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At least 595 records · Page 33

Parallel solution of closely coupled systems

The odd-even permutation and associated unitary transformations for reordering the matrix coefficient A are employed as means of breaking the strong seriality which is characteristic of closely coupled systems. The nested dissection technique is also reviewed, and the equivalence between reordering A and dissecting its network is established. The effect of transforming A with odd-even permutation on its topology and the topology of its Cholesky factors is discussed. This leads to the construction of directed graphs showing the computational steps required for factoring A, their precedence relationships and their sequential and concurrent assignment to the available processors. Expressions for the speed-up and efficiency of using N processors in parallel relative to the sequential use of a single processor are derived from the directed graph. Similar expressions are also derived when the number of available processors is fewer than required.

Utku, S.↗

Viscous-flow analysis of a subsonic transport aircraft high-lift system and correlation with flight data

High-lift system aerodynamics has been gaining attention in recent years. In an effort to improve aircraft performance, comprehensive studies of multi-element airfoil systems are being undertaken in wind-tunnel and flight experiments. Recent developments in Computational Fluid Dynamics (CFD) offer a relatively inexpensive alternative for studying complex viscous flows by numerically solving the Navier-Stokes (N-S) equations. Current limitations in computer resources restrict practical high-lift N-S computations to two dimensions, but CFD predictions can yield tremendous insight into flow structure, interactions between airfoil elements, and effects of changes in airfoil geometry or free-stream conditions. These codes are very accurate when compared to strictly 2D data provided by wind-tunnel testing, as will be shown here. Yet, additional challenges must be faced in the analysis of a production aircraft wing section, such as that of the NASA Langley Transport Systems Research Vehicle (TSRV). A primary issue is the sweep theory used to correlate 2D predictions with 3D flight results, accounting for sweep, taper, and finite wing effects. Other computational issues addressed here include the effects of surface roughness of the geometry, cove shape modeling, grid topology, and transition specification. The sensitivity of the flow to changing free-stream conditions is investigated. In addition, the effects of Gurney flaps on the aerodynamic characteristics of the airfoil system are predicted.

Potter, R. C.↗

A Framework for Optimization-Based ISRU Tool Design Using Discrete Element Modeling

Novel robotic excavation technologies are needed to perform in-situ resource utilization (ISRU) tasks at levels required to sustain a long-term presence on the lunar surface. Developing and testing multiple iterations of functional hardware is time and cost prohibitive, thus slowing down the pace of progress and delaying humanity’s settlement of the Moon. High-fidelity, physics-based simulation can reduce the time and effort required to develop and deploy robotic systems [1]. We have adopted this approach to create high-fidelity models of robotic test hardware to enable rapid virtual design and optimization of excavation technologies [2]. Such models can leverage modern computational tools like Discrete Element Method (DEM) simulations that can be coupled with automated design approaches like topology optimization to reduce the amount of prototyping and physical testing needed to realize useful tools.

ISRU↗

Variably Premixed Rotating Detonation Engine for Evaluation of Detonation Cycle Dynamics

A variably premixed rotating detonation engine using gaseous hydrogen and air reactants is introduced to enable investigation of key cycle processes while varying the homogeneity of the reactant inlet conditions. Two chamber configurations are investigated, the first with reactants filling the entire span of a straight annular channel and the second with a slightly larger channel and a backward-facing step. The first configuration permits both premixed and non-premixed fuel injection, enabling mixing quality modulation. The second configuration is operated only at fully premixed conditions. Operating modes and detonation wave speeds are characterized using exhaust-plume imaging, while the chamber heat release field is captured by transverse imaging through a transparent outer body. Tests using the first configuration were characterized by unstable counterpropagating modes with low detonation wave speeds regardless of the state of premixing, while the second configuration rendered single-wave behavior with wave speeds up to 86% of the Chapman–Jouguet velocity. Comparisons with a simple computational fluid dynamics model of the second configuration indicate that reactant preheating significantly influences the detonation wave topology, highlighting the potential utility of the test platform for isolating key physics associated with the effects of reactant premixing, preheating, and chamber geometry on rotating detonation engine operation.

Detonation↗

Analysis of the SiMPL Method for Density-Based Topology Optimization

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides pointwise bound-preserving design updates and faster convergence than other popular first-order topology optimization methods. Due to its strong bound preservation, the method is exceptionally robust, as demonstrated in numerous examples here and in the companion article [D. Kim et al., Struct. Multidiscip. Optim., 68 (2025), 74]. Furthermore, it is easy to implement with clear structure and analytical expressions for the updates. Our analysis covers two versions of the method, characterized by the employed line search strategies. We consider a modified Armijo backtracking line search and a Bregman backtracking line search. For both line search algorithms, our algorithm delivers a strict monotone decrease in the objective function and further intuitive convergence properties, e.g., strong and pointwise convergence of the density variables on the active sets, norm convergence to zero of the increments, convergence of the Lagrange multipliers, and more. In addition, the numerical experiments demonstrate apparent mesh-independent convergence of the algorithm. Here, we refer to the new algorithm as the SiMPL method (pronounced “simple”), which stands for Sigmoidal Mirror descent with a Projected Latent variable.

97 MATHEMATICS AND COMPUTING↗

Numerical simulation of the tip vortex off a low-aspect-ratio wing at transonic speed

The viscous transonic flow around a low aspect ratio wing was computed by an implicit, three dimensional, thin-layer Navier-Stokes solver. The grid around the geometry of interest is obtained numerically as a solution to a Dirichlet problem for the cube. A low aspect ratio wing with large sweep, twist, taper, and camber is the chosen geometry. The topology chosen to wrap the mesh around the wing with good tip resolution is a C-O type mesh. The flow around the wing was computed for a free stream Mach number of 0.82 at an angle of attack of 5 deg. At this Mach number, an oblique shock forms on the upper surface of the wing, and a tip vortex and three dimensional flow separation off the wind surface are observed. Particle path lines indicate that the three dimensional flow separation on the wing surface is part of the roots of the tip vortex formation. The lifting of the tip vortex before the wing trailing edge is observed by following the trajectory of particles release around the wing tip.

Mansour, N. N.↗

The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V – E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χ m ) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χ m has an elegant topological interpretation through the concept of orbifolds. Alternatively, χ m can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

97 MATHEMATICS AND COMPUTING↗

Topological Machine Learning Methods for Power System Responses to Contingencies

While deep learning tools, coupled with the emerging machinery of topological data analysis, are proven to deliver various performance gains in a broad range of applications, from image classification to biosurveillance to blockchain fraud detection, their utility in areas of high societal importance such as power system modeling and, particularly, resilience quantification in the energy sector yet remains untapped. To provide fast acting synthetic regulation and contingency reserve services to the grid while having minimal disruptions on customer quality of service, we propose a new topology-based system that depends on a neural network architecture for impact metric classification and prediction in power systems. This novel topology-based system allows one to evaluate the impact of three power system contingency types, in conjunction with transmission lines, transformers, and transmission lines combined with transformers. We show that the proposed new neural network architecture equipped with local topological measures facilitates more accurate classification of unserved load as well as the amount of unserved load. In addition, we are able to learn more about the complex relationships between electrical properties and local topological measurements on their simulated response to contingencies for the NREL-SIIP power system.

contingency analysis↗

Biomorphic Multi-Agent Architecture for Persistent Computing

A multi-agent software/hardware architecture, inspired by the multicellular nature of living organisms, has been proposed as the basis of design of a robust, reliable, persistent computing system. Just as a multicellular organism can adapt to changing environmental conditions and can survive despite the failure of individual cells, a multi-agent computing system, as envisioned, could adapt to changing hardware, software, and environmental conditions. In particular, the computing system could continue to function (perhaps at a reduced but still reasonable level of performance) if one or more component( s) of the system were to fail. One of the defining characteristics of a multicellular organism is unity of purpose. In biology, the purpose is survival of the organism. The purpose of the proposed multi-agent architecture is to provide a persistent computing environment in harsh conditions in which repair is difficult or impossible. A multi-agent, organism-like computing system would be a single entity built from agents or cells. Each agent or cell would be a discrete hardware processing unit that would include a data processor with local memory, an internal clock, and a suite of communication equipment capable of both local line-of-sight communications and global broadcast communications. Some cells, denoted specialist cells, could contain such additional hardware as sensors and emitters. Each cell would be independent in the sense that there would be no global clock, no global (shared) memory, no pre-assigned cell identifiers, no pre-defined network topology, and no centralized brain or control structure. Like each cell in a living organism, each agent or cell of the computing system would contain a full description of the system encoded as genes, but in this case, the genes would be components of a software genome.

Lodding, Kenneth N.↗

Topologically trivial gap-filling in superconducting Fe(Se,Te) by one-dimensional defects

Abstract Structural distortions and imperfections are a crucial aspect of materials science, on the macroscopic scale providing strength, but also enhancing corrosion and reducing electrical and thermal conductivity. At the nanometre scale, multi-atom imperfections, such as atomic chains and crystalline domain walls have conversely been proposed as a route to topological superconductivity, whose most prominent characteristic is the emergence of Majorana Fermions that can be used for error-free quantum computing. Here, we shed more light on the nature of purported domain walls in Fe(Se,Te) that may host 1D dispersing Majorana modes. We show that the displacement shift of the atomic lattice at these line-defects results from sub-surface impurities that warp the topmost layer(s). Using the electric field between the tip and sample, we manage to reposition the sub-surface impurities, directly visualizing the displacement shift and the underlying defect-free lattice. These results, combined with observations of a completely different type of 1D defect where superconductivity remains fully gapped, highlight the topologically trivial nature of 1D defects in Fe(Se,Te).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Study of hypervelocity meteoroid impact on orbital space stations

Structural damage resulting in hypervelocity impact of a meteorite on a spacecraft is discussed. Of particular interest is the backside spallation caused by such a collision. To treat this phenomenon two numerical schemes were developed in the course of this study to compute the elastic-plastic flow fracture of a solid. The numerical schemes are a five-point finite difference scheme and a four-node finite element scheme. The four-node finite element scheme proved to be less sensitive to the type of boundary conditions and loadings. Although further development work is needed to improve the program versatility (generalization of the network topology, secondary storage for large systems, improving of the coding to reduce the run time, etc.), the basic framework is provided for a utilitarian computer program which may be used in a wide variety of situations. Analytic results showing the program output are given for several test cases.

Leimbach, K. R.↗

TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state (t) and previous context (over timestamps [t–1,t–l], l is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp t. We consider diverse benchmarks with varying levels of "novelty" as measured by the TEA (Temporal Edge Appearance) plots. Here, our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.

97 MATHEMATICS AND COMPUTING↗

Analysis of 100Mb/s Ethernet for the Whitney Commodity Computing Testbed

We evaluate the performance of a Fast Ethernet network configured with a single large switch, a single hub, and a 4x4 2D torus topology in a testbed cluster of "commodity" Pentium Pro PCs. We also evaluated a mixed network composed of ethernet hubs and switches. An MPI collective communication benchmark, and the NAS Parallel Benchmarks version 2.2 (NPB2) show that the torus network performs best for all sizes that we were able to test (up to 16 nodes). For larger networks the ethernet switch outperforms the hub, though its performance is far less than peak. The hub/switch combination tests indicate that the NAS parallel benchmarks are relatively insensitive to hub densities of less than 7 nodes per hub.

Fineberg, Samuel A.↗

Numerical simulation of rotorcraft

The objective of the research is to develop and validate accurate, user-oriented viscous CFD codes (with inviscid options) for three-dimensional, unsteady aerodynamic flows about arbitrary rotorcraft configurations. Unsteady, three-dimensional Euler and Navier-Stokes codes are developed, adapted, and extended to rotor-body combinations. Flow solvers are coupled with zonal grid topologies, including rotating and nonrotating blocks. Special grid clustering and wave-fitting techniques were developed to capture low-level radiating acoustic waves. Significant progress was made in computing the propagation of acoustic waves due to the interaction of a concentrated vortex and a helicopter airfoil. The need for higher-order schemes was firmly established in relatively inexpensive two-dimensional calculations. In three dimensions, the number of grid points required to capture the low-level acoustic waves becomes very large, so that large supercomputer memory becomes essential. Good agreement was obtained between the numerical results obtained with a thin-layer Navier-Stokes code and experimental data from a model rotor. In addition, several nonrotating configurations that are sometimes proposed to simulate rotor blade tips in conventional wind tunnels were examined, and the complex flow around the radical tip shape of the world's fastest helicopter is under investigation. These studies demonstrate the flexibility and power of CFD to gain physical insight, study novel ideas, and examine various possibilities that might be difficult or impossible to set up in physical experiments. As a prelude to studies of rotor-body aerodynamic interactions, a preliminary grid topology and moving-interface strategy were developed. A new Euler/Navier-Stokes code using these techniques computes the vortical wake directly, rather than modeling it, as in most previous rotorcraft studies. Several hover cases were run for conventional and advanced-geometry blades. Numerical schemes using multi-zones and/or adaptive grids appear to be necessary to simulate the complex vortical flows in rotor wakes.

Mccroskey, William J.↗

Computer-Aided Modeling and Analysis of Power Processing Systems (CAMAPPS), phase 1

The large-signal behaviors of a regulator depend largely on the type of power circuit topology and control. Thus, for maximum flexibility, it is best to develop models for each functional block a independent modules. A regulator can then be configured by collecting appropriate pre-defined modules for each functional block. In order to complete the component model generation for a comprehensive spacecraft power system, the following modules were developed: solar array switching unit and control; shunt regulators; and battery discharger. The capability of each module is demonstrated using a simplified Direct Energy Transfer (DET) system. Large-signal behaviors of solar array power systems were analyzed. Stability of the solar array system operating points with a nonlinear load is analyzed. The state-plane analysis illustrates trajectories of the system operating point under various conditions. Stability and transient responses of the system operating near the solar array's maximum power point are also analyzed. The solar array system mode of operation is described using the DET spacecraft power system. The DET system is simulated for various operating conditions. Transfer of the software program CAMAPPS (Computer Aided Modeling and Analysis of Power Processing Systems) to NASA/GSFC (Goddard Space Flight Center) was accomplished.

Kim, S.↗

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗

Numerical Investigation of Plasma Detachment in Magnetic Nozzle Experiments

At present there exists no generally accepted theoretical model that provides a consistent physical explanation of plasma detachment from an externally-imposed magnetic nozzle. To make progress towards that end, simulation of plasma flow in the magnetic nozzle of an arcjet experiment is performed using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The aim is to compare the computational results with various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver (see Fig. I), and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kuriki and Okada. This geometry is modeled because there is a substantial amount of experimental data that can be compared to the computational results, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how they scale with different input parameters. Further studies will focus on modeling literature experiments both for the purpose of additional code validation and to extract physical insight regarding the mechanisms driving detachment.

Sankaran, Kamesh↗

Navier-Stokes computations for circulation controlled airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, T. H.↗