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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an essential role in capturing the shape of scalar field data. Herein we present a state–of–the–art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time–varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Peer-to-Peer Communication Trade-Offs for Smart Grid Applications: Preprint

Peer-to-peer energy management systems for smart grids require developers to consider the trade-offs between the amount of communication traffic generated and the quality and speed of convergence of the control algorithms that are deployed. Employing a fully connected communication causes messages to scale exponentially with the number of nodes, while using a sparse connectivity causes less information dissemination leading to degradation of the algorithm performance. The best communication topology for a particular application lies somewhere in between and often requires empirical evaluation by application designers. Existing methods do not put focus on the needs for smart grid applications, which is information dissemination throughout the network and they do not provide a flexible solution for application developers to prototype and deploy different topologies without modifying the application code. This paper introduces a configurable virtual communication topology framework TopLinkMgr, allowing users to specify any chosen communication topology and deploy peer-to-peer applications using it. It also introduces a self-adaptive, fault-tolerant topology management algorithm, Bounded Path Dissemination that can ensure the dissemination of information to all peers within a specified threshold for a sparsely connected topology. Experiments show that the algorithm improves on convergence speed and accuracy over state-of-the-art methods and is also robust against node failures. The results indicate the possibility of achieving a close-to optimal convergence without overloading the network allowing the realization of peer-to-peer control platforms covering larger and more complex power systems.

Bounded Path Dissemination↗
DOE OSTI2024

Role of bath-induced many-body interactions in the dissipative phases of the Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. In conclusion, we also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.

1-dimensional systems↗
DOE OSTI2024

Off-shell Partition Functions in 3d Gravity

We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of PSL(2,R) Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface Σ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form Σ×S 1 , where Σ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of n asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{M}$ g,n , which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces Σ. As a result, there is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.

Classical and Quantum Gravity↗
NASA NTRS1993

Program Helps Simulate Neural Networks

Neural Network Environment on Transputer System (NNETS) computer program provides users high degree of flexibility in creating and manipulating wide variety of neural-network topologies at processing speeds not found in conventional computing environments. Supports back-propagation and back-propagation-related algorithms. Back-propagation algorithm used is implementation of Rumelhart's generalized delta rule. NNETS developed on INMOS Transputer(R). Predefines back-propagation network, Jordan network, and reinforcement network to assist users in learning and defining own networks. Also enables users to configure other neural-network paradigms from NNETS basic architecture. Small portion of software written in OCCAM(R) language.

Villarreal, James↗
DOE OSTI2021

Probing polarization dynamics at specific domain configurations: Computer-vision based automated experiment in piezoresponse force microscopy

Topological defects in ferroelectric materials have attracted much attention due to the emergence of conductive, ferroic, and magnetic functionalities. However, many topological configurations dynamically evolve during the switching processes, making them a challenge to characterize via traditional techniques. Here, we implement an automated experimentation approach for the exploration of functional properties in BiFeO 3 thin films. Specifically, we visualize the ferroelectric domain structures via single frequency piezoresponse force microscopy and implement a computer vision-based algorithm to discover features of interest at which spectroscopic measurements are taken. Subsequently, we employ dimensionality reduction techniques to reveal characteristic polarization behaviors at these features. This approach can be extended to other spectroscopies and modalities to probe only specific features of interest, ultimately enabling dynamical processes in ferroelectrics to be studied.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Reconfigurable topologies for decentralized control of spacecraft formations in Deep Space

This paper discusses control and communication topologies that asynchronously distribute the sensing, communication and computation tasks amongst the spacecraft in the formation. Our approach allows the dynamic reconfiguration of the measurement and communication topologies while maintaining the specified formation performance objectives. An illustrative simulation example is presented.

Hadaegh, Fred Y.↗
DOE OSTI2024

Simulating long-time evolution of driven many-body systems with next generation quantum computers (Final Report)

This project is focused on performing the best science possible on current generation quantum computers. As such, we have focused on developing techniques that involve robust algorithms that are either insensitive to noise, or are extremely low depth. We also have worked on determining topological properties and employing the robustness of topology to noise to allow for robust quantum computation. The ultimate goal is to be able to do new science on quantum computers that cannot be achieved on classical computers. The main effort of the work we have completed is on time-evolution of quantum systems and robust calculation of properties of systems enabled by being able to perform time evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Distributed Finite-Time Termination for Consensus Algorithm in Switching Topologies

Here, in this article, we present a finite-time stopping criterion for consensus algorithms in networks with dynamic communication topology. Prior state of the art has established convergence to the consensus value; however, the asymptotic convergence of these algorithms poses a challenge in practical settings where the response from agents is required in finite time. To this end, we propose a maximum-minimum protocol that propagates the global maximum and minimum values of agent states (while running the consensus algorithm) in the network. This article focuses on establishing that the global maximum and minimum values are strictly monotonic even for a dynamic topology, and they can be used to distributively ascertain the closeness to convergence in finite time. We rigorously show that each node can have access to the global maximum and minimum by running the proposed maximum-minimum protocol to realize a finite-time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1995

The National Grid Project: A system overview

The National Grid Project (NGP) is a comprehensive numerical grid generation software system that is being developed at the National Science Foundation (NSF) Engineering Research Center (ERC) for Computational Field Simulation (CFS) at Mississippi State University (MSU). NGP is supported by a coalition of U.S. industries and federal laboratories. The objective of the NGP is to significantly decrease the amount of time it takes to generate a numerical grid for complex geometries and to increase the quality of these grids to enable computational field simulations for applications in industry. A geometric configuration can be discretized into grids (or meshes) that have two fundamental forms: structured and unstructured. Structured grids are formed by intersecting curvilinear coordinate lines and are composed of quadrilateral (2D) and hexahedral (3D) logically rectangular cells. The connectivity of a structured grid provides for trivial identification of neighboring points by incrementing coordinate indices. Unstructured grids are composed of cells of any shape (commonly triangles, quadrilaterals, tetrahedra and hexahedra), but do not have trivial identification of neighbors by incrementing an index. For unstructured grids, a set of points and an associated connectivity table is generated to define unstructured cell shapes and neighboring points. Hybrid grids are a combination of structured grids and unstructured grids. Chimera (overset) grids are intersecting or overlapping structured grids. The NGP system currently provides a user interface that integrates both 2D and 3D structured and unstructured grid generation, a solid modeling topology data management system, an internal Computer Aided Design (CAD) system based on Non-Uniform Rational B-Splines (NURBS), a journaling language, and a grid/solution visualization system.

Gaither, Adam↗
DOE OSTI2023

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. Further, this result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

General Bayesian Inference over the Stiefel Manifold via the Givens Transform

We introduce here an approach based on the Givens representation for posterior inference in statistical models with orthogonal matrix parameters, such as factor models and probabilistic principal component analysis (PPCA). We show how the Givens representation can be used to develop practical methods for transforming densities over the Stiefel manifold into densities over subsets of Euclidean space. We demonstrate how to deal with issues arising from the topology of the Stiefel manifold and how to inexpensively compute the change-of-measure terms. We introduce an auxiliary parameter approach that limits the impact of topological issues. We provide both analysis of our methods and numerical examples demonstrating the effectiveness of the approach. We also discuss how our Givens representation can be used to define general classes of distributions over the space of orthogonal matrices. We then give demonstrations on several examples showing how the Givens approach performs in practice in comparison with other methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Topology and boundary shape optimization as an integrated design tool

The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD type input-output facilities.

Bendsoe, Martin Philip↗
NASA NTRS2011

Contact Graph Routing

Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic. The information carried by CGR contact plan messages is useful not only for dynamic route computation, but also for the implementation of rate control, congestion forecasting, transmission episode initiation and termination, timeout interval computation, and retransmission timer suspension and resumption.

Burleigh, Scott C.↗
DOE OSTI2025

Object detection with deep learning for rare event search in the GADGET II TPC

In the pursuit of identifying rare two-particle events within the GADGET II Time Projection Chamber (TPC), this paper presents a comprehensive approach for leveraging Convolutional Neural Networks (CNNs) and various data processing methods. To address the inherent complexities of 3D TPC track reconstructions, the data is expressed in 2D projections and 1D quantities. This approach capitalizes on the diverse data modalities of the TPC, allowing for the efficient representation of the distinct features of the 3D events, with no loss in topology uniqueness. Additionally, it leverages the computational efficiency of 2D CNNs and benefits from the extensive availability of pre-trained models. Given the scarcity of real training data for the rare events of interest, simulated events are used to train the models to detect real events. To account for potential distribution shifts when predominantly depending on simulations, significant perturbations are embedded within the simulations. This produces a broad parameter space that works to account for potential physics parameter and detector response variations and uncertainties. These parameter-varied simulations are used to train sensitive 2D CNN object detectors. When combined with 1D histogram peak detection algorithms, this multi-modal detection framework is highly adept at identifying rare, two-particle events in data taken during experiment 21072 at the Facility for Rare Isotope Beams (FRIB), demonstrating a 100% recall for events of interest. Here, we present the methods and outcomes of our investigation and discuss the potential future applications of these techniques.

Convolutional neural network↗
DOE OSTI2021

Electronic properties of the bulk and surface states of Fe 1+y Te 1-x Se x

The idea of employing non-Abelian statistics for error-free quantum computing ignited interest in reports of topological surface superconductivity and Majorana zero modes (MZMs) in FeTe 0.55 Se 0.45 . However, the topological features and superconducting properties are not observed uniformly across the sample surface. The understanding and practical control of these electronic inhomogeneities present a prominent challenge for potential applications. Here, we combine neutron scattering, scanning angle-resolved photoemission spectroscopy, and microprobe composition and resistivity measurements to characterize the electronic state of Fe 1+y Te 1-x Se x . Furthermore, we establish a phase diagram in which the superconductivity is observed only at sufficiently low Fe concentration, in association with distinct antiferromagnetic correlations, whereas the coexisting topological surface state occurs only at sufficiently high Te concentration. We find that FeTe 0.55 Se 0.45 is located very close to both phase boundaries, which explains the inhomogeneity of superconducting and topological states. Our results demonstrate the compositional control required for use of topological MZMs in practical applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗