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This paper discusses how to numerically test a subroutine for the solution of ordinary differential equations. Results obtained with a variable order Adams method are given for eleven simple test cases.-
A digital local linearization technique was used to solve a system of stiff differential equations which simulate a magnetic bearing assembly. The results prove the technique to be accurate, stable, and efficient when compared to a general purpose variable order Adams method with a stiff option.
ANISAP is a 3-D finite element FORTRAN 77 computer code for linear elastic, small strain, analysis of laminated composites with arbitrary geometry including free edges and holes. Individual layers may be isotropic or transversely isotropic in material principal coordinates; individual layers may be rotated off-axis about a global z-axis. The laminate may be a hybrid. Three different isoparametric elements, variable order of gaussian integration, calculation of stresses at element boundaries, and loading by either nodal displacement of forces are included in the program capability. Post processing capability includes failure analysis using the tensor polynominal failure criterion.
The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.
Incorporating the full geochemical cycles of stable water isotopes (HDO and H2O-18) into an atmospheric general circulation model (GCM) allows an improved understanding of global delta-D and delta-O-18 distributions and might even allow an analysis of the GCM's hydrological cycle. A detailed sensitivity analysis using the NASA/Goddard Institute for Space Studies (GISS) model II GCM is presented that examines the nature of isotope modeling. The tests indicate that delta-D and delta-O-18 values in nonpolar regions are not strongly sensitive to details in the model precipitation parameterizations. This result, while implying that isotope modeling has limited potential use in the calibration of GCM convection schemes, also suggests that certain necessarily arbitrary aspects of these schemes are adequate for many isotope studies. Deuterium excess, a second-order variable, does show some sensitivity to precipitation parameterization and thus may be more useful for GCM calibration.
An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.
GOES-7 VAS measurements during the Pathfinder period (1987-88) have been analysed to reveal seasonal and interannual variations in moisture transport. Long term measurements of quality winds and humidity from satellite estimates show superior benefit in diagnosing middle and upper tropospheric large scale climate variations such as ENSO events and direct circulation systems such as the Hadley Cell. A water Vapor Transport Index (WVTI) has been developed to diagnose preferred regions of strong moisture transport and to gauge the seasonal and interannual intensities detected in the GOES viewing area. Second-order variables that may be derived from GOES winds will be also discussed on the poster.
A geosynchronous Lidar would enable synoptic measurement of atmospheric winds; temperature; and moisture, which are key first-order variables of the Earth's weather equation. Simultaneous measurement of these parameters at fast revisit rates promises large advancements in our weather predictive skills. Such capabilities would: a) yield greatly improved initial conditions for models, b) make obsolete existing (discrete) measurement approaches which are both costly and cumbersome, and c) obviate the use of numerical techniques needed to correct data obtained using present methods. Additionally, simultaneous synoptic Lidar observations would lead to improvements in model parameters, and in our knowledge of small-scale weather processes. A Dial Lidar system could simultaneously measure winds, temperatures, and humidity through a combination of Doppler and Differential Absorption techniques. Also, such a system would provide basic aerosol (dry dust) measurement capabilities that could have an impact on Earth radiation budget measurements. On the technical side, a geosynchronous Lidar DAR system would require transmit optics of a few meters in diameter, a hundred meter diameter receive telescope, fineness of both optical systems scaled to the wavelength, and scanning for the transmit system. Potential technology issues include optical quality of large transmit and receive telescope optics, the large detector area needed, the transmit scanning system, signal detection (S/N ratio of detector system) for the extremely weak return signal at GEO, and power demands in the KW range.
An observing system comprised of two lidars in geosynchronous orbit would enable the synoptic and meso-scale measurement of atmospheric winds and moisture, both of which are key first-order variables of the Earth's weather equation. Simultaneous measurement of these parameters at fast revisit rates promises large advancements in our weather prediction skills. Such capabilities would be unprecedented and yield greatly improved and finer resolution initial conditions for models, make existing costly and cumbersome measurement approaches obsolete, and obviate the use of numerical techniques needed to correct data obtained using present observing systems. Additionally, simultaneous synoptic wind and moisture observations would lead to improvements in model parameterizations, and in our knowledge of small-scale weather processes. Technology and science data product assessments are ongoing. Results will be presented during the conference.
An observing system comprised of two lidars in geosychronous orbit would enable the synoptic and meso-scale measurement of atmospheric winds and moisture both of which are key first-order variables of the Earth's weather equation. Simultaneous measurement of these parameters at fast revisit rates promises large advancements in our weather prediction skills. Such capabilities would be unprecedented and a) yield greatly improved and finer resolution initial conditions for models, b) make existing costly and cumbersome measurement approaches obsolete, and c) obviate the use of numerical techniques needed to correct data obtained using present observing systems. Additionally, simultaneous synoptic wind and moisture observations would lead to improvements in model parameterizations, and in our knowledge of small-scale weather processes. Technology and science data product assessments are ongoing. Results will be presented during the conference.
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.
The cometary meteoroid ejection model of Jones and Brown (1996b) was used to simulate ejection from comets 55P/Tempel-Tuttle during the last 12 revolutions, and the last 9 apparitions of 109P/Swift-Tuttle. Using cometary ephemerides generated by the Jet Propulsion Laboratory s (JPL) HORIZONS Solar System Data and Ephemeris Computation Service, two independent ejection schemes were simulated. In the first case, ejection was simulated in 1 hour time steps along the comet s orbit while it was within 2.5 AU of the Sun. In the second case, ejection was simulated to occur at the hour the comet reached perihelion. A 4th order variable step-size Runge-Kutta integrator was then used to integrate meteoroid position and velocity forward in time, accounting for the effects of radiation pressure, Poynting-Robertson drag, and the gravitational forces of the planets, which were computed using JPL s DE406 planetary ephemerides. An impact parameter was computed for each particle approaching the Earth to create a flux profile, and the results compared to observations of the 1998 and 1999 Leonid showers, and the 1993 and 2004 Perseids.
Eight international laboratories specializing in the determination of marine pigment concentrations using high performance liquid chromatography (HPLC) were intercompared using in situ samples and a variety of laboratory standards. The field samples were collected primarily from eutrophic waters, although mesotrophic waters were also sampled to create a dynamic range in chlorophyll concentration spanning approximately two orders of magnitude (0.3 25.8 mg m-3). The intercomparisons were used to establish the following: a) the uncertainties in quantitating individual pigments and higher-order variables (sums, ratios, and indices); b) an evaluation of spectrophotometric versus HPLC uncertainties in the determination of total chlorophyll a; and c) the reduction in uncertainties as a result of applying quality assurance (QA) procedures associated with extraction, separation, injection, degradation, detection, calibration, and reporting (particularly limits of detection and quantitation). In addition, the remote sensing requirements for the in situ determination of total chlorophyll a were investigated to determine whether or not the average uncertainty for this measurement is being satisfied. The culmination of the activity was a validation of the round-robin methodology plus the development of the requirements for validating an individual HPLC method. The validation process includes the measurements required to initially demonstrate a pigment is validated, and the measurements that must be made during sample analysis to confirm a method remains validated. The so-called performance-based metrics developed here describe a set of thresholds for a variety of easily-measured parameters with a corresponding set of performance categories. The aggregate set of performance parameters and categories establish a) the overall performance capability of the method, and b) whether or not the capability is consistent with the required accuracy objectives.
In Linear Temporal Logic (LTL) model checking, we check LTL formulas representing desired behaviors against a formal model of the system designed to exhibit these behaviors. To accomplish this task, the LTL formulas must be translated into automata [21]. We focus on LTL compilation by investigating LTL satisfiability checking via a reduction to model checking. Having shown that symbolic LTL compilation algorithms are superior to explicit automata construction algorithms for this task [16], we concentrate here on seeking a better symbolic algorithm.We present experimental data comparing algorithmic variations such as normal forms, encoding methods, and variable ordering and examine their effects on performance metrics including processing time and scalability. Safety critical systems, such as air traffic control, life support systems, hazardous environment controls, and automotive control systems, pervade our daily lives, yet testing and simulation alone cannot adequately verify their reliability [3]. Model checking is a promising approach to formal verification for safety critical systems which involves creating a formal mathematical model of the system and translating desired safety properties into a formal specification for this model. The complement of the specification is then checked against the system model. When the model does not satisfy the specification, model-checking tools accompany this negative answer with a counterexample, which points to an inconsistency between the system and the desired behaviors and aids debugging efforts.
A Validation Network (VN) prototype is currently underway that compares data from the Precipitation Radar (PR) instrument on NASA's Tropical Rainfall Measuring Mission (TRMM) satellite to similar measurements from the U.S. national network of operational weather radars. This prototype is being conducted as part of the ground validation activities of NASA's Global Precipitation Measurement (GPM) mission. GPM will carry a Dual-frequency Precipitation Radar instrument (DPR) with similar characteristics to the TRMM PR. The purpose of the VN is to identify and resolve significant discrepancies between the U.S. national network of ground radar (GR) observations and satellite observations. The ultimate goal of such comparisons is to understand and resolve the first order variability and bias of precipitation retrievals in different meteorological/hydrological regimes at large scales. This paper presents a description of, and results from, an improved algorithm for volume matching and comparison of PR and ground radar observations.
Seven international laboratories specializing in the determination of marine pigment concentrations using high performance liquid chromatography (HPLC) were intercompared using in situ samples and a mixed pigment sample. The field samples were collected primarily from oligotrophic waters, although mesotrophic and eutrophic waters were also sampled to create a dynamic range in chlorophyll concentration spanning approximately two orders of magnitude (0.020 1.366 mg m^{-3}) The intercomparisons were used to establish the following: a) the uncertainties in quantitating individual pigments and higher-order variables (sums, ratios, and indices); b) the reduction in uncertainties as a result of applying quality assurance (QA) procedures; c) the importance of establishing a properly defined referencing system in the computation of uncertainties; d) the analytical benefits of performance metrics, and e) the utility of a laboratory mix in understanding method performance. In addition, the remote sensing requirements for the in situ determination of total chlorophyll a were investigated to determine whether or not the average uncertainty for this measurement is being satisfied.
Ten international laboratories specializing in the determination of marine pigment concentrations using high performance liquid chromatography (HPLC) were intercompared using in situ samples and a mixed pigment sample. Although prior Sea-viewing Wide Field-of-view Sensor (SeaWiFS) High Performance Liquid Chromatography (HPLC) Round-Robin Experiment (SeaHARRE) activities conducted in open-ocean waters covered a wide dynamic range in productivity, and some of the samples were collected in the coastal zone, none of the activities involved exclusively coastal samples. Consequently, SeaHARRE-4 was organized and executed as a strictly coastal activity and the field samples were collected from primarily eutrophic waters within the coastal zone of Denmark. The more restrictive perspective limited the dynamic range in chlorophyll concentration to approximately one and a half orders of magnitude (previous activities covered more than two orders of magnitude). The method intercomparisons were used for the following objectives: a) estimate the uncertainties in quantitating individual pigments and higher-order variables formed from sums and ratios; b) confirm if the chlorophyll a accuracy requirements for ocean color validation activities (approximately 25%, although 15% would allow for algorithm refinement) can be met in coastal waters; c) establish the reduction in uncertainties as a result of applying QA procedures; d) show the importance of establishing a properly defined referencing system in the computation of uncertainties; e) quantify the analytical benefits of performance metrics, and f) demonstrate the utility of a laboratory mix in understanding method performance. In addition, the remote sensing requirements for the in situ determination of total chlorophyll a were investigated to determine whether or not the average uncertainty for this measurement is being satisfied.