Search NASA⌕ Search

SEARCH · Search NASA

Results for “low dimensional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.↗

Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.

Data-driven↗

Quantitative three-dimensional low-speed wake surveys

Theoretical and practical aspects of conducting three-dimensional wake measurements in large wind tunnels are reviewed with emphasis on applications in low-speed aerodynamics. Such quantitative wake surveys furnish separate values for the components of drag, such as profile drag and induced drag, but also measure lift without the use of a balance. In addition to global data, details of the wake flowfield as well as spanwise distributions of lift and drag are obtained. The paper demonstrates the value of this measurement technique using data from wake measurements conducted by Boeing on a variety of low-speed configurations including the complex high-lift system of a transport aircraft.

Brune, G. W.↗

A competition between 2D and 3D magnetic orderings in novel mixed valent copper frameworks

Low-dimensional hybrid inorganic–organic frameworks exhibit high structural flexibility and allow for the inclusion of various magnetic and optically-active species into their host structures. The emergence of copper-based hybrid structures for various optical applications provides a promising foundation for exploring the integration of magnetic sublattices, paving the way for advancements in magneto-optical coupling and multifunctional materials. Herein, we introduce a novel class of hybrid copper frameworks with covalently-connected alternating magnetic 2D copper(II) formate and non-magnetic copper(I) bromide layers. The anionic framework is stabilized by A + cations to form ACu 5 Br 4 (COOH) 4 (A + = Na + , K + , Rb + , NH 4 + ) semiconductors (bandgaps 2.1–2.2 eV) with optical transitions suitable for optoelectronic applications. Comprehensive magnetometry studies show that ACu 5 Br 4 (COOH) 4 compounds exhibit low-dimensional 2D short-range antiferromagnetic order within the formate layers, characterized by strong exchange coupling (J/k B ∼ −100 K). Upon further temperature reduction, interactions between Cu(II) layers give rise to 3D long-range magnetic order at ∼40 K, despite the large (8.6–8.8 Å) spatial separation of the magnetic Cu(II) formate layers by nonmagnetic Cu(I)–Br bridging layers. This transition is further supported by electron paramagnetic resonance (EPR) spectroscopy. In conclusion, this study expands our understanding of low-dimensional hybrid frameworks and opens new avenues for the design of 2D multifunctional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Layer-dependent topological phase in a two-dimensional quasicrystal and approximant

The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing “forbidden” symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta 1.6 Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta 21 Te 13 , reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.

36 MATERIALS SCIENCE↗

A comparison of probabilistic generative frameworks for molecular simulations

Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.

Artificial intelligence↗

Enhanced thermoelectric efficiency in nanocrystalline bismuth telluride nanotubes

We report on the thermal and thermoelectric properties of individual nanocrystalline Bi 2 Te 3 nanotubes synthesized by the solution phase method using 3ω method and a microfabricated testbench. Measurements show that the nanotubes offer improved ZT compared to bulk Bi 2 Te 3 near room temperature due to an enhanced Seebeck coefficient and suppressed thermal conductivity. This improvement in ZT originates from the nanocrystalline nature and low dimensionality of the nanotubes. Domain boundary filtering of low-energy electrons provides an enhanced Seebeck coefficient. The scattering of phonons at the surface of the nanotube leads to suppressed thermal conductivity. These have been theoretically analyzed using the Boltzmann equation based on the relaxation time approximation and Landauer approach. This work clearly demonstrates the possibility of achieving enhancement in thermoelectric efficiency by combining nanocrystalline and low-dimensional systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Catalytic cathode for a lithium-oxygen battery

A metal-air battery includes an anode; a low-dimensional catalyst cathode; and an electrolyte; wherein: the low-dimensional catalyst cathode comprises a functional metal layer on a carbon support overcoated with a catalyst layer; the electrolyte comprises an aprotic solvent that is an ether-based solvent, a fluorinated ether-based solvent, an oligo (ethylene oxide) solvent, or a mixture of any two or more thereof; and the electrolyte is free of carbonate solvents.

25 ENERGY STORAGE↗

The Impact of High-Dimensional Phase Space Correlations on the Beam Dynamics in a Linear Accelerator

Hadron beams develop intensity-dependent transverse-longitudinal correlations within radio-frequency quadrupole (RFQ) accelerating structures. These correlations are only visible in six-dimensional phase space and are destroyed by reconstructions from low-dimensional projections. In this work, we estimate the effect of artificial decorrelation on the beam dynamics in the Spallation Neutron Source (SNS) linac and Beam Test Facility (BTF). We show that the evolution of a realistic initial distribution and its decorrelated twin converge during the early acceleration stages; thus, low-dimensional projections are probably sufficient for detailed predictions in high-power linacs.

Hoover, Austin↗

Inverse Analysis with Variational Autoencoders: A Comparison of Shallow and Deep Networks

Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.

97 MATHEMATICS AND COMPUTING↗

Probabilistic Modeling of Heavy Machinery Using Machine Learning

NASA Glenn Research Center’s facility operations seeks to leverage its extensive instrumentation and historical data with machine learning to increase system efficiencies. The ultimate goal of this effort is to probabilistically model the behavior of Glenn’s central air service compressors for optimal decision making and planning. This project is a first step in that direction. We propose a multimodel approach that uses high-dimensional models to ask simple questions about complex dependent structures, and low-dimensional models to ask complex questions about simple dependent structures. While the low-dimensional models make strong assumptions, they can be visualized and they can be insightful. We show good fits for univariate models of compressor sensors, and preliminary work on high-dimensional multivariate models.

Machine learning↗

Spin-related phenomena in spin 3/2 charge carrier holes systems

Charge carrier holes provide a remarkable system for spintronics and quantum information technology. In this review paper, I discuss spin-related phenomena in three-dimensional and low-dimensional hole systems. Special attention is paid to the mutual transformation of heavy and light holes at the boundary of quantum wells and wires that governs values of parameters defining hole spectra in quantum wells, wires and dots, such as effective masses, g-factors and Rashba and Dresselhaus spin–orbit constants. Recently, topological phenomena in condensed matter systems, such as emergence of Majorana zero modes and non-Abelian phases in the fractional quantum Hall effect, sparked considerable interest of researchers. Charge carrier holes turn out to be a remarkable setting for possible observation of these phenomena and advancing topological quantum computing. I discuss the spectra and wavefunctions of two-dimensional holes in magnetic field. While there is a semiclassical range of parameters when heavy and light holes can be described by equidistant Landau levels, ground-level holes and holes in a few low-lying excited states behave as species completely different from electrons. Especially interesting are crossings in hole spectra in magnetic field. Hole–hole interactions can substantially differ from electron–electron interactions. Apart from the difference in exchange splitting, this shows in possible emergence of even denominator fractional quantum Hall state in the ground hole level in magnetic field. I also briefly discuss spintronic phenomena, such as mutual transformation of angular momentum (spin) of holes and electric current, as well as spin-related interference effects in hole transport. Recent developments in a system of Ge hole quantum dots offer new perspectives for hole-based systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems’ stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. In this work, we first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

36 MATERIALS SCIENCE↗

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

fracture mechanics↗

A graph embedding‐based approach for automatic cyber‐physical power system risk assessment to prevent and mitigate threats at scale

Abstract Power systems are facing an increasing number of cyber incidents, potentially leading to damaging consequences to both physical and cyber aspects. However, the development of analytical methods for the study of large‐scale power infrastructures as cyber‐physical systems is still in its early stages. Drawing inspiration from machine‐learning techniques, the authors introduce a method inspired by the principles of graph embedding that is tailored for quantitative risk assessment and the exploration of possible mitigation strategies of large‐scale cyber‐physical power systems. The primary advantage of the graph embedding approach lies in its ability to generate numerous random walks on a graph, simulating potential access paths. Meanwhile, it enables capturing high‐dimensional structures in low‐dimensional spaces, facilitating advanced machine‐learning applications, and ensuring scalability and adaptability for comprehensive network analysis. By employing this graph embedding‐based approach, the authors present a structured and methodical framework for risk assessment in cyber‐physical systems. The proposed graph embedding‐based risk analysis framework aims to provide a more insightful perspective on cyber‐physical risk assessment and situation awareness for power systems. To validate and demonstrate its applicability, the method has been tested on two cyber‐physical power system models: the Western System Coordinating Council (WSCC) 9‐Bus System and the Illinois 200‐Bus System , thereby showing its advantages in enhancing the accuracy of risk analysis and comprehensiveness of situational awareness.

Sun, Shining↗

Anomalous Charge Transfer from Organic Ligands to Metal Halides in Zero‐Dimensional [(C 6 H 5 ) 4 P] 2 SbCl 5 Enabled by Pressure‐Induced Lone Pair‐π Interaction

Abstract Low‐dimensional (low‐D) organic metal halide hybrids (OMHHs) have emerged as fascinating candidates for optoelectronics due to their integrated properties from both organic and inorganic components. However, for most of low‐D OMHHs, especially the zero‐D (0D) compounds, the inferior electronic coupling between organic ligands and inorganic metal halides prevents efficient charge transfer at the hybrid interfaces and thus limits their further tunability of optical and electronic properties. Here, using pressure to regulate the interfacial interactions, efficient charge transfer from organic ligands to metal halides is achieved, which leads to a near‐unity photoluminescence quantum yield (PLQY) at around 6.0 GPa in a 0D OMHH, [(C 6 H 5 ) 4 P] 2 SbCl 5 . In situ experimental characterizations and theoretical simulations reveal that the pressure‐induced electronic coupling between the lone‐pair electrons of Sb 3+ and the π electrons of benzene ring (lp‐π interaction) serves as an unexpected “bridge” for the charge transfer. Our work opens a versatile strategy for the new materials design by manipulating the lp‐π interactions in organic–inorganic hybrid systems.

Luo, Hui↗

High-Pressure Synthesis of Bulk Cobalt Cementite, Co 3 C

Transition metal carbides find use in a wide range of advanced high-resilience applications including high-strength steels, heat shields, and deep-earth drills. However, carbides of the mid-to-late transition metals remain difficult to isolate and characterize on account of their metastability, which precludes the preparation of high-quality bulk single crystal samples using traditional solid-state methods. Herein, we report a combined computational and experimental survey of the cobalt-carbon binary system under high pressures and demonstrate that pressure offers a route toward the bulk synthesis of the metastable cementite-type cobalt carbide, Co 3 C, which under ambient conditions can only be prepared in low-dimensional thin film or nanoparticle forms. First-principles calculations reveal two competitive low-energy stoichiometric phases under ambient pressures - Pnnm-Co 2 C (Fe 2 C-type) and Pnma-Co 3 C (Fe 3 Ctype) - consistent with the known low-dimensional phases that have been studied for their promising magnetic properties. However, the calculated formation enthalpy of Pnma-Co 3 C decreases steadily with the applied pressure, while that of Pnnm-Co 2 C increases. Here, we pursue these results using high-pressure laser-heated synthesis methods coupled with in situ X-ray diffraction and observe the formation of Pnma-Co 3 C above 4.8 GPa. We determine the experimental bulk modulus of Co 3 C to be K o = 237 GPa (K p = 4.0). First-principles calculations of the phonon modes in Co 3 C reveal dynamical instabilities at ambient pressure that are absent under compression. These results offer a promising new route for the synthesis of rare-earth-free magnets.

36 MATERIALS SCIENCE↗

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗