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NASA NTRS1982

Countercurrent distribution of biological cells

Detailed physiochemical studies of dextran/poly(ethylene glycol) (PEG) two phase systems were carried out to characterize and provide understanding of the properties of the systems which determine cell partition and the electrophoretic behavior of phase drops responsible for electric field driven phase separation. A detailed study of the electrostatic and electrokinetic potentials developed in these systems was carried out. The salt partition was examined both in phase systems and with pure polymer solutions via equilibrium dialysis and mechanism of sulfate, chloride and phosphate partition shown to be exclusion by PEG rather than binding by dextran. Salt partition was shown to have a strong effect on the polymer compositions of the phases as well, an effect which produces large changes in the interfacial tension between them. These effects were characterized and the interfacial tension shown to obey a power law with respect to its dependence on the length of the tie line describing the system composition on a phase diagram. The electrostatic potential differences measured via salt bridges were shown to obey thermodynamic predictions. The electrophoretic mobilities measured were utilized to provide a partial test of Levine's incomplete theory of phase drop electrophoresis. The data were consistent with Levine's expression over a limited range of the variables tested.

Brooks, D. E.↗

NASA NTRS1984

Buoyant production and consumption of turbulence kinetic energy in cloud-topped mixed layers

It is pointed out that studies of the entraining planetary boundary layer (PBL) have generally emphasized the role of buoyancy fluxes in driving entrainment. The buoyancy flux is proportional to the rate of conversion of the potential energy of the mean flow into the kinetic energy of the turbulence. It is not unusual for conversion to proceed in both directions simultaneously. This occurs, for instance, in both clear and cloudy convective mixed layers which are capped by inversions. A partitioning of the net conversion into positive parts, generating turbulence kinetic energy (TKE), and negative parts (TKE-consuming), would make it possible to include the positive part in the gross production rate, and closure would be achieved. Three different approaches to partitioning have been proposed. The present investigation is concerned with a comparison of the three partitioning theories. Particular attention is given to the cloud-topped mixed layer because in this case the differences between two partitioning approaches are most apparent.

Randall, D. A.↗

NASA NTRS1986

Multiply scaled constrained nonlinear equation solvers

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

Padovan, Joe↗

NASA NTRS1986

A distributable APSE

A distributed Ada program library is a key element in a distributed Ada Program Support Environment (APSE). To implement this successfully, the program library universe as defined by the Ada Reference Manual must be broken up into independently manageable pieces. This in turn requires the support of a distributed database system, as well as a mechanism for identifying compilation units, linkable subprograms, and Ada types in a decentralized way, to avoid falling victim to the bottlenecks of a global database and/or global unique-identifier manager. It was found that the ability to decentralize Ada program library activity is a major advantage in the management of large Ada programs. Currently, there are 18 resource-catalog revision sets, each in its own Host Interface (HIF) partition, plus 18 partitions for testing each of these, plus 11 partitions for the top-level compiler/linker/program library manager components. Compiling and other development work can proceed in parallel in each of these partitions, without suffering the performance bottlenecks of global locks or global unique-identifier generation.

Taft, Tucker, S.↗

NASA NTRS1989

Run-time scheduling and execution of loops on message passing machines

Sparse system solvers and general purpose codes for solving partial differential equations are examples of the many types of problems whose irregularity can result in poor performance on distributed memory machines. Often, the data structures used in these problems are very flexible. Crucial details concerning loop dependences are encoded in these structures rather than being explicitly represented in the program. Good methods for parallelizing and partitioning these types of problems require assignment of computations in rather arbitrary ways. Naive implementations of programs on distributed memory machines requiring general loop partitions can be extremely inefficient. Instead, the scheduling mechanism needs to capture the data reference patterns of the loops in order to partition the problem. First, the indices assigned to each processor must be locally numbered. Next, it is necessary to precompute what information is needed by each processor at various points in the computation. The precomputed information is then used to generate an execution template designed to carry out the computation, communication, and partitioning of data, in an optimized manner. The design is presented for a general preprocessor and schedule executer, the structures of which do not vary, even though the details of the computation and of the type of information are problem dependent.

Crowley, Kay↗

NASA NTRS1989

Unconditionally stable concurrent procedures for transient finite-element analysis

A family of algorithms was outlined which would appear to be particularly well-suited for implementation in a parallel environment. This is due to the fact that for any partition of the mesh each subdomain in the partition can be processed over a time step simultaneously and independently of the rest. The method eliminates the need for assembling and factorizing large global arrays while retaining the unconditional stability properties of the algorithms used at the local level. To critically appraise the proposed methodology, two limiting cases were considered: element-by-element mesh partitions, and coarse mesh partitions. It was concluded that while the proposed methodology can be useful in sequential machines, it would appear to be promising as it bears on computation. It should also be emphasized that extensions of the method to nonlinear problems are possible.

Ortiz, Michael↗

NASA NTRS1988

Efficiency of shear induced entrainment in convectively mixed layers

Lidar data of mixed layer height are used to compare the model of process partitioning to that of Eulerian partitioning. It is found that the Eulerian partitioning model more closely follows the data and that the process partitioning model underpredicts the mixed layer depth. The results suggest that shear production and consumption of turbulent kinetic energy at the mixed layer top are local processes.

Boers, Reinout↗

NASA NTRS1990

Run-time scheduling and execution of loops on message passing machines

Saltz, Joel↗

NASA NTRS1992

Evidence for a high temperature differentiation in a molten earth: A preliminary appraisal

If the earth were molten during its later stages of accretion as indicated by the present understanding of planetary accretion process, the differentiation that led to the formation of the core and mantle must have occurred at high temperatures in the range of 3000-5000 K because of the effect of pressure on the temperature of melting in the interior of the earth. This calls into question the use of low-temperature laboratory measurements of partition coefficients of trace elements to make inferences about earth accretion and differentiation. The low temperature partition coefficients cannot be directly applied to high temperature fractionations because partition coefficients refer to an equilibrium specific to a temperature for a given reaction, and must change in some proportion to exp 1/RT. There are no laboratory data on partition coefficients at the high temperatures relevant to differentiation in the interior of the earth, and an attempt to estimate high temperature distribution coefficients of siderophile elements was made by considering the chemical potential of a given element at equilibrium and how this potential changes with temperature, under some specific assumptions.

Murthy, V. Rama↗

NASA NTRS1992

Terrestrial magma ocean and core segregation in the earth

According to the recent theories of formation of the earth, the outer layer of the proto-earth was molten and the terrestrial magma ocean was formed when its radius exceeded 3000 km. Core formation should have started in this magma ocean stage, since segregation of metallic iron occurs effectively by melting of the proto-earth. Therefore, interactions between magma, mantle minerals, and metallic iron in the magma ocean stage controlled the geochemistry of the mantle and core. We have studied the partitioning behaviors of elements into the silicate melt, high pressure minerals, and metallic iron under the deep upper mantle and lower mantle conditions. We employed the multi-anvil apparatus for preparing the equilibrating samples in the ranges from 16 to 27 GPa and 1700-2400 C. Both the electron probe microanalyzer (EPMA) and the Secondary Ion Mass spectrometer (SIMS) were used for analyzing the run products. We obtained the partition coefficients of various trace elements between majorite, Mg-perovskite, and liquid, and magnesiowustite, Mg-perovskite, and metallic iron. The examples of the partition coefficients of some key elements are summarized in figures, together with the previous data. We may be able to assess the origin of the mantle abundances of the elements such as transition metals by using the partitioning data obtained above. The mantle abundances of some transition metals expected by the core-mantle equilibrium under the lower mantle conditions cannot explain the observed abundance of some elements such as Mn and Ge in the mantle. Estimations of the densities of the ultrabasic magma Mg-perovskite at high pressure suggest existence of a density crossover in the deep lower mantle; flotation of Mg-perovskite occurs in the deep magma ocean under the lower mantle conditions. The observed depletion of some transition metals such as V, Cr, Mn, Fe, Co, and Ni in the mantle may be explained by the two stage process, the core-mantle equilibrium under the lower mantle conditions in the first stage, and subsequent downwards separation of the ultrabasic liquid (and magnesiowustite) and flotation of Mg-perovskite in the lower mantle.

Ohtani, Eiji↗

NASA NTRS1992

Physical processes within the nocturnal stratus-topped boundary layer

There are many physical processes involved in the stratus-topped boundary layer: longwave radiation cooling, entrainment, latent heating, surface heating, solar heating, and drizzling, for example. The manner in which the processes combine to maintain the turbulence within the stratus-topped boundary layer remains an unsolved problem. The large eddy simulation technique is used to examine the first four physical processes mentioned above. First, the contribution of each physical process to the thermodynamic differences between the updraft and downdraft branches of turbulent circulations is examined through a conditional sampling. Second, these mean thermodynamic differences are shown to express well the vertical distributions of heat and moisture fluxes within stratus-topped boundary layers. These provide a method to validate the process partitioning technique. (This technique assumes that the net flux profile can be partitioned into different component-flux profiles according to physical processes, and that each partitioned component flux is linear in height.) In this paper, the heat and moisture fluxes are process partitioned, and each component-flux is found to contribute to the net flux in a way that is consistent with its corresponding process contribution to the mean thermodynamic differences between updrafts and downdrafts. Also, the net flux obtained by summing all component-fluxes agrees very well with that obtained directly from the large-eddy simulations.

Moeng, Chin-Hoh↗

NASA NTRS1993

Multiphase complete exchange: A theoretical analysis

Complete Exchange requires each of N processors to send a unique message to each of the remaining N-1 processors. For a circuit switched hypercube with N = 2(sub d) processors, the Direct and Standard algorithms for Complete Exchange are optimal for very large and very small message sizes, respectively. For intermediate sizes, a hybrid Multiphase algorithm is better. This carries out Direct exchanges on a set of subcubes whose dimensions are a partition of the integer d. The best such algorithm for a given message size m could hitherto only be found by enumerating all partitions of d. The Multiphase algorithm is analyzed assuming a high performance communication network. It is proved that only algorithms corresponding to equipartitions of d (partitions in which the maximum and minimum elements differ by at most 1) can possibly be optimal. The run times of these algorithms plotted against m form a hull of optimality. It is proved that, although there is an exponential number of partitions, (1) the number of faces on this hull is Theta(square root of d), (2) the hull can be found in theta(square root of d) time, and (3) once it has been found, the optimal algorithm for any given m can be found in Theta(log d) time. These results provide a very fast technique for minimizing communication overhead in many important applications, such as matrix transpose, Fast Fourier transform, and ADI.

Bokhari, Shahid H.↗

NASA NTRS1993

Experience with parametric binary dissection

Parametric Binary Dissection (PBD) is a new algorithm that can be used for partitioning graphs embedded in 2- or 3-dimensional space. It partitions explicitly on the basis of nodes + (lambda)x(edges cut), where lambda is the ratio of time to communicate over an edge to the time to compute at a node. The new algorithm is faster than the original binary dissection algorithm and attempts to obtain better partitions than the older algorithm, which only takes nodes into account. The performance of parametric dissection with plain binary dissection on 3 large unstructured 3-d meshes obtained from computational fluid dynamics and on 2 random graphs were compared. It was showm that the new algorithm can usually yield partitions that are substantially superior, but that its performance is heavily dependent on the input data.

Bokhari, Shahid H.↗

NASA NTRS1994

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗

NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗

NASA NTRS1996

The Parent Magmas of the Cumulate Eucrites: A Mass Balance Approach

The cumulate eucrite meteorites are gabbros that are related to the eucrite basalt meteorites. The eucrite basalts are relatively primitive (nearly flat REE patterns with La approx. 8-30 x CI), but the parent magmas of the cumulate eucrites have been inferred as extremely evolved (La to greater than 100 x CI). This inference has been based on mineral/magma partitioning, and on mass balance considering the cumulate eucrites as adcumulates of plagioclase + pigeonite only; both approaches have been criticized as inappropriate. Here, mass balance including magma + equilibrium pigeonite + equilibrium plagiociase is used to test a simple model for the cumulate eucrites: that they formed from known eucritic magma types, that they consisted only of magma + crystals in chemical equilibrium with the magma, and that they were closed to chemical exchange after the accumulation of crystals. This model is tested for major and Rare Earth Elements (REE). The cumulate eucrites Serra de Mage and Moore County are consistent, in both REE and major elements, with formation by this simple model from a eucrite magma with a composition similar to the Nuevo Laredo meteorite: Serra de Mage as 14% magma, 47.5% pigeonite, and 38.5% plagioclase; Moore County as 35% magma, 37.5% pigeonite, and 27.5% plagioclase. These results are insensitive to the choice of mineral/magma partition coefficients. Results for the Moama cumulate eucrite are strongly dependent on choice of partition coefficients; for one reasonable choice, Moama's composition can be modeled as 4% Nuevo Laredo magma, 60% pigeonite, and 36% plagioclase. Selection of parent magma composition relies heavily on major elements; the REE cannot uniquely indicate a parent magma among the eucrite basalts. The major element composition of Y-791195 can be fit adequately as a simple cumulate from any basaltic eucrite composition. However, Y-791195 has LREE abundances and La/Lu too low to be accommodated within the model using any basaltic eucrite composition and any reasonable partition coefficients. Postcumulus loss of incompatible elements seems possible. It is intriguing that Serra de Mage, Moore County, and Moama are consistent with the same parental magma; could they be from the same igneous body on the eucrite parent asteroid (4 Vesta)?

Treiman, Allan H.↗

NASA NTRS1998

Influence of Soil Heterogeneity on Mesoscale Land Surface Fluxes During Washita '92

The influence of soil heterogeneity on the partitioning of mesoscale land surface energy fluxes at diurnal time scales is investigated over a 10(exp 6) sq km domain centered on the Little Washita Basin, Oklahoma, for the period June 10 - 18, 1992. The sensitivity study is carried out using MM5/PLACE, the Penn State/NCAR MM5 model enhanced with the Parameterization for Land-Atmosphere-Cloud Exchange or PLACE. PLACE is a one-dimensional land surface model possessing detailed plant and soil water physics algorithms, multiple soil layers, and the capacity to model subgrid heterogeneity. A series of 12-hour simulations were conducted with identical atmospheric initialization and land surface characterization but with different initial soil moisture and texture. A comparison then was made of the simulated land surface energy flux fields, the partitioning of net radiation into latent and sensible heat, and the soil moisture fields. Results indicate that heterogeneity in both soil moisture and texture affects the spatial distribution and partitioning of mesoscale energy balance. Spatial averaging results in an overprediction of latent heat flux, and an underestimation of sensible heat flux. In addition to the primary focus on the partitioning of the land surface energy, the modeling effort provided an opportunity to examine the issue of initializing the soil moisture fields for coupled three-dimensional models. For the present case, the initial soil moisture and temperature were determined from off-line modeling using PLACE at each grid box, driven with a combination of observed and assimilated data fields.

Jasinski, Michael F.↗

NASA NTRS2000

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗