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NASA NTRS1979

Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Fymat, A. L.↗

DOE OSTI2020

Kirigami-Inspired Self-Assembly of 3D Structures

Self-assembly of 3D structures introduce an attractive and scalable route to realize reconfigurable and functionally capable mesoscale devices without human intervention. A common approach for achieving this is to utilize stimuli-responsive folding of hinged structures, which requires the integration of different materials and/or geometric arrangements along the hinges. It is also demonstrated that the inclusion of Kirigami cuts in planar, hingeless bilayer thin sheets can be used to produce complex 3D shapes in an on-demand manner. Nonlinear finite element models are developed to elucidate the mechanics of shape morphing in bilayer thin sheets and verify the predictions through swelling experiments of planar, millimeter-scaled PDMS (polydimethylsiloxane) bilayers in organic solvents. Building upon the mechanistic understandings, The transformation of Kirigami-cut simple bilayers into 3D shapes such as letters from the Roman alphabet (to make “ADVANCED FUNCTIONAL MATERIALS”) and open/closed polyhedral architectures is experimentally demonstrated. A possible application of the bilayers as tether-less optical metamaterials with dynamically tunable light transmission and reflection behaviors is also shown. As the proposed mechanistic design principles could be applied to a variety of materials, this research broadly contributes toward the development of smart, tetherless, and reconfigurable multifunctional systems.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Alchemy: A Model-Based Approach for 2D to 3D Autonomous Nuclear System Design

Engineering design of nuclear power plant (NPP) piping and equipment systems frequently bypasses crucial 2D system planning, instead moving straight to 3D modeling. This often leads to designs that exceed building envelope constraints, forcing expensive and time-consuming redesigns. When 2D modeling is employed, it typically involves labor-intensive manual workflows that convert 2D drawings into 3D models, resulting in inefficiencies and errors across design iterations. These workflows further suffer from poor software interoperability and dependence on proprietary software ecosystems, thereby contributing to schedule delays and cost overruns. This paper presents Alchemy, an autonomous framework that transforms 2D system definitions into Industry Foundation Classes (IFC)-compliant 3D building information models (BIMs) for expediting nuclear facility design at the conceptual preliminary phase. Using a model-based approach, the framework treats the 2D system diagram as the central reference model employed to automatically generate all subsequent outputs, ensuring consistency between the system definition and the resulting physical design. A web-based interface enables engineers to define hierarchical system topologies including associated equipment, geometric properties, and connectivity requirements. A two-phase equipment layout optimization algorithm automatically computes collision-free spatial configurations within predefined building envelopes. An artificial intelligence (AI)-assisted pipe routing module then generates orthogonal, collision-free routing paths, allowing the user to select either an A* search-based method or an Ant Colony Optimization (ACO)-based method. All outputs are authored natively in IFC format, relying on open-source technologies and standardized formats in order to ensure extensibility and eliminate proprietary software dependencies. The proposed framework is validated on two representative pressurized-water reactor (PWR)-based case studies, for which it autonomously generates IFC-compliant 3D models in minutes, drastically reducing workflows that typically require hours of manual effort. The generated model demonstrates topologically correct equipment placement, physically plausible spatial relationships, and collision-free pipe routing consistent with known PWR loop configurations. This work represents a foundational step toward digital engineering for nuclear facility preliminary design, with future ongoing development targeting design code compliance and expanded system complexity.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Rotation of polarization by a moving gravitational lens

We present a simple prescription for the rotation of polarization produced by a relativistically moving gravitational lens, applicable to arbitrary deflection angle and arbitrary velocity of the lens. When geometric optics is applicable, two independent components contribute to the total rotation of polarization: (i) in the frame of the lens the polarization vector experiences minimal rotation defined by the deflection angle (as measured by a set of remote observers, or no rotation if defined in terms of a parallel-propagated tetrad); (ii) the effect of the motion of the lens on the polarization can be taken into account exactly using special-relativistic Lorentz transformation of polarization. The effects of the gravitational lensing are thus parametrized by the deflection angle of the null geodesics (not necessarily small) and the motion of the lens (not necessarily with velocities much smaller than that of light).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

From crystal color symmetry to quantum spacetime

More than one hundred years after the inception of relativistic physics, the concept of time remains incompletely understood. Relativity provides means to perform calculations of geometrical properties of spacetime, such as distances or curvature, and to interpret them in terms of physical observations, for instance as time dilation or gravitational effects. However, an intuitive understanding of spacetime is complicated, not so much because it is four-dimensional (which, after all, can be evaded by visualizing twodimensional cross sections) but mainly because its geometry does not obey Euclid’s axioms even in the absence of curvature. Through a well defined and clever transformation (RBS: renormalized blended spacetime), Venkatraman Gopalan (2021) has demonstrated how the hyperbolic geometry in Minkowski spacetime can be mapped to a circular Euclidean geometry. In particular, Lorentzian boosts become Euclidean rotations which enables new frontiers of exploration in color symmetry and magnetic crystals. His idea of general relativistic spacetime crystals and how to obtain them is both powerful and broad, although the notion of relativistic crystals and lattices in two dimensions has existed for a while (Janner & Ascher, 1969a,b). Finally, the breadth of this new work is underlined by the present opinion piece, written by two co-authors with distinct yet connected areas of expertise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1989

Terrain mapping for a roving planetary explorer

A prototype legged vehicle is being developed for an exploratory mission on another planet, conceivably Mars, where it is to traverse uncharted areas and collect material samples. The rover can construct from range imagery a geometric terrain representation; i.e., elevation map that includes uncertainty, unknown areas, and local features. An algorithm for constructing an elevation map from a single range image is presented: by virtue of working in spherical-polar space, the algorithm is independent of the desired map resolution and the orientation of the sensor, unlike algorithms that work in Cartesian space. Also presented is a two-stage matching technique (feature matching followed by iconic matching) that identifies the transformation T corresponding to the vehicle displacement between two viewing positions. To support legged locomotion over rough terrain, methods for evaluating regions of the constructed elevation maps as footholds are developed.

Hebert, M.↗

DOE OSTI2015

SU-E-T-653: Quantifying Inter-Fraction Range Uncertainty for Input Into Robust Proton Planning

Purpose: To provide a method for quantifying centre- and tumour site-specific population range uncertainty due to inter-fraction motion for use within robust proton planning and plan analysis. PTV-based and probabilistic/robust plans depend upon accurate knowledge of geometric and range uncertainties. If the uncertainty model is inaccurate, both types of plan, PTV or probabilistic, could produce under-dosing of the target and/or overdosing of OAR. Methods: Daily mega-voltage volumetric imaging data from previously treated radiotherapy patients has been used to investigate inter-fraction changes to water equivalent path-length (WEPL). Daily image-guidance scans were carried out for each patient and corrected for changes in CTV position (using rigid transformations). An effective depth algorithm was used to determine residual range changes, after corrections were applied, by comparing WEPL within the CTV at each fraction for several beam angles. This method has been demonstrated for nine prostate and seven head and neck. Results: Inter-fraction range changes for the head and neck patient sample were Σ=3.39mm, σ=4.72mm and overall mean =−1.82mm; for prostate Σ=5.64mm, σ=5.91mm and overall mean =0.98 mm. The choice of beam angle for head and neck did not affect the inter-fraction range error significantly; however this was not the same for prostate. Greater range changes were seen using a lateral beam compared to an anterior beam for prostate due to relative motion of the prostate and femoral heads. Conclusion: A method has been developed to quantify population range changes due to inter-fraction motion. The results show a non-zero mean for these samples, as well as significant Σ and σ, highlighting the importance of quantifying uncertainties and use of image guidance. Such information can be used in robust optimisation algorithms and for analysing treatment plan robustness. It may also help in establishing beam start conditions at planning and for establishing adaptive planning protocols.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS2013

Implementation of a Wavefront-Sensing Algorithm

A computer program has been written as a unique implementation of an image-based wavefront-sensing algorithm reported in "Iterative-Transform Phase Retrieval Using Adaptive Diversity" (GSC-14879-1), NASA Tech Briefs, Vol. 31, No. 4 (April 2007), page 32. This software was originally intended for application to the James Webb Space Telescope, but is also applicable to other segmented-mirror telescopes. The software is capable of determining optical-wavefront information using, as input, a variable number of irradiance measurements collected in defocus planes about the best focal position. The software also uses input of the geometrical definition of the telescope exit pupil (otherwise denoted the pupil mask) to identify the locations of the segments of the primary telescope mirror. From the irradiance data and mask information, the software calculates an estimate of the optical wavefront (a measure of performance) of the telescope generally and across each primary mirror segment specifically. The software is capable of generating irradiance data, wavefront estimates, and basis functions for the full telescope and for each primary-mirror segment. Optionally, each of these pieces of information can be measured or computed outside of the software and incorporated during execution of the software.

Smith, Jeffrey S.↗

DOE OSTI2016

Synthesis, crystal structure and magnetic properties of the two polymorphs of novel S=1 osmate; Li{sub 4}MgOsO{sub 6}

Li{sub 4}MgOsO{sub 6} was synthesized by two different solid-state reaction procedures. The crystal structures were determined by X-ray powder diffraction technique and it was revealed that Li{sub 4}MgOsO{sub 6} crystallizes in two different crystal symmetries in ordered rock salt structure type, namely monoclinic C2/m and orthorhombic Fddd. The unit cell constants for the monoclinic system are a=5.1074(4) Å, b=8.8182(4) Å, c=5.0902(2) Å, and β=109.845(4)° and those of the orthorhombic structure are a=5.8485(1) Å, b=8.3821(1) Å, and c=17.6212(3) Å. In both systems, Os{sup 6+} ions reside exclusively in a specific crystallographic position while Li{sup +} and Mg{sup 2+} ions exhibit mix occupancy. The temperature dependent magnetic susceptibility data for both S=1 osmate systems do not support the occurrence of any magnetic transition down to 2 K. The Curie–Weiss fit to the paramagnetic regime of the magnetic susceptibility data reveal highly negative θ value (−114.81 K and −121.87 K for C2/m and for Fddd systems, respectively), which are indicative of predominant antiferromagnetic (AFM) interactions in both systems. The experimental effective magnetic moment (μ{sub eff}) value for the monoclinic phase is 2.13 μB and that of the orthorhombic system is 2.34 μB. Due to the rather strong AFM interactions and lack of magnetic transition down to 2 K, both of these novel osmates are placed in the class of highly frustrated magnets. Low temperature magnetic susceptibility (below 2 K) and dynamic magnetic properties studies (μsr studies) are in order to better understand the magnetic ground states of these two polymorphs of Li{sub 4}MgOsO{sub 6}. - Graphical abstract: The structural transformation between two modifications of highly frustrated Li{sub 4}MgOsO{sub 6}. - Highlights: • Li4MgOsO{sub 6} was synthesized in two different crystal systems. • The monoclinic variant crystallizes in C2/m space group, while the orthorhombic version forms in Fddd space group. • The Os{sup 6+} ions are fully ordered while Li{sup +} and Mg{sup 2+} are mixed occupied. • These systems are the first Os{sup 6+} compounds in ordered NaCl structure type. • Both compounds exhibit high degree of geometric magnetic frustration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Conceptual Advances from Werner Complexes to Metal–Organic Frameworks

Alfred Werner's work on the geometric aspects of how ligands bind to metal ions at the end of the 19th century has given rise, in the molecular realm, to organometallic, bioinorganic, and cluster chemistries. By stitching together organic and inorganic units into crystalline porous metal-organic frameworks (MOFs), the connectivity, spatial arrangement, and geometry of those molecular complexes can now be fixed in space and become directly addressable. The fact that MOFs are porous provides additional space within which molecules can further be transformed and their chemistry controlled. Finally, an aspect not available in molecular chemistry but a direct consequence of Werner's analysis of coordination complexes is the ability to have multivariable functionality in MOFs to bring about a continuum of chemical environments, within the repeating order of the framework, from which a substrate can sample and be transformed in ways not possible in molecular complex chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Enhancing phonon flow through one-dimensional interfaces by impedance matching

We extend concepts from microwave engineering to thermal interfaces and explore the principles of impedance matching in 1D. The extension is based on the generalization of acoustic impedance to nonlinear dispersions using the contact broadening matrix Γ(ω), extracted from the phonon self energy. For a single junction, we find that for coherent and incoherent phonons, the optimal thermal conductance occurs when the matching Γ(ω) equals the Geometric Mean of the contact broadenings. This criterion favors the transmission of both low and high frequency phonons by requiring that (1) the low frequency acoustic impedance of the junction matches that of the two contacts by minimizing the sum of interfacial resistances and (2) the cut-off frequency is near the minimum of the two contacts, thereby reducing the spillage of the states into the tunneling regime. For an ultimately scaled single atom/spring junction, the matching criterion transforms to the arithmetic mean for mass and the harmonic mean for spring constant. The matching can be further improved using a composite graded junction with an exponential varying broadening that functions like a broadband antireflection coating. There is, however, a trade off as the increased length of the interface brings in additional intrinsic sources of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

Comparison of transform coding methods with an optimal predictor for the data compression of digital elevation models

Statistical encoding techniques enable the reduction of the number of bits required to encode a set of symbols, and are derived from their probabilities. Huffman encoding is an example of statistical encoding that has been used for error-free data compression. The degree of compression given by Huffman encoding in this application can be improved by the use of prediction methods. These replace the set of elevations by a set of corrections that have a more advantageous probability distribution. In particular, the method of Lagrange Multipliers for minimization of the mean square error has been applied to local geometrical predictors. Using this technique, an 8-point predictor achieved about a 7 percent improvement over an existing simple triangular predictor.

Lewis, Michael↗

NASA NTRS1985

Directional reflectance factor distributions for cover types of Northern Africa

Directional reflectance factors that spanned the entire exitance hemisphere were collected on the ground throughout the morning period for common cover types in Tunisia, Africa. NOAA 7/8 AVHRR bands 1(0.58-0.68 micron) and 2 (0.7301.1 micron) were used in data collection. The cover types reported were a plowed field, annual grassland, steppe grassland, hard wheat, salt plain, and irrigated wheat. Several of these cover types had geometric structures that are extreme as compared to those reported in the literature. Comparisons were made between the dynamics of the observed reflectance distributions and those reported in the literature. It was found that the dynamics of the measured data could be explained by a combination of soil and vegetation scattering components. The data and analysis further validated physical principles that cause the reflectance distribution dynamics as proposed by field and simulation studies in the literature. Finally, the normalized difference transformation (Band 2 - Band 1)/(Band 1 + Band 2), which is useful in monitoring vegetation cover, generally decreased the variation in signal with changing view angle. However, several exceptions were noted.

Kimes, D. S.↗

NASA NTRS1995

NASA-IGES Translator and Viewer

NASA-IGES Translator (NIGEStranslator) is a batch program that translates a general IGES (Initial Graphics Exchange Specification) file to a NASA-IGES-Nurbs-Only (NINO) file. IGES is the most popular geometry exchange standard among Computer Aided Geometric Design (CAD) systems. NINO format is a subset of IGES, implementing the simple and yet the most popular NURBS (Non-Uniform Rational B-Splines) representation. NIGEStranslator converts a complex IGES file to the simpler NINO file to simplify the tasks of CFD grid generation for models in CAD format. The NASA-IGES Viewer (NIGESview) is an Open-Inventor-based, highly interactive viewer/ editor for NINO files. Geometry in the IGES files can be viewed, copied, transformed, deleted, and inquired. Users can use NIGEStranslator to translate IGES files from CAD systems to NINO files. The geometry then can be examined with NIGESview. Extraneous geometries can be interactively removed, and the cleaned model can be written to an IGES file, ready to be used in grid generation.

Chou, Jin J.↗

NASA NTRS1993

Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams

A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.

Noor, Ahmed K.↗

NASA NTRS2007

Derivation and Application of a Global Albedo yielding an Optical Brightness To Physical Size Transformation Free of Systematic Errors

Orbital object data acquired via optical telescopes can play a crucial role in accurately defining the space environment. Radar systems probe the characteristics of small debris by measuring the reflected electromagnetic energy from an object of the same order of size as the wavelength of the radiation. This signal is affected by electrical conductivity of the bulk of the debris object, as well as its shape and orientation. Optical measurements use reflected solar radiation with wavelengths much smaller than the size of the objects. Just as with radar, the shape and orientation of an object are important, but we only need to consider the surface electrical properties of the debris material (i.e., the surface albedo), not the bulk electromagnetic properties. As a result, these two methods are complementary in that they measure somewhat independent physical properties to estimate the same thing, debris size. Short arc optical observations such as are typical of NASA's Liquid Mirror Telescope (LMT) give enough information to estimate an Assumed Circular Orbit (ACO) and an associated range. This information, combined with the apparent magnitude, can be used to estimate an "absolute" brightness (scaled to a fixed range and phase angle). This absolute magnitude is what is used to estimate debris size. However, the shape and surface albedo effects make the size estimates subject to systematic and random errors, such that it is impossible to ascertain the size of an individual object with any certainty. However, as has been shown with radar debris measurements, that does not preclude the ability to estimate the size distribution of a number of objects statistically. After systematic errors have been eliminated (range errors, phase function assumptions, photometry) there remains a random geometric albedo distribution that relates object size to absolute magnitude. Measurements by the LMT of a subset of tracked debris objects with sizes estimated from their radar cross sections indicate that the random variations in the albedo follow a log-normal distribution quite well. In addition, this distribution appears to be independent of object size over a considerable range in size. Note that this relation appears to hold for debris only, where the shapes and other properties are not primarily the result of human manufacture, but of random processes. With this information in hand, it now becomes possible to estimate the actual size distribution we are sampling from. We have identified two characteristics of the space debris population that make this process tractable and by extension have developed a methodology for performing the transformation.

Mulrooney, Dr. Mark K.↗

DOE OSTI2023

Trigger Detection for the sPHENIX Experiment via Bipartite Graph Networks with Set Transformer

Trigger (interesting events) detection is crucial to high-energy and nuclear physics experiments because it improves data acquisition efficiency. It also plays a vital role in facilitating the downstream offline data analysis process. The sPHENIX detector, located at the Relativistic Heavy Ion Collider in Brookhaven National Laboratory, is one of the largest nuclear physics experiments on a world scale and is optimized to detect physics processes involving charm and beauty quarks. Furthermore, these particles are produced in collisions involving two proton beams, two gold nuclei beams, or a combination of the two and give critical insights into the formation of the early universe. This paper presents a model architecture for trigger detection with geometric information from two fast silicon detectors. Transverse momentum is introduced as an intermediate feature from physics heuristics. We also prove its importance through our training experiments. Each event consists of tracks and can be viewed as a graph. A bipartite graph neural network is integrated with the attention mechanism to design a binary classification model. Compared with the state-of-the-art algorithm for trigger detection, our model is parsimonious and increases the accuracy and the AUC score by more than 15%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Advancing Additive Manufacturing Through Artificial Intelligence–Powered, High-Throughput, Nondestructive Characterization and Process Optimization

This Cooperative Research and Development Agreement (CRADA) between Oak Ridge National Laboratory (ORNL) and ZEISS Industrial Metrology has demonstrated the transformative potential of artificial intelligence (AI)-enabled x-ray computed tomography (XCT) to accelerate the qualification and certification of additively manufactured (AM) parts. At the core of this effort is Simurgh, an AI-powered XCT reconstruction framework jointly advanced by ORNL and ZEISS that integrates computer-aided design (CAD) models, physics-based simulations, and deep learning to overcome the long-standing challenges of metal artifact correction, long scan durations, and limited flaw detectability in dense and geometrically complex components. Simurgh enables high-throughput, high-quality 3D reconstruction from sparse and fast scans, which reduces XCT acquisition times by more than an order of magnitude and simultaneously improves defect detection limits by up to fourfold compared with industry-standard approaches. This capability reduces scan costs by more than 50%, lowers labor overhead, and makes XCT characterization economically viable for routine industrial use. By enabling reliable flaw detection in minutes rather than hours, Simurgh facilitates real-time feedback loops for process parameter optimization, which was highlighted in a recent npj Computational Materials (a Nature journal) issue. In the published study, more than 100 alloy coupons were characterized within a single day. This work represents a tenfold acceleration in the development of novel AM alloys and processes compared with conventional workflows. The ZEISS collaboration has also demonstrated the scalability of Simurgh to diverse application domains, including aerospace, nuclear, automotive, and biomedical components; in these applications, ensuring structural integrity is paramount. By drastically reducing barriers to XCT adoption, this partnership has laid the foundation for digital twins and data-driven certification pipelines and directly addressed bottlenecks in qualifying new materials and designs. Together, ORNL and ZEISS have shown that Simurgh advances the state of the art in nondestructive evaluation and aligns with the broader mission of enabling Industry 4.0 manufacturing ecosystems, in which intelligent, cost-effective, rapid quality assurance is integral to accelerating innovation and ensuring safety in critical applications.

36 MATERIALS SCIENCE↗