASA Technical Reports Server (NTRS)

Jeng, Duen-Ren; De Witt, Kenneth J.; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Skyshine radiation from a pressurized water reactor containment dome

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, W.H.

1986-06-01

The radiation dose rates resulting from airborne activities inside a postaccident pressurized water reactor containment are calculated by a discrete ordinates/Monte Carlo combined method. The calculated total dose rates and the skyshine component are presented as a function of distance from the containment at three different elevations for various gamma-ray source energies. The one-dimensional (ANISN code) is used to approximate the skyshine dose rates from the hemisphere dome, and the results are compared favorably to more rigorous results calculated by a three-dimensional Monte Carlo code.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

General Purpose Fortran Program for Discrete-Ordinate-Method Radiative Transfer in Scattering and Emitting Layered Media: An Update of DISORT

NASA Technical Reports Server (NTRS)

Tsay, Si-Chee; Stamnes, Knut; Wiscombe, Warren; Laszlo, Istvan; Einaudi, Franco (Technical Monitor)

2000-01-01

This update reports a state-of-the-art discrete ordinate algorithm for monochromatic unpolarized radiative transfer in non-isothermal, vertically inhomogeneous, but horizontally homogeneous media. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, and surface bidirectional reflection. The system may be driven by parallel or isotropic diffuse radiation incident at the top boundary, as well as by internal thermal sources and thermal emission from the boundaries. Radiances, fluxes, and mean intensities are returned at user-specified angles and levels. DISORT has enjoyed considerable popularity in the atmospheric science and other communities since its introduction in 1988. Several new DISORT features are described in this update: intensity correction algorithms designed to compensate for the 8-M forward-peak scaling and obtain accurate intensities even in low orders of approximation; a more general surface bidirectional reflection option; and an exponential-linear approximation of the Planck function allowing more accurate solutions in the presence of large temperature gradients. DISORT has been designed to be an exemplar of good scientific software as well as a program of intrinsic utility. An extraordinary effort has been made to make it numerically well-conditioned, error-resistant, and user-friendly, and to take advantage of robust existing software tools. A thorough test suite is provided to verify the program both against published results, and for consistency where there are no published results. This careful attention to software design has been just as important in DISORT's popularity as its powerful algorithmic content.

A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

NASA Technical Reports Server (NTRS)

Weng, Fuzhong

1992-01-01

A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.

Ordinal preference elicitation methods in health economics and health services research: using discrete choice experiments and ranking methods.

PubMed

Ali, Shehzad; Ronaldson, Sarah

2012-09-01

The predominant method of economic evaluation is cost-utility analysis, which uses cardinal preference elicitation methods, including the standard gamble and time trade-off. However, such approach is not suitable for understanding trade-offs between process attributes, non-health outcomes and health outcomes to evaluate current practices, develop new programmes and predict demand for services and products. Ordinal preference elicitation methods including discrete choice experiments and ranking methods are therefore commonly used in health economics and health service research. Cardinal methods have been criticized on the grounds of cognitive complexity, difficulty of administration, contamination by risk and preference attitudes, and potential violation of underlying assumptions. Ordinal methods have gained popularity because of reduced cognitive burden, lower degree of abstract reasoning, reduced measurement error, ease of administration and ability to use both health and non-health outcomes. The underlying assumptions of ordinal methods may be violated when respondents use cognitive shortcuts, or cannot comprehend the ordinal task or interpret attributes and levels, or use 'irrational' choice behaviour or refuse to trade-off certain attributes. CURRENT USE AND GROWING AREAS: Ordinal methods are commonly used to evaluate preference for attributes of health services, products, practices, interventions, policies and, more recently, to estimate utility weights. AREAS FOR ON-GOING RESEARCH: There is growing research on developing optimal designs, evaluating the rationalization process, using qualitative tools for developing ordinal methods, evaluating consistency with utility theory, appropriate statistical methods for analysis, generalizability of results and comparing ordinal methods against each other and with cardinal measures.

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Clouds in the atmospheres of extrasolar planets. IV. On the scattering greenhouse effect of CO2 ice particles: Numerical radiative transfer studies

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Patzer, A. B. C.; Rauer, H.

2013-09-01

Context. Owing to their wavelength-dependent absorption and scattering properties, clouds have a strong impact on the climate of planetary atmospheres. The potential greenhouse effect of CO2 ice clouds in the atmospheres of terrestrial extrasolar planets is of particular interest because it might influence the position and thus the extension of the outer boundary of the classic habitable zone around main sequence stars. Such a greenhouse effect, however, is a complicated function of the CO2 ice particles' optical properties. Aims: We study the radiative effects of CO2 ice particles obtained by different numerical treatments to solve the radiative transfer equation. To determine the effectiveness of the scattering greenhouse effect caused by CO2 ice clouds, the radiative transfer calculations are performed over the relevant wide range of particle sizes and optical depths, employing different numerical methods. Methods: We used Mie theory to calculate the optical properties of particle polydispersion. The radiative transfer calculations were done with a high-order discrete ordinate method (DISORT). Two-stream radiative transfer methods were used for comparison with previous studies. Results: The comparison between the results of a high-order discrete ordinate method and simpler two-stream approaches reveals large deviations in terms of a potential scattering efficiency of the greenhouse effect. The two-stream methods overestimate the transmitted and reflected radiation, thereby yielding a higher scattering greenhouse effect. For the particular case of a cool M-type dwarf, the CO2 ice particles show no strong effective scattering greenhouse effect by using the high-order discrete ordinate method, whereas a positive net greenhouse effect was found for the two-stream radiative transfer schemes. As a result, previous studies of the effects of CO2 ice clouds using two-stream approximations overrated the atmospheric warming caused by the scattering greenhouse effect. Consequently, the scattering greenhouse effect of CO2 ice particles seems to be less effective than previously estimated. In general, higher order radiative transfer methods are needed to describe the effects of CO2 ice clouds accurately as indicated by our numerical radiative transfer studies.

Fast and Accurate Hybrid Stream PCRTMSOLAR Radiative Transfer Model for Reflected Solar Spectrum Simulation in the Cloudy Atmosphere

NASA Technical Reports Server (NTRS)

Yang, Qiguang; Liu, Xu; Wu, Wan; Kizer, Susan; Baize, Rosemary R.

2016-01-01

A hybrid stream PCRTM-SOLAR model has been proposed for fast and accurate radiative transfer simulation. It calculates the reflected solar (RS) radiances with a fast coarse way and then, with the help of a pre-saved matrix, transforms the results to obtain the desired high accurate RS spectrum. The methodology has been demonstrated with the hybrid stream discrete ordinate (HSDO) radiative transfer (RT) model. The HSDO method calculates the monochromatic radiances using a 4-stream discrete ordinate method, where only a small number of monochromatic radiances are simulated with both 4-stream and a larger N-stream (N = 16) discrete ordinate RT algorithm. The accuracy of the obtained channel radiance is comparable to the result from N-stream moderate resolution atmospheric transmission version 5 (MODTRAN5). The root-mean-square errors are usually less than 5x10(exp -4) mW/sq cm/sr/cm. The computational speed is three to four-orders of magnitude faster than the medium speed correlated-k option MODTRAN5. This method is very efficient to simulate thousands of RS spectra under multi-layer clouds/aerosols and solar radiation conditions for climate change study and numerical weather prediction applications.

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

NASA Astrophysics Data System (ADS)

Gong, Chunye; Liu, Jie; Chi, Lihua; Huang, Haowei; Fang, Jingyue; Gong, Zhenghu

2011-07-01

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates ( Sn) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.

Application of the first collision source method to CSNS target station shielding calculation

NASA Astrophysics Data System (ADS)

Zheng, Ying; Zhang, Bin; Chen, Meng-Teng; Zhang, Liang; Cao, Bo; Chen, Yi-Xue; Yin, Wen; Liang, Tian-Jiao

2016-04-01

Ray effects are an inherent problem of the discrete ordinates method. RAY3D, a functional module of ARES, which is a discrete ordinates code system, employs a semi-analytic first collision source method to mitigate ray effects. This method decomposes the flux into uncollided and collided components, and then calculates them with an analytical method and discrete ordinates method respectively. In this article, RAY3D is validated by the Kobayashi benchmarks and applied to the neutron beamline shielding problem of China Spallation Neutron Source (CSNS) target station. The numerical results of the Kobayashi benchmarks indicate that the solutions of DONTRAN3D with RAY3D agree well with the Monte Carlo solutions. The dose rate at the end of the neutron beamline is less than 10.83 μSv/h in the CSNS target station neutron beamline shutter model. RAY3D can effectively mitigate the ray effects and obtain relatively reasonable results. Supported by Major National S&T Specific Program of Large Advanced Pressurized Water Reactor Nuclear Power Plant (2011ZX06004-007), National Natural Science Foundation of China (11505059, 11575061), and the Fundamental Research Funds for the Central Universities (13QN34).

Functional data analysis: An approach for environmental ordination and matching discrete with continuous observations

EPA Science Inventory

Investigators are frequently confronted with data sets that include both discrete observations and extended time series of environmental data that had been collected by autonomous recorders. Evaluating the relationships between these two kinds of data is challenging. A common a...

Two-dimensional HID light source radiative transfer using discrete ordinates method

NASA Astrophysics Data System (ADS)

Ghrib, Basma; Bouaoun, Mohamed; Elloumi, Hatem

2016-08-01

This paper shows the implementation of the Discrete Ordinates Method for handling radiation problems in High Intensity Discharge (HID) lamps. Therefore, we start with presenting this rigorous method for treatment of radiation transfer in a two-dimensional, axisymmetric HID lamp. Furthermore, the finite volume method is used for the spatial discretization of the Radiative Transfer Equation. The atom and electron densities were calculated using temperature profiles established by a 2D semi-implicit finite-element scheme for the solution of conservation equations relative to energy, momentum, and mass. Spectral intensities as a function of position and direction are first calculated, and then axial and radial radiative fluxes are evaluated as well as the net emission coefficient. The results are given for a HID mercury lamp on a line-by-line basis. A particular attention is paid on the 253.7 nm resonance and 546.1 nm green lines.

Verification of Three Dimensional Triangular Prismatic Discrete Ordinates Transport Code ENSEMBLE-TRIZ by Comparison with Monte Carlo Code GMVP

NASA Astrophysics Data System (ADS)

Homma, Yuto; Moriwaki, Hiroyuki; Ohki, Shigeo; Ikeda, Kazumi

2014-06-01

This paper deals with verification of three dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at beginning of cycle of an initial core and at beginning and end of cycle of equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multi-plication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity.

A Deep Penetration Problem Calculation Using AETIUS:An Easy Modeling Discrete Ordinates Transport Code UsIng Unstructured Tetrahedral Mesh, Shared Memory Parallel

NASA Astrophysics Data System (ADS)

KIM, Jong Woon; LEE, Young-Ouk

2017-09-01

As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

The effect of multiple scattering on the validity of the Beer-Lambert law is discussed for a wide range of particle-size parameters and optical depths. To predict the amount of received radiant power, appropriate correction terms are introduced. For particles larger than or comparable to the wavelength of radiation, the small-angle approximation is adequate; whereas for small densely packed particles, the diffusion theory is advantageously employed. These two approaches are used in the context of the problem of laser-beam propagation in a dense aerosol medium. In addition, preliminary results obtained by using a two-dimensional finite-element discrete-ordinates transport code are described. Multiple-scatteringmore » effects for laser propagation in fog, cloud, rain, and aerosol cloud are modeled.« less

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tominaga, Nozomu; Shibata, Sanshiro; Blinnikov, Sergei I., E-mail: tominaga@konan-u.ac.jp, E-mail: sshibata@post.kek.jp, E-mail: Sergei.Blinnikov@itep.ru

We develop a time-dependent, multi-group, multi-dimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids that are involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) which evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed-frame approach; the source functionmore » is evaluated in the comoving frame, whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated using various test problems and comparisons with the results from a relativistic Monte Carlo code. These validations confirm that the code correctly calculates the intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates the first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.« less

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

Parallelization of PANDA discrete ordinates code using spatial decomposition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humbert, P.

2006-07-01

We present the parallel method, based on spatial domain decomposition, implemented in the 2D and 3D versions of the discrete Ordinates code PANDA. The spatial mesh is orthogonal and the spatial domain decomposition is Cartesian. For 3D problems a 3D Cartesian domain topology is created and the parallel method is based on a domain diagonal plane ordered sweep algorithm. The parallel efficiency of the method is improved by directions and octants pipelining. The implementation of the algorithm is straightforward using MPI blocking point to point communications. The efficiency of the method is illustrated by an application to the 3D-Ext C5G7more » benchmark of the OECD/NEA. (authors)« less

PRIM versus CART in subgroup discovery: when patience is harmful.

PubMed

Abu-Hanna, Ameen; Nannings, Barry; Dongelmans, Dave; Hasman, Arie

2010-10-01

We systematically compare the established algorithms CART (Classification and Regression Trees) and PRIM (Patient Rule Induction Method) in a subgroup discovery task on a large real-world high-dimensional clinical database. Contrary to current conjectures, PRIM's performance was generally inferior to CART's. PRIM often considered "peeling of" a large chunk of data at a value of a relevant discrete ordinal variable unattractive, ultimately missing an important subgroup. This finding has considerable significance in clinical medicine where ordinal scores are ubiquitous. PRIM's utility in clinical databases would increase when global information about (ordinal) variables is better put to use and when the search algorithm keeps track of alternative solutions.

Spectrally-Invariant Approximation Within Atmospheric Radiative Transfer

NASA Technical Reports Server (NTRS)

Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.

2011-01-01

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in clouddominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction. and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with ID radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Population Fisher information matrix and optimal design of discrete data responses in population pharmacodynamic experiments.

PubMed

Ogungbenro, Kayode; Aarons, Leon

2011-08-01

In the recent years, interest in the application of experimental design theory to population pharmacokinetic (PK) and pharmacodynamic (PD) experiments has increased. The aim is to improve the efficiency and the precision with which parameters are estimated during data analysis and sometimes to increase the power and reduce the sample size required for hypothesis testing. The population Fisher information matrix (PFIM) has been described for uniresponse and multiresponse population PK experiments for design evaluation and optimisation. Despite these developments and availability of tools for optimal design of population PK and PD experiments much of the effort has been focused on repeated continuous variable measurements with less work being done on repeated discrete type measurements. Discrete data arise mainly in PDs e.g. ordinal, nominal, dichotomous or count measurements. This paper implements expressions for the PFIM for repeated ordinal, dichotomous and count measurements based on analysis by a mixed-effects modelling technique. Three simulation studies were used to investigate the performance of the expressions. Example 1 is based on repeated dichotomous measurements, Example 2 is based on repeated count measurements and Example 3 is based on repeated ordinal measurements. Data simulated in MATLAB were analysed using NONMEM (Laplace method) and the glmmML package in R (Laplace and adaptive Gauss-Hermite quadrature methods). The results obtained for Examples 1 and 2 showed good agreement between the relative standard errors obtained using the PFIM and simulations. The results obtained for Example 3 showed the importance of sampling at the most informative time points. Implementation of these expressions will provide the opportunity for efficient design of population PD experiments that involve discrete type data through design evaluation and optimisation.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Goal-based h-adaptivity of the 1-D diamond difference discrete ordinate method

NASA Astrophysics Data System (ADS)

Jeffers, R. S.; Kópházi, J.; Eaton, M. D.; Févotte, F.; Hülsemann, F.; Ragusa, J.

2017-04-01

The quantity of interest (QoI) associated with a solution of a partial differential equation (PDE) is not, in general, the solution itself, but a functional of the solution. Dual weighted residual (DWR) error estimators are one way of providing an estimate of the error in the QoI resulting from the discretisation of the PDE. This paper aims to provide an estimate of the error in the QoI due to the spatial discretisation, where the discretisation scheme being used is the diamond difference (DD) method in space and discrete ordinate (SN) method in angle. The QoI are reaction rates in detectors and the value of the eigenvalue (Keff) for 1-D fixed source and eigenvalue (Keff criticality) neutron transport problems respectively. Local values of the DWR over individual cells are used as error indicators for goal-based mesh refinement, which aims to give an optimal mesh for a given QoI.

Graphical aids for visualizing and interpreting patterns in departures from agreement in ordinal categorical observer agreement data.

PubMed

Bangdiwala, Shrikant I

2017-01-01

When studying the agreement between two observers rating the same n units into the same k discrete ordinal categories, Bangdiwala (1985) proposed using the "agreement chart" to visually assess agreement. This article proposes that often it is more interesting to focus on the patterns of disagreement and visually understanding the departures from perfect agreement. The article reviews the use of graphical techniques for descriptively assessing agreement and disagreements, and also reviews some of the available summary statistics that quantify such relationships.

Newsracks and the First Amendment.

ERIC Educational Resources Information Center

Stevens, George E.

1989-01-01

Discusses court cases dealing with whether a community may ban newsracks, how much discretion city officials may exercise in regulating vending machines, and what limitations in display and placement are reasonable. Finds that acceptable city ordinances are narrow and content neutral. (RS)

Numerical Model of Multiple Scattering and Emission from Layering Snowpack for Microwave Remote Sensing

NASA Astrophysics Data System (ADS)

Jin, Y.; Liang, Z.

2002-12-01

The vector radiative transfer (VRT) equation is an integral-deferential equation to describe multiple scattering, absorption and transmission of four Stokes parameters in random scatter media. From the integral formal solution of VRT equation, the lower order solutions, such as the first-order scattering for a layer medium or the second order scattering for a half space, can be obtained. The lower order solutions are usually good at low frequency when high-order scattering is negligible. It won't be feasible to continue iteration for obtaining high order scattering solution because too many folds integration would be involved. In the space-borne microwave remote sensing, for example, the DMSP (Defense Meterological Satellite Program) SSM/I (Special Sensor Microwave/Imager) employed seven channels of 19, 22, 37 and 85GHz. Multiple scattering from the terrain surfaces such as snowpack cannot be neglected at these channels. The discrete ordinate and eigen-analysis method has been studied to take into account for multiple scattering and applied to remote sensing of atmospheric precipitation, snowpack etc. Snowpack was modeled as a layer of dense spherical particles, and the VRT for a layer of uniformly dense spherical particles has been numerically studied by the discrete ordinate method. However, due to surface melting and refrozen crusts, the snowpack undergoes stratifying to form inhomegeneous profiles of the ice grain size, fractional volume and physical temperature etc. It becomes necessary to study multiple scattering and emission from stratified snowpack of dense ice grains. But, the discrete ordinate and eigen-analysis method cannot be simply applied to multi-layers model, because numerically solving a set of multi-equations of VRT is difficult. Stratifying the inhomogeneous media into multi-slabs and employing the first order Mueller matrix of each thin slab, this paper developed an iterative method to derive high orders scattering solutions of whole scatter media. High order scattering and emission from inhomogeneous stratifying media of dense spherical particles are numerically obtained. The brightness temperature at low frequency such as 5.3 GHz without high order scattering and at SSM/I channels with high order scattering are obtained. This approach is also compared with the conventional discrete ordinate method for an uniform layer model. Numerical simulation for inhomogeneous snowpack is also compared with the measurements of microwave remote sensing.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

Shock-wave structure in a partially ionized gas

NASA Technical Reports Server (NTRS)

Lu, C. S.; Huang, A. B.

1974-01-01

The structure of a steady plane shock in a partially ionized gas has been investigated using the Boltzmann equation with a kinetic model as the governing equation and the discrete ordinate method as a tool. The effects of the electric field induced by the charge separation on the shock structure have also been studied. Although the three species of an ionized gas travel with approximately the same macroscopic velocity, the individual distribution functions are found to be very different. In a strong shock the atom distribution function may have double peaks, while the ion distribution function has only one peak. Electrons are heated up much earlier than ions and atoms in a partially ionized gas. Because the interactions of electrons with atoms and with ions are different, the ion temperature can be different from the atom temperature.

Applying Multivariate Discrete Distributions to Genetically Informative Count Data.

PubMed

Kirkpatrick, Robert M; Neale, Michael C

2016-03-01

We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.

On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media

NASA Astrophysics Data System (ADS)

Godoy, William F.; DesJardin, Paul E.

2010-05-01

The application of flux limiters to the discrete ordinates method (DOM), SN, for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to "exact" solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.

3D unstructured-mesh radiation transport codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

Power and sample size evaluation for the Cochran-Mantel-Haenszel mean score (Wilcoxon rank sum) test and the Cochran-Armitage test for trend.

PubMed

Lachin, John M

2011-11-10

The power of a chi-square test, and thus the required sample size, are a function of the noncentrality parameter that can be obtained as the limiting expectation of the test statistic under an alternative hypothesis specification. Herein, we apply this principle to derive simple expressions for two tests that are commonly applied to discrete ordinal data. The Wilcoxon rank sum test for the equality of distributions in two groups is algebraically equivalent to the Mann-Whitney test. The Kruskal-Wallis test applies to multiple groups. These tests are equivalent to a Cochran-Mantel-Haenszel mean score test using rank scores for a set of C-discrete categories. Although various authors have assessed the power function of the Wilcoxon and Mann-Whitney tests, herein it is shown that the power of these tests with discrete observations, that is, with tied ranks, is readily provided by the power function of the corresponding Cochran-Mantel-Haenszel mean scores test for two and R > 2 groups. These expressions yield results virtually identical to those derived previously for rank scores and also apply to other score functions. The Cochran-Armitage test for trend assesses whether there is an monotonically increasing or decreasing trend in the proportions with a positive outcome or response over the C-ordered categories of an ordinal independent variable, for example, dose. Herein, it is shown that the power of the test is a function of the slope of the response probabilities over the ordinal scores assigned to the groups that yields simple expressions for the power of the test. Copyright © 2011 John Wiley & Sons, Ltd.

MCNP (Monte Carlo Neutron Photon) capabilities for nuclear well logging calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Forster, R.A.; Little, R.C.; Briesmeister, J.F.

The Los Alamos Radiation Transport Code System (LARTCS) consists of state-of-the-art Monte Carlo and discrete ordinates transport codes and data libraries. The general-purpose continuous-energy Monte Carlo code MCNP (Monte Carlo Neutron Photon), part of the LARTCS, provides a computational predictive capability for many applications of interest to the nuclear well logging community. The generalized three-dimensional geometry of MCNP is well suited for borehole-tool models. SABRINA, another component of the LARTCS, is a graphics code that can be used to interactively create a complex MCNP geometry. Users can define many source and tally characteristics with standard MCNP features. The time-dependent capabilitymore » of the code is essential when modeling pulsed sources. Problems with neutrons, photons, and electrons as either single particle or coupled particles can be calculated with MCNP. The physics of neutron and photon transport and interactions is modeled in detail using the latest available cross-section data. A rich collections of variance reduction features can greatly increase the efficiency of a calculation. MCNP is written in FORTRAN 77 and has been run on variety of computer systems from scientific workstations to supercomputers. The next production version of MCNP will include features such as continuous-energy electron transport and a multitasking option. Areas of ongoing research of interest to the well logging community include angle biasing, adaptive Monte Carlo, improved discrete ordinates capabilities, and discrete ordinates/Monte Carlo hybrid development. Los Alamos has requested approval by the Department of Energy to create a Radiation Transport Computational Facility under their User Facility Program to increase external interactions with industry, universities, and other government organizations. 21 refs.« less

Quasi-heterogeneous efficient 3-D discrete ordinates CANDU calculations using Attila

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preeti, T.; Rulko, R.

2012-07-01

In this paper, 3-D quasi-heterogeneous large scale parallel Attila calculations of a generic CANDU test problem consisting of 42 complete fuel channels and a perpendicular to fuel reactivity device are presented. The solution method is that of discrete ordinates SN and the computational model is quasi-heterogeneous, i.e. fuel bundle is partially homogenized into five homogeneous rings consistently with the DRAGON code model used by the industry for the incremental cross-section generation. In calculations, the HELIOS-generated 45 macroscopic cross-sections library was used. This approach to CANDU calculations has the following advantages: 1) it allows detailed bundle (and eventually channel) power calculationsmore » for each fuel ring in a bundle, 2) it allows the exact reactivity device representation for its precise reactivity worth calculation, and 3) it eliminates the need for incremental cross-sections. Our results are compared to the reference Monte Carlo MCNP solution. In addition, the Attila SN method performance in CANDU calculations characterized by significant up scattering is discussed. (authors)« less

WWER-1000 core and reflector parameters investigation in the LR-0 reactor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaritsky, S. M.; Alekseev, N. I.; Bolshagin, S. N.

2006-07-01

Measurements and calculations carried out in the core and reflector of WWER-1000 mock-up are discussed: - the determination of the pin-to-pin power distribution in the core by means of gamma-scanning of fuel pins and pin-to-pin calculations with Monte Carlo code MCU-REA and diffusion codes MOBY-DICK (with WIMS-D4 cell constants preparation) and RADAR - the fast neutron spectra measurements by proton recoil method inside the experimental channel in the core and inside the channel in the baffle, and corresponding calculations in P{sub 3}S{sub 8} approximation of discrete ordinates method with code DORT and BUGLE-96 library - the neutron spectra evaluations (adjustment)more » in the same channels in energy region 0.5 eV-18 MeV based on the activation and solid state track detectors measurements. (authors)« less

Generalized Fokker-Planck theory for electron and photon transport in biological tissues: application to radiotherapy.

PubMed

Olbrant, Edgar; Frank, Martin

2010-12-01

In this paper, we study a deterministic method for particle transport in biological tissues. The method is specifically developed for dose calculations in cancer therapy and for radiological imaging. Generalized Fokker-Planck (GFP) theory [Leakeas and Larsen, Nucl. Sci. Eng. 137 (2001), pp. 236-250] has been developed to improve the Fokker-Planck (FP) equation in cases where scattering is forward-peaked and where there is a sufficient amount of large-angle scattering. We compare grid-based numerical solutions to FP and GFP in realistic medical applications. First, electron dose calculations in heterogeneous parts of the human body are performed. Therefore, accurate electron scattering cross sections are included and their incorporation into our model is extensively described. Second, we solve GFP approximations of the radiative transport equation to investigate reflectance and transmittance of light in biological tissues. All results are compared with either Monte Carlo or discrete-ordinates transport solutions.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

Radiative Transfer Modeling of a Large Pool Fire by Discrete Ordinates, Discrete Transfer, Ray Tracing, Monte Carlo and Moment Methods

NASA Technical Reports Server (NTRS)

Jensen, K. A.; Ripoll, J.-F.; Wray, A. A.; Joseph, D.; ElHafi, M.

2004-01-01

Five computational methods for solution of the radiative transfer equation in an absorbing-emitting and non-scattering gray medium were compared on a 2 m JP-8 pool fire. The temperature and absorption coefficient fields were taken from a synthetic fire due to the lack of a complete set of experimental data for fires of this size. These quantities were generated by a code that has been shown to agree well with the limited quantity of relevant data in the literature. Reference solutions to the governing equation were determined using the Monte Carlo method and a ray tracing scheme with high angular resolution. Solutions using the discrete transfer method, the discrete ordinate method (DOM) with both S(sub 4) and LC(sub 11) quadratures, and moment model using the M(sub 1) closure were compared to the reference solutions in both isotropic and anisotropic regions of the computational domain. DOM LC(sub 11) is shown to be the more accurate than the commonly used S(sub 4) quadrature technique, especially in anisotropic regions of the fire domain. This represents the first study where the M(sub 1) method was applied to a combustion problem occurring in a complex three-dimensional geometry. The M(sub 1) results agree well with other solution techniques, which is encouraging for future applications to similar problems since it is computationally the least expensive solution technique. Moreover, M(sub 1) results are comparable to DOM S(sub 4).

The potential influence of multiple scattering on longwave flux and heating rate simulations with clouds

NASA Astrophysics Data System (ADS)

Kuo, C. P.; Yang, P.; Huang, X.; Feldman, D.; Flanner, M.; Kuo, C.; Mlawer, E. J.

2017-12-01

Clouds, which cover approximately 67% of the globe, serve as one of the major modulators in adjusting radiative energy on the Earth. Since rigorous radiative transfer computations including multiple scattering are costly, only absorption is considered in the longwave spectral bands in the radiation sub-models of the general circulation models (GCMs). Quantification of the effect of ignoring longwave scattering for flux and heating rate simulations is performed by using the GCM version of the Longwave Rapid Radiative Transfer Model (RRTMG_LW) with an implementation with the 16-stream Discrete Ordinates Radiative Transfer (DISORT) Program for a Multi-Layered Plane-Parallel Medium in conjunction with the 2010 CCCM products that merge satellite observations from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), the CloudSat, the Clouds and the Earth's Radiant Energy System (CERES) and the Moderate Resolution Imaging Spectrometer (MODIS). One-year global simulations show that neglecting longwave scattering overestimates upward flux at the top of the atmosphere (TOA) and underestimates downward flux at the surface by approximately 2.63 and 1.15 W/m2, respectively. Furthermore, when longwave scattering is included in the simulations, the tropopause is cooled by approximately 0.018 K/day and the surface is heated by approximately 0.028 K/day. As a result, the radiative effects of ignoring longwave scattering and doubling CO2 are comparable in magnitude.

Implementation of radiation shielding calculation methods. Volume 2: Seminar/Workshop notes

NASA Technical Reports Server (NTRS)

Capo, M. A.; Disney, R. K.

1971-01-01

Detailed descriptions are presented of the input data for each of the MSFC computer codes applied to the analysis of a realistic nuclear propelled vehicle. The analytical techniques employed include cross section data, preparation, one and two dimensional discrete ordinates transport, point kernel, and single scatter methods.

Efficient and Accurate Computation of Non-Negative Anisotropic Group Scattering Cross Sections for Discrete Ordinates and Monte Carlo Radiation Transport

DTIC Science & Technology

2002-07-01

Date Kirk A. Mathews (Advisor) James T. Moore (Dean’s Representative) Charles J. Bridgman (Member...Adler-Adler, and Kalbach -Mann representations of the scatter cross sections that are used for some isotopes in ENDF/B-VI are not included. They are not

Empirical Histograms in Item Response Theory with Ordinal Data

ERIC Educational Resources Information Center

Woods, Carol M.

2007-01-01

The purpose of this research is to describe, test, and illustrate a new implementation of the empirical histogram (EH) method for ordinal items. The EH method involves the estimation of item response model parameters simultaneously with the approximation of the distribution of the random latent variable (theta) as a histogram. Software for the EH…

Ordinal probability effect measures for group comparisons in multinomial cumulative link models.

PubMed

Agresti, Alan; Kateri, Maria

2017-03-01

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals Φ(β/2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf Φ and effect β that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1+exp(β)] with the log-log link and equals approximately exp(β/2)/[1+exp(β/2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example. © 2016, The International Biometric Society.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

NASA Astrophysics Data System (ADS)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

A Bayesian hierarchical model for discrete choice data in health care.

PubMed

Antonio, Anna Liza M; Weiss, Robert E; Saigal, Christopher S; Dahan, Ely; Crespi, Catherine M

2017-01-01

In discrete choice experiments, patients are presented with sets of health states described by various attributes and asked to make choices from among them. Discrete choice experiments allow health care researchers to study the preferences of individual patients by eliciting trade-offs between different aspects of health-related quality of life. However, many discrete choice experiments yield data with incomplete ranking information and sparsity due to the limited number of choice sets presented to each patient, making it challenging to estimate patient preferences. Moreover, methods to identify outliers in discrete choice data are lacking. We develop a Bayesian hierarchical random effects rank-ordered multinomial logit model for discrete choice data. Missing ranks are accounted for by marginalizing over all possible permutations of unranked alternatives to estimate individual patient preferences, which are modeled as a function of patient covariates. We provide a Bayesian version of relative attribute importance, and adapt the use of the conditional predictive ordinate to identify outlying choice sets and outlying individuals with unusual preferences compared to the population. The model is applied to data from a study using a discrete choice experiment to estimate individual patient preferences for health states related to prostate cancer treatment.

Computing Radiative Transfer in a 3D Medium

NASA Technical Reports Server (NTRS)

Von Allmen, Paul; Lee, Seungwon

2012-01-01

A package of software computes the time-dependent propagation of a narrow laser beam in an arbitrary three- dimensional (3D) medium with absorption and scattering, using the transient-discrete-ordinates method and a direct integration method. Unlike prior software that utilizes a Monte Carlo method, this software enables simulation at very small signal-to-noise ratios. The ability to simulate propagation of a narrow laser beam in a 3D medium is an improvement over other discrete-ordinate software. Unlike other direct-integration software, this software is not limited to simulation of propagation of thermal radiation with broad angular spread in three dimensions or of a laser pulse with narrow angular spread in two dimensions. Uses for this software include (1) computing scattering of a pulsed laser beam on a material having given elastic scattering and absorption profiles, and (2) evaluating concepts for laser-based instruments for sensing oceanic turbulence and related measurements of oceanic mixed-layer depths. With suitable augmentation, this software could be used to compute radiative transfer in ultrasound imaging in biological tissues, radiative transfer in the upper Earth crust for oil exploration, and propagation of laser pulses in telecommunication applications.

Radiant heat exchange calculations in radiantly heated and cooled enclosures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chapman, K.S.; Zhang, P.

1995-08-01

This paper presents the development of a three-dimensional mathematical model to compute the radiant heat exchange between surfaces separated by a transparent and/or opaque medium. The model formulation accommodates arbitrary arrangements of the interior surfaces, as well as arbitrary placement of obstacles within the enclosure. The discrete ordinates radiation model is applied and has the capability to analyze the effect of irregular geometries and diverse surface temperatures and radiative properties. The model is verified by comparing calculated heat transfer rates to heat transfer rates determined from the exact radiosity method for four different enclosures. The four enclosures were selected tomore » provide a wide range of verification. This three-dimensional model based on the discrete ordinates method can be applied to a building to assist the design engineer in sizing a radiant heating system. By coupling this model with a convective and conductive heat transfer model and a thermal comfort model, the comfort levels throughout the room can be easily and efficiently mapped for a given radiant heater location. In addition, objects such as airplanes, trucks, furniture, and partitions can be easily incorporated to determine their effect on the performance of the radiant heating system.« less

Ex-vessel neutron dosimetry analysis for westinghouse 4-loop XL pressurized water reactor plant using the RadTrack{sup TM} Code System with the 3D parallel discrete ordinates code RAPTOR-M3G

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, J.; Alpan, F. A.; Fischer, G.A.

2011-07-01

Traditional two-dimensional (2D)/one-dimensional (1D) SYNTHESIS methodology has been widely used to calculate fast neutron (>1.0 MeV) fluence exposure to reactor pressure vessel in the belt-line region. However, it is expected that this methodology cannot provide accurate fast neutron fluence calculation at elevations far above or below the active core region. A three-dimensional (3D) parallel discrete ordinates calculation for ex-vessel neutron dosimetry on a Westinghouse 4-Loop XL Pressurized Water Reactor has been done. It shows good agreement between the calculated results and measured results. Furthermore, the results show very different fast neutron flux values at some of the former plate locationsmore » and elevations above and below an active core than those calculated by a 2D/1D SYNTHESIS method. This indicates that for certain irregular reactor internal structures, where the fast neutron flux has a very strong local effect, it is required to use a 3D transport method to calculate accurate fast neutron exposure. (authors)« less

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Discontinuous finite element method for vector radiative transfer

NASA Astrophysics Data System (ADS)

Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping

2017-03-01

The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.

Sub-Scale Analysis of New Large Aircraft Pool Fire-Suppression

DTIC Science & Technology

2016-01-01

discrete ordinates radiation and single step Khan and Greeves soot model provided radiation and soot interaction. Agent spray dynamics were...Notable differences observed showed a modeled increase in the mockup surface heat-up rate as well as a modeled decreased rate of soot production...488 K SUPPRESSION STARTED  Large deviation between sensors due to sensor alignment challenges and asymmetric fuel surface ignition  Unremarkable

Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

NASA Astrophysics Data System (ADS)

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive, nevertheless, the present GKUAs for kinetic model Boltzmann equations in conjunction with current available high-performance parallel computer power can provide a vital engineering tool for analyzing rarefied gas flows covering the whole range of flow regimes in aerospace engineering applications.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

A DEIM Induced CUR Factorization

DTIC Science & Technology

2015-09-18

CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a...CUR approximations based on leverage scores. 1 Introduction This work presents a new CUR matrix factorization based upon the Discrete Empirical...SUPPLEMENTARY NOTES 14. ABSTRACT We derive a CUR approximate matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given

Discrete factor approximations in simultaneous equation models: estimating the impact of a dummy endogenous variable on a continuous outcome.

PubMed

Mroz, T A

1999-10-01

This paper contains a Monte Carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models. When the true model has bivariate normal disturbances, estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias; these approximation estimators dominate all the other estimators examined when the disturbances are non-normal. The experiments also indicate that one should liberally add points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages.

A Theoretical Understanding of Circular Polarization Memory in Random Media

NASA Astrophysics Data System (ADS)

Dark, Julia

Radiative transport theory describes the propagation of light in random media that absorb, scatter, and emit radiation. To describe the propagation of light, the full polarization state is quantified using the Stokes parameters. For the sake of mathematical convenience, the polarization state of light is often neglected leading to the scalar radiative transport equation for the intensity only. For scalar transport theory, there is a well-established body of literature on numerical and analytic approximations to the radiative transport equation. We extend the scalar theory to the vector radiative transport equation (vRTE). In particular, we are interested in the theoretical basis for a phenomena called circular polarization memory. Circular polarization memory is the physical phenomena whereby circular polarization retains its ellipticity and handedness when propagating in random media. This is in contrast to the propagation of linear polarization in random media, which depolarizes at a faster rate, and specular reflection of circular polarization, whereby the circular polarization handedness flips. We investigate two limits that are of known interest in the phenomena of circular polarization memory. The first limit we investigate is that of forward-peaked scattering, i.e. the limit where most scattering events occur in the forward or near-forward directions. The second limit we consider is that of strong scattering and weak absorption. In the forward-peaked scattering limit we approximate the vRTE by a system of partial differential equations motivated by the scalar Fokker-Planck approximation. We call the leading order approximation the vector Fokker-Planck approximation. The vector Fokker Planck approximation predicts that strongly forward-peaked media exhibit circular polarization memory where the strength of the effect can be calculated from the expansion of the scattering matrix in special functions. In addition, we find in this limit that total intensity, linear polarization, and circular polarization decouple. From this result we conclude, that in the Fokker-Planck limit the scalar approximation is an appropriate leading order approximation. In the strong scattering and weak absorbing limit the vector radiative transport equation can be analyzed using boundary layer theory. In this case, the problem of light scattering in an optically thick medium is reduced to a 1D vRTE near the boundary and a 3D diffusion equation in the interior. We develop and implement a numerical solver for the boundary layer problem by using a discrete ordinate solver in the boundary layer and a spectral method to solve the diffusion approximation in the interior. We implement the method in Fortran 95 with external dependencies on BLAS, LAPACK, and FFTW. By analyzing the spectrum of the discretized vRTE in the boundary layer, we are able to predict the presence of circular polarization memory in a given medium.

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

A new spherical model for computing the radiation field available for photolysis and heating at twilight

NASA Technical Reports Server (NTRS)

Dahlback, Arne; Stamnes, Knut

1991-01-01

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

A solar radiation model for use in climate studies

NASA Technical Reports Server (NTRS)

Chou, Ming-Dah

1992-01-01

A solar radiation routine is developed for use in climate studies that includes absorption and scattering due to ozone, water vapor, oxygen, carbon dioxide, clouds, and aerosols. Rayleigh scattering is also included. Broadband parameterization is used to compute the absorption by water vapor in a clear atmosphere, and the k-distribution method is applied to compute fluxes in a scattering atmosphere. The reflectivity and transmissivity of a scattering layer are computed analytically using the delta-four-stream discrete-ordinate approximation. The two-stream adding method is then applied to compute fluxes for a composite of clear and scattering layers. Compared to the results of high spectral resolution and detailed multiple-scattering calculations, fluxes and heating rate are accurately computed to within a few percent. The high accuracy of the flux and heating-rate calculations is achieved with a reasonable amount of computing time. With the UV and visible region grouped into four bands, this solar radiation routine is useful not only for climate studies but also for studies on photolysis in the upper atmosphere and photosynthesis in the biosphere.

Vectorization of transport and diffusion computations on the CDC Cyber 205

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abu-Shumays, I.K.

1986-01-01

The development and testing of alternative numerical methods and computational algorithms specifically designed for the vectorization of transport and diffusion computations on a Control Data Corporation (CDC) Cyber 205 vector computer are described. Two solution methods for the discrete ordinates approximation to the transport equation are summarized and compared. Factors of 4 to 7 reduction in run times for certain large transport problems were achieved on a Cyber 205 as compared with run times on a CDC-7600. The solution of tridiagonal systems of linear equations, central to several efficient numerical methods for multidimensional diffusion computations and essential for fluid flowmore » and other physics and engineering problems, is also dealt with. Among the methods tested, a combined odd-even cyclic reduction and modified Cholesky factorization algorithm for solving linear symmetric positive definite tridiagonal systems is found to be the most effective for these systems on a Cyber 205. For large tridiagonal systems, computation with this algorithm is an order of magnitude faster on a Cyber 205 than computation with the best algorithm for tridiagonal systems on a CDC-7600.« less

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors.

PubMed

Yu, Jinpeng; Shi, Peng; Yu, Haisheng; Chen, Bing; Lin, Chong

2015-07-01

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

A revised radiation package of G-packed McICA and two-stream approximation: Performance evaluation in a global weather forecasting model

NASA Astrophysics Data System (ADS)

Baek, Sunghye

2017-07-01

For more efficient and accurate computation of radiative flux, improvements have been achieved in two aspects, integration of the radiative transfer equation over space and angle. First, the treatment of the Monte Carlo-independent column approximation (MCICA) is modified focusing on efficiency using a reduced number of random samples ("G-packed") within a reconstructed and unified radiation package. The original McICA takes 20% of CPU time of radiation in the Global/Regional Integrated Model systems (GRIMs). The CPU time consumption of McICA is reduced by 70% without compromising accuracy. Second, parameterizations of shortwave two-stream approximations are revised to reduce errors with respect to the 16-stream discrete ordinate method. Delta-scaled two-stream approximation (TSA) is almost unanimously used in Global Circulation Model (GCM) but contains systematic errors which overestimate forward peak scattering as solar elevation decreases. These errors are alleviated by adjusting the parameterizations of each scattering element—aerosol, liquid, ice and snow cloud particles. Parameterizations are determined with 20,129 atmospheric columns of the GRIMs data and tested with 13,422 independent data columns. The result shows that the root-mean-square error (RMSE) over the all atmospheric layers is decreased by 39% on average without significant increase in computational time. Revised TSA developed and validated with a separate one-dimensional model is mounted on GRIMs for mid-term numerical weather forecasting. Monthly averaged global forecast skill scores are unchanged with revised TSA but the temperature at lower levels of the atmosphere (pressure ≥ 700 hPa) is slightly increased (< 0.5 K) with corrected atmospheric absorption.

A fast radiative transfer model for visible through shortwave infrared spectral reflectances in clear and cloudy atmospheres

NASA Astrophysics Data System (ADS)

Wang, Chenxi; Yang, Ping; Nasiri, Shaima L.; Platnick, Steven; Baum, Bryan A.; Heidinger, Andrew K.; Liu, Xu

2013-02-01

A computationally efficient radiative transfer model (RTM) for calculating visible (VIS) through shortwave infrared (SWIR) reflectances is developed for use in satellite and airborne cloud property retrievals. The full radiative transfer equation (RTE) for combinations of cloud, aerosol, and molecular layers is solved approximately by using six independent RTEs that assume the plane-parallel approximation along with a single-scattering approximation for Rayleigh scattering. Each of the six RTEs can be solved analytically if the bidirectional reflectance/transmittance distribution functions (BRDF/BTDF) of the cloud/aerosol layers are known. The adding/doubling (AD) algorithm is employed to account for overlapped cloud/aerosol layers and non-Lambertian surfaces. Two approaches are used to mitigate the significant computational burden of the AD algorithm. First, the BRDF and BTDF of single cloud/aerosol layers are pre-computed using the discrete ordinates radiative transfer program (DISORT) implemented with 128 streams, and second, the required integral in the AD algorithm is numerically implemented on a twisted icosahedral mesh. A concise surface BRDF simulator associated with the MODIS land surface product (MCD43) is merged into a fast RTM to accurately account for non-isotropic surface reflectance. The resulting fast RTM is evaluated with respect to its computational accuracy and efficiency. The simulation bias between DISORT and the fast RTM is large (e.g., relative error >5%) only when both the solar zenith angle (SZA) and the viewing zenith angle (VZA) are large (i.e., SZA>45° and VZA>70°). For general situations, i.e., cloud/aerosol layers above a non-Lambertian surface, the fast RTM calculation rate is faster than that of the 128-stream DISORT by approximately two orders of magnitude.

Numerical modelling of soot formation and oxidation in laminar coflow non-smoking and smoking ethylene diffusion flames

NASA Astrophysics Data System (ADS)

Liu, Fengshan; Guo, Hongsheng; Smallwood, Gregory J.; Gülder, Ömer L.

2003-06-01

A numerical study of soot formation and oxidation in axisymmetric laminar coflow non-smoking and smoking ethylene diffusion flames was conducted using detailed gas-phase chemistry and complex thermal and transport properties. A modified two-equation soot model was employed to describe soot nucleation, growth and oxidation. Interaction between the gas-phase chemistry and soot chemistry was taken into account. Radiation heat transfer by both soot and radiating gases was calculated using the discrete-ordinates method coupled with a statistical narrow-band correlated-k based band model, and was used to evaluate the simple optically thin approximation. The governing equations in fully elliptic form were solved. The current models in the literature describing soot oxidation by O2 and OH have to be modified in order to predict the smoking flame. The modified soot oxidation model has only moderate effects on the calculation of the non-smoking flame, but dramatically affects the soot oxidation near the flame tip in the smoking flame. Numerical results of temperature, soot volume fraction and primary soot particle size and number density were compared with experimental data in the literature. Relatively good agreement was found between the prediction and the experimental data. The optically thin approximation radiation model significantly underpredicts temperatures in the upper portion of both flames, seriously affecting the soot prediction.

Heat transfer analysis of a lab scale solar receiver using the discrete ordinates model

NASA Astrophysics Data System (ADS)

Dordevich, Milorad C. W.

This thesis documents the development, implementation and simulation outcomes of the Discrete Ordinates Radiation Model in ANSYS FLUENT simulating the radiative heat transfer occurring in the San Diego State University lab-scale Small Particle Heat Exchange Receiver. In tandem, it also serves to document how well the Discrete Ordinates Radiation Model results compared with those from the in-house developed Monte Carlo Ray Trace Method in a number of simplified geometries. The secondary goal of this study was the inclusion of new physics, specifically buoyancy. Implementation of an additional Monte Carlo Ray Trace Method software package known as VEGAS, which was specifically developed to model lab scale solar simulators and provide directional, flux and beam spread information for the aperture boundary condition, was also a goal of this study. Upon establishment of the model, test cases were run to understand the predictive capabilities of the model. It was shown that agreement within 15% was obtained against laboratory measurements made in the San Diego State University Combustion and Solar Energy Laboratory with the metrics of comparison being the thermal efficiency and outlet, wall and aperture quartz temperatures. Parametric testing additionally showed that the thermal efficiency of the system was very dependent on the mass flow rate and particle loading. It was also shown that the orientation of the small particle heat exchange receiver was important in attaining optimal efficiency due to the fact that buoyancy induced effects could not be neglected. The analyses presented in this work were all performed on the lab-scale small particle heat exchange receiver. The lab-scale small particle heat exchange receiver is 0.38 m in diameter by 0.51 m tall and operated with an input irradiation flux of 3 kWth and a nominal mass flow rate of 2 g/s with a suspended particle mass loading of 2 g/m3. Finally, based on acumen gained during the implementation and development of the model, a new and improved design was simulated to predict how the efficiency within the small particle heat exchange receiver could be improved through a few simple internal geometry design modifications. It was shown that the theoretical calculated efficiency of the small particle heat exchange receiver could be improved from 64% to 87% with adjustments to the internal geometry, mass flow rate, and mass loading.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richers, Sherwood; Nagakura, Hiroki; Ott, Christian D.

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DOmore » method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.« less

A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

DOE PAGES

Richers, Sherwood; Nagakura, Hiroki; Ott, Christian D.; ...

2017-10-03

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. In this paper, we carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to bothmore » methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Finally, included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.« less

A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richers, Sherwood; Nagakura, Hiroki; Ott, Christian D.

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. In this paper, we carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to bothmore » methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Finally, included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.« less

Dyscalculia and the Calculating Brain.

PubMed

Rapin, Isabelle

2016-08-01

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals. Copyright © 2016 Elsevier Inc. All rights reserved.

A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

NASA Astrophysics Data System (ADS)

Richers, Sherwood; Nagakura, Hiroki; Ott, Christian D.; Dolence, Joshua; Sumiyoshi, Kohsuke; Yamada, Shoichi

2017-10-01

The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.

The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

NASA Technical Reports Server (NTRS)

Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

1976-01-01

The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

Ridit Analysis for Cooper-Harper and Other Ordinal Ratings for Sparse Data - A Distance-based Approach

DTIC Science & Technology

2016-09-01

is to fit empirical Beta distributions to observed data, and then to use a randomization approach to make inferences on the difference between...a Ridit analysis on the often sparse data sets in many Flying Qualities applicationsi. The method of this paper is to fit empirical Beta ...One such measure is the discrete- probability-distribution version of the (squared) ‘Hellinger Distance’ (Yang & Le Cam , 2000) 2(, ) = 1

Rescaling quality of life values from discrete choice experiments for use as QALYs: a cautionary tale

PubMed Central

Flynn, Terry N; Louviere, Jordan J; Marley, Anthony AJ; Coast, Joanna; Peters, Tim J

2008-01-01

Background Researchers are increasingly investigating the potential for ordinal tasks such as ranking and discrete choice experiments to estimate QALY health state values. However, the assumptions of random utility theory, which underpin the statistical models used to provide these estimates, have received insufficient attention. In particular, the assumptions made about the decisions between living states and the death state are not satisfied, at least for some people. Estimated values are likely to be incorrectly anchored with respect to death (zero) in such circumstances. Methods Data from the Investigating Choice Experiments for the preferences of older people CAPability instrument (ICECAP) valuation exercise were analysed. The values (previously anchored to the worst possible state) were rescaled using an ordinal model proposed previously to estimate QALY-like values. Bootstrapping was conducted to vary artificially the proportion of people who conformed to the conventional random utility model underpinning the analyses. Results Only 26% of respondents conformed unequivocally to the assumptions of conventional random utility theory. At least 14% of respondents unequivocally violated the assumptions. Varying the relative proportions of conforming respondents in sensitivity analyses led to large changes in the estimated QALY values, particularly for lower-valued states. As a result these values could be either positive (considered to be better than death) or negative (considered to be worse than death). Conclusion Use of a statistical model such as conditional (multinomial) regression to anchor quality of life values from ordinal data to death is inappropriate in the presence of respondents who do not conform to the assumptions of conventional random utility theory. This is clearest when estimating values for that group of respondents observed in valuation samples who refuse to consider any living state to be worse than death: in such circumstances the model cannot be estimated. Only a valuation task requiring respondents to make choices in which both length and quality of life vary can produce estimates that properly reflect the preferences of all respondents. PMID:18945358

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Benchmark gamma-ray skyshine experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nason, R.R.; Shultis, J.K.; Faw, R.E.

1982-01-01

A benchmark gamma-ray skyshine experiment is descibed in which /sup 60/Co sources were either collimated into an upward 150-deg conical beam or shielded vertically by two different thicknesses of concrete. A NaI(Tl) spectrometer and a high pressure ion chamber were used to measure, respectively, the energy spectrum and the 4..pi..-exposure rate of the air-reflected gamma photons up to 700 m from the source. Analyses of the data and comparison to DOT discrete ordinates calculations are presented.

S4 solution of the transport equation for eigenvalues using Legendre polynomials

NASA Astrophysics Data System (ADS)

Öztürk, Hakan; Bülbül, Ahmet

2017-09-01

Numerical solution of the transport equation for monoenergetic neutrons scattered isotropically through the medium of a finite homogeneous slab is studied for the determination of the eigenvalues. After obtaining the discrete ordinates form of the transport equation, separated homogeneous and particular solutions are formed and then the eigenvalues are calculated using the Gauss-Legendre quadrature set. Then, the calculated eigenvalues for various values of the c0, the mean number of secondary neutrons per collision, are given in the tables.

APC: A New Code for Atmospheric Polarization Computations

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2014-01-01

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

Extending radiative transfer models by use of Bayes rule. [in atmospheric science

NASA Technical Reports Server (NTRS)

Whitney, C.

1977-01-01

This paper presents a procedure that extends some existing radiative transfer modeling techniques to problems in atmospheric science where curvature and layering of the medium and dynamic range and angular resolution of the signal are important. Example problems include twilight and limb scan simulations. Techniques that are extended include successive orders of scattering, matrix operator, doubling, Gauss-Seidel iteration, discrete ordinates and spherical harmonics. The procedure for extending them is based on Bayes' rule from probability theory.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

NASA Technical Reports Server (NTRS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.

2016-01-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarized radiative transfer of a cirrus cloud consisting of randomly oriented hexagonal ice crystals: The 3×3 approximation for non-spherical particles

NASA Astrophysics Data System (ADS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K. N.; Stamnes, K.

2017-05-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 ×103 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling-adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error < 2 ×10-6 for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Design Analysis of SNS Target StationBiological Shielding Monoligh with Proton Power Uprate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bekar, Kursat B.; Ibrahim, Ahmad M.

2017-05-01

This report documents the analysis of the dose rate in the experiment area outside the Spallation Neutron Source (SNS) target station shielding monolith with proton beam energy of 1.3 GeV. The analysis implemented a coupled three dimensional (3D)/two dimensional (2D) approach that used both the Monte Carlo N-Particle Extended (MCNPX) 3D Monte Carlo code and the Discrete Ordinates Transport (DORT) two dimensional deterministic code. The analysis with proton beam energy of 1.3 GeV showed that the dose rate in continuously occupied areas on the lateral surface outside the SNS target station shielding monolith is less than 0.25 mrem/h, which compliesmore » with the SNS facility design objective. However, the methods and codes used in this analysis are out of date and unsupported, and the 2D approximation of the target shielding monolith does not accurately represent the geometry. We recommend that this analysis is updated with modern codes and libraries such as ADVANTG or SHIFT. These codes have demonstrated very high efficiency in performing full 3D radiation shielding analyses of similar and even more difficult problems.« less

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

High performance computation of radiative transfer equation using the finite element method

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Favennec, Y.

2018-05-01

This article deals with an efficient strategy for numerically simulating radiative transfer phenomena using distributed computing. The finite element method alongside the discrete ordinate method is used for spatio-angular discretization of the monochromatic steady-state radiative transfer equation in an anisotropically scattering media. Two very different methods of parallelization, angular and spatial decomposition methods, are presented. To do so, the finite element method is used in a vectorial way. A detailed comparison of scalability, performance, and efficiency on thousands of processors is established for two- and three-dimensional heterogeneous test cases. Timings show that both algorithms scale well when using proper preconditioners. It is also observed that our angular decomposition scheme outperforms our domain decomposition method. Overall, we perform numerical simulations at scales that were previously unattainable by standard radiative transfer equation solvers.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

3D numerical modelling of the propagation of radiative intensity through a X-ray tomographied ligament

NASA Astrophysics Data System (ADS)

Le Hardy, David; Badri, Mohd Afeef; Rousseau, Benoit; Chupin, Sylvain; Rochais, Denis; Favennec, Yann

2017-06-01

In order to explain the macroscopic radiative behaviour of an open-cell ceramic foam, knowledge of its solid phase distribution in space and the radiative contributions by this solid phase is required. The solid phase in an open-cell ceramic foam is arranged as a porous skeleton, which is itself composed of an interconnected network of ligament. Typically, ligaments being based on the assembly of grains more or less compacted, exhibit an anisotropic geometry with a concave cross section having a lateral size of one hundred microns. Therefore, ligaments are likely to emit, absorb and scatter thermal radiation. This framework explains why experimental investigations at this scale must be developed to extract accurate homogenized radiative properties regardless the shape and size of ligaments. To support this development, a 3D numerical investigation of the radiative intensity propagation through a real world ligament, beforehand scanned by X-Ray micro-tomography, is presented in this paper. The Radiative Transfer Equation (RTE), applied to the resulting meshed volume, is solved by combining Discrete Ordinate Method (DOM) and Streamline upwind Petrov-Garlekin (SUPG) numerical scheme. A particular attention is paid to propose an improved discretization procedure (spatial and angular) based on ordinate parallelization with the aim to reach fast convergence. Towards the end of this article, we present the effects played by the local radiative properties of three ceramic materials (silicon carbide, alumina and zirconia), which are often used for designing open-cell refractory ceramic foams.

Inferring network structure in non-normal and mixed discrete-continuous genomic data.

PubMed

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2018-03-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.

Inferring network structure in non-normal and mixed discrete-continuous genomic data

PubMed Central

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2017-01-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. PMID:28437848

Analysis of early life influences on cognitive development in childhood using multilevel ordinal models

PubMed Central

Li, Leah

2012-01-01

Summary Studies of cognitive development in children are often based on tests designed for specific ages. Examination of the changes of these scores over time may not be meaningful. This paper investigates the influence of early life factors on cognitive development using maths and reading test scores at ages 7, 11, and 16 years in a British birth cohort born in 1958. The distributions of these test scores differ between ages, for example, 20% participants scored the top mark in the reading test at 7 and the distribution of reading score at 16 is heavily skewed. In this paper, we group participants into 5 ordered categories, approximately 20% in each category according to their test scores at each age. Multilevel models for a repeated ordinal outcome are applied to relate the ordinal scale of maths and reading ability to early life factors. PMID:22661923

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Tycho 2: A Proxy Application for Kinetic Transport Sweeps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrett, Charles Kristopher; Warsa, James S.

2016-09-14

Tycho 2 is a proxy application that implements discrete ordinates (SN) kinetic transport sweeps on unstructured, 3D, tetrahedral meshes. It has been designed to be small and require minimal dependencies to make collaboration and experimentation as easy as possible. Tycho 2 has been released as open source software. The software is currently in a beta release with plans for a stable release (version 1.0) before the end of the year. The code is parallelized via MPI across spatial cells and OpenMP across angles. Currently, several parallelization algorithms are implemented.

Ray Effect Mitigation Through Reference Frame Rotation

DOE PAGES

Tencer, John

2016-05-01

The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. Moreover, when ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. It is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.

An S N Algorithm for Modern Architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Randal Scott

2016-08-29

LANL discrete ordinates transport packages are required to perform large, computationally intensive time-dependent calculations on massively parallel architectures, where even a single such calculation may need many months to complete. While KBA methods scale out well to very large numbers of compute nodes, we are limited by practical constraints on the number of such nodes we can actually apply to any given calculation. Instead, we describe a modified KBA algorithm that allows realization of the reductions in solution time offered by both the current, and future, architectural changes within a compute node.

Shielding Analyses for VISION Beam Line at SNS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popova, Irina; Gallmeier, Franz X

2014-01-01

Full-scale neutron and gamma transport analyses were performed to design shielding around the VISION beam line, instrument shielding enclosure, beam stop, secondary shutter including a temporary beam stop for the still closed neighboring beam line to meet requirement is to achieve dose rates below 0.25 mrem/h at 30 cm from the shielding surface. The beam stop and the temporary beam stop analyses were performed with the discrete ordinate code DORT additionally to Monte Carlo analyses with the MCNPX code. Comparison of the results is presented.

Snow Microwave Radiative Transfer (SMRT): A new model framework to simulate snow-microwave interactions for active and passive remote sensing applications

NASA Astrophysics Data System (ADS)

Loewe, H.; Picard, G.; Sandells, M. J.; Mätzler, C.; Kontu, A.; Dumont, M.; Maslanka, W.; Morin, S.; Essery, R.; Lemmetyinen, J.; Wiesmann, A.; Floury, N.; Kern, M.

2016-12-01

Forward modeling of snow-microwave interactions is widely used to interpret microwave remote sensing data from active and passive sensors. Though different models are yet available for that purpose, a joint effort has been undertaken in the past two years within the ESA Project "Microstructural origin of electromagnetic signatures in microwave remote sensing of snow". The new Snow Microwave Radiative Transfer (SMRT) model primarily facilitates a flexible treatment of snow microstructure as seen by X-ray tomography and seeks to unite respective advantages of existing models. In its main setting, SMRT considers radiation transfer in a plane-parallel snowpack consisting of homogeneous layers with a layer microstructure represented by an autocorrelation function. The electromagnetic model, which underlies permittivity, absorption and scattering calculations within a layer, is based on the improved Born approximation. The resulting vector-radiative transfer equation in the snowpack is solved using spectral decomposition of the discrete ordinates discretization. SMRT is implemented in Python and employs an object-oriented, modular design which intends to i) provide an intuitive and fail-safe API for basic users ii) enable efficient community developments for extensions (e.g. for improvements of sub-models for microstructure, permittivity, soil or interface reflectivity) from advanced users and iii) encapsulate the numerical core which is maintained by the developers. For cross-validation and inter-model comparison, SMRT implements various ingredients of existing models as selectable options (e.g. Rayleigh or DMRT-QCA phase functions) and shallow wrappers to invoke legacy model code directly (MEMLS, DMRT-QMS, HUT). In this paper we give an overview of the model components and show examples and results from different validation schemes.

Year End Progress Report on Rattlesnake Improvements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yaqi; DeHart, Mark David; Gleicher, Frederick Nathan

Rattlesnake is a MOOSE-based radiation transport application developed at INL to support modern multi-physics simulations. At the beginning of the last year, Rattlesnake was able to perform steady-state, transient and eigenvalue calculations for the multigroup radiation transport equations. Various discretization schemes, including continuous finite element method (FEM) with discrete ordinates method (SN) and spherical harmonics expansion method (PN) for the self-adjoint angular flux (SAAF) formulation, continuous FEM (CFEM) with SN for the least square (LS) formulation, diffusion approximation with CFEM and discontinuous FEM (DFEM), have been implemented. A separate toolkit, YAKXS, for multigroup cross section management was developed to supportmore » Rattlesnake calculations with feedback both from changes in the field variables, such as fuel temperature, coolant density, and etc., and in isotope inventory. The framework for doing nonlinear diffusion acceleration (NDA) within Rattlesnake has been set up, and both NDA calculations with SAAF-SN-CFEM scheme and Monte Carlo with OpenMC have been performed. It was also used for coupling BISON and RELAP-7 for the full-core multiphysics simulations. Within the last fiscal year, significant improvements have been made in Rattlesnake. Rattlesnake development was migrated into our internal GITLAB development environment at the end of year 2014. Since then total 369 merge requests has been accepted into Rattlesnake. It is noted that the MOOSE framework that Rattlesnake is based on is under continuous developments. Improvements made in MOOSE can improve the Rattlesnake. It is acknowledged that MOOSE developers spent efforts on patching Rattlesnake for the improvements made on the framework side. This report will not cover the code restructuring for better readability and modularity and documentation improvements, which we have spent tremendous effort on. It only details some of improvements in the following sections.« less

Radiative heat transfer in strongly forward scattering media of circulating fluidized bed combustors

NASA Astrophysics Data System (ADS)

Ates, Cihan; Ozen, Guzide; Selçuk, Nevin; Kulah, Gorkem

2016-10-01

Investigation of the effect of particle scattering on radiative incident heat fluxes and source terms is carried out in the dilute zone of the lignite-fired 150 kWt Middle East Technical University Circulating Fluidized Bed Combustor (METU CFBC) test rig. The dilute zone is treated as an axisymmetric cylindrical enclosure containing grey/non-grey, absorbing, emitting gas with absorbing, emitting non/isotropically/anisotropically scattering particles surrounded by grey diffuse walls. A two-dimensional axisymmetric radiation model based on Method of Lines (MOL) solution of Discrete Ordinates Method (DOM) coupled with Grey Gas (GG)/Spectral Line-Based Weighted Sum of Grey Gases Model (SLW) and Mie theory/geometric optics approximation (GOA) is extended for incorporation of anisotropic scattering by using normalized Henyey-Greenstein (HG)/transport approximation for the phase function. Input data for the radiation model is obtained from predictions of a comprehensive model previously developed and benchmarked against measurements on the same CFBC burning low calorific value indigenous lignite with high volatile matter/fixed carbon (VM/FC) ratio in its own ash. Predictive accuracy and computational efficiency of nonscattering, isotropic scattering and forward scattering with transport approximation are tested by comparing their predictions with those of forward scattering with HG. GG and GOA based on reflectivity with angular dependency are found to be accurate and CPU efficient. Comparisons reveal that isotropic assumption leads to under-prediction of both incident heat fluxes and source terms for which discrepancy is much larger. On the other hand, predictions obtained by neglecting scattering were found to be in favorable agreement with those of forward scattering at significantly less CPU time. Transport approximation is as accurate and CPU efficient as HG. These findings indicate that negligence of scattering is a more practical choice in solution of the radiative transfer equation (RTE) in conjunction with conservation equations for the system under consideration.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Analog 65/130 nm CMOS 5 GHz Sub-Arrays with ROACH-2 FPGA Beamformers for Hybrid Aperture-Array Receivers

DTIC Science & Technology

2017-03-20

sub-array, which is based on all-pass filters (APFs) is realized using 130 nm CMOS technology. Approximate- discrete Fourier transform (a-DFT...fixed beams are directed at known directions [9]. The proposed approximate- discrete Fourier transform (a-DFT) based multi-beamformer [9] yields L...to digital conversion daughter board. occurs in the discrete time domain (in ROACH-2 FPGA platform) following signal digitization (see Figs. 1(d) and

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Effective Hamiltonian for travelling discrete breathers

NASA Astrophysics Data System (ADS)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

Corrigendum to "The discrete dipole approximation: An overview and recent developments" [J. Quant. Spectrosc. Radiat. Transfer 106 (2007) 558-589

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Hoekstra, Alfons G.

2016-03-01

The review [1] is still widely used as a general reference to the discrete dipole approximation, which motivates keeping it as accurate as possible. In the following we correct several errors, mostly typographical ones, which were uncovered over the years.

Discrete Morse flow for Ricci flow and porous medium equation

NASA Astrophysics Data System (ADS)

Ma, Li; Witt, Ingo

2018-06-01

In this paper, we study the discrete Morse flow for the Ricci flow on the American football, which is the 2-sphere with the north and south poles removed and equipped with a metric g0 of constant scalar curvature, and for the porous medium equation on a bounded regular domain in the plane. We show that under suitable assumptions on the initial metric g(0) one has a weak approximate discrete Morse flow for the approximated Ricci flow and porous medium equation on any time interval.

Extension of the Bgl Broad Group Cross Section Library

NASA Astrophysics Data System (ADS)

Kirilova, Desislava; Belousov, Sergey; Ilieva, Krassimira

2009-08-01

The broad group cross-section libraries BUGLE and BGL are applied for reactor shielding calculation using the DOORS package based on discrete ordinates method and multigroup approximation of the neutron cross-sections. BUGLE and BGL libraries are problem oriented for PWR or VVER type of reactors respectively. They had been generated by collapsing the problem independent fine group library VITAMIN-B6 applying PWR and VVER one-dimensional radial model of the reactor middle plane using the SCALE software package. The surveillance assemblies (SA) of VVER-1000/320 are located on the baffle above the reactor core upper edge in a region where geometry and materials differ from those of the middle plane and the neutron field gradient is very high which would result in a different neutron spectrum. That is why the application of the fore-mentioned libraries for the neutron fluence calculation in the region of SA could lead to an additional inaccuracy. This was the main reason to study the necessity for an extension of the BGL library with cross-sections appropriate for the SA region. Comparative analysis of the neutron spectra of the SA region calculated by the VITAMIN-B6 and BGL libraries using the two-dimensional code DORT have been done with purpose to evaluate the BGL applicability for SA calculation.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Fire Suppression M and S Validation (Status and Challenges), Systems Fire Protection Information Exchange

DTIC Science & Technology

2015-10-14

rate Kinetics •14 Species & 12 reactionsCombustion Model •Participating Media Discrete Ordinate Method •WSG model for CO2, H2O and SootRadiation Model...Inhibition of JP-8 Combustion Physical Acting Agents • Dilute heat • Dilute reactants Ex: water, nitrogen Chemical Acting Agents • Reduce flame...Release; distribution is unlimited 5 Overview of Reduced Kinetics Scheme for FM200 • R1: JP-8 + O2 => CO + CO2 + H2O • R2: CO + O2 <=> CO2 • R3: HFP + JP-8

Multitasking TORT under UNICOS: Parallel performance models and measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnett, A.; Azmy, Y.Y.

1999-09-27

The existing parallel algorithms in the TORT discrete ordinates code were updated to function in a UNICOS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead.

Multitasking TORT Under UNICOS: Parallel Performance Models and Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azmy, Y.Y.; Barnett, D.A.

1999-09-27

The existing parallel algorithms in the TORT discrete ordinates were updated to function in a UNI-COS environment. A performance model for the parallel overhead was derived for the existing algorithms. The largest contributors to the parallel overhead were identified and a new algorithm was developed. A parallel overhead model was also derived for the new algorithm. The results of the comparison of parallel performance models were compared to applications of the code to two TORT standard test problems and a large production problem. The parallel performance models agree well with the measured parallel overhead.

Implementation of radiation shielding calculation methods. Volume 1: Synopsis of methods and summary of results

NASA Technical Reports Server (NTRS)

Capo, M. A.; Disney, R. K.

1971-01-01

The work performed in the following areas is summarized: (1) Analysis of Realistic nuclear-propelled vehicle was analyzed using the Marshall Space Flight Center computer code package. This code package includes one and two dimensional discrete ordinate transport, point kernel, and single scatter techniques, as well as cross section preparation and data processing codes, (2) Techniques were developed to improve the automated data transfer in the coupled computation method of the computer code package and improve the utilization of this code package on the Univac-1108 computer system. (3) The MSFC master data libraries were updated.

The LBM program at the EPFL/LOTUS Facility

DOE Office of Scientific and Technical Information (OSTI.GOV)

File, J.; Jassby, D.L.; Tsang, F.Y.

1986-11-01

An experimental program of neutron transport studies of the Lithium Blanket Module (LBM) is being carried out with the LOTUS point-neutron source facility at Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland. Preliminary experiments use passive neutron dosimetry within the fuel rods in the LBM central zone, as well as, both thermal extraction and dissolution methods to assay tritium bred in Li/sub 2/O diagnostic wafers and LBM pellets. These measurements are being compared and reconciled with each other and with the predictions of two-dimensional discrete-ordinates and continuous-energy Monte-Carlo analyses of the Lotus/LBM system.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Data approximation using a blending type spline construction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dalmo, Rune; Bratlie, Jostein

2014-11-18

Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C{sup k}-smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which aremore » necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.« less

A Varifold Approach to Surface Approximation

NASA Astrophysics Data System (ADS)

Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon

2017-11-01

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.

Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas.

PubMed

Yan, Xin-Zhong

2011-07-01

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

Comparing methods for modelling spreading cell fronts.

PubMed

Markham, Deborah C; Simpson, Matthew J; Maini, Philip K; Gaffney, Eamonn A; Baker, Ruth E

2014-07-21

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and the asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performance of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made. Copyright © 2014 Elsevier Ltd. All rights reserved.

PWR Facility Dose Modeling Using MCNP5 and the CADIS/ADVANTG Variance-Reduction Methodology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blakeman, Edward D; Peplow, Douglas E.; Wagner, John C

2007-09-01

The feasibility of modeling a pressurized-water-reactor (PWR) facility and calculating dose rates at all locations within the containment and adjoining structures using MCNP5 with mesh tallies is presented. Calculations of dose rates resulting from neutron and photon sources from the reactor (operating and shut down for various periods) and the spent fuel pool, as well as for the photon source from the primary coolant loop, were all of interest. Identification of the PWR facility, development of the MCNP-based model and automation of the run process, calculation of the various sources, and development of methods for visually examining mesh tally filesmore » and extracting dose rates were all a significant part of the project. Advanced variance reduction, which was required because of the size of the model and the large amount of shielding, was performed via the CADIS/ADVANTG approach. This methodology uses an automatically generated three-dimensional discrete ordinates model to calculate adjoint fluxes from which MCNP weight windows and source bias parameters are generated. Investigative calculations were performed using a simple block model and a simplified full-scale model of the PWR containment, in which the adjoint source was placed in various regions. In general, it was shown that placement of the adjoint source on the periphery of the model provided adequate results for regions reasonably close to the source (e.g., within the containment structure for the reactor source). A modification to the CADIS/ADVANTG methodology was also studied in which a global adjoint source is weighted by the reciprocal of the dose response calculated by an earlier forward discrete ordinates calculation. This method showed improved results over those using the standard CADIS/ADVANTG approach, and its further investigation is recommended for future efforts.« less

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

NASA Technical Reports Server (NTRS)

Cliff, E. M.

1975-01-01

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Cramer-Rao Bound for Gaussian Random Processes and Applications to Radar Processing of Atmospheric Signals

NASA Technical Reports Server (NTRS)

Frehlich, Rod

1993-01-01

Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

DSSPcont: continuous secondary structure assignments for proteins

PubMed Central

Carter, Phil; Andersen, Claus A. F.; Rost, Burkhard

2003-01-01

The DSSP program automatically assigns the secondary structure for each residue from the three-dimensional co-ordinates of a protein structure to one of eight states. However, discrete assignments are incomplete in that they cannot capture the continuum of thermal fluctuations. Therefore, DSSPcont (http://cubic.bioc.columbia.edu/services/DSSPcont) introduces a continuous assignment of secondary structure that replaces ‘static’ by ‘dynamic’ states. Technically, the continuum results from calculating weighted averages over 10 discrete DSSP assignments with different hydrogen bond thresholds. A DSSPcont assignment for a particular residue is a percentage likelihood of eight secondary structure states, derived from a weighted average of the ten DSSP assignments. The continuous assignments have two important features: (i) they reflect the structural variations due to thermal fluctuations as detected by NMR spectroscopy; and (ii) they reproduce the structural variation between many NMR models from one single model. Therefore, functionally important variation can be extracted from a single X-ray structure using the continuous assignment procedure. PMID:12824310

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Spatial homogenization methods for pin-by-pin neutron transport calculations

NASA Astrophysics Data System (ADS)

Kozlowski, Tomasz

For practical reactor core applications low-order transport approximations such as SP3 have been shown to provide sufficient accuracy for both static and transient calculations with considerably less computational expense than the discrete ordinate or the full spherical harmonics methods. These methods have been applied in several core simulators where homogenization was performed at the level of the pin cell. One of the principal problems has been to recover the error introduced by pin-cell homogenization. Two basic approaches to treat pin-cell homogenization error have been proposed: Superhomogenization (SPH) factors and Pin-Cell Discontinuity Factors (PDF). These methods are based on well established Equivalence Theory and Generalized Equivalence Theory to generate appropriate group constants. These methods are able to treat all sources of error together, allowing even few-group diffusion with one mesh per cell to reproduce the reference solution. A detailed investigation and consistent comparison of both homogenization techniques showed potential of PDF approach to improve accuracy of core calculation, but also reveal its limitation. In principle, the method is applicable only for the boundary conditions at which it was created, i.e. for boundary conditions considered during the homogenization process---normally zero current. Therefore, there exists a need to improve this method, making it more general and environment independent. The goal of proposed general homogenization technique is to create a function that is able to correctly predict the appropriate correction factor with only homogeneous information available, i.e. a function based on heterogeneous solution that could approximate PDFs using homogeneous solution. It has been shown that the PDF can be well approximated by least-square polynomial fit of non-dimensional heterogeneous solution and later used for PDF prediction using homogeneous solution. This shows a promise for PDF prediction for off-reference conditions, such as during reactor transients which provide conditions that can not typically be anticipated a priori.

Fast All-Sky Radiation Model for Solar Applications (FARMS): A Brief Overview of Mechanisms, Performance, and Applications: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Yu; Sengupta, Manajit

Solar radiation can be computed using radiative transfer models, such as the Rapid Radiation Transfer Model (RRTM) and its general circulation model applications, and used for various energy applications. Due to the complexity of computing radiation fields in aerosol and cloudy atmospheres, simulating solar radiation can be extremely time-consuming, but many approximations--e.g., the two-stream approach and the delta-M truncation scheme--can be utilized. To provide a new fast option for computing solar radiation, we developed the Fast All-sky Radiation Model for Solar applications (FARMS) by parameterizing the simulated diffuse horizontal irradiance and direct normal irradiance for cloudy conditions from the RRTMmore » runs using a 16-stream discrete ordinates radiative transfer method. The solar irradiance at the surface was simulated by combining the cloud irradiance parameterizations with a fast clear-sky model, REST2. To understand the accuracy and efficiency of the newly developed fast model, we analyzed FARMS runs using cloud optical and microphysical properties retrieved using GOES data from 2009-2012. The global horizontal irradiance for cloudy conditions was simulated using FARMS and RRTM for global circulation modeling with a two-stream approximation and compared to measurements taken from the U.S. Department of Energy's Atmospheric Radiation Measurement Climate Research Facility Southern Great Plains site. Our results indicate that the accuracy of FARMS is comparable to or better than the two-stream approach; however, FARMS is approximately 400 times more efficient because it does not explicitly solve the radiative transfer equation for each individual cloud condition. Radiative transfer model runs are computationally expensive, but this model is promising for broad applications in solar resource assessment and forecasting. It is currently being used in the National Solar Radiation Database, which is publicly available from the National Renewable Energy Laboratory at http://nsrdb.nrel.gov.« less

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Discrete linear canonical transforms based on dilated Hermite functions.

PubMed

Pei, Soo-Chang; Lai, Yun-Chiu

2011-08-01

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

Fisher Scoring Method for Parameter Estimation of Geographically Weighted Ordinal Logistic Regression (GWOLR) Model

NASA Astrophysics Data System (ADS)

Widyaningsih, Purnami; Retno Sari Saputro, Dewi; Nugrahani Putri, Aulia

2017-06-01

GWOLR model combines geographically weighted regression (GWR) and (ordinal logistic reression) OLR models. Its parameter estimation employs maximum likelihood estimation. Such parameter estimation, however, yields difficult-to-solve system of nonlinear equations, and therefore numerical approximation approach is required. The iterative approximation approach, in general, uses Newton-Raphson (NR) method. The NR method has a disadvantage—its Hessian matrix is always the second derivatives of each iteration so it does not always produce converging results. With regard to this matter, NR model is modified by substituting its Hessian matrix into Fisher information matrix, which is termed Fisher scoring (FS). The present research seeks to determine GWOLR model parameter estimation using Fisher scoring method and apply the estimation on data of the level of vulnerability to Dengue Hemorrhagic Fever (DHF) in Semarang. The research concludes that health facilities give the greatest contribution to the probability of the number of DHF sufferers in both villages. Based on the number of the sufferers, IR category of DHF in both villages can be determined.

Economic impacts of the Pueblo Smoke-Free Air Act.

PubMed

Young, Walter F; Szychowski, Jeffery; Karp, Shelley; Liu, Lucia; Diedrich, Robert T

2010-03-01

On July 1, 2003, the city of Pueblo CO enacted a smokefree ordinance (Pueblo Smoke-Free Air Act [PSFAA]) that prohibited smoking in public places and workplaces, including taverns and restaurants. Opponents to this ordinance argued that it would have a negative impact on tavern and restaurant sales. The purpose of this study was to determine whether the PSFAA had a negative economic impact on tavern and restaurant sales tax revenues. With data gathered in 2007, this study implemented an interrupted time-series model in 2008, using 42 months of pre- and post-intervention sales tax revenue data for Pueblo to determine whether implementation of this ordinance had an effect on tavern and restaurant sales tax revenues. Ratios of tavern and restaurant openings to closings were also computed for the pre- and post-intervention periods. Pre-post sales tax revenue data showed slight losses in sales tax revenue for taverns, and gains for restaurants, which more than offset the tavern losses. After adjusting for the consumer price index, the city of Pueblo experienced a 20.3% gain in combined tavern and restaurant sales tax revenues from the pre-ordinance period to the post-ordinance period. The ratio of tavern openings to closings improved from 1:1 pre-period to 3.3:1 post-period and the restaurant ratio remained unchanged at approximately 1.78:1 from pre- to post-period. There is no evidence that the PSFAA had a negative economic impact on consumer price index-adjusted tavern and restaurant sales tax revenues. From a fiscal policy perspective, this ordinance may have contributed to a net increase in sales tax revenues for the city of Pueblo. The business openings/closings data suggest that the confidence Pueblo's business sector had in the local hospitality industry was not negatively influenced by the PSFAA. Copyright (c) 2010 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.

Numerical Computation of Flame Spread over a Thin Solid in Forced Concurrent Flow with Gas-phase Radiation

NASA Technical Reports Server (NTRS)

Jiang, Ching-Biau; T'ien, James S.

1994-01-01

Excerpts from a paper describing the numerical examination of concurrent-flow flame spread over a thin solid in purely forced flow with gas-phase radiation are presented. The computational model solves the two-dimensional, elliptic, steady, and laminar conservation equations for mass, momentum, energy, and chemical species. Gas-phase combustion is modeled via a one-step, second order finite rate Arrhenius reaction. Gas-phase radiation considering gray non-scattering medium is solved by a S-N discrete ordinates method. A simplified solid phase treatment assumes a zeroth order pyrolysis relation and includes radiative interaction between the surface and the gas phase.

Linear Characteristic Spatial Quadrature for Discrete Ordinates Neutral Particle Transport on Arbitrary Triangles

DTIC Science & Technology

1993-06-01

1•) + ) •,(v)(•,L) = ()(Q)+ sEXT (F). (4) The scalar flux, 0, is related to the angular flux, W, by (F)= f (dQ Vh) (5) and the particle current, J...J," v,p’) u +at(U, v) w(u, U, p’)= as(u, v) O(u, v) + SEXT (uv)] (92) 0 Ul,(V) I Assuming the area of the triangle is sufficiently small that cross...M + SEXT () (98) Wvn and WoUT are angular flux averages along the input and output edges, respectively, and are defined by WD Iv = f- ds. V(s.v) (99

Heat Transfer Modelling of Glass Media within TPV Systems

NASA Astrophysics Data System (ADS)

Bauer, Thomas; Forbes, Ian; Penlington, Roger; Pearsall, Nicola

2004-11-01

Understanding and optimisation of heat transfer, and in particular radiative heat transfer in terms of spectral, angular and spatial radiation distributions is important to achieve high system efficiencies and high electrical power densities for thermophtovoltaics (TPV). This work reviews heat transfer models and uses the Discrete Ordinates method. Firstly one-dimensional heat transfer in fused silica (quartz glass) shields was examined for the common arrangement, radiator-air-glass-air-PV cell. It has been concluded that an alternative arrangement radiator-glass-air-PV cell with increased thickness of fused silica should have advantages in terms of improved transmission of convertible radiation and enhanced suppression of non-convertible radiation.

Measurement and modeling of advanced coal conversion processes, Volume II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solomon, P.R.; Serio, M.A.; Hamblen, D.G.

1993-06-01

A two dimensional, steady-state model for describing a variety of reactive and nonreactive flows, including pulverized coal combustion and gasification, is presented. The model, referred to as 93-PCGC-2 is applicable to cylindrical, axi-symmetric systems. Turbulence is accounted for in both the fluid mechanics equations and the combustion scheme. Radiation from gases, walls, and particles is taken into account using a discrete ordinates method. The particle phase is modeled in a lagrangian framework, such that mean paths of particle groups are followed. A new coal-general devolatilization submodel (FG-DVC) with coal swelling and char reactivity submodels has been added.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE PAGES

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Hybrid discrete ordinates and characteristics method for solving the linear Boltzmann equation

NASA Astrophysics Data System (ADS)

Yi, Ce

With the ability of computer hardware and software increasing rapidly, deterministic methods to solve the linear Boltzmann equation (LBE) have attracted some attention for computational applications in both the nuclear engineering and medical physics fields. Among various deterministic methods, the discrete ordinates method (SN) and the method of characteristics (MOC) are two of the most widely used methods. The SN method is the traditional approach to solve the LBE for its stability and efficiency. While the MOC has some advantages in treating complicated geometries. However, in 3-D problems requiring a dense discretization grid in phase space (i.e., a large number of spatial meshes, directions, or energy groups), both methods could suffer from the need for large amounts of memory and computation time. In our study, we developed a new hybrid algorithm by combing the two methods into one code, TITAN. The hybrid approach is specifically designed for application to problems containing low scattering regions. A new serial 3-D time-independent transport code has been developed. Under the hybrid approach, the preferred method can be applied in different regions (blocks) within the same problem model. Since the characteristics method is numerically more efficient in low scattering media, the hybrid approach uses a block-oriented characteristics solver in low scattering regions, and a block-oriented SN solver in the remainder of the physical model. In the TITAN code, a physical problem model is divided into a number of coarse meshes (blocks) in Cartesian geometry. Either the characteristics solver or the SN solver can be chosen to solve the LBE within a coarse mesh. A coarse mesh can be filled with fine meshes or characteristic rays depending on the solver assigned to the coarse mesh. Furthermore, with its object-oriented programming paradigm and layered code structure, TITAN allows different individual spatial meshing schemes and angular quadrature sets for each coarse mesh. Two quadrature types (level-symmetric and Legendre-Chebyshev quadrature) along with the ordinate splitting techniques (rectangular splitting and PN-TN splitting) are implemented. In the S N solver, we apply a memory-efficient 'front-line' style paradigm to handle the fine mesh interface fluxes. In the characteristics solver, we have developed a novel 'backward' ray-tracing approach, in which a bi-linear interpolation procedure is used on the incoming boundaries of a coarse mesh. A CPU-efficient scattering kernel is shared in both solvers within the source iteration scheme. Angular and spatial projection techniques are developed to transfer the angular fluxes on the interfaces of coarse meshes with different discretization grids. The performance of the hybrid algorithm is tested in a number of benchmark problems in both nuclear engineering and medical physics fields. Among them are the Kobayashi benchmark problems and a computational tomography (CT) device model. We also developed an extra sweep procedure with the fictitious quadrature technique to calculate angular fluxes along directions of interest. The technique is applied in a single photon emission computed tomography (SPECT) phantom model to simulate the SPECT projection images. The accuracy and efficiency of the TITAN code are demonstrated in these benchmarks along with its scalability. A modified version of the characteristics solver is integrated in the PENTRAN code and tested within the parallel engine of PENTRAN. The limitations on the hybrid algorithm are also studied.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wan, Xiaoliang; Yu, Haijun

2017-02-01

This paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method (MAM) for a spatially extended system when employing the large deviation principle (LDP) to study the effects of small random perturbations. A dynamic solver is used to approximate the unperturbed system, and a minimum action method is used to approximate the LDP, which corresponds to solving an Euler-Lagrange equation related to but more complicated than the unperturbed system. We will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the LDP, based on which we propose to define both the dynamic solver and the MAM on the same approximation space for spatial discretization. The semi-discrete LDP can then be regarded as the exact LDP of the semi-discrete unperturbed system, which is a finite-dimensional ODE system. We achieve this methodology for the two-dimensional Navier-Stokes equations using a divergence-free approximation space. The method developed can be used to study the nonlinear instability of wall-bounded parallel shear flows, and be generalized straightforwardly to three-dimensional cases. Numerical experiments are presented.

Computing approximate solutions of the protein structure determination problem using global constraints on discrete crystal lattices.

PubMed

Dal Palù, Alessandro; Dovier, Agostino; Pontelli, Enrico

2010-01-01

Crystal lattices are discrete models of the three-dimensional space that have been effectively employed to facilitate the task of determining proteins' natural conformation. This paper investigates alternative global constraints that can be introduced in a constraint solver over discrete crystal lattices. The objective is to enhance the efficiency of lattice solvers in dealing with the construction of approximate solutions of the protein structure determination problem. Some of them (e.g., self-avoiding-walk) have been explicitly or implicitly already used in previous approaches, while others (e.g., the density constraint) are new. The intrinsic complexities of all of them are studied and preliminary experimental results are discussed.

Electrophysiological Markers of Newly Acquired Symbolic Numerical Representations: The Role of Magnitude and Ordinal Information

ERIC Educational Resources Information Center

Merkley, Rebecca; Shimi, Andria; Scerif, Gaia

2016-01-01

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

Past, Present and Future. Dull Knife Memorial College (Indian Action Program Inc.).

ERIC Educational Resources Information Center

1978

Five vocational training programs as well as academic coursework are offered on the Northern Cheyenne Reservation by Dull Knife Memorial College. Established and operated by the Northern Cheyenne, and located in Lame Deer, Montana, the college was chartered by a tribal ordinance in 1975. Approximately 75 trainees are currently involved in the…

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

1997-01-01

Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

PubMed

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Comparison of the performance of the activPAL Professional physical activity logger to a discrete accelerometer-based activity monitor.

PubMed

Godfrey, A; Culhane, K M; Lyons, G M

2007-10-01

The aim of this study was to assess the accuracy of the 'activPAL Professional' physical activity logger by comparing its output to that of a proven discrete accelerometer-based activity monitor during extended measurements on healthy subjects while performing activities of daily living (ADL). Ten healthy adults, with unrestricted mobility, wore both the activPAL and the discrete dual accelerometer (Analog Devices ADXL202)-based activity monitor that recorded in synchronization with each other. The accelerometer derived data were then compared to that generated by the activPAL and a complete statistical and error analysis was performed using a Matlab program. This program determined trunk and thigh inclination angles to distinguish between sitting/lying, standing and stepping for the discrete accelerometer device and amount of time spent on each activity. Analysis was performed on a second-by-second basis and then categorized at 15s intervals in direct comparison with the activPAL generated data. Of the total time monitored (approximately 60 h) the detection accuracies for static and dynamic activities were approximately 98%. In a population of healthy adults, the data obtained from the activPAL Professional physical activity logger for both static and dynamic activities showed a close match to a proven discrete accelerometer data with an offset of approximately 2% between the two systems.

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Approximate Locality for Quantum Systems on Graphs

NASA Astrophysics Data System (ADS)

Osborne, Tobias J.

2008-10-01

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)1557-2862]: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Exponential Characteristic Spatial Quadrature for Discrete Ordinates Neutral Particle Transport in Slab Geometry

DTIC Science & Technology

1992-03-01

left bdy = 0 vacuum current incident at left boundary = I type of current incident at left bdy = 0 isotropic surface Src region# cR SigmaR SourceR nc...0 type of current incident at left bdy = 0 isotropic surface Src region# cR SigmaR SourceR nc Right Bdy 1 0.5000 .3OD+00 0.0000D+00 256. 16.0000 2... SigmaR SourceR nc Right Bdy 1 0.1000 1.0000D+00 0.0000D+00 256. 16.0000 2 0.9500 1.0(OOD+00 1.0000D+00 256. 32.0000 type of right bdy = 0 vacuum current

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Durlofsky, L. J.

2016-10-01

A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.

Prediction of spectral acceleration response ordinates based on PGA attenuation

USGS Publications Warehouse

Graizer, V.; Kalkan, E.

2009-01-01

Developed herein is a new peak ground acceleration (PGA)-based predictive model for 5% damped pseudospectral acceleration (SA) ordinates of free-field horizontal component of ground motion from shallow-crustal earthquakes. The predictive model of ground motion spectral shape (i.e., normalized spectrum) is generated as a continuous function of few parameters. The proposed model eliminates the classical exhausted matrix of estimator coefficients, and provides significant ease in its implementation. It is structured on the Next Generation Attenuation (NGA) database with a number of additions from recent Californian events including 2003 San Simeon and 2004 Parkfield earthquakes. A unique feature of the model is its new functional form explicitly integrating PGA as a scaling factor. The spectral shape model is parameterized within an approximation function using moment magnitude, closest distance to the fault (fault distance) and VS30 (average shear-wave velocity in the upper 30 m) as independent variables. Mean values of its estimator coefficients were computed by fitting an approximation function to spectral shape of each record using robust nonlinear optimization. Proposed spectral shape model is independent of the PGA attenuation, allowing utilization of various PGA attenuation relations to estimate the response spectrum of earthquake recordings.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

Characteristic correlation study of UV disinfection performance for ballast water treatment

NASA Astrophysics Data System (ADS)

Ba, Te; Li, Hongying; Osman, Hafiiz; Kang, Chang-Wei

2016-11-01

Characteristic correlation between ultraviolet disinfection performance and operating parameters, including ultraviolet transmittance (UVT), lamp power and water flow rate, was studied by numerical and experimental methods. A three-stage model was developed to simulate the fluid flow, UV radiation and the trajectories of microorganisms. Navier-Stokes equation with k-epsilon turbulence was solved to model the fluid flow, while discrete ordinates (DO) radiation model and discrete phase model (DPM) were used to introduce UV radiation and microorganisms trajectories into the model, respectively. The UV dose statistical distribution for the microorganisms was found to move to higher value with the increase of UVT and lamp power, but moves to lower value when the water flow rate increases. Further investigation shows that the fluence rate increases exponentially with UVT but linearly with the lamp power. The average and minimum resident time decreases linearly with the water flow rate while the maximum resident time decrease rapidly in a certain range. The current study can be used as a digital design and performance evaluation tool of the UV reactor for ballast water treatment.

The compulsory psychiatric regime in Hong Kong: Constitutional and ethical perspectives.

PubMed

Cheung, Daisy

This article examines the compulsory psychiatric regime in Hong Kong. Under section 36 of the Mental Health Ordinance, which authorises long-term detention of psychiatric patients, a District Judge is required to countersign the form filled out by the registered medical practitioners in order for the detention to be valid. Case law, however, has shown that the role of the District Judge is merely administrative. This article suggests that, as it currently stands, the compulsory psychiatric regime in Hong Kong is unconstitutional because it fails the proportionality test. In light of this conclusion, the author proposes two solutions to deal with the issue, by common law or by legislative reform. The former would see an exercise of discretion by the courts read into section 36, while the latter would involve piecemeal reform of the relevant provisions to give the courts an explicit discretion to consider substantive issues when reviewing compulsory detention applications. The author argues that these solutions would introduce effective judicial supervision into the compulsory psychiatric regime and safeguard against abuse of process. Copyright © 2016 Elsevier Ltd. All rights reserved.

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

The Evolution and Discharge of Electric Fields within a Thunderstorm

NASA Astrophysics Data System (ADS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-05-01

A 3-dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed. If the spatial derivatives are approximated by a method akin to the ☐ scheme and if the temporal derivative is approximated by either a backward difference or the Crank-Nicholson scheme, we show that the resulting discretization is unconditionally stable. The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity. Max-norm error estimates for the discrete approximations are established. To handle the propagation of lightning, special numerical techniques are devised based on the Inverse Matrix Modification Formula and Cholesky updates. Numerical comparisons between the model and theoretical results of Wilson and Holzer-Saxon are presented. We also apply our model to a storm observed at the Kennedy Space Center on July 11, 1978.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

Phase computations and phase models for discrete molecular oscillators.

PubMed

Suvak, Onder; Demir, Alper

2012-06-11

Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations.

Phase computations and phase models for discrete molecular oscillators

PubMed Central

2012-01-01

Background Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. Results In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. Conclusions The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations. PMID:22687330

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadia T.

1999-01-01

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

NASA Astrophysics Data System (ADS)

Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.

2018-01-01

We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

DTIC Science & Technology

2015-08-13

conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed

In Praise of Numerical Computation

NASA Astrophysics Data System (ADS)

Yap, Chee K.

Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

2002-01-01

We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G

2013-01-01

In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and themore » recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work.« less

Discrete ordinate quadrature selection for reactor-based Eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jarrell, J. J.; Evans, T. M.; Davidson, G. G.

2013-07-01

In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and themore » recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work. (authors)« less

Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions

DTIC Science & Technology

2012-08-01

small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately...implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This...probability distribution is given by the inverse of the Hessian of the negative log likelihood function. For Gaussian data noise and model error, this

High order discretization techniques for real-space ab initio simulations

NASA Astrophysics Data System (ADS)

Anderson, Christopher R.

2018-03-01

In this paper, we present discretization techniques to address numerical problems that arise when constructing ab initio approximations that use real-space computational grids. We present techniques to accommodate the singular nature of idealized nuclear and idealized electronic potentials, and we demonstrate the utility of using high order accurate grid based approximations to Poisson's equation in unbounded domains. To demonstrate the accuracy of these techniques, we present results for a Full Configuration Interaction computation of the dissociation of H2 using a computed, configuration dependent, orbital basis set.

Invariant patterns in crystal lattices: Implications for protein folding algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

HART,WILLIAM E.; ISTRAIL,SORIN

2000-06-01

Crystal lattices are infinite periodic graphs that occur naturally in a variety of geometries and which are of fundamental importance in polymer science. Discrete models of protein folding use crystal lattices to define the space of protein conformations. Because various crystal lattices provide discretizations of the same physical phenomenon, it is reasonable to expect that there will exist invariants across lattices related to fundamental properties of the protein folding process. This paper considers whether performance-guaranteed approximability is such an invariant for HP lattice models. The authors define a master approximation algorithm that has provable performance guarantees provided that a specificmore » sublattice exists within a given lattice. They describe a broad class of crystal lattices that are approximable, which further suggests that approximability is a general property of HP lattice models.« less

Modeling potential effects of reduced calories in kids' meals with toy giveaways.

PubMed

Freij, Maysoun Y; Sell, Randall L; Bozack, Anne K; Weiss, Linda J; Garcia, Ana C

2014-02-01

Given the large proportion of daily calories attributable to fast food, there is growing interest in considering whether ordinances that restrict calories in kids' meals with toy giveaways could avert weight gain among children. Based upon a literature review and stakeholder feedback, a model was developed to estimate the potential number of children that could be affected by a statewide toy giveaway ordinance and the caloric savings should such a policy effectively reduce the number of calories in kids' meals with toy giveaways. Assumptions included the estimated number of children that eat fast food each day, the proportion that choose a kids' meal with a toy, the caloric savings of a kids' meal that meets nutrition standards, and the degree to which these savings could result in weight gain averted per child per year. Using New York as a case study, the model estimates that, on a typical day, 5% (163,571) of children 0-12 years of age in New York could be affected by a toy ordinance. A child who typically consumes fast food two times per week could avoid gaining approximately 2 pounds per year with an ordinance requiring kids' meals to be ≤550 calories. The amount of weight gain averted would vary according to the calorie limit set by the law and the frequency of consumption per week. Our model indicates that a reduction in calories in kids' meals with toy giveaways has the potential to positively affect weight gain in a considerable percentage of children. Limitations of the model are considered.

Starfish (Asteroidea, Echinodermata) from the Faroe Islands; spatial distribution and abundance

NASA Astrophysics Data System (ADS)

Ringvold, H.; Andersen, T.

2016-01-01

"Marine benthic fauna of the Faroe Islands" (BIOFAR) is a large programme with a focus on collecting invertebrate fauna from the Faroes (62°N and 7°W). Cruises were undertaken from 1987 to 1990, and starfish (Asteroidea, Echinodermata) collected during this time were analysed. Asteroidea were sampled at ~50% of all BIOFAR stations. A Detritus sledge and a Triangular dredge proved to be the most efficient equipment, collecting over 60% of the specimens. In total 2473 specimens were collected from 20 to 1500 m depth, including 41 species from 17 families and 31 genera. Henricia pertusa (O. F. Müller, 1776) group, Pontaster tenuispinus (Düben & Koren, 1846), and Leptychaster arcticus (M. Sars, 1851) showed highest relative abundance. Maximum species diversity was found at 500-700 m depth, which coincides with the transition zone of water masses (North Icelandic Winter Water and Arctic Intermediate Water (NI/AI)) at approximately 400-600 m depth. 63% of the species were recorded at an average-weighted depth above 600 m. Two different ordination methods (detrended correspondence analysis (DCA) and nonmetric multidimensional scaling (NMDS)) gave highly consistent representations of the community structure gradients. The first ordination axis scores did not show significant relationships with any environmental variable. Biological covariates like the presence of Lophelia corals were not significantly related to ordination scores on any axis. The second ordination axis scores were significantly correlated with depth. Temperature and salinity were highly correlated (r=0.90), and both negatively correlated with depth (r=-0.69 and r=-0.57, respectively).

Among-character rate variation distributions in phylogenetic analysis of discrete morphological characters.

PubMed

Harrison, Luke B; Larsson, Hans C E

2015-03-01

Likelihood-based methods are commonplace in phylogenetic systematics. Although much effort has been directed toward likelihood-based models for molecular data, comparatively less work has addressed models for discrete morphological character (DMC) data. Among-character rate variation (ACRV) may confound phylogenetic analysis, but there have been few analyses of the magnitude and distribution of rate heterogeneity among DMCs. Using 76 data sets covering a range of plants, invertebrate, and vertebrate animals, we used a modified version of MrBayes to test equal, gamma-distributed and lognormally distributed models of ACRV, integrating across phylogenetic uncertainty using Bayesian model selection. We found that in approximately 80% of data sets, unequal-rates models outperformed equal-rates models, especially among larger data sets. Moreover, although most data sets were equivocal, more data sets favored the lognormal rate distribution relative to the gamma rate distribution, lending some support for more complex character correlations than in molecular data. Parsimony estimation of the underlying rate distributions in several data sets suggests that the lognormal distribution is preferred when there are many slowly evolving characters and fewer quickly evolving characters. The commonly adopted four rate category discrete approximation used for molecular data was found to be sufficient to approximate a gamma rate distribution with discrete characters. However, among the two data sets tested that favored a lognormal rate distribution, the continuous distribution was better approximated with at least eight discrete rate categories. Although the effect of rate model on the estimation of topology was difficult to assess across all data sets, it appeared relatively minor between the unequal-rates models for the one data set examined carefully. As in molecular analyses, we argue that researchers should test and adopt the most appropriate model of rate variation for the data set in question. As discrete characters are increasingly used in more sophisticated likelihood-based phylogenetic analyses, it is important that these studies be built on the most appropriate and carefully selected underlying models of evolution. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

ON THE ROLE OF INVOLUTIONS IN THE DISCONTINUOUS GALERKIN DISCRETIZATION OF MAXWELL AND MAGNETOHYDRODYNAMIC SYSTEMS

NASA Technical Reports Server (NTRS)

Barth, Timothy

2005-01-01

The role of involutions in energy stability of the discontinuous Galerkin (DG) discretization of Maxwell and magnetohydrodynamic (MHD) systems is examined. Important differences are identified in the symmetrization of the Maxwell and MHD systems that impact the construction of energy stable discretizations using the DG method. Specifically, general sufficient conditions to be imposed on the DG numerical flux and approximation space are given so that energy stability is retained These sufficient conditions reveal the favorable energy consequence of imposing continuity in the normal component of the magnetic induction field at interelement boundaries for MHD discretizations. Counterintuitively, this condition is not required for stability of Maxwell discretizations using the discontinuous Galerkin method.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV - Multi-discrete time method

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1987-01-01

It is shown that a discrete multi-time method can be constructed to obtain approximations to the periodic solutions of a special class of second-order nonlinear difference equations containing a small parameter. Three examples illustrating the method are presented.

Denoising embolic Doppler ultrasound signals using Dual Tree Complex Discrete Wavelet Transform.

PubMed

Serbes, Gorkem; Aydin, Nizamettin

2010-01-01

Early and accurate detection of asymptomatic emboli is important for monitoring of preventive therapy in stroke-prone patients. One of the problems in detection of emboli is the identification of an embolic signal caused by very small emboli. The amplitude of the embolic signal may be so small that advanced processing methods are required to distinguish these signals from Doppler signals arising from red blood cells. In this study instead of conventional discrete wavelet transform, the Dual Tree Complex Discrete Wavelet Transform was used for denoising embolic signals. Performances of both approaches were compared. Unlike the conventional discrete wavelet transform discrete complex wavelet transform is a shift invariant transform with limited redundancy. Results demonstrate that the Dual Tree Complex Discrete Wavelet Transform based denoising outperforms conventional discrete wavelet denoising. Approximately 8 dB improvement is obtained by using the Dual Tree Complex Discrete Wavelet Transform compared to the improvement provided by the conventional Discrete Wavelet Transform (less than 5 dB).

Utilization of O4 slant column density to derive aerosol layer height from a spaceborne UV-visible hyperspectral sensor: sensitivity and case study

NASA Astrophysics Data System (ADS)

Park, S. S.; Kim, J.; Lee, H.; Torres, O.; Lee, K.-M.; Lee, S. D.

2015-03-01

The sensitivities of oxygen-dimer (O4) slant column densities (SCDs) to changes in aerosol layer height are investigated using simulated radiances by a radiative transfer model, Linearized Discrete Ordinate Radiative Transfer (LIDORT), and Differential Optical Absorption Spectroscopy (DOAS) technique. The sensitivities of the O4 SCDs to aerosol types and optical properties are also evaluated and compared. Among the O4 absorption bands at 340, 360, 380, and 477 nm, the O4 absorption band at 477 nm is found to be the most suitable to retrieve the aerosol effective height. However, the O4 SCD at 477 nm is significantly influenced not only by the aerosol layer effective height but also by aerosol vertical profiles, optical properties including single scattering albedo (SSA), aerosol optical depth (AOD), and surface albedo. Overall, the error of the retrieved aerosol effective height is estimated to be 414 m (16.5%), 564 m (22.4%), and 1343 m (52.5%) for absorbing, dust, and non-absorbing aerosol, respectively, assuming knowledge on the aerosol vertical distribution type. Using radiance data from the Ozone Monitoring Instrument (OMI), a new algorithm is developed to derive the aerosol effective height over East Asia after the determination of the aerosol type and AOD from the MODerate resolution Imaging Spectroradiometer (MODIS). The retrieved aerosol effective heights are lower by approximately 300 m (27 %) compared to those obtained from the ground-based LIDAR measurements.

Benchmark measurements and calculations of a 3-dimensional neutron streaming experiment

NASA Astrophysics Data System (ADS)

Barnett, D. A., Jr.

1991-02-01

An experimental assembly known as the Dog-Legged Void assembly was constructed to measure the effect of neutron streaming in iron and void regions. The primary purpose of the measurements was to provide benchmark data against which various neutron transport calculation tools could be compared. The measurements included neutron flux spectra at four places and integral measurements at two places in the iron streaming path as well as integral measurements along several axial traverses. These data have been used in the verification of Oak Ridge National Laboratory's three-dimensional discrete ordinates code, TORT. For a base case calculation using one-half inch mesh spacing, finite difference spatial differencing, an S(sub 16) quadrature and P(sub 1) cross sections in the MUFT multigroup structure, the calculated solution agreed to within 18 percent with the spectral measurements and to within 24 percent of the integral measurements. Variations on the base case using a fewgroup energy structure and P(sub 1) and P(sub 3) cross sections showed similar agreement. Calculations using a linear nodal spatial differencing scheme and fewgroup cross sections also showed similar agreement. For the same mesh size, the nodal method was seen to require 2.2 times as much CPU time as the finite difference method. A nodal calculation using a typical mesh spacing of 2 inches, which had approximately 32 times fewer mesh cells than the base case, agreed with the measurements to within 34 percent and yet required on 8 percent of the CPU time.

Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

2016-02-15

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

The nonconforming virtual element method for eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

Introduction of Parallel GPGPU Acceleration Algorithms for the Solution of Radiative Transfer

NASA Technical Reports Server (NTRS)

Godoy, William F.; Liu, Xu

2011-01-01

General-purpose computing on graphics processing units (GPGPU) is a recent technique that allows the parallel graphics processing unit (GPU) to accelerate calculations performed sequentially by the central processing unit (CPU). To introduce GPGPU to radiative transfer, the Gauss-Seidel solution of the well-known expressions for 1-D and 3-D homogeneous, isotropic media is selected as a test case. Different algorithms are introduced to balance memory and GPU-CPU communication, critical aspects of GPGPU. Results show that speed-ups of one to two orders of magnitude are obtained when compared to sequential solutions. The underlying value of GPGPU is its potential extension in radiative solvers (e.g., Monte Carlo, discrete ordinates) at a minimal learning curve.

Development and validation of P-MODTRAN7 and P-MCScene, 1D and 3D polarimetric radiative transfer models

NASA Astrophysics Data System (ADS)

Hawes, Frederick T.; Berk, Alexander; Richtsmeier, Steven C.

2016-05-01

A validated, polarimetric 3-dimensional simulation capability, P-MCScene, is being developed by generalizing Spectral Sciences' Monte Carlo-based synthetic scene simulation model, MCScene, to include calculation of all 4 Stokes components. P-MCScene polarimetric optical databases will be generated by a new version (MODTRAN7) of the government-standard MODTRAN radiative transfer algorithm. The conversion of MODTRAN6 to a polarimetric model is being accomplished by (1) introducing polarimetric data, by (2) vectorizing the MODTRAN radiation calculations and by (3) integrating the newly revised and validated vector discrete ordinate model VDISORT3. Early results, presented here, demonstrate a clear pathway to the long-term goal of fully validated polarimetric models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitzmann, D., E-mail: daniel.kitzmann@csh.unibe.ch

Carbon dioxide ice clouds are thought to play an important role for cold terrestrial planets with thick CO{sub 2} dominated atmospheres. Various previous studies showed that a scattering greenhouse effect by carbon dioxide ice clouds could result in a massive warming of the planetary surface. However, all of these studies only employed simplified two-stream radiative transfer schemes to describe the anisotropic scattering. Using accurate radiative transfer models with a general discrete ordinate method, this study revisits this important effect and shows that the positive climatic impact of carbon dioxide clouds was strongly overestimated in the past. The revised scattering greenhousemore » effect can have important implications for the early Mars, but also for planets like the early Earth or the position of the outer boundary of the habitable zone.« less

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

A study of stationarity in time series by using wavelet transform

NASA Astrophysics Data System (ADS)

Dghais, Amel Abdoullah Ahmed; Ismail, Mohd Tahir

2014-07-01

In this work the core objective is to apply discrete wavelet transform (DWT) functions namely Haar, Daubechies, Symmlet, Coiflet and discrete approximation of the meyer wavelets in non-stationary financial time series data from US stock market (DJIA30). The data consists of 2048 daily data of closing index starting from December 17, 2004 until October 23, 2012. From the unit root test the results show that the data is non stationary in the level. In order to study the stationarity of a time series, the autocorrelation function (ACF) is used. Results indicate that, Haar function is the lowest function to obtain noisy series as compared to Daubechies, Symmlet, Coiflet and discrete approximation of the meyer wavelets. In addition, the original data after decomposition by DWT is less noisy series than decomposition by DWT for return time series.

Analytical approximation of a distorted reflector surface defined by a discrete set of points

NASA Technical Reports Server (NTRS)

Acosta, Roberto J.; Zaman, Afroz A.

1988-01-01

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

NASA Astrophysics Data System (ADS)

Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor

2017-01-01

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

Development of a total hydrocarbon ordinal job-exposure matrix for workers responding to the Deepwater Horizon disaster: The GuLF STUDY.

PubMed

Stewart, Patricia A; Stenzel, Mark R; Ramachandran, Gurumurthy; Banerjee, Sudipto; Huynh, Tran B; Groth, Caroline P; Kwok, Richard K; Blair, Aaron; Engel, Lawrence S; Sandler, Dale P

2018-05-01

The GuLF STUDY is a cohort study investigating the health of workers who responded to the Deepwater Horizon oil spill in the Gulf of Mexico in 2010. The objective of this effort was to develop an ordinal job-exposure matrix (JEM) of airborne total hydrocarbons (THC), dispersants, and particulates to estimate study participants' exposures. Information was collected on participants' spill-related tasks. A JEM of exposure groups (EGs) was developed from tasks and THC air measurements taken during and after the spill using relevant exposure determinants. THC arithmetic means were developed for the EGs, assigned ordinal values, and linked to the participants using determinants from the questionnaire. Different approaches were taken for combining exposures across EGs. EGs for dispersants and particulates were based on questionnaire responses. Considerable differences in THC exposure levels were found among EGs. Based on the maximum THC level participants experienced across any job held, ∼14% of the subjects were identified in the highest exposure category. Approximately 10% of the cohort was exposed to dispersants or particulates. Considerable exposure differences were found across the various EGs, facilitating investigation of exposure-response relationships. The JEM is flexible to allow for different assumptions about several possibly relevant exposure metrics.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Developing a Game Interface to Assess Risk Perception with Respect to Two Key Dimensions of Risk (Frequency and Severity) in Contexts Where Risks Are Elevated from Their Accepted, "Typical" Values.

PubMed

Goodman, William M; Ma, Zhenfeng; Andrade, Angie

2015-06-01

This four-stage study culminated in a game interface designed to calibrate people's perceptions of net risk (combining frequency and severity), in contexts where risks are elevated from their accepted, "typical" values, as when avalanche threats elevate the risks of "skiing" above levels skiers normally accept. Risk prompts are displayed dynamically, in naturalistic language, and not, for example, as static displays of dollar amounts or probabilities. Individual differences are measured. In Stage 1 (pilot), focus groups (n=9) piloted procedures, visual prompts, and examples of contexts where risks elevated from the "usual," for use in upcoming stages. In Stage 2 (exploratory), participants (primarily students; n=119; mean age, 20.1 years; 64 percent male) were assigned to risk contexts, answered demographic and risk-history questions, and then matched risk-description prompts to perceived "appropriate" levels along an ordinal risk scale. Descriptive measures and graphs showed response distributions; chi-squared analyses compared responses for different demographics. In Stage 3 (manipulating "cards"), participants (n=80; mean age, 37 years; 60 percent male) matched naturalistic risk prompts with ordinal risk positions. Regressions compared cards' placements with their "expected" (per exploratory Stage 2) placements. In Stage 4, the interface was coded in the Unity(®) (implemented at Business and IT Capstone, University of Ontario Institute of Technology, Oshawa, ON, Canada) development environment. In Stage 1, ambiguities in draft wordings/displays for Stage 2 were identified and corrected. Three risk contexts emerged: traffic/hidden intersection; skiing/avalanche; and swimming/drowning. In Stage 2, for traffic and skiing contexts, responses relating ordinal risk categories to realistic examples were observed to cluster around values potentially usable as markers. No associations appeared with demographic variables. In Stage 3, actual and "expected" ordinal-risk-category assignments for naturalistic risk markers were well correlated. "Approximate mappings" between markers and categories appeared stable. In Stage 4, the interface design incorporated the "approximate mappings"-yet also incorporated a "tuning phase," for measuring and recording individual differences. The interface can capture individual differences in risk perception on two key dimensions (frequency and severity)-viewed in dynamic, naturalistic scenarios, where risk levels are increased.

Design and Implementation of Parallel Algorithms

DTIC Science & Technology

1992-05-01

Alon, N., Y. Azar, and Y. Ravid [1990]. "Universal sequences for complete graphs," SIAM J. Discrete Math 27. Alon, N., A. Bar-Noy, N. Linial, and D...SIAM J. Discrete Math .’ Klein, P., S. A. Plotkin, C. Stein, and E. Tardos [19911. "Faster approximation algorithms for the unit capacity concurrent

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1991-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Gottlieb, David; Tadmor, Eitan

1990-01-01

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

PubMed

Mendonça, J Ricardo G; Gevorgyan, Yeva

2017-05-01

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

Scattering of electromagnetic waves from a half-space of randomly distributed discrete scatterers and polarized backscattering ratio law

NASA Technical Reports Server (NTRS)

Zhu, P. Y.

1991-01-01

The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Application of the discrete generalized multigroup method to ultra-fine energy mesh in infinite medium calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibson, N. A.; Forget, B.

2012-07-01

The Discrete Generalized Multigroup (DGM) method uses discrete Legendre orthogonal polynomials to expand the energy dependence of the multigroup neutron transport equation. This allows a solution on a fine energy mesh to be approximated for a cost comparable to a solution on a coarse energy mesh. The DGM method is applied to an ultra-fine energy mesh (14,767 groups) to avoid using self-shielding methodologies without introducing the cost usually associated with such energy discretization. Results show DGM to converge to the reference ultra-fine solution after a small number of recondensation steps for multiple infinite medium compositions. (authors)

Algebraic perturbation theory for dense liquids with discrete potentials

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2007-06-01

A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

Phase-space finite elements in a least-squares solution of the transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

A fast radiative transfer method for the simulation of visible satellite imagery

NASA Astrophysics Data System (ADS)

Scheck, Leonhard; Frèrebeau, Pascal; Buras-Schnell, Robert; Mayer, Bernhard

2016-05-01

A computationally efficient radiative transfer method for the simulation of visible satellite images is presented. The top of atmosphere reflectance is approximated by a function depending on vertically integrated optical depths and effective particle sizes for water and ice clouds, the surface albedo, the sun and satellite zenith angles and the scattering angle. A look-up table (LUT) for this reflectance function is generated by means of the discrete ordinate method (DISORT). For a constant scattering angle the reflectance is a relatively smooth and symmetric function of the two zenith angles, which can be well approximated by the lowest-order terms of a 2D Fourier series. By storing only the lowest Fourier coefficients and adopting a non-equidistant grid for the scattering angle, the LUT is reduced to a size of 21 MB per satellite channel. The computation of the top of atmosphere reflectance requires only the calculation of the cloud parameters from the model state and the evaluation and interpolation of the reflectance function using the compressed LUT and is thus orders of magnitude faster than DISORT. The accuracy of the method is tested by generating synthetic satellite images for the 0.6 μm and 0.8 μm channels of the SEVIRI instrument for operational COSMO-DE model forecasts from the German Weather Service (DWD) and comparing them to DISORT results. For a test period in June the root mean squared absolute reflectance error is about 10-2 and the mean relative reflectance error is less than 2% for both channels. For scattering angles larger than 170 ° the rapid variation of reflectance with the particle size related to the backscatter glory reduces the accuracy and the errors increase by a factor of 3-4. Speed and accuracy of the new method are sufficient for operational data assimilation and high-resolution model verification applications.

Is Best-Worst Scaling Suitable for Health State Valuation? A Comparison with Discrete Choice Experiments.

PubMed

Krucien, Nicolas; Watson, Verity; Ryan, Mandy

2017-12-01

Health utility indices (HUIs) are widely used in economic evaluation. The best-worst scaling (BWS) method is being used to value dimensions of HUIs. However, little is known about the properties of this method. This paper investigates the validity of the BWS method to develop HUI, comparing it to another ordinal valuation method, the discrete choice experiment (DCE). Using a parametric approach, we find a low level of concordance between the two methods, with evidence of preference reversals. BWS responses are subject to decision biases, with significant effects on individuals' preferences. Non parametric tests indicate that BWS data has lower stability, monotonicity and continuity compared to DCE data, suggesting that the BWS provides lower quality data. As a consequence, for both theoretical and technical reasons, practitioners should be cautious both about using the BWS method to measure health-related preferences, and using HUI based on BWS data. Given existing evidence, it seems that the DCE method is a better method, at least because its limitations (and measurement properties) have been extensively researched. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

NASA Technical Reports Server (NTRS)

Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen

1995-01-01

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Discrete gravity on random tensor network and holographic Rényi entropy

NASA Astrophysics Data System (ADS)

Han, Muxin; Huang, Shilin

2017-11-01

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Extinction efficiencies from DDA calculations solved for finite circular cylinders and disks

NASA Technical Reports Server (NTRS)

Withrow, J. R.; Cox, S. K.

1993-01-01

One of the most commonly noted uncertainties with respect to the modeling of cirrus clouds and their effect upon the planetary radiation balance is the disputed validity of the use of Mie scattering results as an approximation to the scattering results of the hexagonal plates and columns found in cirrus clouds. This approximation has historically been a kind of default, a result of the lack of an appropriate analytical solution of Maxwell's equations to particles other than infinite cylinders and spheroids. Recently, however, the use of such approximate techniques as the Discrete Dipole Approximation has made scattering solutions on such particles a computationally intensive but feasible possibility. In this study, the Discrete Dipole Approximation (DDA) developed by Flatau (1992) is used to find such solutions for homogeneous, circular cylinders and disks. This can serve to not only assess the validity of the current radiative transfer schemes which are available for the study of cirrus but also to extend the current approximation of equivalent spheres to an approximation of second order, homogeneous finite circular cylinders and disks. The results will be presented in the form of a single variable, the extinction efficiency.

Adaptive hybrid simulations for multiscale stochastic reaction networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

A Monte Carlo Application to Approximate the Integral from a to b of e Raised to the x Squared.

ERIC Educational Resources Information Center

Easterday, Kenneth; Smith, Tommy

1992-01-01

Proposes an alternative means of approximating the value of complex integrals, the Monte Carlo procedure. Incorporating a discrete approach and probability, an approximation is obtained from the ratio of computer-generated points falling under the curve to the number of points generated in a predetermined rectangle. (MDH)

On Studying Common Factor Dominance and Approximate Unidimensionality in Multicomponent Measuring Instruments with Discrete Items

ERIC Educational Resources Information Center

Raykov, Tenko; Marcoulides, George A.

2018-01-01

This article outlines a procedure for examining the degree to which a common factor may be dominating additional factors in a multicomponent measuring instrument consisting of binary items. The procedure rests on an application of the latent variable modeling methodology and accounts for the discrete nature of the manifest indicators. The method…

Numerical treatment of a geometrically nonlinear planar Cosserat shell model

NASA Astrophysics Data System (ADS)

Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

2016-05-01

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.

An efficient algorithm for choosing the degree of a polynomial to approximate discrete nonoscillatory data

NASA Technical Reports Server (NTRS)

Hedgley, D. R.

1978-01-01

An efficient algorithm for selecting the degree of a polynomial that defines a curve that best approximates a data set was presented. This algorithm was applied to both oscillatory and nonoscillatory data without loss of generality.

The emergence of temporal language in Nicaraguan Sign Language

PubMed Central

Kocab, Annemarie; Senghas, Ann; Snedeker, Jesse

2016-01-01

Understanding what uniquely human properties account for the creation and transmission of language has been a central goal of cognitive science. Recently, the study of emerging sign languages, such as Nicaraguan Sign Language (NSL), has offered the opportunity to better understand how languages are created and the roles of the individual learner and the community of users. Here, we examined the emergence of two types of temporal language in NSL, comparing the linguistic devices for conveying temporal information among three sequential age cohorts of signers. Experiment 1 showed that while all three cohorts of signers could communicate about linearly ordered discrete events, only the second and third generations of signers successfully communicated information about events with more complex temporal structure. Experiment 2 showed that signers could discriminate between the types of temporal events in a nonverbal task. Finally, Experiment 3 investigated the ordinal use of numbers (e.g., first, second) in NSL signers, indicating that one strategy younger signers might have for accurately describing events in time might be to use ordinal numbers to mark each event. While the capacity for representing temporal concepts appears to be present in the human mind from the onset of language creation, the linguistic devices to convey temporality do not appear immediately. Evidently, temporal language emerges over generations of language transmission, as a product of individual minds interacting within a community of users. PMID:27591549

The emergence of temporal language in Nicaraguan Sign Language.

PubMed

Kocab, Annemarie; Senghas, Ann; Snedeker, Jesse

2016-11-01

Understanding what uniquely human properties account for the creation and transmission of language has been a central goal of cognitive science. Recently, the study of emerging sign languages, such as Nicaraguan Sign Language (NSL), has offered the opportunity to better understand how languages are created and the roles of the individual learner and the community of users. Here, we examined the emergence of two types of temporal language in NSL, comparing the linguistic devices for conveying temporal information among three sequential age cohorts of signers. Experiment 1 showed that while all three cohorts of signers could communicate about linearly ordered discrete events, only the second and third generations of signers successfully communicated information about events with more complex temporal structure. Experiment 2 showed that signers could discriminate between the types of temporal events in a nonverbal task. Finally, Experiment 3 investigated the ordinal use of numbers (e.g., first, second) in NSL signers, indicating that one strategy younger signers might have for accurately describing events in time might be to use ordinal numbers to mark each event. While the capacity for representing temporal concepts appears to be present in the human mind from the onset of language creation, the linguistic devices to convey temporality do not appear immediately. Evidently, temporal language emerges over generations of language transmission, as a product of individual minds interacting within a community of users. Copyright © 2016 Elsevier B.V. All rights reserved.

Generating Multivariate Ordinal Data via Entropy Principles.

PubMed

Lee, Yen; Kaplan, David

2018-03-01

When conducting robustness research where the focus of attention is on the impact of non-normality, the marginal skewness and kurtosis are often used to set the degree of non-normality. Monte Carlo methods are commonly applied to conduct this type of research by simulating data from distributions with skewness and kurtosis constrained to pre-specified values. Although several procedures have been proposed to simulate data from distributions with these constraints, no corresponding procedures have been applied for discrete distributions. In this paper, we present two procedures based on the principles of maximum entropy and minimum cross-entropy to estimate the multivariate observed ordinal distributions with constraints on skewness and kurtosis. For these procedures, the correlation matrix of the observed variables is not specified but depends on the relationships between the latent response variables. With the estimated distributions, researchers can study robustness not only focusing on the levels of non-normality but also on the variations in the distribution shapes. A simulation study demonstrates that these procedures yield excellent agreement between specified parameters and those of estimated distributions. A robustness study concerning the effect of distribution shape in the context of confirmatory factor analysis shows that shape can affect the robust [Formula: see text] and robust fit indices, especially when the sample size is small, the data are severely non-normal, and the fitted model is complex.

Method of Implementing Digital Phase-Locked Loops

NASA Technical Reports Server (NTRS)

Stephens, Scott A. (Inventor); Thomas, J. Brooks (Inventor)

1997-01-01

In a new formulation for digital phase-locked loops, loop-filter constants are determined from loop roots that can each be selectively placed in the s-plane on the basis of a new set of parameters, each with simple and direct physical meaning in terms of loop noise bandwidth, root-specific decay rate, and root-specific damping. Loops of first to fourth order are treated in the continuous-update approximation (B(sub L)T approaches 0) and in a discrete-update formulation with arbitrary B(sub L)T. Deficiencies of the continuous-update approximation in large-B(sub L)T applications are avoided in the new discrete-update formulation.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Stepwise shockwave velocity determinator

NASA Technical Reports Server (NTRS)

Roth, Timothy E.; Beeson, Harold

1992-01-01

To provide an uncomplicated and inexpensive method for measuring the far-field velocity of a surface shockwave produced by an explosion, a stepwise shockwave velocity determinator (SSVD) was developed. The velocity determinator is constructed of readily available materials and works on the principle of breaking discrete sensors composed of aluminum foil contacts. The discrete sensors have an average breaking threshold of approximately 7 kPa. An incremental output step of 250 mV is created with each foil contact breakage and is logged by analog-to-digital instrumentation. Velocity data obtained from the SSVD is within approximately 11 percent of the calculated surface shockwave velocity of a muzzle blast from a 30.06 rifle.

Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation. [electromagnetic scattering and absorption by interstellar grains

NASA Technical Reports Server (NTRS)

Draine, B. T.; Goodman, Jeremy

1993-01-01

We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Coordinate control of initiative mating device for autonomous underwater vehicle based on TDES

NASA Astrophysics Data System (ADS)

Yan, Zhe-Ping; Hou, Shu-Ping

2005-06-01

A novel initiative mating device, which has four 2-degree manipulators around the mating skirt, is proposed to mate between a skirt of AUV (autonomons underwater vehicle) and a disabled submarine. The primary function of the device is to keep exact mating between skirt and disabled submarine in a badly sub sea environment. According to the characteristic of rescue, an automaton model is brought foward to describe the mating proceed between AUV and manipulators. The coordinated control is implemented by the TDES (time discrete event system). After taking into account the time problem, it is a useful method to control mating by simulation testing. The result shows that it reduces about 70 seconds after using intelligent co-ordinate control based on TDES through the whole mating procedure.

The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions.

PubMed

Arridge, S R; Dehghani, H; Schweiger, M; Okada, E

2000-01-01

We present a method for handling nonscattering regions within diffusing domains. The method develops from an iterative radiosity-diffusion approach using Green's functions that was computationally slow. Here we present an improved implementation using a finite element method (FEM) that is direct. The fundamental idea is to introduce extra equations into the standard diffusion FEM to represent nondiffusive light propagation across a nonscattering region. By appropriate mesh node ordering the computational time is not much greater than for diffusion alone. We compare results from this method with those from a discrete ordinate transport code, and with Monte Carlo calculations. The agreement is very good, and, in addition, our scheme allows us to easily model time-dependent and frequency domain problems.

Revisiting the Scattering Greenhouse Effect of CO2 Ice Clouds

NASA Astrophysics Data System (ADS)

Kitzmann, D.

2016-02-01

Carbon dioxide ice clouds are thought to play an important role for cold terrestrial planets with thick CO2 dominated atmospheres. Various previous studies showed that a scattering greenhouse effect by carbon dioxide ice clouds could result in a massive warming of the planetary surface. However, all of these studies only employed simplified two-stream radiative transfer schemes to describe the anisotropic scattering. Using accurate radiative transfer models with a general discrete ordinate method, this study revisits this important effect and shows that the positive climatic impact of carbon dioxide clouds was strongly overestimated in the past. The revised scattering greenhouse effect can have important implications for the early Mars, but also for planets like the early Earth or the position of the outer boundary of the habitable zone.

Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao

In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

PubMed Central

Rubinsten, Orly; Sury, Dana

2011-01-01

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information. PMID:21935374

Processing ordinality and quantity: the case of developmental dyscalculia.

PubMed

Rubinsten, Orly; Sury, Dana

2011-01-01

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

Important features of home-based support services for older Australians and their informal carers.

PubMed

McCaffrey, Nikki; Gill, Liz; Kaambwa, Billingsley; Cameron, Ian D; Patterson, Jan; Crotty, Maria; Ratcliffe, Julie

2015-11-01

In Australia, newly initiated, publicly subsidised 'Home-Care Packages' designed to assist older people (≥ 65 years of age) living in their own home must now be offered on a 'consumer-directed care' (CDC) basis by service providers. However, CDC models have largely developed in the absence of evidence on users' views and preferences. The aim of this study was to determine what features (attributes) of consumer-directed, home-based support services are important to older people and their informal carers to inform the design of a discrete choice experiment (DCE). Semi-structured, face-to-face interviews were conducted in December 2012-November 2013 with 17 older people receiving home-based support services and 10 informal carers from 5 providers located in South Australia and New South Wales. Salient service characteristics important to participants were determined using thematic and constant comparative analysis and formulated into attributes and attribute levels for presentation within a DCE. Initially, eight broad themes were identified: information and knowledge, choice and control, self-managed continuum, effective co-ordination, effective communication, responsiveness and flexibility, continuity and planning. Attributes were formulated for the DCE by combining overlapping themes such as effective communication and co-ordination, and the self-managed continuum and planning into single attributes. Six salient service features that characterise consumer preferences for the provision of home-based support service models were identified: choice of provider, choice of support worker, flexibility in care activities provided, contact with the service co-ordinator, managing the budget and saving unspent funds. Best practice indicates that qualitative research with individuals who represent the population of interest should guide attribute selection for a DCE and this is the first study to employ such methods in aged care service provision. Further development of services could incorporate methods of consumer engagement such as DCEs which facilitate the identification and quantification of users' views and preferences on alternative models of delivery. © 2015 John Wiley & Sons Ltd.

Morphology and mixing state of aged soot particles at a remote marine free troposphere site: Implications for optical properties

DOE PAGES

China, Swarup; Scarnato, Barbara; Owen, Robert C.; ...

2015-01-14

The radiative properties of soot particles depend on their morphology and mixing state, but their evolution during transport is still elusive. In this paper, we report observations from an electron microscopy analysis of individual particles transported in the free troposphere over long distances to the remote Pico Mountain Observatory in the Azores in the North Atlantic. Approximately 70% of the soot particles were highly compact and of those 26% were thinly coated. Discrete dipole approximation simulations indicate that this compaction results in an increase in soot single scattering albedo by a factor of ≤2.17. The top of the atmosphere directmore » radiative forcing is typically smaller for highly compact than mass-equivalent lacy soot. Lastly, the forcing estimated using Mie theory is within 12% of the forcing estimated using the discrete dipole approximation for a high surface albedo, implying that Mie calculations may provide a reasonable approximation for compact soot above remote marine clouds.« less

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, ourmore » FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.« less

Singular perturbation and time scale approaches in discrete control systems

NASA Technical Reports Server (NTRS)

Naidu, D. S.; Price, D. B.

1988-01-01

After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.

Fuzziness In Approximate And Common-Sense Reasoning In Knowledge-Based Robotics Systems

NASA Astrophysics Data System (ADS)

Dodds, David R.

1987-10-01

Fuzzy functions, a major key to inexact reasoning, are described as they are applied to the fuzzification of robot co-ordinate systems. Linguistic-variables, a means of labelling ranges in fuzzy sets, are used as computationally pragmatic means of representing spatialization metaphors, themselves an extraordinarily rich basis for understanding concepts in orientational terms. Complex plans may be abstracted and simplified in a system which promotes conceptual planning by means of the orientational representation.

The effect of ordinances requiring smoke-free restaurants and bars on revenues: a follow-up.

PubMed Central

Glantz, S A; Smith, L R

1997-01-01

OBJECTIVES: The purpose of this study was to extend an earlier evaluation of the economic effects of ordinances requiring smoke-free restaurants and bars. METHODS: Sales tax data for 15 cities with smoke-free restaurant ordinances, 5 cities and 2 counties with smoke-free bar ordinances, and matched comparison locations were analyzed by multiple regression, including time and a dummy variable for the ordinance. RESULTS: Ordinances had no significant effect on the fraction of total retail sales that went to eating and drinking places or on the ratio between sales in communities with ordinances and sales in comparison communities. Ordinances requiring smoke-free bars had no significant effect on the fraction of revenues going to eating and drinking places that serve all types of liquor. CONCLUSIONS: Smoke-free ordinances do not adversely affect either restaurant or bar sales. PMID:9357356

Numerical predictors of arithmetic success in grades 1-6.

PubMed

Lyons, Ian M; Price, Gavin R; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel

2014-09-01

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1-6. In grades 1-2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing. © 2014 John Wiley & Sons Ltd.

Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra

NASA Astrophysics Data System (ADS)

Rezakhah, Saeid; Maleki, Yasaman

2016-07-01

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.

Adaptive Discrete Hypergraph Matching.

PubMed

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Independent Pixel and Two Dimensional Estimates of LANDSAT-Derived Cloud Field Albedo

NASA Technical Reports Server (NTRS)

Chambers, L. H.; Wielicki, Bruce A.; Evans, K. F.

1996-01-01

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane parallel (PP-IPA) and independent pixel (IPA-2D) approximations for a wide range of 2D cloud fields obtained from LANDSAT. They include single layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter Y (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP-IPA bias, -0.12 for IPA-2D bias) for large v. On a scene average basis PP-IPA bias can reach 0.30, while IPA-2D bias reaches its largest magnitude at -0.07. Biases due to horizontal transport (IPA-2D) are much smaller than PP-IPA biases but account for 20% RMS of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The LANDSAT data used may also be affected by radiative smoothing.

Sensitivity Studies for Space-based Measurement of Atmospheric Total Column Carbon Dioxide Using Reflected Sunlight

NASA Technical Reports Server (NTRS)

Mao, Jianping; Kawa, S. Randolph

2003-01-01

A series of sensitivity studies is carried out to explore the feasibility of space-based global carbon dioxide (CO2) measurements for global and regional carbon cycle studies. The detection method uses absorption of reflected sunlight in the CO2 vibration-rotation band at 1.58 microns. The sensitivities of the detected radiances are calculated using the line-by-line model (LBLRTM), implemented with the DISORT (Discrete Ordinates Radiative Transfer) model to include atmospheric scattering in this band. The results indicate that (a) the small (approx.1%) changes in CO2 near the Earth's surface are detectable in this CO2 band provided adequate sensor signal-to-noise ratio and spectral resolution are achievable; (b) the radiance signal or sensitivity to CO2 change near the surface is not significantly diminished even in the presence of aerosols and/or thin cirrus clouds in the atmosphere; (c) the modification of sunlight path length by scattering of aerosols and cirrus clouds could lead to large systematic errors in the retrieval; therefore, ancillary aerosol/cirrus cloud data are important to reduce retrieval errors; (d) CO2 retrieval requires good knowledge of the atmospheric temperature profile, e.g. approximately 1K RMS error in layer temperature; (e) the atmospheric path length, over which the CO2 absorption occurs, must be known in order to correctly interpret horizontal gradients of CO2 from the total column CO2 measurement; thus an additional sensor for surface pressure measurement needs to be attached for a complete measurement package.

On recent advances and future research directions for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Soliman, M. O.; Manhardt, P. D.

1986-01-01

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

A Discrete Approximation Framework for Hereditary Systems.

DTIC Science & Technology

1980-05-01

schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger absolute error values, it shows similar convergence rates as the other split schemes, but does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much to fast. Despite this, the finding of this new scheme illustrates the potential of our discretization framework as a toolbox to find and to study new FE schemes based on new combinations of FE spaces. [1] Bauer, W. [2016], A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM - International Journal on Geomathematics, 7(1), 31-101.

Non-holonomic integrators

NASA Astrophysics Data System (ADS)

Cortés, J.; Martínez, S.

2001-09-01

We introduce a discretization of the Lagrange-d'Alembert principle for Lagrangian systems with non-holonomic constraints, which allows us to construct numerical integrators that approximate the continuous flow. We study the geometric invariance properties of the discrete flow which provide an explanation for the good performance of the proposed method. This is tested on two examples: a non-holonomic particle with a quadratic potential and a mobile robot with fixed orientation.

Discrete Conformal Approximation of Complex Earthquake Maps

DTIC Science & Technology

2005-08-01

Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 1. AGENCY USE ONLY...ing when my dreams were not yours. Thank you for teaching me that books are my friends (though I may have taken that a little too much to heart), and...61 4.2 Hyperbolic Projections ....... ...................... 63 4.3 Discrete Shearing Maps ............................. 64

Problems with heterogeneous and non-isotropic media or distorted grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, J.; Shashkov, M.; Steinberg, S.

1996-08-01

This paper defines discretizations of the divergence and flux operators that produce symmetric, positive-definite, and accurate approximations to steady-state diffusion problems. Because discontinuous material properties and highly distorted grids are allowed, the flux operator, rather than the gradient, is used as a fundamental operator to be discretized. Resulting finite-difference scheme is similar to those obtained from the mixed finite-element method.

High mobility of large mass movements: a study by means of FEM/DEM simulations

NASA Astrophysics Data System (ADS)

Manzella, I.; Lisjak, A.; Grasselli, G.

2013-12-01

Large mass movements, such as rock avalanches and large volcanic debris avalanches are characterized by extremely long propagation, which cannot be modelled using normal sliding friction law. For this reason several studies and theories derived from field observation, physical theories and laboratory experiments, exist to try to explain their high mobility. In order to investigate more into deep some of the processes recalled by these theories, simulations have been run with a new numerical tool called Y-GUI based on the Finite Element-Discrete Element Method FEM/DEM. The FEM/DEM method is a numerical technique developed by Munjiza et al. (1995) where Discrete Element Method (DEM) algorithms are used to model the interaction between different solids, while Finite Element Method (FEM) principles are used to analyze their deformability being also able to explicitly simulate material sudden loss of cohesion (i.e. brittle failure). In particular numerical tests have been run, inspired by the small-scale experiments done by Manzella and Labiouse (2013). They consist of rectangular blocks released on a slope; each block is a rectangular discrete element made of a mesh of finite elements enabled to fragment. These simulations have highlighted the influence on the propagation of block packing, i.e. whether the elements are piled into geometrical ordinate structure before failure or they are chaotically disposed as a loose material, and of the topography, i.e. whether the slope break is smooth and regular or not. In addition the effect of fracturing, i.e. fragmentation, on the total runout have been studied and highlighted.

Squeezing Interval Change From Ordinal Panel Data: Latent Growth Curves With Ordinal Outcomes

ERIC Educational Resources Information Center

Mehta, Paras D.; Neale, Michael C.; Flay, Brian R.

2004-01-01

A didactic on latent growth curve modeling for ordinal outcomes is presented. The conceptual aspects of modeling growth with ordinal variables and the notion of threshold invariance are illustrated graphically using a hypothetical example. The ordinal growth model is described in terms of 3 nested models: (a) multivariate normality of the…

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Discrete differential geometry: The nonplanar quadrilateral mesh

NASA Astrophysics Data System (ADS)

Twining, Carole J.; Marsland, Stephen

2012-06-01

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

Method of conditional moments (MCM) for the Chemical Master Equation: a unified framework for the method of moments and hybrid stochastic-deterministic models.

PubMed

Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J

2014-09-01

The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.

Protection, Profit, or Privacy: Exploring Strategic Solutions for Integrating Unmanned Aerial Systems (UAS) and the Delicate Balance Between Commercial Opportunity and Public Safety

DTIC Science & Technology

2016-12-01

United States v. Knotts.9 Analysis of previous cases provides a starting point for discussion between government officials and the public they...authorized under this ordinance to deploy this technology. At the start of the legislative session in the fall of 2015, Senator John Kavanagh, a...2015, through April 30, 2016 (a span of approximately 15 months). The start date of this query is intended to correspond with the operational

Calculations of the skyshine gamma-ray dose rates from independent spent fuel storage installations (ISFSI) under worst case accident conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pace, J.V. III; Cramer, S.N.; Knight, J.R.

1980-09-01

Calculations of the skyshine gamma-ray dose rates from three spent fuel storage pools under worst case accident conditions have been made using the discrete ordinates code DOT-IV and the Monte Carlo code MORSE and have been compared to those of two previous methods. The DNA 37N-21G group cross-section library was utilized in the calculations, together with the Claiborne-Trubey gamma-ray dose factors taken from the same library. Plots of all results are presented. It was found that the dose was a strong function of the iron thickness over the fuel assemblies, the initial angular distribution of the emitted radiation, and themore » photon source near the top of the assemblies. 16 refs., 11 figs., 7 tabs.« less

Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pautz, Shawn D.; Bailey, Teresa S.

Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amountmore » of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.« less

Coexistence of cyclic (CH3OH)2(H2O)8 heterodecamer and acyclic water trimer in the channels of silver-azelate framework

NASA Astrophysics Data System (ADS)

Luo, Geng-Geng; Zhu, Rui-Min; He, Wei-Jun; Li, Ming-Zhi; Zhao, Qing-Hua; Li, Dong-Xu; Dai, Jing-Cao

2012-08-01

Flexible azelaic acid (H2aze) and 1,3-bis(4-pyridyl)propane) (bpp) react ultrasonically with silver(I) oxide, generating a new metal-organic framework [Ag2(bpp)2(aze)·7H2O·CH3OH]n (1) that forms a 3D supramolecular structure through H-bonding interactions between solvent molecules and carboxylate O atoms with void spaces. Two kinds of solvent clusters, discrete cyclic (CH3OH)2(H2O)8 heterodecameric and acyclic water trimeric clusters occupy the channels in the structure. Furthermore, 1 exhibits strong photoluminescence maximized at 500 nm upon 350 nm excitation at room temperature, of which CIE chromaticity ordinate (x = 0.28, y = 0.44) is close to that of edge of green component.

Combustion chamber analysis code

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Lai, Y. G.; Krishnan, A.; Avva, R. K.; Giridharan, M. G.

1993-01-01

A three-dimensional, time dependent, Favre averaged, finite volume Navier-Stokes code has been developed to model compressible and incompressible flows (with and without chemical reactions) in liquid rocket engines. The code has a non-staggered formulation with generalized body-fitted-coordinates (BFC) capability. Higher order differencing methodologies such as MUSCL and Osher-Chakravarthy schemes are available. Turbulent flows can be modeled using any of the five turbulent models present in the code. A two-phase, two-liquid, Lagrangian spray model has been incorporated into the code. Chemical equilibrium and finite rate reaction models are available to model chemically reacting flows. The discrete ordinate method is used to model effects of thermal radiation. The code has been validated extensively against benchmark experimental data and has been applied to model flows in several propulsion system components of the SSME and the STME.

Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions

DOE PAGES

Pautz, Shawn D.; Bailey, Teresa S.

2016-11-29

Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amountmore » of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.« less

Measured and calculated fast neutron spectra in a depleted uranium and lithium hydride shielded reactor

NASA Technical Reports Server (NTRS)

Lahti, G. P.; Mueller, R. A.

1973-01-01

Measurements of MeV neutron were made at the surface of a lithium hydride and depleted uranium shielded reactor. Four shield configurations were considered: these were assembled progressively with cylindrical shells of 5-centimeter-thick depleted uranium, 13-centimeter-thick lithium hydride, 5-centimeter-thick depleted uranium, 13-centimeter-thick lithium hydride, 5-centimeter-thick depleted uranium, and 3-centimeter-thick depleted uranium. Measurements were made with a NE-218 scintillation spectrometer; proton pulse height distributions were differentiated to obtain neutron spectra. Calculations were made using the two-dimensional discrete ordinates code DOT and ENDF/B (version 3) cross sections. Good agreement between measured and calculated spectral shape was observed. Absolute measured and calculated fluxes were within 50 percent of one another; observed discrepancies in absolute flux may be due to cross section errors.

Calculation and experimental validation of spectral properties of microsize grains surrounded by nanoparticles.

PubMed

Yu, Haitong; Liu, Dong; Duan, Yuanyuan; Wang, Xiaodong

2014-04-07

Opacified aerogels are particulate thermal insulating materials in which micrometric opacifier mineral grains are surrounded by silica aerogel nanoparticles. A geometric model was developed to characterize the spectral properties of such microsize grains surrounded by much smaller particles. The model represents the material's microstructure with the spherical opacifier's spectral properties calculated using the multi-sphere T-matrix (MSTM) algorithm. The results are validated by comparing the measured reflectance of an opacified aerogel slab against the value predicted using the discrete ordinate method (DOM) based on calculated optical properties. The results suggest that the large particles embedded in the nanoparticle matrices show different scattering and absorption properties from the single scattering condition and that the MSTM and DOM algorithms are both useful for calculating the spectral and radiative properties of this particulate system.

Reactor Dosimetry Applications Using RAPTOR-M3G:. a New Parallel 3-D Radiation Transport Code

NASA Astrophysics Data System (ADS)

Longoni, Gianluca; Anderson, Stanwood L.

2009-08-01

The numerical solution of the Linearized Boltzmann Equation (LBE) via the Discrete Ordinates method (SN) requires extensive computational resources for large 3-D neutron and gamma transport applications due to the concurrent discretization of the angular, spatial, and energy domains. This paper will discuss the development RAPTOR-M3G (RApid Parallel Transport Of Radiation - Multiple 3D Geometries), a new 3-D parallel radiation transport code, and its application to the calculation of ex-vessel neutron dosimetry responses in the cavity of a commercial 2-loop Pressurized Water Reactor (PWR). RAPTOR-M3G is based domain decomposition algorithms, where the spatial and angular domains are allocated and processed on multi-processor computer architectures. As compared to traditional single-processor applications, this approach reduces the computational load as well as the memory requirement per processor, yielding an efficient solution methodology for large 3-D problems. Measured neutron dosimetry responses in the reactor cavity air gap will be compared to the RAPTOR-M3G predictions. This paper is organized as follows: Section 1 discusses the RAPTOR-M3G methodology; Section 2 describes the 2-loop PWR model and the numerical results obtained. Section 3 addresses the parallel performance of the code, and Section 4 concludes this paper with final remarks and future work.

An efficient direct solver for rarefied gas flows with arbitrary statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz, Manuel A., E-mail: f99543083@ntu.edu.tw; Yang, Jaw-Yen, E-mail: yangjy@iam.ntu.edu.tw; Center of Advanced Study in Theoretical Science, National Taiwan University, Taipei 10167, Taiwan

2016-01-15

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes themore » limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.« less

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Deregulation, Distrust, and Democracy: State and Local Action to Ensure Equitable Access to Healthy, Sustainably Produced Food.

PubMed

Wiley, Lindsay F

2015-01-01

Environmental, public health, alternative food, and food justice advocates are working together to achieve incremental agricultural subsidy and nutrition assistance reforms that increase access to fresh fruits and vegetables. When it comes to targeting food and beverage products for increased regulation and decreased consumption, however, the priorities of various food reform movements diverge. This article argues that foundational legal issues, including preemption of state and local authority to protect the public's health and welfare, increasing First Amendment protection for commercial speech, and eroding judicial deference to legislative policy judgments, present a more promising avenue for collaboration across movements than discrete food reform priorities around issues like sugary drinks, genetic modification, or organics. Using the Vermont Genetically Modified Organism (GMO) Labeling Act litigation, the Kauai GMO Cultivation Ordinance litigation, the New York City Sugary Drinks Portion Rule litigation, and the Cleveland Trans Fat Ban litigation as case studies, I discuss the foundational legal challenges faced by diverse food reformers, even when their discrete reform priorities diverge. I also 'explore the broader implications of cooperation among groups that respond differently to the "irrationalities" (from the public health perspective) or "values" (from the environmental and alternative food perspective) that permeate public risk perception for democratic governance in the face of scientific uncertainty.

Dislocation pileup as a representation of strain accumulation on a strike-slip fault

USGS Publications Warehouse

Savage, J.C.

2006-01-01

The conventional model of strain accumulation on a vertical transform fault is a discrete screw dislocation in an elastic half-space with the Burgers vector of the dislocation increasing at the rate of relative plate motion. It would be more realistic to replace that discrete dislocation by a dislocation distribution, presumably a pileup in which the individual dislocations are in equilibrium. The length of the pileup depends upon the applied stress and the amount of slip that has occurred at depth. I argue here that the dislocation pileup (the transition on the fault from no slip to slip at the full plate rate) occupies a substantial portion of the lithosphere thickness. A discrete dislocation at an adjustable depth can reproduce the surface deformation profile predicted by a pileup so closely that it will be difficult to distinguish between the two models. The locking depth (dislocation depth) of that discrete dislocation approximation is substantially (???30%) larger than that (depth to top of the pileup) in the pileup model. Thus, in inverting surface deformation data using the discrete dislocation model, the locking depth in the model should not be interpreted as the true locking depth. Although dislocation pileup models should provide a good explanation of the surface deformation near the fault trace, that explanation may not be adequate at greater distances from the fault trace because approximating the expected horizontally distributed deformation at subcrustal depths by uniform slip concentrated on the fault is not justified.

High sensitivity operation of discrete solid state detectors at 4 K

NASA Technical Reports Server (NTRS)

Rieke, G. H.; Montgomery, E. F.; Lebofsky, M. J.; Eisenhardt, P. R.

1981-01-01

Techniques are described to allow operation of discrete, solid state detectors at 4 K with optimized JFET amplifiers. Three detector types cover the 0.6 to 4 mm spectral range with NEP approximately equal to 10 to the 16th power Hz (-1/2) for two of the types and potential improvement to this performance for the third. Lower NEP's are anticipated at longer infrared wavelengths.

On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space.

PubMed

Wu, Chase Q; Wang, Li

2017-10-10

Sensor networks have been used in a rapidly increasing number of applications in many fields. This work generalizes a sensor deployment problem to place a minimum set of wireless sensors at candidate locations in constrained 3D space to k -cover a given set of target objects. By exhausting the combinations of discreteness/continuousness constraints on either sensor locations or target objects, we formulate four classes of sensor deployment problems in 3D space: deploy sensors at Discrete/Continuous Locations (D/CL) to cover Discrete/Continuous Targets (D/CT). We begin with the design of an approximate algorithm for DLDT and then reduce DLCT, CLDT, and CLCT to DLDT by discretizing continuous sensor locations or target objects into a set of divisions without sacrificing sensing precision. Furthermore, we consider a connected version of each problem where the deployed sensors must form a connected network, and design an approximation algorithm to minimize the number of deployed sensors with connectivity guarantee. For performance comparison, we design and implement an optimal solution and a genetic algorithm (GA)-based approach. Extensive simulation results show that the proposed deployment algorithms consistently outperform the GA-based heuristic and achieve a close-to-optimal performance in small-scale problem instances and a significantly superior overall performance than the theoretical upper bound.

An approach to solve group-decision-making problems with ordinal interval numbers.

PubMed

Fan, Zhi-Ping; Liu, Yang

2010-10-01

The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.

Clean Indoor Air Ordinance Coverage in the Appalachian Region of the United States

PubMed Central

Liber, Alex; Pennell, Michael; Nealy, Darren; Hammer, Jana; Berman, Micah

2010-01-01

Objectives. We sought to quantitatively examine the pattern of, and socioeconomic factors associated with, adoption of clean indoor air ordinances in Appalachia. Methods. We collected and reviewed clean indoor air ordinances in Appalachian communities in 6 states and rated the ordinances for completeness of coverage in workplaces, restaurants, and bars. Additionally, we computed a strength score to measure coverage in 7 locations. We fit mixed-effects models to determine whether the presence of a comprehensive ordinance and the ordinance strength were related to community socioeconomic disadvantage. Results. Of the 332 communities included in the analysis, fewer than 20% had adopted a comprehensive workplace, restaurant, or bar ordinance. Most ordinances were weak, achieving on average only 43% of the total possible points. Communities with a higher unemployment rate were less likely and those with a higher education level were more likely to have a strong ordinance. Conclusions. The majority of residents in these communities are not protected from secondhand smoke. Efforts to pass strong statewide clean indoor air laws should take priority over local initiatives in these states. PMID:20466957

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

City curfew ordinances and teenage motor vehicle injury.

PubMed

Preusser, D F; Williams, A F; Lund, A K; Zador, P L

1990-08-01

Several U.S. cities have curfew ordinances that limit the late night activities of minor teenagers in public places including highways. Detroit, Cleveland, and Columbus, which have curfew ordinances, were compared to Cincinnati, which does not have such an ordinance. The curfew ordinances were associated with a 23% reduction in motor vehicle related injury for 13- to 17-year-olds as passengers, drivers, pedestrians, or bicyclists during the curfew hours. It was concluded that city curfew ordinances, like the statewide driving curfews studied in other states, can reduce motor vehicle injury to teenagers during the particularly hazardous late night hours.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

PubMed

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Method of implementing digital phase-locked loops

NASA Technical Reports Server (NTRS)

Stephens, Scott A. (Inventor); Thomas, Jess Brooks, Jr. (Inventor)

1993-01-01

In a new formulation for digital phase-locked loops, loop-filter constants are determined from loop roots that can each be selectively placed in the s-plane on the basis of a new set of parameters, each with simple and direct physical meaning in terms of loop noise bandwidth, root-specific decay rate, or root-specific damping. Loops of first to fourth order are treated in the continuous-update approximation (BLT yields 0) and in a discrete-update formulation with arbitrary BLT. Deficiencies of the continuous-update approximation in large-BLT applications are avoided in the new discrete-update formulation. A new method for direct, transient-free acquisition with third- and fourth-order loops can improve the versatility and reliability of acquisition with such loops.

Breit-Wigner Approximation and the Distributionof Resonances

NASA Astrophysics Data System (ADS)

Petkov, Vesselin; Zworski, Maciej

For operators with a discrete spectrum, {λj2}, the counting function of λj's, N (λ), trivially satisfies N ( λ+δ ) -N ( λ-δ ) =∑jδλj((λ-δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λj∈+, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that where ω+ is the harmonic measure of the upper of half plane and δ can be taken dependent on λ. This provides a precise high energy version of the Breit-Wigner approximation, and relates the properties of s (λ) to the distribution of resonances close to the real axis.

Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.

2008-11-06

This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use,more » a filtering algorithm based on linear approximations of the real observations is proposed.« less

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

NASA Astrophysics Data System (ADS)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

Gap-minimal systems of notations and the constructible hierarchy

NASA Technical Reports Server (NTRS)

Lucian, M. L.

1972-01-01

If a constructibly countable ordinal alpha is a gap ordinal, then the order type of the set of index ordinals smaller than alpha is exactly alpha. The gap ordinals are the only points of discontinuity of a certain ordinal-valued function. The notion of gap minimality for well ordered systems of notations is defined, and the existence of gap-minimal systems of notations of arbitrarily large constructibly countable length is established.

78 FR 54670 - Miami Tribe of Oklahoma-Liquor Control Ordinance

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-05

... Tribe of Oklahoma--Liquor Control Ordinance AGENCY: Bureau of Indian Affairs, Interior. ACTION: Notice. SUMMARY: This notice publishes the Miami Tribe of Oklahoma--Liquor Control Ordinance. This Ordinance... Oklahoma, increases the ability of the tribal government to control the distribution and possession of...

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

Tax revenue in Mississippi communities following implementation of smoke-free ordinances: an examination of tourism and economic development tax revenues.

PubMed

McMillen, Robert; Shackelford, Signe

2012-10-01

There is no safe level of exposure to tobacco smoke. More than 60 Mississippi communities have passed smoke-free ordinances in the past six years. Opponents claim that these ordinances harm local businesses. Mississippi law allows municipalities to place a tourism and economic development (TED) tax on local restaurants and hotels/motels. The objective of this study is to examine the impact of these ordinances on TED tax revenues. This study applies a pre/post quasi-experimental design to compare TED tax revenue before and after implementing ordinances. Descriptive analyses indicated that inflation-adjusted tax revenues increased during the 12 months following implementation of smoke-free ordinances while there was no change in aggregated control communities. Multivariate fixed-effects analyses found no statistically significant effect of smoke-free ordinances on hospitality tax revenue. No evidence was found that smoke-free ordinances have an adverse effect on the local hospitality industry.

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

PubMed

Beard, D A; Schlick, T

2001-01-01

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels. Copyright 2000 John Wiley & Sons, Inc.

The forgotten guidelines: cross-sectional analysis of participation in muscle strengthening and balance & co-ordination activities by adults and older adults in Scotland.

PubMed

Strain, Tessa; Fitzsimons, Claire; Kelly, Paul; Mutrie, Nanette

2016-10-21

In 2011, the UK physical activity guidelines were updated to include recommendations for muscle strengthening and balance & coordination (at least two sessions of relevant activities per week). However, monitoring and policy efforts remain focussed on aerobic activity. This study aimed to assess differences by gender and age in the a) prevalence of muscle strengthening and balance & co-ordination guidelines, and b) participation in guideline-specific activities. The sample for the muscle strengthening analyses was 10,488 adult (16-64 years) and 3857 older adult (≥65 years) 2012-2014 Scottish Health Survey respondents. The balance & co-ordination analyses used only the older adult responses. Differences by gender and (where possible) age in guideline prevalence and activity participation were assessed using logistic regression and t-tests. Thirty-one percent of men and 24 % of women met the muscle strengthening guideline, approximately half that of published figures for aerobic physical activity. Nineteen percent of older men and 12 % of older women met the balance & co-ordination guidelines. The oldest age groups were less likely to meet both guidelines compared to the youngest age groups. Differences by gender were only evident for muscle strengthening: more men met the guidelines than women in all age groups, with the largest difference amongst 16-24 year olds (55 % men compared with 40 % women). Participation in relevant activities differed by gender for both guidelines. 'Workout at gym' was the most popular activity to improve muscle strength for men (18 % participated), while swimming was for women (15 % participated). Golf was the most popular activity to improve balance & co-ordination for older men (11 % participated) and aerobics was for older women (6 % participated). Participation decreased in most muscle strengthening activities for both men and women. One exception was golf, where participation levels were as high amongst older men as in younger age groups, although overall levels were low (3 % of all men). Physical activity policy should aim to increase prevalence of these 'forgotten' guidelines, particularly amongst young women (for muscle strengthening) and older age groups (both guidelines). Gender and age participation differences should be considered when designing population-level interventions.

75 FR 65373 - Klamath Tribes Liquor Control Ordinance

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-22

... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Klamath Tribes Liquor Control Ordinance AGENCY... certification of the amendment to the Klamath Tribes Liquor Control Ordinance. The first Ordinance was published... and controls the sale, possession and distribution of liquor within the tribal lands. The tribal lands...

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levi, Decio; Scimiterna, Christian

2010-03-08

In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

Ordinality and the nature of symbolic numbers.

PubMed

Lyons, Ian M; Beilock, Sian L

2013-10-23

The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.

Comparing performance in discrete and continuous comparison tasks.

PubMed

Leibovich, Tali; Henik, Avishai

2014-05-01

The approximate number system (ANS) theory suggests that all magnitudes, discrete (i.e., number of items) or continuous (i.e., size, density, etc.), are processed by a shared system and comply with Weber's law. The current study reexamined this notion by comparing performance in discrete (comparing numerosities of dot arrays) and continuous (comparisons of area of squares) tasks. We found that: (a) threshold of discrimination was higher for continuous than for discrete comparisons; (b) while performance in the discrete task complied with Weber's law, performance in the continuous task violated it; and (c) performance in the discrete task was influenced by continuous properties (e.g., dot density, dot cumulative area) of the dot array that were not predictive of numerosities or task relevant. Therefore, we propose that the magnitude processing system (MPS) is actually divided into separate (yet interactive) systems for discrete and continuous magnitude processing. Further subdivisions are discussed. We argue that cooperation between these systems results in a holistic comparison of magnitudes, one that takes into account continuous properties in addition to numerosities. Considering the MPS as two systems opens the door to new and important questions that shed light on both normal and impaired development of the numerical system.

Social Host Ordinances and Policies. Prevention Update

ERIC Educational Resources Information Center

Higher Education Center for Alcohol, Drug Abuse, and Violence Prevention, 2011

2011-01-01

Social host liability laws (also known as teen party ordinances, loud or unruly gathering ordinances, or response costs ordinances) target the location in which underage drinking takes place. Social host liability laws hold noncommercial individuals responsible for underage drinking events on property they own, lease, or otherwise control. They…

25 CFR 522.8 - Publication of class III ordinance and approval.

Code of Federal Regulations, 2010 CFR

2010-04-01

... Section 522.8 Indians NATIONAL INDIAN GAMING COMMISSION, DEPARTMENT OF THE INTERIOR APPROVAL OF CLASS II AND CLASS III ORDINANCES AND RESOLUTIONS SUBMISSION OF GAMING ORDINANCE OR RESOLUTION § 522.8 Publication of class III ordinance and approval. The Chairman shall publish a class III tribal gaming...

27 CFR 478.24 - Compilation of State laws and published ordinances.

Code of Federal Regulations, 2010 CFR

2010-04-01

... and published ordinances. 478.24 Section 478.24 Alcohol, Tobacco Products, and Firearms BUREAU OF... published ordinances. (a) The Director shall annually revise and furnish Federal firearms licensees with a compilation of State laws and published ordinances which are relevant to the enforcement of this part. The...

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

A high-order staggered meshless method for elliptic problems

DOE PAGES

Trask, Nathaniel; Perego, Mauro; Bochev, Pavel Blagoveston

2017-03-21

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attainsmore » $$O(h^{m})$$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.« less

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

NASA Astrophysics Data System (ADS)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

Computation of Steady and Unsteady Laminar Flames: Theory

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Radhakrishnan, Krishnan; Zhou, Ruhai

1999-01-01

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Holographic representation of space-variant systems: system theory.

PubMed

Marks Ii, R J; Krile, T F

1976-09-01

System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

DOE PAGES

Seleson, Pablo; Du, Qiang; Parks, Michael L.

2016-08-16

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Furthermore, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.« less

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Equivalent Discrete-Time Channel Modeling for Molecular Communication With Emphasize on an Absorbing Receiver.

PubMed

Damrath, Martin; Korte, Sebastian; Hoeher, Peter Adam

2017-01-01

This paper introduces the equivalent discrete-time channel model (EDTCM) to the area of diffusion-based molecular communication (DBMC). Emphasis is on an absorbing receiver, which is based on the so-called first passage time concept. In the wireless communications community the EDTCM is well known. Therefore, it is anticipated that the EDTCM improves the accessibility of DBMC and supports the adaptation of classical wireless communication algorithms to the area of DBMC. Furthermore, the EDTCM has the capability to provide a remarkable reduction of computational complexity compared to random walk based DBMC simulators. Besides the exact EDTCM, three approximations thereof based on binomial, Gaussian, and Poisson approximation are proposed and analyzed in order to further reduce computational complexity. In addition, the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is adapted to all four channel models. Numerical results show the performance of the exact EDTCM, illustrate the performance of the adapted BCJR algorithm, and demonstrate the accuracy of the approximations.

Using ordinal partition transition networks to analyze ECG data

NASA Astrophysics Data System (ADS)

Kulp, Christopher W.; Chobot, Jeremy M.; Freitas, Helena R.; Sprechini, Gene D.

2016-07-01

Electrocardiogram (ECG) data from patients with a variety of heart conditions are studied using ordinal pattern partition networks. The ordinal pattern partition networks are formed from the ECG time series by symbolizing the data into ordinal patterns. The ordinal patterns form the nodes of the network and edges are defined through the time ordering of the ordinal patterns in the symbolized time series. A network measure, called the mean degree, is computed from each time series-generated network. In addition, the entropy and number of non-occurring ordinal patterns (NFP) is computed for each series. The distribution of mean degrees, entropies, and NFPs for each heart condition studied is compared. A statistically significant difference between healthy patients and several groups of unhealthy patients with varying heart conditions is found for the distributions of the mean degrees, unlike for any of the distributions of the entropies or NFPs.

Convergence of Spectral Discretizations of the Vlasov--Poisson System

DOE PAGES

Manzini, G.; Funaro, D.; Delzanno, G. L.

2017-09-26

Here we prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1Vmore » case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.« less

Confirmatory Factor Analysis of Ordinal Variables with Misspecified Models

ERIC Educational Resources Information Center

Yang-Wallentin, Fan; Joreskog, Karl G.; Luo, Hao

2010-01-01

Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is…

75 FR 51102 - Liquor Ordinance of the Wichita and Affiliated Tribes; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-18

... Tribes; Correction AGENCY: Bureau of Indian Affairs, Interior ACTION: Notice; correction SUMMARY: The... Liquor Ordinance of the Wichita and Affiliated Tribes. The notice refers to an amended ordinance of the Wichita and Affiliated Tribes when in fact the Liquor Ordinance adopted by Resolution No. WT-10-31 on May...

Estimating Ordinal Reliability for Likert-Type and Ordinal Item Response Data: A Conceptual, Empirical, and Practical Guide

ERIC Educational Resources Information Center

Gadermann, Anne M.; Guhn, Martin; Zumbo, Bruno D.

2012-01-01

This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach's alpha, are calculated using a Pearson…

The effect of ordinances requiring smoke-free restaurants on restaurant sales.

PubMed Central

Glantz, S A; Smith, L R

1994-01-01

OBJECTIVES: The effect on restaurant revenues of local ordinances requiring smoke-free restaurants is an important consideration for restauranteurs themselves and the cities that depend on sales tax revenues to provide services. METHODS: Data were obtained from the California State Board of Equalization and Colorado State Department of Revenue on taxable restaurant sales from 1986 (1982 for Aspen) through 1993 for all 15 cities where ordinances were in force, as well as for 15 similar control communities without smoke-free ordinances during this period. These data were analyzed using multiple regression, including time and a dummy variable for whether an ordinance was in force. Total restaurant sales were analyzed as a fraction of total retail sales and restaurant sales in smoke-free cities vs the comparison cities similar in population, median income, and other factors. RESULTS. Ordinances had no significant effect on the fraction of total retail sales that went to restaurants or on the ratio of restaurant sales in communities with ordinances compared with those in the matched control communities. CONCLUSIONS. Smoke-free restaurant ordinances do not adversely affect restaurant sales. PMID:8017529

Ordinal measures for iris recognition.

PubMed

Sun, Zhenan; Tan, Tieniu

2009-12-01

Images of a human iris contain rich texture information useful for identity authentication. A key and still open issue in iris recognition is how best to represent such textural information using a compact set of features (iris features). In this paper, we propose using ordinal measures for iris feature representation with the objective of characterizing qualitative relationships between iris regions rather than precise measurements of iris image structures. Such a representation may lose some image-specific information, but it achieves a good trade-off between distinctiveness and robustness. We show that ordinal measures are intrinsic features of iris patterns and largely invariant to illumination changes. Moreover, compactness and low computational complexity of ordinal measures enable highly efficient iris recognition. Ordinal measures are a general concept useful for image analysis and many variants can be derived for ordinal feature extraction. In this paper, we develop multilobe differential filters to compute ordinal measures with flexible intralobe and interlobe parameters such as location, scale, orientation, and distance. Experimental results on three public iris image databases demonstrate the effectiveness of the proposed ordinal feature models.

Food marketing to children through toys: response of restaurants to the first U.S. toy ordinance.

PubMed

Otten, Jennifer J; Hekler, Eric B; Krukowski, Rebecca A; Buman, Matthew P; Saelens, Brian E; Gardner, Christopher D; King, Abby C

2012-01-01

On August 9, 2010, Santa Clara County CA became the first U.S. jurisdiction to implement an ordinance that prohibits the distribution of toys and other incentives to children in conjunction with meals, foods, or beverages that do not meet minimal nutritional criteria. Restaurants had many different options for complying with this ordinance, such as introducing more healthful menu options, reformulating current menu items, or changing marketing or toy distribution practices. To assess how ordinance-affected restaurants changed their child menus, marketing, and toy distribution practices relative to non-affected restaurants. Children's menu items and child-directed marketing and toy distribution practices were examined before and at two time points after ordinance implementation (from July through November 2010) at ordinance-affected fast-food restaurants compared with demographically matched unaffected same-chain restaurants using the Children's Menu Assessment tool. Affected restaurants showed a 2.8- to 3.4-fold improvement in Children's Menu Assessment scores from pre- to post-ordinance with minimal changes at unaffected restaurants. Response to the ordinance varied by restaurant. Improvements were seen in on-site nutritional guidance; promotion of healthy meals, beverages, and side items; and toy marketing and distribution activities. The ordinance appears to have positively influenced marketing of healthful menu items and toys as well as toy distribution practices at ordinance-affected restaurants, but did not affect the number of healthful food items offered. Copyright © 2012 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.

SMRT: A new, modular snow microwave radiative transfer model

NASA Astrophysics Data System (ADS)

Picard, Ghislain; Sandells, Melody; Löwe, Henning; Dumont, Marie; Essery, Richard; Floury, Nicolas; Kontu, Anna; Lemmetyinen, Juha; Maslanka, William; Mätzler, Christian; Morin, Samuel; Wiesmann, Andreas

2017-04-01

Forward models of radiative transfer processes are needed to interpret remote sensing data and derive measurements of snow properties such as snow mass. A key requirement and challenge for microwave emission and scattering models is an accurate description of the snow microstructure. The snow microwave radiative transfer model (SMRT) was designed to cater for potential future active and/or passive satellite missions and developed to improve understanding of how to parameterize snow microstructure. SMRT is implemented in Python and is modular to allow easy intercomparison of different theoretical approaches. Separate modules are included for the snow microstructure model, electromagnetic module, radiative transfer solver, substrate, interface reflectivities, atmosphere and permittivities. An object-oriented approach is used with carefully specified exchanges between modules to allow future extensibility i.e. without constraining the parameter list requirements. This presentation illustrates the capabilities of SMRT. At present, five different snow microstructure models have been implemented, and direct insertion of the autocorrelation function from microtomography data is also foreseen with SMRT. Three electromagnetic modules are currently available. While DMRT-QCA and Rayleigh models need specific microstructure models, the Improved Born Approximation may be used with any microstructure representation. A discrete ordinates approach with stream connection is used to solve the radiative transfer equations, although future inclusion of 6-flux and 2-flux solvers are envisioned. Wrappers have been included to allow existing microwave emission models (MEMLS, HUT, DMRT-QMS) to be run with the same inputs and minimal extra code (2 lines). Comparisons between theoretical approaches will be shown, and evaluation against field experiments in the frequency range 5-150 GHz. SMRT is simple and elegant to use whilst providing a framework for future development within the community.

Review of Hybrid (Deterministic/Monte Carlo) Radiation Transport Methods, Codes, and Applications at Oak Ridge National Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wagner, John C; Peplow, Douglas E.; Mosher, Scott W

2011-01-01

This paper provides a review of the hybrid (Monte Carlo/deterministic) radiation transport methods and codes used at the Oak Ridge National Laboratory and examples of their application for increasing the efficiency of real-world, fixed-source Monte Carlo analyses. The two principal hybrid methods are (1) Consistent Adjoint Driven Importance Sampling (CADIS) for optimization of a localized detector (tally) region (e.g., flux, dose, or reaction rate at a particular location) and (2) Forward Weighted CADIS (FW-CADIS) for optimizing distributions (e.g., mesh tallies over all or part of the problem space) or multiple localized detector regions (e.g., simultaneous optimization of two or moremore » localized tally regions). The two methods have been implemented and automated in both the MAVRIC sequence of SCALE 6 and ADVANTG, a code that works with the MCNP code. As implemented, the methods utilize the results of approximate, fast-running 3-D discrete ordinates transport calculations (with the Denovo code) to generate consistent space- and energy-dependent source and transport (weight windows) biasing parameters. These methods and codes have been applied to many relevant and challenging problems, including calculations of PWR ex-core thermal detector response, dose rates throughout an entire PWR facility, site boundary dose from arrays of commercial spent fuel storage casks, radiation fields for criticality accident alarm system placement, and detector response for special nuclear material detection scenarios and nuclear well-logging tools. Substantial computational speed-ups, generally O(102-4), have been realized for all applications to date. This paper provides a brief review of the methods, their implementation, results of their application, and current development activities, as well as a considerable list of references for readers seeking more information about the methods and/or their applications.« less

Validation of a Solid Rocket Motor Internal Environment Model

NASA Technical Reports Server (NTRS)

Martin, Heath T.

2017-01-01

In a prior effort, a thermal/fluid model of the interior of Penn State University's laboratory-scale Insulation Test Motor (ITM) was constructed to predict both the convective and radiative heat transfer to the interior walls of the ITM with a minimum of empiricism. These predictions were then compared to values of total and radiative heat flux measured in a previous series of ITM test firings to assess the capabilities and shortcomings of the chosen modeling approach. Though the calculated fluxes reasonably agreed with those measured during testing, this exercise revealed means of improving the fidelity of the model to, in the case of the thermal radiation, enable direct comparison of the measured and calculated fluxes and, for the total heat flux, compute a value indicative of the average measured condition. By replacing the P1-Approximation with the discrete ordinates (DO) model for the solution of the gray radiative transfer equation, the radiation intensity field in the optically thin region near the radiometer is accurately estimated, allowing the thermal radiation flux to be calculated on the heat-flux sensor itself, which was then compared directly to the measured values. Though the fully coupling the wall thermal response with the flow model was not attempted due to the excessive computational time required, a separate wall thermal response model was used to better estimate the average temperature of the graphite surfaces upstream of the heat flux gauges and improve the accuracy of both the total and radiative heat flux computations. The success of this modeling approach increases confidence in the ability of state-of-the-art thermal and fluid modeling to accurately predict SRM internal environments, offers corrections to older methods, and supplies a tool for further studies of the dynamics of SRM interiors.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Computational analysis of Variable Thrust Engine (VTE) performance

NASA Technical Reports Server (NTRS)

Giridharan, M. G.; Krishnan, A.; Przekwas, A. J.

1993-01-01

The Variable Thrust Engine (VTE) of the Orbital Maneuvering Vehicle (OMV) uses a hypergolic propellant combination of Monomethyl Hydrazine (MMH) and Nitrogen Tetroxide (NTO) as fuel and oxidizer, respectively. The performance of the VTE depends on a number of complex interacting phenomena such as atomization, spray dynamics, vaporization, turbulent mixing, convective/radiative heat transfer, and hypergolic combustion. This study involved the development of a comprehensive numerical methodology to facilitate detailed analysis of the VTE. An existing Computational Fluid Dynamics (CFD) code was extensively modified to include the following models: a two-liquid, two-phase Eulerian-Lagrangian spray model; a chemical equilibrium model; and a discrete ordinate radiation heat transfer model. The modified code was used to conduct a series of simulations to assess the effects of various physical phenomena and boundary conditions on the VTE performance. The details of the models and the results of the simulations are presented.

Radiative transfer simulations of the two-dimensional ocean glint reflectance and determination of the sea surface roughness.

PubMed

Lin, Zhenyi; Li, Wei; Gatebe, Charles; Poudyal, Rajesh; Stamnes, Knut

2016-02-20

An optimized discrete-ordinate radiative transfer model (DISORT3) with a pseudo-two-dimensional bidirectional reflectance distribution function (BRDF) is used to simulate and validate ocean glint reflectances at an infrared wavelength (1036 nm) by matching model results with a complete set of BRDF measurements obtained from the NASA cloud absorption radiometer (CAR) deployed on an aircraft. The surface roughness is then obtained through a retrieval algorithm and is used to extend the simulation into the visible spectral range where diffuse reflectance becomes important. In general, the simulated reflectances and surface roughness information are in good agreement with the measurements, and the diffuse reflectance in the visible, ignored in current glint algorithms, is shown to be important. The successful implementation of this new treatment of ocean glint reflectance and surface roughness in DISORT3 will help improve glint correction algorithms in current and future ocean color remote sensing applications.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Radiative Transfer Simulations of the Two-Dimensional Ocean Glint Reflectance and Determination of the Sea Surface Roughness

NASA Technical Reports Server (NTRS)

Lin, Zhenyi; Li, Wei; Gatebe, Charles; Poudyal, Rajesh; Stamnes, Knut

2016-01-01

An optimized discrete-ordinate radiative transfer model (DISORT3) with a pseudo-two-dimensional bidirectional reflectance distribution function (BRDF) is used to simulate and validate ocean glint reflectances at an infrared wavelength (1036 nm) by matching model results with a complete set of BRDF measurements obtained from the NASA cloud absorption radiometer (CAR) deployed on an aircraft. The surface roughness is then obtained through a retrieval algorithm and is used to extend the simulation into the visible spectral range where diffuse reflectance becomes important. In general, the simulated reflectances and surface roughness information are in good agreement with the measurements, and the diffuse reflectance in the visible, ignored in current glint algorithms, is shown to be important. The successful implementation of this new treatment of ocean glint reflectance and surface roughness in DISORT3 will help improve glint correction algorithms in current and future ocean color remote sensing applications.

Non-destructive testing of ceramic materials using mid-infrared ultrashort-pulse laser

NASA Astrophysics Data System (ADS)

Sun, S. C.; Qi, Hong; An, X. Y.; Ren, Y. T.; Qiao, Y. B.; Ruan, Liming M.

2018-04-01

The non-destructive testing (NDT) of ceramic materials using mid-infrared ultrashort-pulse laser is investigated in this study. The discrete ordinate method is applied to solve the transient radiative transfer equation in 2D semitransparent medium and the emerging radiative intensity on boundary serves as input for the inverse analysis. The sequential quadratic programming algorithm is employed as the inverse technique to optimize objective function, in which the gradient of objective function with respect to reconstruction parameters is calculated using the adjoint model. Two reticulated porous ceramics including partially stabilized zirconia and oxide-bonded silicon carbide are tested. The retrieval results show that the main characteristics of defects such as optical properties, geometric shapes and positions can be accurately reconstructed by the present model. The proposed technique is effective and robust in NDT of ceramics even with measurement errors.

Automated variance reduction for MCNP using deterministic methods.

PubMed

Sweezy, J; Brown, F; Booth, T; Chiaramonte, J; Preeg, B

2005-01-01

In order to reduce the user's time and the computer time needed to solve deep penetration problems, an automated variance reduction capability has been developed for the MCNP Monte Carlo transport code. This new variance reduction capability developed for MCNP5 employs the PARTISN multigroup discrete ordinates code to generate mesh-based weight windows. The technique of using deterministic methods to generate importance maps has been widely used to increase the efficiency of deep penetration Monte Carlo calculations. The application of this method in MCNP uses the existing mesh-based weight window feature to translate the MCNP geometry into geometry suitable for PARTISN. The adjoint flux, which is calculated with PARTISN, is used to generate mesh-based weight windows for MCNP. Additionally, the MCNP source energy spectrum can be biased based on the adjoint energy spectrum at the source location. This method can also use angle-dependent weight windows.

Some Remarks on GMRES for Transport Theory

NASA Technical Reports Server (NTRS)

Patton, Bruce W.; Holloway, James Paul

2003-01-01

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Los Alamos radiation transport code system on desktop computing platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briesmeister, J.F.; Brinkley, F.W.; Clark, B.A.

The Los Alamos Radiation Transport Code System (LARTCS) consists of state-of-the-art Monte Carlo and discrete ordinates transport codes and data libraries. These codes were originally developed many years ago and have undergone continual improvement. With a large initial effort and continued vigilance, the codes are easily portable from one type of hardware to another. The performance of scientific work-stations (SWS) has evolved to the point that such platforms can be used routinely to perform sophisticated radiation transport calculations. As the personal computer (PC) performance approaches that of the SWS, the hardware options for desk-top radiation transport calculations expands considerably. Themore » current status of the radiation transport codes within the LARTCS is described: MCNP, SABRINA, LAHET, ONEDANT, TWODANT, TWOHEX, and ONELD. Specifically, the authors discuss hardware systems on which the codes run and present code performance comparisons for various machines.« less

Delta Clipper-Experimental In-Ground Effect on Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See

1998-01-01

A quasitransient in-ground effect method is developed to study the effect of vertical landing on a launch vehicle base-heating environment. This computational methodology is based on a three-dimensional, pressure-based, viscous flow, chemically reacting, computational fluid dynamics formulation. Important in-ground base-flow physics such as the fountain-jet formation, plume growth, air entrainment, and plume afterburning are captured with the present methodology. Convective and radiative base-heat fluxes are computed for comparison with those of a flight test. The influence of the laminar Prandtl number on the convective heat flux is included in this study. A radiative direction-dependency test is conducted using both the discrete ordinate and finite volume methods. Treatment of the plume afterburning is found to be very important for accurate prediction of the base-heat fluxes. Convective and radiative base-heat fluxes predicted by the model using a finite rate chemistry option compared reasonably well with flight-test data.

Assessment and validation of the community radiative transfer model for ice cloud conditions

NASA Astrophysics Data System (ADS)

Yi, Bingqi; Yang, Ping; Weng, Fuzhong; Liu, Quanhua

2014-11-01

The performance of the Community Radiative Transfer Model (CRTM) under ice cloud conditions is evaluated and improved with the implementation of MODIS collection 6 ice cloud optical property model based on the use of severely roughened solid column aggregates and a modified Gamma particle size distribution. New ice cloud bulk scattering properties (namely, the extinction efficiency, single-scattering albedo, asymmetry factor, and scattering phase function) suitable for application to the CRTM are calculated by using the most up-to-date ice particle optical property library. CRTM-based simulations illustrate reasonable accuracy in comparison with the counterparts derived from a combination of the Discrete Ordinate Radiative Transfer (DISORT) model and the Line-by-line Radiative Transfer Model (LBLRTM). Furthermore, simulations of the top of the atmosphere brightness temperature with CRTM for the Crosstrack Infrared Sounder (CrIS) are carried out to further evaluate the updated CRTM ice cloud optical property look-up table.

Neutron skyshine from intense 14-MeV neutron source facility

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakamura, T.; Hayashi, K.; Takahashi, A.

1985-07-01

The dose distribution and the spectrum variation of neutrons due to the skyshine effect have been measured with the high-efficiency rem counter, the multisphere spectrometer, and the NE-213 scintillator in the environment surrounding an intense 14-MeV neutron source facility. The dose distribution and the energy spectra of neutrons around the facility used as a skyshine source have also been measured to enable the absolute evaluation of the skyshine effect. The skyshine effect was analyzed by two multigroup Monte Carlo codes, NIMSAC and MMCR-2, by two discrete ordinates S /sub n/ codes, ANISN and DOT3.5, and by the shield structure designmore » code for skyshine, SKYSHINE-II. The calculated results show good agreement with the measured results in absolute values. These experimental results should be useful as benchmark data for shyshine analysis and for shielding design of fusion facilities.« less

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Damageable contact between an elastic body and a rigid foundation

NASA Astrophysics Data System (ADS)

Campo, M.; Fernández, J. R.; Silva, A.

2009-02-01

In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

PROTEUS-SN User Manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shemon, Emily R.; Smith, Micheal A.; Lee, Changho

2016-02-16

PROTEUS-SN is a three-dimensional, highly scalable, high-fidelity neutron transport code developed at Argonne National Laboratory. The code is applicable to all spectrum reactor transport calculations, particularly those in which a high degree of fidelity is needed either to represent spatial detail or to resolve solution gradients. PROTEUS-SN solves the second order formulation of the transport equation using the continuous Galerkin finite element method in space, the discrete ordinates approximation in angle, and the multigroup approximation in energy. PROTEUS-SN’s parallel methodology permits the efficient decomposition of the problem by both space and angle, permitting large problems to run efficiently on hundredsmore » of thousands of cores. PROTEUS-SN can also be used in serial or on smaller compute clusters (10’s to 100’s of cores) for smaller homogenized problems, although it is generally more computationally expensive than traditional homogenized methodology codes. PROTEUS-SN has been used to model partially homogenized systems, where regions of interest are represented explicitly and other regions are homogenized to reduce the problem size and required computational resources. PROTEUS-SN solves forward and adjoint eigenvalue problems and permits both neutron upscattering and downscattering. An adiabatic kinetics option has recently been included for performing simple time-dependent calculations in addition to standard steady state calculations. PROTEUS-SN handles void and reflective boundary conditions. Multigroup cross sections can be generated externally using the MC2-3 fast reactor multigroup cross section generation code or internally using the cross section application programming interface (API) which can treat the subgroup or resonance table libraries. PROTEUS-SN is written in Fortran 90 and also includes C preprocessor definitions. The code links against the PETSc, METIS, HDF5, and MPICH libraries. It optionally links against the MOAB library and is a part of the SHARP multi-physics suite for coupled multi-physics analysis of nuclear reactors. This user manual describes how to set up a neutron transport simulation with the PROTEUS-SN code. A companion methodology manual describes the theory and algorithms within PROTEUS-SN.« less

25 CFR 522.7 - Disapproval of a class III ordinance.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 25 Indians 2 2010-04-01 2010-04-01 false Disapproval of a class III ordinance. 522.7 Section 522.7 Indians NATIONAL INDIAN GAMING COMMISSION, DEPARTMENT OF THE INTERIOR APPROVAL OF CLASS II AND CLASS III ORDINANCES AND RESOLUTIONS SUBMISSION OF GAMING ORDINANCE OR RESOLUTION § 522.7 Disapproval of a class III...

25 CFR 522.5 - Disapproval of a class II ordinance.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 25 Indians 2 2010-04-01 2010-04-01 false Disapproval of a class II ordinance. 522.5 Section 522.5 Indians NATIONAL INDIAN GAMING COMMISSION, DEPARTMENT OF THE INTERIOR APPROVAL OF CLASS II AND CLASS III ORDINANCES AND RESOLUTIONS SUBMISSION OF GAMING ORDINANCE OR RESOLUTION § 522.5 Disapproval of a class II...

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis with Ordinal Data

ERIC Educational Resources Information Center

Lee, Chun-Ting; Zhang, Guangjian; Edwards, Michael C.

2012-01-01

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable.…

Local Area Co-Ordination: Strengthening Support for People with Learning Disabilities in Scotland

ERIC Educational Resources Information Center

Stalker, Kirsten Ogilvie; Malloch, Margaret; Barry, Monica Anne; Watson, June Ann

2008-01-01

This paper reports the findings of a study commissioned by the Scottish Executive which examined the introduction and implementation of local area co-ordination (LAC) in Scotland. A questionnaire about their posts was completed by 44 local area co-ordinators, interviews were conducted with 35 local area co-ordinators and 14 managers and case…

Means and Variances without Calculus

ERIC Educational Resources Information Center

Kinney, John J.

2005-01-01

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

Factorizable Schemes for the Equations of Fluid Flow

NASA Technical Reports Server (NTRS)

Sidilkover, David

1999-01-01

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

NASA Astrophysics Data System (ADS)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

[The relationship between Ridit analysis and rank sum test for one-way ordinal contingency table in medical research].

PubMed

Wang, Ling; Xia, Jie-lai; Yu, Li-li; Li, Chan-juan; Wang, Su-zhen

2008-06-01

To explore several numerical methods of ordinal variable in one-way ordinal contingency table and their interrelationship, and to compare corresponding statistical analysis methods such as Ridit analysis and rank sum test. Formula deduction was based on five simplified grading approaches including rank_r(i), ridit_r(i), ridit_r(ci), ridit_r(mi), and table scores. Practical data set was verified by SAS8.2 in clinical practice (to test the effect of Shiwei solution in treatment for chronic tracheitis). Because of the linear relationship of rank_r(i) = N ridit_r(i) + 1/2 = N ridit_r(ci) = (N + 1) ridit_r(mi), the exact chi2 values in Ridit analysis based on ridit_r(i), ridit_r(ci), and ridit_r(mi), were completely the same, and they were equivalent to the Kruskal-Wallis H test. Traditional Ridit analysis was based on ridit_r(i), and its corresponding chi2 value calculated with an approximate variance (1/12) was conservative. The exact chi2 test of Ridit analysis should be used when comparing multiple groups in the clinical researches because of its special merits such as distribution of mean ridit value on (0,1) and clear graph expression. The exact chi2 test of Ridit analysis can be output directly by proc freq of SAS8.2 with ridit and modridit option (SCORES =). The exact chi2 test of Ridit analysis is equivalent to the Kruskal-Wallis H test, and should be used when comparing multiple groups in the clinical researches.

Multimodal observational assessment of quality and productivity benefits from the implementation of wireless technology for out of hours working

PubMed Central

Blakey, John D; Guy, Debbie; Simpson, Carl; Fearn, Andrew; Cannaby, Sharon; Wilson, Petra

2012-01-01

Objectives The authors investigated if a wireless system of call handling and task management for out of hours care could replace a standard pager-based system and improve markers of efficiency, patient safety and staff satisfaction. Design Prospective assessment using both quantitative and qualitative methods, including interviews with staff, a standard satisfaction questionnaire, independent observation, data extraction from work logs and incident reporting systems and analysis of hospital committee reports. Setting A large teaching hospital in the UK. Participants Hospital at night co-ordinators, clinical support workers and junior doctors handling approximately 10 000 tasks requested out of hours per month. Outcome measures Length of hospital stay, incidents reported, co-ordinator call logging activity, user satisfaction questionnaire, staff interviews. Results Users were more satisfied with the new system (satisfaction score 62/90 vs 82/90, p=0.0080). With the new system over 70 h/week of co-ordinator time was released, and there were fewer untoward incidents related to handover and medical response (OR=0.30, p=0.02). Broad clinical measures (cardiac arrest calls for peri-arrest situations and length of hospital stay) improved significantly in the areas covered by the new system. Conclusions The introduction of call handling software and mobile technology over a medical-grade wireless network improved staff satisfaction with the Hospital at Night system. Improvements in efficiency and information flow have been accompanied by a reduction in untoward incidents, length of stay and peri-arrest calls. PMID:22466035

Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening

NASA Technical Reports Server (NTRS)

Diskin, Boris

1999-01-01

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation, deformation of a cantilever bracket, and Boycott effects). The applicability of the method is not limited to flow in porous media, but can also be employed to describe many other physical systems governed by a similar set of equations, including e.g. multi-component materials.

Tourism and hotel revenues before and after passage of smoke-free restaurant ordinances.

PubMed

Glantz, S A; Charlesworth, A

1999-05-26

Claims that ordinances requiring smoke-free restaurants will adversely affect tourism have been used to argue against passing such ordinances. Data exist regarding the validity of these claims. To determine the changes in hotel revenues and international tourism after passage of smoke-free restaurant ordinances in locales where the effect has been debated. Comparison of hotel revenues and tourism rates before and after passage of 100% smoke-free restaurant ordinances and comparison with US hotel revenue overall. Three states (California, Utah, and Vermont) and 6 cities (Boulder, Colo; Flagstaff, Ariz; Los Angeles, Calif; Mesa, Ariz; New York, NY; and San Francisco, Calif) in which the effect on tourism of smoke-free restaurant ordinances had been debated. Hotel room revenues and hotel revenues as a fraction of total retail sales compared with preordinance revenues and overall US revenues. In constant 1997 dollars, passage of the smoke-free restaurant ordinance was associated with a statistically significant increase in the rate of change of hotel revenues in 4 localities, no significant change in 4 localities, and a significant slowing in the rate of increase (but not a decrease) in 1 locality. There was no significant change in the rate of change of hotel revenues as a fraction of total retail sales (P=.16) or total US hotel revenues associated with the ordinances when pooled across all localities (P = .93). International tourism was either unaffected or increased following implementation of the smoke-free ordinances. Smoke-free ordinances do not appear to adversely affect, and may increase, tourist business.

Co-ordinated action between youth-care and sports: facilitators and barriers.

PubMed

Hermens, Niels; de Langen, Lisanne; Verkooijen, Kirsten T; Koelen, Maria A

2017-07-01

In the Netherlands, youth-care organisations and community sports clubs are collaborating to increase socially vulnerable youths' participation in sport. This is rooted in the idea that sports clubs are settings for youth development. As not much is known about co-ordinated action involving professional care organisations and community sports clubs, this study aims to generate insight into facilitators of and barriers to successful co-ordinated action between these two organisations. A cross-sectional study was conducted using in-depth semi-structured qualitative interview data. In total, 23 interviews were held at five locations where co-ordinated action between youth-care and sports takes place. Interviewees were youth-care workers, representatives from community sports clubs, and Care Sport Connectors who were assigned to encourage and manage the co-ordinated action. Using inductive coding procedures, this study shows that existing and good relationships, a boundary spanner, care workers' attitudes, knowledge and competences of the participants, organisational policies and ambitions, and some elements external to the co-ordinated action were reported to be facilitators or barriers. In addition, the participants reported that the different facilitators and barriers influenced the success of the co-ordinated action at different stages of the co-ordinated action. Future research is recommended to further explore the role of boundary spanners in co-ordinated action involving social care organisations and community sports clubs, and to identify what external elements (e.g. events, processes, national policies) are turning points in the formation, implementation and continuation of such co-ordinated action. © 2017 John Wiley & Sons Ltd.

Survey of local forestry-related ordinances and regulations in the south

Treesearch

Jonathan J. Spink; Karry L. Haney; John L. Greene

2000-01-01

A survey of the 13 southern states was conducted in 1999-2000 to obtain a comprehensive list of forestry-related ordinances enacted by various local governments. Each ordinance was examined to determine the date of adoption, regulatory objective, and its regu1atory provisions. Based on the regulatory objective, the ordinances were categorized into five general types:...

Knowledge of the ordinal position of list items in pigeons.

PubMed

Scarf, Damian; Colombo, Michael

2011-10-01

Ordinal knowledge is a fundamental aspect of advanced cognition. It is self-evident that humans represent ordinal knowledge, and over the past 20 years it has become clear that nonhuman primates share this ability. In contrast, evidence that nonprimate species represent ordinal knowledge is missing from the comparative literature. To address this issue, in the present experiment we trained pigeons on three 4-item lists and then tested them with derived lists in which, relative to the training lists, the ordinal position of the items was either maintained or changed. Similar to the findings with human and nonhuman primates, our pigeons performed markedly better on the maintained lists compared to the changed lists, and displayed errors consistent with the view that they used their knowledge of ordinal position to guide responding on the derived lists. These findings demonstrate that the ability to acquire ordinal knowledge is not unique to the primate lineage. (PsycINFO Database Record (c) 2011 APA, all rights reserved).

Least squares regression methods for clustered ROC data with discrete covariates.

PubMed

Tang, Liansheng Larry; Zhang, Wei; Li, Qizhai; Ye, Xuan; Chan, Leighton

2016-07-01

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerical study of the effects of lamp configuration and reactor wall roughness in an open channel water disinfection UV reactor.

PubMed

Sultan, Tipu

2016-07-01

This article describes the assessment of a numerical procedure used to determine the UV lamp configuration and surface roughness effects on an open channel water disinfection UV reactor. The performance of the open channel water disinfection UV reactor was numerically analyzed on the basis of the performance indictor reduction equivalent dose (RED). The RED values were calculated as a function of the Reynolds number to monitor the performance. The flow through the open channel UV reactor was modelled using a k-ε model with scalable wall function, a discrete ordinate (DO) model for fluence rate calculation, a volume of fluid (VOF) model to locate the unknown free surface, a discrete phase model (DPM) to track the pathogen transport, and a modified law of the wall to incorporate the reactor wall roughness effects. The performance analysis was carried out using commercial CFD software (ANSYS Fluent 15.0). Four case studies were analyzed based on open channel UV reactor type (horizontal and vertical) and lamp configuration (parallel and staggered). The results show that lamp configuration can play an important role in the performance of an open channel water disinfection UV reactor. The effects of the reactor wall roughness were Reynolds number dependent. The proposed methodology is useful for performance optimization of an open channel water disinfection UV reactor. Copyright © 2016 Elsevier Ltd. All rights reserved.

Satellite Remote Sensing of Tropical Precipitation and Ice Clouds for GCM Verification

NASA Technical Reports Server (NTRS)

Evans, K. Franklin

2001-01-01

This project, supported by the NASA New Investigator Program, has primarily been funding a graduate student, Darren McKague. Since August 1999 Darren has been working part time at Raytheon, while continuing his PhD research. Darren is planning to finish his thesis work in May 2001, thus some of the work described here is ongoing. The proposed research was to use GOES visible and infrared imager data and SSM/I microwave data to obtain joint distributions of cirrus cloud ice mass and precipitation for a study region in the Eastern Tropical Pacific. These joint distributions of cirrus cloud and rainfall were to be compared to those from the CSU general circulation model to evaluate the cloud microphysical amd cumulus parameterizations in the GCM. Existing algorithms were to be used for the retrieval of cloud ice water path from GOES (Minnis) and rainfall from SSM/I (Wilheit). A theoretical study using radiative transfer models and realistic variations in cloud and precipitation profiles was to be used to estimate the retrieval errors. Due to the unavailability of the GOES satellite cloud retrieval algorithm from Dr. Minnis (a co-PI), there was a change in the approach and emphasis of the project. The new approach was to develop a completely new type of remote sensing algorithm - one to directly retrieve joint probability density functions (pdf's) of cloud properties from multi-dimensional histograms of satellite radiances. The usual approach is to retrieve individual pixels of variables (i.e. cloud optical depth), and then aggregate the information. Only statistical information is actually needed, however, and so a more direct method is desirable. We developed forward radiative transfer models for the SSM/I and GOES channels, originally for testing the retrieval algorithms. The visible and near infrared ice scattering information is obtained from geometric ray tracing of fractal ice crystals (Andreas Macke), while the mid-infrared and microwave scattering is computed with Mie scattering. The radiative transfer is performed with the Spherical Harmonic Discrete Ordinate Method (developed by the PI), and infrared molecular absorption is included with the correlated k-distribution method. The SHDOM radiances have been validated by comparison to version 2 of DISORT (the community "standard" discrete-ordinates radiative transfer model), however we use SHDOM since it is computationally more efficient.

Galerkin v. discrete-optimal projection in nonlinear model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

The Semigeostrophic Equations Discretized in Reference and Dual Variables

NASA Astrophysics Data System (ADS)

Cullen, Mike; Gangbo, Wilfrid; Pisante, Giovanni

2007-08-01

We study the evolution of a system of n particles {\\{(x_i, v_i)\\}_{i=1}n} in {mathbb{R}^{2d}} . That system is a conservative system with a Hamiltonian of the form {H[μ]=W22(μ, νn)} , where W 2 is the Wasserstein distance and μ is a discrete measure concentrated on the set {\\{(x_i, v_i)\\}_{i=1}n} . Typically, μ(0) is a discrete measure approximating an initial L ∞ density and can be chosen randomly. When d = 1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that the limiting densities are absolutely continuous with respect to the Lebesgue measure. When {\\{ν^n\\}_{n=1}^infty} converges to a measure concentrated on a special d-dimensional set, we obtain the Vlasov-Monge-Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov-Poisson system.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP

DTIC Science & Technology

2007-01-01

differentiability, fluid-solid interaction, error estimation, re-discretization, moving meshes 16. SECURITY CLASSIFICATION OF: 17 . LIMITATION OF 18. NUMBER...method the weight function is an indepen- dent function v = 0 6 4Ph , with v = 0 on F, if W = W0 on F1. 2. Galerkin method (GM): If Wh is an approximation...This can be demonstrated by considering a simple I-D case (like described above) in which the discretization 17 is uniform with characteristic length

A discrete speech recognition system for dermatology: 8 years of daily experience in a medical dermatology office.

PubMed

Smith, Kevin C

2002-09-01

A discrete speech recognition system was customized to recognize approximately 9,000 phrases and terms commonly used in dermatology, and has been used on a daily basis since 1984 to produce as many as 65 consult and follow up letters daily. The systems and procedures necessary for the practical use of this system are described, together with a discussion of the advantages and disadvantages of using this system to automate the transcription of dermatological dictation.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Urban Runoff: Model Ordinances for Erosion and Sediment Control

EPA Pesticide Factsheets

The model ordinance in this section borrows language from the erosion and sediment control ordinance features that might help prevent erosion and sedimentation and protect natural resources more fully.

Probability Elicitation Under Severe Time Pressure: A Rank-Based Method.

PubMed

Jaspersen, Johannes G; Montibeller, Gilberto

2015-07-01

Probability elicitation protocols are used to assess and incorporate subjective probabilities in risk and decision analysis. While most of these protocols use methods that have focused on the precision of the elicited probabilities, the speed of the elicitation process has often been neglected. However, speed is also important, particularly when experts need to examine a large number of events on a recurrent basis. Furthermore, most existing elicitation methods are numerical in nature, but there are various reasons why an expert would refuse to give such precise ratio-scale estimates, even if highly numerate. This may occur, for instance, when there is lack of sufficient hard evidence, when assessing very uncertain events (such as emergent threats), or when dealing with politicized topics (such as terrorism or disease outbreaks). In this article, we adopt an ordinal ranking approach from multicriteria decision analysis to provide a fast and nonnumerical probability elicitation process. Probabilities are subsequently approximated from the ranking by an algorithm based on the principle of maximum entropy, a rule compatible with the ordinal information provided by the expert. The method can elicit probabilities for a wide range of different event types, including new ways of eliciting probabilities for stochastically independent events and low-probability events. We use a Monte Carlo simulation to test the accuracy of the approximated probabilities and try the method in practice, applying it to a real-world risk analysis recently conducted for DEFRA (the U.K. Department for the Environment, Farming and Rural Affairs): the prioritization of animal health threats. © 2015 Society for Risk Analysis.

Self-assembly of discrete metal complexes in aqueous solution via block copolypeptide amphiphiles.

PubMed

Kuroiwa, Keita; Masaki, Yoshitaka; Koga, Yuko; Deming, Timothy J

2013-01-21

The integration of discrete metal complexes has been attracting significant interest due to the potential of these materials for soft metal-metal interactions and supramolecular assembly. Additionally, block copolypeptide amphiphiles have been investigated concerning their capacity for self-assembly into structures such as nanoparticles, nanosheets and nanofibers. In this study, we combined these two concepts by investigating the self-assembly of discrete metal complexes in aqueous solution using block copolypeptides. Normally, discrete metal complexes such as [Au(CN)(2)]-, when molecularly dispersed in water, cannot interact with one another. Our results demonstrated, however, that the addition of block copolypeptide amphiphiles such as K(183)L(19) to [Au(CN)(2)]- solutions induced one-dimensional integration of the discrete metal complex, resulting in photoluminescence originating from multinuclear complexes with metal-metal interactions. Transmission electron microscopy (TEM) showed a fibrous nanostructure with lengths and widths of approximately 100 and 20 nm, respectively, which grew to form advanced nanoarchitectures, including those resembling the weave patterns of Waraji (traditional Japanese straw sandals). This concept of combining block copolypeptide amphiphiles with discrete coordination compounds allows the design of flexible and functional supramolecular coordination systems in water.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

Indirect iterative learning control for a discrete visual servo without a camera-robot model.

PubMed

Jiang, Ping; Bamforth, Leon C A; Feng, Zuren; Baruch, John E F; Chen, YangQuan

2007-08-01

This paper presents a discrete learning controller for vision-guided robot trajectory imitation with no prior knowledge of the camera-robot model. A teacher demonstrates a desired movement in front of a camera, and then, the robot is tasked to replay it by repetitive tracking. The imitation procedure is considered as a discrete tracking control problem in the image plane, with an unknown and time-varying image Jacobian matrix. Instead of updating the control signal directly, as is usually done in iterative learning control (ILC), a series of neural networks are used to approximate the unknown Jacobian matrix around every sample point in the demonstrated trajectory, and the time-varying weights of local neural networks are identified through repetitive tracking, i.e., indirect ILC. This makes repetitive segmented training possible, and a segmented training strategy is presented to retain the training trajectories solely within the effective region for neural network approximation. However, a singularity problem may occur if an unmodified neural-network-based Jacobian estimation is used to calculate the robot end-effector velocity. A new weight modification algorithm is proposed which ensures invertibility of the estimation, thus circumventing the problem. Stability is further discussed, and the relationship between the approximation capability of the neural network and the tracking accuracy is obtained. Simulations and experiments are carried out to illustrate the validity of the proposed controller for trajectory imitation of robot manipulators with unknown time-varying Jacobian matrices.

On the ordinality of numbers: A review of neural and behavioral studies.

PubMed

Lyons, I M; Vogel, S E; Ansari, D

2016-01-01

The last several years have seen steady growth in research on the cognitive and neuronal mechanisms underlying how numbers are represented as part of ordered sequences. In the present review, we synthesize what is currently known about numerical ordinality from behavioral and neuroimaging research, point out major gaps in our current knowledge, and propose several hypotheses that may bear further investigation. Evidence suggests that how we process ordinality differs from how we process cardinality, but that this difference depends strongly on context-in particular, whether numbers are presented symbolically or nonsymbolically. Results also reveal many commonalities between numerical and nonnumerical ordinal processing; however, the degree to which numerical ordinality can be reduced to domain-general mechanisms remains unclear. One proposal is that numerical ordinality relies upon more general short-term memory mechanisms as well as more numerically specific long-term memory representations. It is also evident that numerical ordinality is highly multifaceted, with symbolic representations in particular allowing for a wide range of different types of ordinal relations, the complexity of which appears to increase over development. We examine the proposal that these relations may form the basis of a richer set of associations that may prove crucial to the emergence of more complex math abilities and concepts. In sum, ordinality appears to be an important and relatively understudied facet of numerical cognition that presents substantial opportunities for new and ground-breaking research. © 2016 Elsevier B.V. All rights reserved.

Convergence of generalized MUSCL schemes

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point E scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Modeling Wind Wave Evolution from Deep to Shallow Water

DTIC Science & Technology

2012-09-30

WORK COMPLETED Development of a Lumped Quadruplet Approximation ( LQA ) A scalable parameterization of non-linear four-wave interactions is being...what we refer to as the Lumped Quadruplet Approximation ( LQA ), in which discrete contributions on the locus are treated as individual wave number...includes inhomogeneous wave fields, but is compatible with the action balance generally used in operational wave models. RESULTS Development LQA

Design and simulation of stratified probability digital receiver with application to the multipath communication

NASA Technical Reports Server (NTRS)

Deal, J. H.

1975-01-01

One approach to the problem of simplifying complex nonlinear filtering algorithms is through using stratified probability approximations where the continuous probability density functions of certain random variables are represented by discrete mass approximations. This technique is developed in this paper and used to simplify the filtering algorithms developed for the optimum receiver for signals corrupted by both additive and multiplicative noise.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form.

PubMed

Jagannathan, Sarangapani; He, Pingan

2008-12-01

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.

A new approach for modeling composite materials

NASA Astrophysics Data System (ADS)

Alcaraz de la Osa, R.; Moreno, F.; Saiz, J. M.

2013-03-01

The increasing use of composite materials is due to their ability to tailor materials for special purposes, with applications evolving day by day. This is why predicting the properties of these systems from their constituents, or phases, has become so important. However, assigning macroscopical optical properties for these materials from the bulk properties of their constituents is not a straightforward task. In this research, we present a spectral analysis of three-dimensional random composite typical nanostructures using an Extension of the Discrete Dipole Approximation (E-DDA code), comparing different approaches and emphasizing the influences of optical properties of constituents and their concentration. In particular, we hypothesize a new approach that preserves the individual nature of the constituents introducing at the same time a variation in the optical properties of each discrete element that is driven by the surrounding medium. The results obtained with this new approach compare more favorably with the experiment than previous ones. We have also applied it to a non-conventional material composed of a metamaterial embedded in a dielectric matrix. Our version of the Discrete Dipole Approximation code, the EDDA code, has been formulated specifically to tackle this kind of problem, including materials with either magnetic and tensor properties.

Semi-supervised learning for ordinal Kernel Discriminant Analysis.

PubMed

Pérez-Ortiz, M; Gutiérrez, P A; Carbonero-Ruz, M; Hervás-Martínez, C

2016-12-01

Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function. Copyright © 2016 Elsevier Ltd. All rights reserved.

Level Density in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Myo, T.; Katō, K.

2005-06-01

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of L(2) basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Reduction from cost-sensitive ordinal ranking to weighted binary classification.

PubMed

Lin, Hsuan-Tien; Li, Ling

2012-05-01

We present a reduction framework from ordinal ranking to binary classification. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranker from the binary classifier. Based on the framework, we show that a weighted 0/1 loss of the binary classifier upper-bounds the mislabeling cost of the ranker, both error-wise and regret-wise. Our framework allows not only the design of good ordinal ranking algorithms based on well-tuned binary classification approaches, but also the derivation of new generalization bounds for ordinal ranking from known bounds for binary classification. In addition, our framework unifies many existing ordinal ranking algorithms, such as perceptron ranking and support vector ordinal regression. When compared empirically on benchmark data sets, some of our newly designed algorithms enjoy advantages in terms of both training speed and generalization performance over existing algorithms. In addition, the newly designed algorithms lead to better cost-sensitive ordinal ranking performance, as well as improved listwise ranking performance.

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1988-01-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tadmor, E.

1988-07-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusionmore » into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).« less

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

NASA Astrophysics Data System (ADS)

Schmidt, Burkhard; Lorenz, Ulf

2017-04-01

WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. The graphical capabilities allow visualization of quantum dynamics 'on the fly', including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry. The present Part I deals with the description of closed quantum systems in terms of Schrödinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization. The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics. The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found.

Toward Optimal Manifold Hashing via Discrete Locally Linear Embedding.

PubMed

Rongrong Ji; Hong Liu; Liujuan Cao; Di Liu; Yongjian Wu; Feiyue Huang

2017-11-01

Binary code learning, also known as hashing, has received increasing attention in large-scale visual search. By transforming high-dimensional features to binary codes, the original Euclidean distance is approximated via Hamming distance. More recently, it is advocated that it is the manifold distance, rather than the Euclidean distance, that should be preserved in the Hamming space. However, it retains as an open problem to directly preserve the manifold structure by hashing. In particular, it first needs to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a two-step coding is problematic and less optimized. Besides, the off-line learning is extremely time and memory consuming, which needs to calculate the similarity matrix of the original data. In this paper, we propose a novel hashing algorithm, termed discrete locality linear embedding hashing (DLLH), which well addresses the above challenges. The DLLH directly reconstructs the manifold structure in the Hamming space, which learns optimal hash codes to maintain the local linear relationship of data points. To learn discrete locally linear embeddingcodes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH, is further introduced, which approximates the large similarity matrix by the product of two low-rank matrices. Experimental results on three widely used benchmark data sets, i.e., CIFAR10, NUS-WIDE, and YouTube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.

On the derivation of approximations to cellular automata models and the assumption of independence.

PubMed

Davies, K J; Green, J E F; Bean, N G; Binder, B J; Ross, J V

2014-07-01

Cellular automata are discrete agent-based models, generally used in cell-based applications. There is much interest in obtaining continuum models that describe the mean behaviour of the agents in these models. Previously, continuum models have been derived for agents undergoing motility and proliferation processes, however, these models only hold under restricted conditions. In order to narrow down the reason for these restrictions, we explore three possible sources of error in deriving the model. These sources are the choice of limiting arguments, the use of a discrete-time model as opposed to a continuous-time model and the assumption of independence between the state of sites. We present a rigorous analysis in order to gain a greater understanding of the significance of these three issues. By finding a limiting regime that accurately approximates the conservation equation for the cellular automata, we are able to conclude that the inaccuracy between our approximation and the cellular automata is completely based on the assumption of independence. Copyright © 2014 Elsevier Inc. All rights reserved.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

PubMed

Yan-Jun Liu; Shu Li; Shaocheng Tong; Chen, C L Philip

2017-07-01

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

Fast mix table construction for material discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, S. R.

2013-07-01

An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mixmore » table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)« less

Fast Mix Table Construction for Material Discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Seth R

2013-01-01

An effective hybrid Monte Carlo--deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a ``mix table,'' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table inmore » $$O(\\text{number of voxels}\\times \\log \\text{number of mixtures})$$ time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation.« less

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

PubMed

Mishchenko, Michael I; Dlugach, Janna M; Yurkin, Maxim A; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R Lee; Travis, Larry D; Yang, Ping; Zakharova, Nadezhda T

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ , or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

PubMed Central

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies. PMID:29657355

Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

PubMed

Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C

2018-04-01

A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.

Comparison of Ordinal and Nominal Classification Trees to Predict Ordinal Expert-Based Occupational Exposure Estimates in a Case–Control Study

PubMed Central

Wheeler, David C.; Archer, Kellie J.; Burstyn, Igor; Yu, Kai; Stewart, Patricia A.; Colt, Joanne S.; Baris, Dalsu; Karagas, Margaret R.; Schwenn, Molly; Johnson, Alison; Armenti, Karla; Silverman, Debra T.; Friesen, Melissa C.

2015-01-01

Objectives: To evaluate occupational exposures in case–control studies, exposure assessors typically review each job individually to assign exposure estimates. This process lacks transparency and does not provide a mechanism for recreating the decision rules in other studies. In our previous work, nominal (unordered categorical) classification trees (CTs) generally successfully predicted expert-assessed ordinal exposure estimates (i.e. none, low, medium, high) derived from occupational questionnaire responses, but room for improvement remained. Our objective was to determine if using recently developed ordinal CTs would improve the performance of nominal trees in predicting ordinal occupational diesel exhaust exposure estimates in a case–control study. Methods: We used one nominal and four ordinal CT methods to predict expert-assessed probability, intensity, and frequency estimates of occupational diesel exhaust exposure (each categorized as none, low, medium, or high) derived from questionnaire responses for the 14983 jobs in the New England Bladder Cancer Study. To replicate the common use of a single tree, we applied each method to a single sample of 70% of the jobs, using 15% to test and 15% to validate each method. To characterize variability in performance, we conducted a resampling analysis that repeated the sample draws 100 times. We evaluated agreement between the tree predictions and expert estimates using Somers’ d, which measures differences in terms of ordinal association between predicted and observed scores and can be interpreted similarly to a correlation coefficient. Results: From the resampling analysis, compared with the nominal tree, an ordinal CT method that used a quadratic misclassification function and controlled tree size based on total misclassification cost had a slightly better predictive performance that was statistically significant for the frequency metric (Somers’ d: nominal tree = 0.61; ordinal tree = 0.63) and similar performance for the probability (nominal = 0.65; ordinal = 0.66) and intensity (nominal = 0.65; ordinal = 0.65) metrics. The best ordinal CT predicted fewer cases of large disagreement with the expert assessments (i.e. no exposure predicted for a job with high exposure and vice versa) compared with the nominal tree across all of the exposure metrics. For example, the percent of jobs with expert-assigned high intensity of exposure that the model predicted as no exposure was 29% for the nominal tree and 22% for the best ordinal tree. Conclusions: The overall agreements were similar across CT models; however, the use of ordinal models reduced the magnitude of the discrepancy when disagreements occurred. As the best performing model can vary by situation, researchers should consider evaluating multiple CT methods to maximize the predictive performance within their data. PMID:25433003

Impact of San Francisco's toy ordinance on restaurants and children's food purchases, 2011-2012.

PubMed

Otten, Jennifer J; Saelens, Brian E; Kapphahn, Kristopher I; Hekler, Eric B; Buman, Matthew P; Goldstein, Benjamin A; Krukowski, Rebecca A; O'Donohue, Laura S; Gardner, Christopher D; King, Abby C

2014-07-17

In 2011, San Francisco passed the first citywide ordinance to improve the nutritional standards of children's meals sold at restaurants by preventing the giving away of free toys or other incentives with meals unless nutritional criteria were met. This study examined the impact of the Healthy Food Incentives Ordinance at ordinance-affected restaurants on restaurant response (eg, toy-distribution practices, change in children's menus), and the energy and nutrient content of all orders and children's-meal-only orders purchased for children aged 0 through 12 years. Restaurant responses were examined from January 2010 through March 2012. Parent-caregiver/child dyads (n = 762) who were restaurant customers were surveyed at 2 points before and 1 seasonally matched point after ordinance enactment at Chain A and B restaurants (n = 30) in 2011 and 2012. Both restaurant chains responded to the ordinance by selling toys separately from children's meals, but neither changed their menus to meet ordinance-specified nutrition criteria. Among children for whom children's meals were purchased, significant decreases in kilocalories, sodium, and fat per order were likely due to changes in children's side dishes and beverages at Chain A. Although the changes at Chain A did not appear to be directly in response to the ordinance, the transition to a more healthful beverage and default side dish was consistent with the intent of the ordinance. Study results underscore the importance of policy wording, support the concept that more healthful defaults may be a powerful approach for improving dietary intake, and suggest that public policies may contribute to positive restaurant changes.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Wind-tunnel investigation of the descent characteristics of bodies of revolution simulating anti-personnel bombs

NASA Technical Reports Server (NTRS)

Sher, S. H.

1951-01-01

An investigation has been conducted in the Langley 20-foot free spinning tunnel to study the relative behavior in descent of a number of homogeneous balsa bodies of revolution simulating anti-personnel bombs with a small cylindrical exploding device suspended approximately 10 feet below the bomb. The bodies of revolution included hemispherical, near-hemispherical, and near-paraboloid shapes. The ordinates of one near-paraboloid shape were specified by the Office of the Chief of Ordnance, U. S. Army. The behavior of the various bodies without the cylinder was also investigated. The results of the investigation indicated that several of the bodies descended vertically with their longitudinal axis, suspension line, and small cylinder in a vertical attitude,. However, the body, the ordinates of which had been specified by the Office of the Chief of Ordnance, U. S. Army, oscillated considerably from a vertical attitude while descending and therefore appeared unsuitable for its intended use. The behavior of this body became satisfactory when its center of gravity was moved well forward from its original position. In general, the results indicated that the descent characteristics of the bodies of revolution become more favorable as their shapes approached that of a hemisphere.

Gaussian-based routines to impute categorical variables in health surveys.

PubMed

Yucel, Recai M; He, Yulei; Zaslavsky, Alan M

2011-12-20

The multivariate normal (MVN) distribution is arguably the most popular parametric model used in imputation and is available in most software packages (e.g., SAS PROC MI, R package norm). When it is applied to categorical variables as an approximation, practitioners often either apply simple rounding techniques for ordinal variables or create a distinct 'missing' category and/or disregard the nominal variable from the imputation phase. All of these practices can potentially lead to biased and/or uninterpretable inferences. In this work, we develop a new rounding methodology calibrated to preserve observed distributions to multiply impute missing categorical covariates. The major attractiveness of this method is its flexibility to use any 'working' imputation software, particularly those based on MVN, allowing practitioners to obtain usable imputations with small biases. A simulation study demonstrates the clear advantage of the proposed method in rounding ordinal variables and, in some scenarios, its plausibility in imputing nominal variables. We illustrate our methods on a widely used National Survey of Children with Special Health Care Needs where incomplete values on race posed a valid threat on inferences pertaining to disparities. Copyright © 2011 John Wiley & Sons, Ltd.

Comments on `Area and power efficient DCT architecture for image compression' by Dhandapani and Ramachandran

NASA Astrophysics Data System (ADS)

Cintra, Renato J.; Bayer, Fábio M.

2017-12-01

In [Dhandapani and Ramachandran, "Area and power efficient DCT architecture for image compression", EURASIP Journal on Advances in Signal Processing 2014, 2014:180] the authors claim to have introduced an approximation for the discrete cosine transform capable of outperforming several well-known approximations in literature in terms of additive complexity. We could not verify the above results and we offer corrections for their work.

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Regional specialization in human nuclei: visualization of discrete sites of transcription by RNA polymerase III.

PubMed Central

Pombo, A; Jackson, D A; Hollinshead, M; Wang, Z; Roeder, R G; Cook, P R

1999-01-01

Mammalian nuclei contain three different RNA polymerases defined by their characteristic locations and drug sensitivities; polymerase I is found in nucleoli, and polymerases II and III in the nucleoplasm. As nascent transcripts made by polymerases I and II are concentrated in discrete sites, the locations of those made by polymerase III were investigated. HeLa cells were lysed with saponin in an improved 'physiological' buffer that preserves transcriptional activity and nuclear ultrastructure; then, engaged polymerases were allowed to extend nascent transcripts in Br-UTP, before the resulting Br-RNA was immunolabelled indirectly with fluorochromes or gold particles. Biochemical analysis showed that approximately 10 000 transcripts were being made by polymerase III at the moment of lysis, while confocal and electron microscopy showed that these transcripts were concentrated in only approximately 2000 sites (diameter approximately 40 nm). Therefore, each site contains approximately five active polymerases. These sites contain specific subunits of polymerase III, but not the hyperphosphorylated form of the largest subunit of polymerase II. The results indicate that the active forms of all three nuclear polymerases are concentrated in their own dedicated transcription sites or 'factories', suggesting that different regions of the nucleus specialize in the transcription of different types of gene. PMID:10205177

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems.

PubMed

Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

2016-01-01

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Accurate Computation of Electric Field Enhancement Factors for Metallic Nanoparticles Using the Discrete Dipole Approximation

PubMed Central

2010-01-01

We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole approximation, in which the spheroid is represented as a collection of polarizable subunits. We compare the results of simulations that employ subunit polarizabilities derived from the Clausius–Mossotti relation with those of simulations that employ polarizabilities that include a local environmental correction for subunits near the spheroid’s surface [Rahmani et al. Opt Lett 27: 2118 (2002)]. The simulations that employ corrected polarizabilities give predictions in very good agreement with exact results obtained by solving Laplace’s equation. In contrast, simulations that employ uncorrected Clausius–Mossotti polarizabilities substantially underestimate the extent of the electric field “hot spot” near the spheroid’s sharp tip, and give predictions for the field enhancement factor near the tip that are 30 to 50% too small. PMID:20672062

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

PubMed

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Multigrid methods for isogeometric discretization

PubMed Central

Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.

2013-01-01

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168

Overstatement in happiness reporting with ordinal, bounded scale.

PubMed

Tanaka, Saori C; Yamada, Katsunori; Kitada, Ryo; Tanaka, Satoshi; Sugawara, Sho K; Ohtake, Fumio; Sadato, Norihiro

2016-02-18

There are various methods by which people can express subjective evaluations quantitatively. For example, happiness can be measured on a scale from 1 to 10, and has been suggested as a measure of economic policy. However, there is resistance to these types of measurement from economists, who often regard welfare to be a cardinal, unbounded quantity. It is unclear whether there are differences between subjective evaluation reported on ordinal, bounded scales and on cardinal, unbounded scales. To answer this question, we developed functional magnetic resonance imaging experimental tasks for reporting happiness from monetary gain and the perception of visual stimulus. Subjects tended to report higher values when they used ordinal scales instead of cardinal scales. There were differences in neural activation between ordinal and cardinal reporting scales. The posterior parietal area showed greater activation when subjects used an ordinal scale instead of a cardinal scale. Importantly, the striatum exhibited greater activation when asked to report happiness on an ordinal scale than when asked to report on a cardinal scale. The finding that ordinal (bounded) scales are associated with higher reported happiness and greater activation in the reward system shows that overstatement bias in happiness data must be considered.

PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces

DOE PAGES

Sarmiento, Adel; Cortes, Adriano; Garcia, Daniel; ...

2016-10-07

We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Lidar cross-sections of soot fractal aggregates: Assessment of equivalent-sphere models

NASA Astrophysics Data System (ADS)

Ceolato, Romain; Gaudfrin, Florian; Pujol, Olivier; Riviere, Nicolas; Berg, Matthew J.; Sorensen, Christopher M.

2018-06-01

This work assesses the ability of equivalent-sphere models to reproduce the optical properties of soot aggregates relevant for lidar remote sensing, i.e. the backscattering and extinction cross sections. Lidar cross-sections are computed with a spectral discrete dipole approximation model over the visible-to-infrared (400-5000 nm) spectrum and compared with equivalent-sphere approximations. It is shown that the equivalent-sphere approximation, applied to fractal aggregates, has a limited ability to calculate such cross-sections well. The approximation should thus be used with caution for the computation of broadband lidar cross-sections, especially backscattering, at small and intermediate wavelengths (e.g. UV to visible).

75 FR 75694 - Klamath Tribes Liquor Control Ordinance Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-06

... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Klamath Tribes Liquor Control Ordinance... Control Ordinance of the Klamath Tribes. This correction removes incorrect references to an amended... follows: SUMMARY: This notice publishes the Secretary's certification of the Klamath Tribes Liquor Control...

Development of a computer program to obtain ordinates for NACA 4-digit, 4-digit modified, 5-digit, and 16 series airfoils

NASA Technical Reports Server (NTRS)

Ladson, C. L.; Brooks, Cuyler W., Jr.

1975-01-01

A computer program developed to calculate the ordinates and surface slopes of any thickness, symmetrical or cambered NACA airfoil of the 4-digit, 4-digit modified, 5-digit, and 16-series airfoil families is presented. The program produces plots of the airfoil nondimensional ordinates and a punch card output of ordinates in the input format of a readily available program for determining the pressure distributions of arbitrary airfoils in subsonic potential viscous flow.

The added value of ordinal analysis in clinical trials: an example in traumatic brain injury.

PubMed

Roozenbeek, Bob; Lingsma, Hester F; Perel, Pablo; Edwards, Phil; Roberts, Ian; Murray, Gordon D; Maas, Andrew Ir; Steyerberg, Ewout W

2011-01-01

In clinical trials, ordinal outcome measures are often dichotomized into two categories. In traumatic brain injury (TBI) the 5-point Glasgow outcome scale (GOS) is collapsed into unfavourable versus favourable outcome. Simulation studies have shown that exploiting the ordinal nature of the GOS increases chances of detecting treatment effects. The objective of this study is to quantify the benefits of ordinal analysis in the real-life situation of a large TBI trial. We used data from the CRASH trial that investigated the efficacy of corticosteroids in TBI patients (n = 9,554). We applied two techniques for ordinal analysis: proportional odds analysis and the sliding dichotomy approach, where the GOS is dichotomized at different cut-offs according to baseline prognostic risk. These approaches were compared to dichotomous analysis. The information density in each analysis was indicated by a Wald statistic. All analyses were adjusted for baseline characteristics. Dichotomous analysis of the six-month GOS showed a non-significant treatment effect (OR = 1.09, 95% CI 0.98 to 1.21, P = 0.096). Ordinal analysis with proportional odds regression or sliding dichotomy showed highly statistically significant treatment effects (OR 1.15, 95% CI 1.06 to 1.25, P = 0.0007 and 1.19, 95% CI 1.08 to 1.30, P = 0.0002), with 2.05-fold and 2.56-fold higher information density compared to the dichotomous approach respectively. Analysis of the CRASH trial data confirmed that ordinal analysis of outcome substantially increases statistical power. We expect these results to hold for other fields of critical care medicine that use ordinal outcome measures and recommend that future trials adopt ordinal analyses. This will permit detection of smaller treatment effects.

Impact of San Francisco’s Toy Ordinance on Restaurants and Children’s Food Purchases, 2011–2012

PubMed Central

Saelens, Brian E.; Kapphahn, Kristopher I.; Hekler, Eric B.; Buman, Matthew P.; Goldstein, Benjamin A.; Krukowski, Rebecca A.; O’Donohue, Laura S.; Gardner, Christopher D.; King, Abby C.

2014-01-01

Introduction In 2011, San Francisco passed the first citywide ordinance to improve the nutritional standards of children’s meals sold at restaurants by preventing the giving away of free toys or other incentives with meals unless nutritional criteria were met. This study examined the impact of the Healthy Food Incentives Ordinance at ordinance-affected restaurants on restaurant response (eg, toy-distribution practices, change in children’s menus), and the energy and nutrient content of all orders and children’s-meal–only orders purchased for children aged 0 through 12 years. Methods Restaurant responses were examined from January 2010 through March 2012. Parent–caregiver/child dyads (n = 762) who were restaurant customers were surveyed at 2 points before and 1 seasonally matched point after ordinance enactment at Chain A and B restaurants (n = 30) in 2011 and 2012. Results Both restaurant chains responded to the ordinance by selling toys separately from children’s meals, but neither changed their menus to meet ordinance-specified nutrition criteria. Among children for whom children’s meals were purchased, significant decreases in kilocalories, sodium, and fat per order were likely due to changes in children’s side dishes and beverages at Chain A. Conclusion Although the changes at Chain A did not appear to be directly in response to the ordinance, the transition to a more healthful beverage and default side dish was consistent with the intent of the ordinance. Study results underscore the importance of policy wording, support the concept that more healthful defaults may be a powerful approach for improving dietary intake, and suggest that public policies may contribute to positive restaurant changes. PMID:25032837

Multivariate decoding of brain images using ordinal regression.

PubMed

Doyle, O M; Ashburner, J; Zelaya, F O; Williams, S C R; Mehta, M A; Marquand, A F

2013-11-01

Neuroimaging data are increasingly being used to predict potential outcomes or groupings, such as clinical severity, drug dose response, and transitional illness states. In these examples, the variable (target) we want to predict is ordinal in nature. Conventional classification schemes assume that the targets are nominal and hence ignore their ranked nature, whereas parametric and/or non-parametric regression models enforce a metric notion of distance between classes. Here, we propose a novel, alternative multivariate approach that overcomes these limitations - whole brain probabilistic ordinal regression using a Gaussian process framework. We applied this technique to two data sets of pharmacological neuroimaging data from healthy volunteers. The first study was designed to investigate the effect of ketamine on brain activity and its subsequent modulation with two compounds - lamotrigine and risperidone. The second study investigates the effect of scopolamine on cerebral blood flow and its modulation using donepezil. We compared ordinal regression to multi-class classification schemes and metric regression. Considering the modulation of ketamine with lamotrigine, we found that ordinal regression significantly outperformed multi-class classification and metric regression in terms of accuracy and mean absolute error. However, for risperidone ordinal regression significantly outperformed metric regression but performed similarly to multi-class classification both in terms of accuracy and mean absolute error. For the scopolamine data set, ordinal regression was found to outperform both multi-class and metric regression techniques considering the regional cerebral blood flow in the anterior cingulate cortex. Ordinal regression was thus the only method that performed well in all cases. Our results indicate the potential of an ordinal regression approach for neuroimaging data while providing a fully probabilistic framework with elegant approaches for model selection. Copyright © 2013. Published by Elsevier Inc.

The Outlier Detection for Ordinal Data Using Scalling Technique of Regression Coefficients

NASA Astrophysics Data System (ADS)

Adnan, Arisman; Sugiarto, Sigit

2017-06-01

The aims of this study is to detect the outliers by using coefficients of Ordinal Logistic Regression (OLR) for the case of k category responses where the score from 1 (the best) to 8 (the worst). We detect them by using the sum of moduli of the ordinal regression coefficients calculated by jackknife technique. This technique is improved by scalling the regression coefficients to their means. R language has been used on a set of ordinal data from reference distribution. Furthermore, we compare this approach by using studentised residual plots of jackknife technique for ANOVA (Analysis of Variance) and OLR. This study shows that the jackknifing technique along with the proper scaling may lead us to reveal outliers in ordinal regression reasonably well.

Curvature and tangential deflection of discrete arcs: a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data.

PubMed

Anderson, I M; Bezdek, J C

1984-01-01

This paper introduces a new theory for the tangential deflection and curvature of plane discrete curves. Our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats: its rationale is drawn from the statistical and geometric properties associated with the eigenvalue-eigenvector structure of sample covariance matrices. Specifically, we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces. And further, we show that this entry is-in certain limiting cases-also proportional to the analytical curvature of the plane curve from which the discrete data are drawn. These results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection; and moreover, they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts. As a concrete example, we develop the commutator vertex detection (CVD) algorithm, which identifies the location of vertices in shape data based on excessive cummulative tangential deflection; and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding (approximate) curvature extrema.

A new discrete dipole kernel for quantitative susceptibility mapping.

PubMed

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Adaptive critic designs for discrete-time zero-sum games with application to H(infinity) control.

PubMed

Al-Tamimi, Asma; Abu-Khalaf, Murad; Lewis, Frank L

2007-02-01

In this correspondence, adaptive critic approximate dynamic programming designs are derived to solve the discrete-time zero-sum game in which the state and action spaces are continuous. This results in a forward-in-time reinforcement learning algorithm that converges to the Nash equilibrium of the corresponding zero-sum game. The results in this correspondence can be thought of as a way to solve the Riccati equation of the well-known discrete-time H(infinity) optimal control problem forward in time. Two schemes are presented, namely: 1) a heuristic dynamic programming and 2) a dual-heuristic dynamic programming, to solve for the value function and the costate of the game, respectively. An H(infinity) autopilot design for an F-16 aircraft is presented to illustrate the results.

25 CFR 522.2 - Submission requirements.

Code of Federal Regulations, 2010 CFR

2010-04-01

... NATIONAL INDIAN GAMING COMMISSION, DEPARTMENT OF THE INTERIOR APPROVAL OF CLASS II AND CLASS III ORDINANCES AND RESOLUTIONS SUBMISSION OF GAMING ORDINANCE OR RESOLUTION § 522.2 Submission requirements. A tribe... officials and key employees; (d) Copies of all tribal gaming regulations; (e) When an ordinance or...

Cable Television Report and Suggested Ordinance.

ERIC Educational Resources Information Center

League of California Cities, Sacramento.

Guidelines and suggested ordinances for cable television regulation by local governments are comprehensively discussed in this report. The emphasis is placed on franchising the cable operator. Seventeen legal aspects of franchising are reviewed, and an exemplary ordinance is presented. In addition, current statistics about cable franchising in…

An account of co-ordination mechanisms for humanitarian assistance during the international response to the 1994 crisis in Rwanda.

PubMed

Borton, J

1996-12-01

This paper examines the co-ordination strategies developed to respond to the Great Lakes crisis following the events of April 1994. It analyses the different functions and mechanisms which sought to achieve a co-ordinated response--ranging from facilitation at one extreme to management and direction at the other. The different regimes developed to facilitate co-ordination within Rwanda and neighbouring countries, focusing on both inter-agency and inter-country co-ordination issues, are then analysed. Finally, the paper highlights the absence of mechanisms to achieve coherence between the humanitarian, political and security domains. It concludes that effective co-ordination is critical not only to achieve programme efficiency, but to ensure that the appropriate instruments and strategies to respond to complex political emergencies are in place. It proposes a radical re-shaping of international humanitarian, political and security institutions, particularly the United Nations, to improve the effectiveness of humanitarian and political responses to crises such as that in the Great Lakes.

No toy for you! The healthy food incentives ordinance: paternalism or consumer protection?

PubMed

Etow, Alexis M

2012-01-01

The newest approach to discouraging children's unhealthy eating habits, amidst increasing rates of childhood obesity and other diet-related diseases, seeks to ban something that is not even edible. In 2010, San Francisco enacted the Healthy Food Incentives Ordinance, which prohibits toys in kids' meals if the meals do not meet certain nutritional requirements. Notwithstanding the Ordinance's impact on interstate commerce or potential infringement on companies' commercial speech rights and on parents' rights to determine what their children eat, this Comment argues that the Ordinance does not violate the dormant Commerce Clause, the First Amendment, or substantive due process. The irony is that although the Ordinance likely avoids the constitutional hurdles that hindered earlier measures aimed at childhood obesity, it intrudes on civil liberties more than its predecessors. This Comment analyzes the legality of the Healthy Food Incentives Ordinance to understand its implications on subsequent legislation aimed at combating childhood obesity and on the progression of public health law.

Modelling sheet-flow sediment transport in wave-bottom boundary layers using discrete-element modelling.

PubMed

Calantoni, Joseph; Holland, K Todd; Drake, Thomas G

2004-09-15

Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.

Discrete wavelet transform: a tool in smoothing kinematic data.

PubMed

Ismail, A R; Asfour, S S

1999-03-01

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Discrete-time stability of continuous-time controller designs for large space structures

NASA Technical Reports Server (NTRS)

Balas, M. J.

1982-01-01

In most of the stable control designs for flexible structures, continuous time is assumed. However, in view of the implementation of the controllers by on-line digital computers, the discrete-time stability of such controllers is an important consideration. In the case of direct-velocity feedback (DVFB), involving negative feedback from collocated force actuators and velocity sensors, it is not immediately apparent how much delay due to digital implementation of DVFB can be tolerated without loss of stability. The present investigation is concerned with such questions. A study is conducted of the discrete-time stability of DVFB, taking into account an employment of Euler's method of approximation of the time derivative. The obtained result gives an indication of the acceptable time-step size for stable digital implementation of DVFB. A result derived in connection with the consideration of the discrete-time stability of stable continuous-time systems provides a general condition under which digital implementation of such a system will remain stable.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

Meshes optimized for discrete exterior calculus (DEC).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mousley, Sarah C.; Deakin, Michael; Knupp, Patrick

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximationmore » of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.« less

A multigrid solver for the semiconductor equations

NASA Technical Reports Server (NTRS)

Bachmann, Bernhard

1993-01-01

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

A Polyhedral Outer-approximation, Dynamic-discretization optimization solver, 1.x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, Rusell; Nagarajan, Harsha; Sundar, Kaarthik

2017-09-25

In this software, we implement an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) to global optimality. The algorithm combines ideas that exploit the structure of convex relaxations to MINLPs and bound tightening procedures

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials.

PubMed

Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong

2013-12-01

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

77 FR 34981 - Stillaguamish Tribe of Indians-Liquor Control Ordinance

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-12

... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Stillaguamish Tribe of Indians--Liquor Control... publishes the Stillaguamish Tribe of Indians' Liquor Control Ordinance. The Ordinance regulates and controls... of the Stillaguamish Tribe of Indians, will increase the ability of the tribal government to control...

7 CFR 1901.204 - Compliance reviews.

Code of Federal Regulations, 2014 CFR

2014-01-01

... Administrator, Community and Business Programs, for each recipient. (4) Mandatory hook-up ordinance. Compliance... under the provisions of a mandatory hook-up ordinance will consist of a certification by the borrower or grantee that the ordinance is still in effect and is being enforced. (5) Forwarding noncompliance report...

7 CFR 1901.204 - Compliance reviews.

Code of Federal Regulations, 2012 CFR

2012-01-01

... Administrator, Community and Business Programs, for each recipient. (4) Mandatory hook-up ordinance. Compliance... under the provisions of a mandatory hook-up ordinance will consist of a certification by the borrower or grantee that the ordinance is still in effect and is being enforced. (5) Forwarding noncompliance report...

7 CFR 1901.204 - Compliance reviews.

Code of Federal Regulations, 2011 CFR

2011-01-01

... Administrator, Community and Business Programs, for each recipient. (4) Mandatory hook-up ordinance. Compliance... under the provisions of a mandatory hook-up ordinance will consist of a certification by the borrower or grantee that the ordinance is still in effect and is being enforced. (5) Forwarding noncompliance report...

7 CFR 1901.204 - Compliance reviews.

Code of Federal Regulations, 2013 CFR

2013-01-01

... Administrator, Community and Business Programs, for each recipient. (4) Mandatory hook-up ordinance. Compliance... under the provisions of a mandatory hook-up ordinance will consist of a certification by the borrower or grantee that the ordinance is still in effect and is being enforced. (5) Forwarding noncompliance report...

Parent-reported symptoms, impairment, helpfulness of treatment, and unmet service needs in a follow-up of outpatient children with attention-deficit/hyperactivity disorder.

PubMed

Sollie, Henrik; Larsson, Bo

2016-11-01

Limited information exists regarding the associations between impairment, symptoms, helpfulness of treatments, and service needs after initial treatment of children with attention-deficit/hyperactivity disorder (ADHD). The aims of this study were to examine persistence rates and associations between parent-reported symptoms, impairment, helpfulness of treatments, and service needs in a retrospective follow-up study of children with ADHD. Parents of 214 children with a mean age of 12.6 years (SD = 2.1) who were diagnosed with ADHD at five child and adolescent mental health clinics (CAMHS) completed questionnaires 1-10 years (mean = 3.7 years, SD = 2.2) after baseline assessment. The response rate was 43.4%. A community comparison group (n = 110) was recruited from the same area. Approximately two-thirds (60.3%) of the sample fulfilled the DSM-IV symptom criteria of ADHD at follow-up, 84.3% were functionally impaired, and most children (84.7%) were on medication. Inattentive and emotional symptoms were the strongest predictors of impairment across impairment areas. Perceived helpfulness of different treatments varied from 71.8-88.7%, and no significant difference was found between the ADHD sub-groups regarding reported helpfulness. 'Adjustment of the school situation' was the most frequent service need, and approximately half of the parents reported needs for care co-ordination. Children fulfilling the symptom criteria of the ADHD Combined sub-group were most impaired and had most service needs. At follow-up, children were highly symptomatic and impaired, despite a high rate of persistent medication treatment. The findings underline the need for more tailored treatment and co-ordinated care over time.

Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

NASA Astrophysics Data System (ADS)

Huang, Zhi-Xiang; Wu, Xian-Liang

Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

A comparison of methods for converting DCE values onto the full health-dead QALY scale.

PubMed

Rowen, Donna; Brazier, John; Van Hout, Ben

2015-04-01

Preference elicitation techniques such as time trade-off (TTO) and standard gamble (SG) receive criticism for their complexity and difficulties of use. Ordinal techniques such as discrete choice experiment (DCE) are arguably easier to understand but generate values that are not anchored onto the full health-dead 1-0 quality-adjusted life-year (QALY) scale required for use in economic evaluation. This article compares existing methods for converting modeled DCE latent values onto the full health-dead QALY scale: 1) anchoring DCE values using dead as valued in the DCE and 2) anchoring DCE values using TTO value for worst state to 2 new methods: 3) mapping DCE values onto TTO and 4) combining DCE and TTO data in a hybrid model. Models are compared using their ability to predict mean TTO health state values. We use postal DCE data (n = 263) and TTO data (n = 307) collected by interview in a general population valuation study of an asthma condition-specific measure (AQL-5D). New methods 3 and 4 using mapping and hybrid models are better able to predict mean TTO health state values (mean absolute difference [MAD], 0.052-0.084) than the anchor-based methods (MAD, 0.075-0.093) and were better able to predict mean TTO health state values even when using in their estimation a subsample of the available TTO data. These new mapping and hybrid methods have a potentially useful role for producing values on the QALY scale from data elicited using ordinal techniques such as DCE for use in economic evaluation that makes best use of the desirable properties of each elicitation technique and elicited data. Further research is encouraged. © The Author(s) 2014.

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

1999-01-01

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.