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At least 973 records · Page 54
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NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗
NASA NTRS2000

Actinic Flux Calculations: A Model Sensitivity Study

calculate direct and diffuse surface irradiance and actinic flux (downwelling (2p) and total (4p)) for the reference model. Sensitivity analysis has shown that the accuracy of the radiative transfer flux calculations for a unit ETS (i.e. atmospheric transmittance) together with a numerical interpolation technique for the constituents' vertical profiles is better than 1% for SZA less than 70(sub o) and wavelengths longer than 310 nm. The differences increase for shorter wavelengths and larger SZA, due to the differences in pseudo-spherical correction techniques and vertical discretetization among the codes. Our sensitivity study includes variation of ozone cross-sections, ETS spectra and the effects of wavelength shifts between vacuum and air scales. We also investigate the effects of aerosols on the spectral flux components in the UV and visible spectral regions. The "aerosol correction factors" (ACFs) were calculated at discrete wavelengths and different SZAs for each flux component (direct, diffuse, reflected) and prescribed IPMMI aerosol parameters. Finally, the sensitivity study was extended to calculation of selected photolysis rates coefficients.

Krotkov, Nickolay A.↗
NASA NTRS2000

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Kouatchou, Jules↗
NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗
NASA NTRS2001

Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example

The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.

Smart, D. F.↗
NASA NTRS1997

Some Experiences with High Order Discretization Schemes for Compressible Fluid Flow

It is widely recognized that the structure and complexity of compressible fluid flow places high demands on numerical discretization techniques for the fluid flow equations. Fluid flows arising in external aerodynamics often contain both flow field discontinuities and fluid boundary-layers. Both must be accurately resolved to provide useful information to aerodynamic design and analysis engineers. These accuracy requirements motivated the present author to examine a class of finite-volume techniques on arbitrary triangulated domains based on linear or quadratic reconstruction of integral-averaged data followed by upwind flux function evaluation and small time evolution. More recently, we have considered some new upwind techniques which yield compact discretizations while maintaining higher order accuracy. In the mini-symposium talk we will discuss both of these techniques as well as demonstrate the relative merits of each method by computing a number of aerodynamic flows containing shock waves and boundary-layers.

Barth, Timothy J.↗
NASA NTRS1998

Three Program Architecture for Design Optimization

In this presentation, I would like to review historical perspective on the program architecture used to build design optimization capabilities based on mathematical programming and other numerical search techniques. It is rather straightforward to classify the program architecture in three categories as shown above. However, the relative importance of each of the three approaches has not been static, instead dynamically changing as the capabilities of available computational resource increases. For example, we considered that the direct coupling architecture would never be used for practical problems, but availability of such computer systems as multi-processor. In this presentation, I would like to review the roles of three architecture from historical as well as current and future perspective. There may also be some possibility for emergence of hybrid architecture. I hope to provide some seeds for active discussion where we are heading to in the very dynamic environment for high speed computing and communication.

Miura, Hirokazu↗
NASA NTRS2002

The Impact of Urbanization on the Precipitation Component of the Water Cycle: A New Perspective

It is estimated that by the year 2025, 60% of the world s population will live in cities (UNFP, 1999). As cities continue to grow, urban sprawl (e.g., the expansion of urban surfaces outward into rural surroundings) creates unique problems related to land use, transportation, agriculture, housing, pollution, and development. Urban expansion also has measurable impacts on environmental processes. Urban areas modify boundary layer processes through the creation of an urban heat island (UHI). The literature indicates that the signature of the urban heat island effect may be resolvable in rainfall patterns over and downwind of metropolitan areas. However, a recent U.S. Weather Research Program panel concluded that more observational and modeling research is needed in this area (Dabberdt et al. 2000). NASA and other agencies initiated programs such as the Atlanta Land-use Analysis: Temperature and Air Quality Project (ATLANTA) (Quattrochi et al. 1998) which aimed to identify and understand how urban heat islands impact the environment. However, a comprehensive assessment of the role of urban-induced rainfall in the global water and energy cycle (GWEC) and cycling of freshwater was not a primary focus of these efforts. NASA's Earth Science Enterprise (ESE) seeks to develop a scientific understanding of the Earth system and its response to natural or human-induced changes to enable improved prediction capability for climate, weather, and natural hazards (NASA, 2000). Within this mission, the ESE has three basic thrusts: science research to increase Earth system knowledge; an applications program to transfer science knowledge to practical use in society; and a technology program to enable new, better, and cheaper capabilities for observing the earth. Within this framework, a research program is underway to further address the co-relationship between land cover use and change (e.g. urban development) and its impact on key components of the GWEC (e.g., precipitation). This presentation discusses the feasibility of using the TRMM or GPM satellite to identify precipitation anomalies likely caused by urbanization (Shepherd et al. 2002). Recent results from analyses of TRMM data around several major U.S. cities (e.g. Dallas, Atlanta, Houston) will be discussed. The presentation also summarizes a NASA-funded research effort to investigate the phenomenon of urban-induced precipitation anomalies using TRMM (future GPM) satellite-based remote sensing, an intensive ground observation/validation effort near Atlanta, and coupled atmosphere-land numerical modeling techniques.

Shephard, J. Marshal↗
NASA NTRS2000

Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation

A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.

Rizzi, Stephen A.↗
NASA NTRS2001

Rapid flow-induced responses in endothelial cells

Endothelial cells alter their morphology, growth rate, and metabolism in response to fluid shear stress. To study rapid flow-induced responses in the 3D endothelial cell morphology and calcium distribution, coupled fluorescence microscopy with optical sectioning, digital imaging, and numerical deconvolution techniques have been utilized. Results demonstrate that within the first minutes of flow application nuclear calcium is increasing. In the same time frame whole cell height and nuclear height are reduced by about 1 microm. Whole cell height changes may facilitate reduction of shear stress gradients on the luminal surface, whereas nuclear structural changes may be important for modulating endothelial growth rate and metabolism. To study the role of the cytoskeleton in these responses, endothelial cells have been treated with specific disrupters (acrylamide, cytochalasin D, and colchicine) of each of the cytoskeleton elements (intermediate filaments, microfilaments, and microtubules, respectively). None of these compounds had any effect on the shear-induced calcium response. Cytochalasin D and acrylamide did not affect the shear-induced nuclear morphology changes. Colchicine, however, completely abrogated the response, indicating that microtubules may be implicated in force transmission from the plasma membrane to the nucleus. A pedagogical model based on tensegrity theory principles is presented that is consistent with the results on the 3D endothelial morphology.

Non-NASA Center↗
NASA NTRS1984

A dynamic model for plant growth: validation study under changing temperatures

A dynamic simulation model to describe vegetative growth of plants, for which some functions and parameter values have been estimated previously by optimization search techniques and numerical experimentation based on data from constant temperature experiments, is validated under conditions of changing temperatures. To test the predictive capacity of the model, dry matter accumulation in the leaves, stems, and roots of tobacco plants (Nicotiana tabacum L.) was measured at 2- or 3-day intervals during a 5-week period when temperatures in controlled-environment rooms were programmed for changes at weekly and daily intervals and in ascending or descending sequences within a range of 14 to 34 degrees C. Simulations of dry matter accumulation and distribution were carried out using the programmed changes for experimental temperatures and compared with the measured values. The agreement between measured and predicted values was close and indicates that the temperature-dependent functional forms derived from constant-temperature experiments are adequate for modelling plant growth responses to conditions of changing temperatures with switching intervals as short as 1 day.

NASA Discipline Number 60-40↗
NASA NTRS1985

Assessment of metabolic bone diseases by quantitative computed tomography

Advances in the radiologic sciences have permitted the development of numerous noninvasive techniques for measuring the mineral content of bone, with varying degrees of precision, accuracy, and sensitivity. The techniques of standard radiography, radiogrammetry, photodensitometry, Compton scattering, neutron activation analysis, single and dual photon absorptiometry, and quantitative computed tomography (QCT) are described and reviewed in depth. Results from previous cross-sectional and longitudinal QCT investigations are given. They then describe a current investigation in which they studied 269 subjects, including 173 normal women, 34 patients with hyperparathyroidism, 24 patients with steroid-induced osteoporosis, and 38 men with idiopathic osteoporosis. Spinal quantitative computed tomography, radiogrammetry, and single photon absorptiometry were performed, and a spinal fracture index was calculated on all patients. The authors found a disproportionate loss of spinal trabecular mineral compared to appendicular mineral in the men with idiopathic osteoporosis and the patients with steroid-induced osteoporosis. They observed roughly equivalent mineral loss in both the appendicular and axial regions in the hyperparathyroid patients. The appendicular cortical measurements correlated moderately well with each other but less well with spinal trabecular QCT. The spinal fracture index correlated well with QCT and less well with the appendicular measurements. Knowledge of appendicular cortical mineral status is important in its own right but is not a valid predictor of axial trabecular mineral status, which may be disproportionately decreased in certain diseases. Quantitative CT provides a reliable means of assessing the latter region of the skeleton, correlates well with the spinal fracture index (a semiquantitative measurement of end-organ failure), and offers the clinician a sensitive means of following the effects of therapy.

Minerals/analysis↗
NASA NTRS2006

Recent Advances in Binary Black Hole Merger Simulations

Recent advances in numerical simulation techniques have lead to dramatic progress in understanding binary black hole merger radiation. I present recent results from simulations performed at Goddard, focusing on the gravitational radiation waveforms, and the application of these results to gravitational wave observations.

Barker, John↗
NASA NTRS1999

Magnetostatic Cleanliness of the Radioistope Thermoelectric

This paper describes the field-mapping technique, the numerical modeling and the compensation approach used for the RTGs with the goal of minimizing its magnetic field interference with Cassini's DC magnetic field science instruments.

Magnetics RTG Cassini↗
NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗