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At least 217 records · Page 12

Towards a theory of automated elliptic mesh generation

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

Cordova, J. Q.↗

Model Rotor Hover Performance at Low Reynolds Number

Hover performance data from four key experiments has been analyzed in detail to shed some light on model rotor hover performance at low Reynolds number. Each experiment used the simplest blade geometry. The blades were constant chord and untwisted. Three experiments used blades with the NACA 0012 airfoil from root to tip. The NACA 0015 was used in the earliest test. The four experiments provide data spanning a Reynolds number range of 136,500 to 548,700. The specific objective of this report is to ask and answer two questions: 1. Does blade aspect ratio influence hover performance or is rotor solidity the fundamental rotor geometry parameter for practical engineering purposes? ANSWER: Rotor solidity is the fundamental rotor geometry parameter for practical engineering purposes. Any effect of blade aspect ratio appears to be such a secondary variable that its effect lies within the range of experimental error. 2. Is Reynolds number a significant factor in scaling up hover performance to full-scale rotor performance? The answer is twofold. ANSWER: (a) Reynolds number effects on the increase of power with thrust do not appear to be a significant factor for practical engineering purposes, and (b) Reynolds number effects on minimum profile power at or very near zero rotor thrust could not be clearly established primarily because the low torque levels could not be accurately measured with the test equipment used. This has led to significant data scatter. A number of other observations can be made based on the analysis provided herein. For instance: 1. The test matrices used in the four key references contained far too few data points. A collective pitch variation of four or five data points is insufficient to establish experimental accuracy and data repeatability. 2. A common property of the power-versus-thrust (raised to the 3/2 exponent) graphs was that this curve was linear below the onset of blade stall. 3. The blade-to-blade interference at or near zero thrust may, in fact, be creating a turbulent flow field such that the effective Reynolds number at a blade element is considerably greater than what theories using two-dimensional (2D) airfoil properties at a blade element would calculate. 4. Definitive experiments answering the two key questions have yet to be made.

Model Rotor Hover Performance↗

Computational insights into hydrogen adsorption energies on medium-entropy oxides

High entropy oxides (HEOs) have emerged as promising catalysts for several important chemical transformations including alkane activation. Hydrogen adsorption energy (HAE) has been used as a key descriptor for many reactions including methane C–H activation and hydrogen evolution reactions. Hence, understanding the relationship between HAEs and the surface chemistry of HEO surfaces could lay the foundation for meaningful correlations among methane C–H activation, HAE, and the complex, local environment of HEO surfaces. Here, we used a medium-entropy oxide as a prototypical system – Mg 0.25 Ni 0.25 Cu 0.25 Zn 0.25 O with a rock-salt structure – to interrogate these relationships. We sampled 2000 different surfaces of its (100) plane and calculated the HAEs at randomly chosen surface O sites using density functional theory (DFT). Our analysis of the 2000 data points reveals that the HAEs at the surface O sites are significantly influenced by the local environment around the adsorption sites, particularly the nature of the metal atom directly below the surface O site where H adsorbs. After comparing several popular graph-neural-network-based machine learning models, we found that the DimeNet++ model performed best achieving satisfactory accuracy in predicting HAEs for both Mg 0.25 Ni 0.25 Cu 0.25 Zn 0.25 O and slightly varied compositions. Our work underscores the promise of such models and the need for further refinement to address the complexity of HEOs.

Song, Haohong [Vanderbilt Univ., Nashville, TN (Un↗

Sequential Test Strategies for Multiple Fault Isolation

In this paper, we consider the problem of constructing near optimal test sequencing algorithms for diagnosing multiple faults in redundant (fault-tolerant) systems. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and Lagrangian relaxation, we present several static and dynamic (on-line or interactive) test sequencing algorithms for the multiple fault isolation problem that provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a static diagnostic directed graph (digraph), instead of a static diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. Computational results based on real-world systems indicate that the size of a static multiple fault strategy is strictly related to the structure of the system, and that the use of an on-line multiple fault strategy can diagnose faults in systems with as many as 10,000 failure sources.

Shakeri, M.↗

The relations between the linear and bilinear atmospheric tidal fields in geometric height and in log-pressure coordinates

Theoretical models of planetary-atmosphere tidal fields are examined analytically, comparing models based on geometric-height coordinates with those employing log-pressure coordinates. The relationship between the linearized meteorological variables in the two systems is explored for classical tidal theory and its reduction to the Laplace tidal equation, and it is shown that identical horizontal and vertical equations are obtained. Also considered are the tidal zonal-mean bilinear flux convergences and their Eliassen-Palm formulations. Numerical results for problems involving the earth and Mars atmospheres are presented in graphs and discussed.

Zurek, Richard W.↗

Superconductivity in sputtered CuMo6S8

The superconducting transition temperature and the superconducting upper critical fields for sputtered films of copper-containing ternary molybdenum chalcogenides (chevrel phases) were determined. The theory presented by Werthamer, Helfand, and Hohenberg (WHH) (1966) was used to make computer-generated plots of the superconducting upper critical field values versus the superconducting transition temperature values for various values of the Maki paramagnetic pair-breaking parameter and the spin-orbit scattering parameter. The interpretation of the graph suggests that the experimental data for at least one sample are above the maximum WHH theoretical limit in the lower temperature range. Possible explanations of this situation are discussed. In other calculations, a scaling law was found suitable for determining pinning force densities; this data was used to calculate critical current values. The relation between resistivity and temperature was studied.

Alterovitz, S.↗

Nonlocal effects on the convective properties of the electrostatic current-driven ion-cyclotron instability

The convective behavior of the current-driven ion-cyclotron instability (CDICI) in the presence of nonlocal magnetic-shear and current-channel-width effects is investigated theoretically using the analytical approach of Bakshi et al. (1983). The results are presented in graphs and discussed. Three different CDICI regimes defined by the ratio of the channel width to the shear length are obtained: a purely nonlocal regime with reduced temporal growth rate and group velocity in the z direction going to zero (ratios greater than about 0.1); a regime corresponding to the results of local theory (ratios less than 0.01); and a regime characterized by decreasing temporal growth rate and by z and y group velocities which become negative when the channel width becomes less than the mean ion Larmor radius (ratios 0.001 or less).

Ganguli, G.↗

On the Current State of Sheaf Theoretic Networking

Advancing the Delay Tolerant Networking (DTN) effort has proven to be a unique and difficult challenge. In the journey to implementing space networking, NASA has considered several strategies. From direct translations of Internet Protocol (IP) to satellite networks to pre-planned routing structures in Contact Graph Routing (CGR), each potential solution for DTN has come with its fair share of setbacks and challenges. Frequently, these challenges can be traced back to specific assumptions made in the development of each protocol that do not carry over from ground networks to space networks. To address these fundamental assumptions, a more general and foundational networking theory is required. In this paper, we survey a novel mathematical foundation for networking using the theory of cellular sheaves. Sheaves form a mathematical tool for modeling local phenomenon that leads to global effects. Sheaves have been introduced a number of times, and our goal here is to summarize the applications and point towards important future work that must be done to build a stronger, cohesive theory for networking.

Sheaves↗

Planetary science: A lunar perspective

An interpretative synthesis of current knowledge on the moon and the terrestrial planets is presented, emphasizing the impact of recent lunar research (using Apollo data and samples) on theories of planetary morphology and evolution. Chapters are included on the exploration of the solar system; geology and stratigraphy; meteorite impacts, craters, and multiring basins; planetary surfaces; planetary crusts; basaltic volcanism; planetary interiors; the chemical composition of the planets; the origin and evolution of the moon and planets; and the significance of lunar and planetary exploration. Photographs, drawings, graphs, tables of quantitative data, and a glossary are provided.

Taylor, S. R.↗

On the theory of H2 rotational excitation

A number of mechanisms for exciting higher-J states in the ground vibrational level are considered. Attention is given to collisions with H atoms and electrons. Other mechanisms involve a cascading down from upper vibrational levels, following absorption and reemission of photons in the Lyman and Werner bands, or a cascading down from upper vibrational levels, following formation of hydrogen molecules in excited vibrational and rotational levels. Theoretical population densities of rotational levels are shown in a graph.

Spitzer, L., Jr.↗

A remark about pointed bubbles

The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.

Garabedian, P. R.↗

Machine learning in materials research: Developments over the last decade and challenges for the future

The number of studies that apply machine learning (ML) to materials science has been growing at a rate of approximately 1.67 times per year over the past decade. In this review, I examine this growth in various contexts. First, I present an analysis of the most commonly used tools (software, databases, materials science methods, and ML methods) used within papers that apply ML to materials science. The analysis demonstrates that despite the growth of deep learning techniques, the use of classical machine learning is still dominant as a whole. It also demonstrates how new research can effectively build upon past research, particular in the domain of ML models trained on density functional theory calculation data. Next, I present the progression of best scores as a function of time on the matbench materials science benchmark for formation enthalpy prediction. In particular, a dramatic improvement of 7 times reduction in error is obtained when progressing from feature-based methods that use conventional ML (random forest, support vector regression, etc.) to the use of graph neural network techniques. Finally, I provide views on future challenges and opportunities, focusing on data size and complexity, extrapolation, interpretation, access, and relevance.

36 MATERIALS SCIENCE↗

One dimensional heavy ion beam transport: Energy independent model

Attempts are made to model the transport problem for heavy ion beams in various targets, employing the current level of understanding of the physics of high-charge and energy (HZE) particle interaction with matter are made. An energy independent transport model, with the most simplified assumptions and proper parameters is presented. The first and essential assumption in this case (energy independent transport) is the high energy characterization of the incident beam. The energy independent equation is solved and application is made to high energy neon (NE-20) and iron (FE-56) beams in water. The numerical solutions is given and compared to a numerical solution to determine the accuracy of the model. The lower limit energy for neon and iron to be high energy beams is calculated due to Barkas and Burger theory by LBLFRG computer program. The calculated values in the density range of interest (50 g/sq cm) of water are: 833.43 MeV/nuc for neon and 1597.68 MeV/nuc for iron. The analytical solutions of the energy independent transport equation gives the flux of different collision terms. The fluxes of individual collision terms are given and the total fluxes are shown in graphs relative to different thicknesses of water. The values for fluxes are calculated by the ANASTP computer code.

Farhat, Hamidullah↗

On the controllability and control law design for an orbiting large flexible antenna system

The controllability and control law synthesis based on a finite element model of the Hoop/Column orbiting antenna system is considered. Graph theoretic techniques are employed to analyze the controllability of the system for posible proposed actuator arrangements which include torquers and point actuators along the mast and a single actuator placed on the hoop assembly. Once controllability is established for a given combination of number and location of actuators, the synthesis of control laws is based on an application of the linear regulator theory and also pole placement techniques. In general, surface torsion and feed mast torsion are among modes having the longest time constants. System transient performance is noticeably degraded when the hoop actuator is not included.

Bainum, P. M.↗

Dirac traces and the Tutte polynomial

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.

Renormalization and Regularization↗

Development and Testing of Pulse Guns for Combustion Instability Testing

To test liquid rocket engines (LREs) for combustion instabilities, devices such as bombs are often used to create pressure wave disturbances. Bombs, while effective, are inherently dangerous, expensive, and difficult to procure. Over the years, pulse guns have been used as a safer and more cost-effective way to generate controlled pressure disturbances in engine chambers. In anticipation of the need for stability testing of prototype LREs at NASA Marshall Space Flight Center (MSFC), a set of pulse guns have been designed, fabricated, tested, and characterized. The pulse gun program is funded by the RS-25 Engine Program managed out of MSFC and funded by NASA’s Space Launch System (SLS) through the MSFC Liquid Engines Office (LEO). A pulse gun is a simple device – like a traditional gun, it has a breech and barrel section. However, unlike a traditional gun, there is no bullet, as the purpose of the pulse gun is strictly to fire a high pressure pulse. Instead of a firing pin and primer that would normally be used in a traditional gun, an initiator is used to activate the gun powder. The initiator is a highly reliable pyrotechnic initiator. For this study, clone versions of the NASA Standard Initiator (NSI) were used. The initiator is used to ignite a pre-measured amount of gun powder loaded into the breech. When the pressure of the burnt gun powder exceeds the set point of a downstream burst disk, the disk ruptures, allowing the high pressure pulse to travel downstream through the barrel section. A ballistic pressure transducer located in the breech section is used to measure the short duration, high pressure pulse. Some configurations of the pulse gun have barrel sections that include one or more additional ballistic pressure transducers. These additional pressure measurements help track the degradation and damping of the pulse as it travels out of the barrel section. The measurements may also be used to determine the velocity of pulse. The objective of this paper is to present the different variants of this newly-developed pulse gun and characterize performance over a range of parameters. The parameters include breech diameter, barrel length, amount of gun powder used, the way the gun powder is packed, and the pressure setting of the burst disk. There are a total of six pulse guns: three with the 0.25 inch breech and three different length barrels, and three with the 0.40 inch breech and three different length barrels. For both breech sizes, the associated barrels are referred to as standard, one-port, and two-port barrels. The standard barrel has no instrumentation and is likely the barrel that will be used for engine stability testing. The one- and two-port barrels were designed specifically for pulse gun component testing to allow measurements of the magnitude and timing of the high pressure pulse as it makes its way through the pulse gun. The burst disks tested were commercially-available burst disks designed to rupture at 8,000, 16,000, and 24,000 psid. Testing was accomplished by firing the pulse gun into a test chamber pressurized with nitrogen at about 2300 psig. A total of four Model 113B23 High frequency ICP® pressure sensors (10k psi) were mounted in the test chamber, in the same plane as the pulse gun. Two of the sensors had “trimmed” adapters, and two did not. Given the symmetrical configuration of the sensors within the test chamber, different amplitudes of pressure measurements are attributed to the use of trimmed versus untrimmed adapters. The untrimmed adapters, with their narrower passages, tended to amplify the pressure amplitudes by as much as 50%. In total, 41 pulse gun tests have been conducted.Data are still being analyzed, but some trends are apparent. For example, measurements taken within the pulse gun are shown in Figures 3 and 4 for Hot-fires (HFs) # 11 and 39, respectively. Both tests were identical in that the 0.40 inch ID breech, two-port barrel, 8,000 psid burst disk, and same amount of gunpowder (6.639 grains for HF# 11, and 6.576 grains for HF# 39) were used, and the back pressure in the nitrogen test chamber was ~2300 psig. Despite keeping all these variables constant, the results from these two tests look quite different. For both tests, the first pressure peak shown in the P2111 trace within the breech is the firing of the initiator. The second peak and any subsequent peaks are from the combustion of the gunpowder. It should be noted that because the sensors are dynamic, the ~2300 psig baseline static pressure is not shown in the figures. For HF# 11, the burst disk clearly ruptured in a little over 0.1 ms from the time the initiator was fired. This is evident from the abrupt rise in pressure for P2112 followed by another abrupt rise in pressure for P2113. The sensors track the movement of the high pressure pulse through the pulse gun. For HF# 39, however, there was nearly 1 ms delay between the initiator firing and the burst disk rupturing. The only difference between these two tests was the way in which the gunpowder was packed within the breech. For HF# 11, the gunpowder was poured directly into the breech, atop the initiator, and held in place with a vegetable fiber wad appropriately sized for the barrel diameter. Once in place, the wad firmly held the gunpowder in place. For HF# 39, the gunpowder was rolled within cigarette paper with the ends of the paper twisted. The rolled gunpowder was gently pushed down into the breech, toward the initiator, and no wad was used. This method of loading the gunpowder consistently produced longer delays in the rupture of the burst disk, presumably because there was a steady, fuller burning of the gunpowder. The burst disk was rated for 8,000 psid, which means that the burst disk should not have opened until the pressure in the breech reached ~10,300 since there was ~2300 psig back pressure in the test chamber. In the case of HF# 11, the breech pressure only reached roughly 4200 psi before there was leakage either through or past the burst disk, but for HF#39, the breech pressure reached 10,600 psi prior to the burst disk opening. The temperature of the burst disk is certainly a factor in determining when the burst disk will rupture. A sharp rise in the burst disk temperature could weaken it and cause it to stray from the designed set point burst pressure. The burst disks are manufactured of Inconel to try to reduce their sensitivity to temperature, but how the burst disks perform above 900°F is not documented. All burst disks were engineered and tested by the manufacturer for ambient temperature conditions. One theory for why rolling the gunpowder in cigarette paper may produce better results is related to a more controlled temperature environment. The cigarette paper may act as a sheath that protects the burst disk from excessive temperatures during the rapid buildup of pressure in the breech. The ultimate benefit of not breeching the burst disk prematurely is shown in Figures 5 and 6, which graphs the resultant pressure pulse produced in the test chamber. For HF #11, the peak pressure on the P2123 trimmed adapter is about 270 psi, while for HF# 39 it is 343 psi, which is about 1.27 times greater in magnitude. In either case, the pressure pulse is ~20 μs in width once it reaches the test chamber. Another pressure rise about 100 μs later can be seen on the sensors located across from the pulse gun port, P2124 and P2121. These pressures are lower due to attenuation of the pressure wave as it moves across the test chamber. After the wave encounters the wall, it reflects back and forth within the chamber until it completely dissipates.

Pulse Gun↗

The REH theory of protein and nucleic acid divergence - A retrospective update

The random evolutionary hits (REH) theory of evolutionary divergence, originally proposed in 1972, is restated with attention to certain aspects of the theory that have caused confusion. The theory assumes that natural selection and stochastic processes interact and that natural selection restricts those codon sites which may fix mutations. The predicted total number of fixed nucleotide replacements agrees with data for cytochrome c, a-hemoglobin, beta-hemoglobin, and myoglobin. The restatement analyzes the magnitude of possible sources of errors and simplifies calculational methodology by supplying polynomial expressions to replace tables and graphs.

Holmquist, R.↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗