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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Efficient hierarchical interconnection for multiprocessor systems

The authors present a novel approach to the design of a class of hierarchical interconnection networks for multiprocessor systems. This approach, based on an architecture providing separate networks for each level, gives a general and flexible way to construct efficient hierarchical networks. The performance and cost-effectiveness of the resulting networks are analyzed and compared in detail, using both unbuffered and buffered network models. It is shown that, if the design parameters are determined based on the degree of locality, the cost-effectiveness of a hierarchical network can be significantly improved. In addition, the authors investigate how to construct a cost-effectiveness hierarchical network by determining appropriate design parameters. Two associated algorithms are developed for this purpose.

Wei, Sizheng↗
DOE OSTI2026

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from highdimensional statistics. Furthermore, our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

MAP estimation↗
DOE OSTI2025

Modular Assembly of FTO|Chromophore-Catalyst Hierarchical Films Based on Strong Dipole Interactions

Here, we have designed and characterized modular self-assembled hierarchical films containing a molecular catalyst tethered to an anchoring molecule by means of dipole-induced dipole interactions. In order to do so, two new Co III -based molecular catalyst candidates were designed, namely, [Co III L 1 (pyrr) 2 ]ClO 4 (Co1) and [Co III L 2 (pyrr) 2 ]ClO 4 (Co2), where L 1 and L 2 are the respective deprotonated forms of N,N′-[4,5-bis(dodecyloxy)-1,2-phenylene]dipicolinamide and N,N′-[4,5-bis(methoxyethoxy)-1,2-phenylene]dipicolinamide and were characterized by electrochemical, electronic, and film formation properties. Species Co1 and Co2 were deposited onto an anchor molecule such as octylphosphonic acid (OPA) or the chromophoric [Ru II (bpy PO3H ) 2 (bpy C7 )]Cl 2 (Ru) previously attached onto conductive fluorine-doped tin oxide (FTO). Four hierarchical films of the form substrate|anchor-catalyst were obtained, namely, FTO|OPA-Co1, FTO|OPA-Co2, FTO|Ru-Co1, and FTO|Ru-Co2, and the role of dipole-dipole interactions between anchor and catalyst modules was assessed. These newly synthesized hierarchical films were characterized by a host of surface-specific methods that include X-ray photoelectron spectroscopy, ellipsometry, X-ray fluorescence, and water contact angle, thus enabling an unprecedented level of analysis. Compared to the weak C-H van der Waals interactions exhibited by Co1, the presence of alkoxy chains in Co2 ensures stronger dipole-dipole interactions with the alkyl chain of the anchors due to O···H formation. The persistence of their redox properties, which include metal oxidation, and directionality of electron transport were probed suggesting direct relevance to catalytic processes such as water oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Hierarchical Chiral Self-Assembly of Nanocylinders Composed of Sequence-Defined Mesogenic Dimers

Chiral ensembles can arise through supramolecular curvature that resolves geometric frustrations in the packing of bent, achiral molecular or colloidal building blocks. Here, we leverage orthogonal protection−deprotection click chemistry to create sequence-defined mesogenic heterodimers exhibiting emergent chirality. We compare the hierarchical self-assembly of the synthesized asymmetric, achiral heterodimers, which differ only in the position of a methyl substituent. Both dimers form chiral spherulites composed of nanocylinders. However, the detailed arrangement of nanocylinders depends on the position of the methyl substituent and the crystallization conditions. Despite the chemical similarity, in one dimer, two crystalline forms are optically active. They form conglomerates of dextrorotatory and levorotatory spherulites. The other dimer forms more highly anisotropic spherulites that mask circular birefringence arising from the misorientation of nanocylinders, while mapping of nanocylinder directors reveals a sense at the spherulite surface. We propose that differences in nanocylinder arrangements may arise from changes in nanocylinder curvature and dimensions dictated by the methyl substituent position, inducing chirality. These results demonstrate multiscale hierarchical assembly relevant to dense systems of tubular structures and highlight the role of sequence and molecular design in directing the bottom-up hierarchical self-assembly and chirality of mesogenic systems.

Alkyls↗
DOE OSTI2026

Hierarchical microstructure of Yb-filled skutterudites through ultrasonically atomized spherical powders for enhanced thermoelectric performance

Hierarchical microstructures are widely explored as a strategy to reduce lattice thermal conductivity in thermoelectric materials while preserving favorable electronic transport. Here we demonstrate that ultrasonic atomization of precursor powders provides an intrinsic pathway to generate such architectures in n-type Yb0.3Co4Sb12 skutterudites. Materials were synthesized by both conventional sealed-ampoule and ultrasonic atomization routes, each yielding essentially single-phase skutterudite after densification. However, the atomized spherical powders undergo a distinct reaction-driven microstructural evolution during thermal treatment prior to densification. Electron microscopy reveals that the skutterudite phase within the particles induces swelling, cracking, and fragmentation of the droplets before consolidation. Multimodal structural and microstructural characterizations show that densification of these fragmented powders produces a hierarchical microstructure consisting of submicron grains, micrometer-scale faceted crystallites, and powder-derived domains separated by oxide-decorated boundaries. Comprehensive thermoelectric transport measurements evidence that this multiscale architecture lowers the lattice thermal conductivity while maintaining favorable electronic transport, leading to an average ~10% enhancement in the thermoelectric figure of merit. Complementary 121Sb Mössbauer spectroscopy further indicates lattice softening in the atomized material. These results demonstrate that ultrasonic atomization provides an effective route to engineer hierarchical microstructures in skutterudite thermoelectrics and offers a promising strategy for tailoring thermal transport in energy-conversion materials.

Bouteiller, Hugo [ORNL] (ORCID:0009000421322962)↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗
DOE OSTI2025

Theoretical and methodological challenges in hierarchical Bayesian inference for model-form uncertainty

This report describes challenges associated with the hierarchical Bayesian approach to inform model-form uncertainty (MFU) representations, which are parameterized modifications to a mathematical models’ governing equations to express uncertainty in form of the equations. To inform model-form uncertainties, hierarchical Bayesian inference is often employed. Here, the MFU parameters are distributed parametrically, and the hyperparameters of the parametric distribution are informed through Bayesian inference, with the aim of determining the MFU parameter distribution that best agrees with calibration data. In practice, however, we have found the hierarchical Bayesian approach falls short of this aim. We discuss theoretical and methodological challenges of the approach, and we present several numerical demonstrations of these challenges. To conclude, we suggest promising alternative approaches for future investigation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Application of a hierarchical structure stochastic learning automation

A hierarchical structure automaton was developed using a two state stochastic learning automato (SLA) in a time shared model. Application of the hierarchical SLA to systems with multidimensional, multimodal performance criteria is described. Results of experiments performed with the hierarchical SLA using a performance index with a superimposed noise component of ? or - delta distributed uniformly over the surface are discussed.

Neville, R. G.↗
NASA NTRS1982

NASA Thesaurus. Volume 1: Hierarchical listing

There are 16,713 postable terms and 3,716 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary.

Source record↗
NASA NTRS1984

A hierarchical finite element approach for integrated thermal-structural analysis

A hierarchical finite element approach for thermal-structural analysis is presented. The approach employs a common nodal discritization and seeks improvements in the accuracy of the analyses by using hierarchical interpolation functions with nodeless variables. The effectiveness of the integrated approach is assessed for three applications with two-dimensional elements by comparison with conventional finite element thermal-structural solutions. Improvements in the accuracy of temperatures and thermal-stresses are demonstrated. The applications demonstrate the practical importance of having flexibility in refining each analysis independently while maintaining a common discretization, and show that the hierarchical approach offers potential for the development of a general method for integrated thermal-structural analysis.

Thornton, E. A.↗
NASA NTRS1984

On the development of hierarchical solution strategies for nonlinear finite element formulations

This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.

Padovan, J.↗
NASA NTRS1985

NASA thesaurus. Volume 1: Hierarchical listing

There are 16,835 postable terms and 3,765 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary.

Source record↗
NASA NTRS1986

A hierarchical approach to reliability modeling of fault-tolerant systems

A methodology for performing fault tolerant system reliability analysis is presented. The method decomposes a system into its subsystems, evaluates vent rates derived from the subsystem's conditional state probability vector and incorporates those results into a hierarchical Markov model of the system. This is done in a manner that addresses failure sequence dependence associated with the system's redundancy management strategy. The method is derived for application to a specific system definition. Results are presented that compare the hierarchical model's unreliability prediction to that of a more complicated tandard Markov model of the system. The results for the example given indicate that the hierarchical method predicts system unreliability to a desirable level of accuracy while achieving significant computational savings relative to component level Markov model of the system.

Gossman, W. E.↗
NASA NTRS1986

Constrained hierarchical least square nonlinear equation solvers

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Padovan, J.↗
NASA NTRS1988

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗
NASA NTRS1988

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions.

Source record↗
NASA NTRS1992

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗