Geometrical model of calculation of planet reflected solar thermal fluxes
Geometrical model for calculation of planet reflected solar thermal fluxes
MATHEMATICAL MODEL↗
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Results for “geometric models”
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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Effects of model geometric accuracy on comparison of wind-tunnel and flight pressure measurements on a launch vehicle
Wind tunnel and flight pressure measurements compared for Ram B Launch Vehicle
FLIGHT TEST VEHICLE↗
Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper II: Local Geometry and Metric Structure
This paper develops the geometric sector of the replication-driven cosmogenesis framework introduced in Paper I. Starting from a pre-geometric spectral substrate and a minimal set of replication axioms, we show how coherent self-replicating units generate a spatial adjacency graph whose continuum limit acquires an effective Riemannian structure. The replication dynamics determines a characteristic correlation length that seeds the local metric, while overlap relations among coherent units produce an isotropic neighborhood geometry with an emergent dimensionality $d_{\rm eff}\simeq 3$ across a broad range of replication factors. As replication slows and causal order stabilizes, a limiting signal speed $c_\ast$ appears, providing the basis for the Lorentzian structure of spacetime without assuming a pre-existing light cone. We derive conditions under which the adjacency graph converges to a smooth three-dimensional manifold, describe the transition from Euclidean to Lorentzian propagation, and identify geometric invariants controlled by the replication parameters. This work establishes the geometric and causal layer of the replication cosmogenesis program, bridging the spectral axioms of Paper I to the cosmological dynamics explored in Paper III.
79 ASTRONOMY AND ASTROPHYSICS↗
AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper I: Foundations and Replication Dynamics
We develop a pre-geometric cosmological framework in which existence is identified with a finite amount of unstructured energy possessing vibration as its only intrinsic property. This vibrational substrate occupies an open, bounded spectral interval $(\omega_{\min},\omega_{\max})$, ensuring finiteness of total energy and excluding infinitely stable configurations. The substrate evolves under two fundamental and competing tendencies---excitation, which amplifies coherence, and randomization, which scrambles it. Their balance produces a metastable unstructured regime in which rare fluctuations may form long-lived self-consistent spectral configurations. Because the substrate is finite and subject to competing order--disorder dynamics, no coherent configuration can be perpetually stable. We show that the only mechanism capable of sustaining long-lived organization is a replication instability: a coherent unit may reproduce into multiple offspring according to a general $1\!\to n$ rule. Replication consumes energy from the finite substrate, breaks the metastable symmetry, and induces a discrete notion of event time through the replication tick $\Delta\tau$. Temporal succession is defined through correlation ordering of spectral microstates, producing an intrinsic pre-causal structure. The compactness of the spectral domain imposes minimal and maximal timescales, bounds the internal coherence of emergent units, and limits their proliferation. These spectral constraints serve as precursors for the emergence of geometry, adjacency, and a limiting propagation speed, developed in subsequent papers of this series. Paper I provides the foundational axioms (PG1--PG9) governing the spectral substrate, its metastable dynamics, the formation of coherent units, and the necessity of replication, establishing a fully pre-geometric stage from which causal and geometric structure naturally emerge.
79 ASTRONOMY AND ASTROPHYSICS↗
AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper III: Cosmological Structure and Predictions
This paper develops the cosmological consequences of the replication-driven cosmogenesis framework introduced in Paper I and the emergent geometric structure established in Paper II. After the replication epoch freezes out, the coherent sector occupies a finite spectral band and contains a population of excited states. The relaxation of these excited coherent configurations does not produce coherent radiation; instead, all released energy flows into the incoherent substrate, where the randomizer acts as a rapid phase-scrambling mechanism. This process generates an effectively thermal radiation bath, providing a natural reheating mechanism that requires neither inflaton oscillations nor scalar-field potentials, and can be contrasted with standard scenarios of nonperturbative reheating dynamics. Subsequent symmetry-breaking transitions in the coherent vacuum inject additional radiation, yielding a multi-stage thermal history with well-defined energy transfers. We derive the effective equations of state for each component—the cosmological vacuum, the coherent vacuum, and the radiation bath—and show how their interplay produces an FRW-like expansion. The discrete sequence of coherent-state relaxations imprints a distinctive multi-peaked stochastic gravitational-wave background, whose spectral structure reflects the underlying hierarchy of coherent frequencies. Potential observational signatures in the LISA and mid-band frequency ranges are highlighted, providing concrete avenues to test this replication-based cosmological framework in the context of standard cosmological gravitational-wave backgrounds and LISA-oriented forecasts.
79 ASTRONOMY AND ASTROPHYSICS↗
Geometric optics model of Thomson scattering enhanced by parametric coupling
We formulate a theory of Thomson scattering (TS) from inhomogeneous plasmas using a ray-tracing approach. The scattered radiation is described within the eikonal approximation, including convective gain arising from scattering instabilities driven by the TS probe laser. In the limit of a weak probe and vanishing gain, the theory recovers the standard TS cross section and scattered power due to volumetric particle noise. The ray-tracing formalism is implemented in a TS fitting framework, enabling accurate analysis of inhomogeneous plasmas whose background profiles can be provided by large-scale hydrodynamic simulations or experimental diagnostics. Here, several examples of synthetic TS spectra are presented, and further extensions of the theory are discussed.
Carleton, D. E. [University of Alberta, Edmonton, ↗
Operational resilience of additively manufactured parts to stealthy cyberphysical attacks using geometric and process digital twins
Cyberphysical attacks on the digital backbone of Additive Manufacturing (AM) can compromise the printed part’s functionality. They can alter features in the digital geometry to introduce geometric defects (e.g., missing fillets) or alter process parameters to create local defects (e.g., voids). Addressing the downtime, waste, and quality deterioration associated with existing solutions requires operational resilience, i.e., rapid elimination or disruption of defect formation (to retain part function) without production stoppage or part disposal (to retain yield). This need is unmet due to the inherently unpredictable nature of attack-induced alterations, lack of access to the original geometric model for identification of altered geometric features, and in-process imposition of unknown process dynamics via attack-driven alteration of real-time-uncontrolled (or exogenous) parameters. This work establishes the above-mentioned operational resilience for the first time by creating two Digital Twins (DT). The Geometric DT (Geo-DT) is based on a unique physical-field-driven soft sensor and topology optimization method. The Process Digital Twin (Pro-DT) combines local defect quantification with a novel Reinforcement Learning formulation and training method. The importance of these methodological advances and the scalability of our approach are examined on a real AM testbed. It is shown that Geo-DT can correct geometric defects without access to the original digital geometry or explicit knowledge of attack-altered geometric features. Further, Pro-DT can accelerate real-time disruption of local defects despite attack-driven imposition of unknown process dynamics. We discuss how our framework goes beyond the contemporary focus on pre-attack security and in-attack detection towards resilience for AM and beyond.
Additive Manufacturing↗
<general dynamics of physical-chemical systems in mammals< fourth quarterly progress report, may 21 - aug. 20, 1965
Work is continuing on the mathematical modelling of the hydrodynamics of the arterial system. Discussion with Dr. McDonald has raised some questions relative to the geometric model of the arterial system. This area is considered important to provide a suitable base for consideration of the actual events taking place in the arteries. Attempts are being made to develop a model which will describe the geometry in terms of diameters against length, changes in cross-sectional area with division, and number of levels of arteries according to diameter. This work will be described in some detail in a technical report which is being prepared and will be submitted during the next quarter.
ARTERY↗
Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system
The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.
36 MATERIALS SCIENCE↗
Gateway Element and Payload Materials Outgassing Analyses: HALO, HERMES, and ERSA
Gateway was intended to be humanity’s first space station around the Moon, but its development has been paused as the National Aeronautics and Space Administration (NASA) shifts focus to achieving the United States’ National Space Policy goals. Instead of an orbiting lunar outpost, NASA will now pursue the development of a lunar surface base to support a sustained human presence on the Moon. Before the program’s pause, Gateway’s Induced Environments team worked to ensure payloads and elements (i.e., modules) complied with induced environment requirements. Methods developed and insights gained from this work will have applicability to NASA’s Moon Base and the potential repurposing of Gateway elements and payloads, as well as to induced environments modeling for future space stations. The Gateway program’s induced environment included molecular contamination, electric thruster plume sputter and redeposition, and lunar dust transfer from the Human Landing System (HLS). Primary sources of external molecular contamination included materials outgassing, chemical thruster plume contamination, and vacuum venting. The focus of this paper will be on element- and payload-level materials outgassing analyses performed for Gateway Configuration 1, extending the previously-developed framework for Gateway system-level external molecular contamination modeling. Gateway Configuration 1 consisted of the Power and Propulsion Element (PPE) and the Habitation and Logistics Outpost (HALO). It also included payloads like the European Radiation Sensor Array (ERSA) attached to PPE and the Heliophysics Environmental and Radiation Measurement Experiment Suite (HERMES) attached to HALO. The element- and payload-level analyses to be introduced in this paper for HALO, HERMES, and ERSA enabled high-fidelity descriptions of Gateway’s external molecular contamination environment. Approaches to geometric modeling, meshing, outgassing rate assignment, molecular transport modeling, and analysis methodology will be presented. Element and payload contaminant deposition onto sensitive Gateway receiver surfaces will be summarized and results compared to induced environment requirements. While these results incorporate refinements made over the course of the program, they were not intended to be final. Therefore, modeling assumptions and inputs, potential improvements, and lessons-learned will be documented to inform future work on Moon Base, repurposed elements and payloads, and other space stations.
Gateway↗
Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation
This Final Scientific and Technical Report summarizes work performed under the Phase IIA SBIR project “Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation” (DE-SC0020906) from August 2023 through August 2025. The objective of the Phase IIA effort was to mature and harden capabilities developed during Phase II, with the goal of enabling practical interoperability between Coreform’s isogeometric analysis (IGA) technologies and the Multiphysics Object-Oriented Simulation Environment (MOOSE), while improving robustness, performance, and scalability for complex, nuclear-relevant geometries. Over the course of Phase IIA, the project established and validated an extraction-based interoperability pathway between Coreform tools and MOOSE. A combined mesh and matrix format was defined collaboratively with MOOSE developers and integrated into the solver, enabling standard MOOSE workflows to operate on data exported from Coreform’s IGA and Flex Representation Method (FRM) pipelines. Early demonstrations validated architectural compatibility using linear solid mechanics problems, while later efforts focused on benchmark testing and external use. By the end of the project period, engineers at BWXT were able to independently set up and execute a simulation using the Coreform–MOOSE workflow and provide direct feedback that informed further refinement. In parallel, substantial effort was devoted to improving the robustness of trimmed U-spline construction for complex CAD geometries. A growing test suite of nuclear-relevant models was compiled through collaboration with multiple stakeholders and used to drive extensive bug fixing and reliability improvements. These efforts resulted in improved robustness and performance, including the addition of fallback capabilities that enhance reliability when the underlying commercial CAD kernel fails. Performance-oriented work progressed later in the project, with the development and demonstration of methods to decompose complex geometries into structured subregions and updated data representations to support more efficient solver processing. Additionally, extensive enhancements to threadsafe parallel data structures and trimming operations established a foundation for scalable processing of large assemblies. Collaboration with Sandia National Laboratories on the SGM geometric modeling kernel advanced to a functioning interface test case, positioning the workflow for future kernel integration. Overall, the Phase IIA effort successfully transitioned the project from architectural proof-of-concept to externally exercised, solver-integrated capability, while clarifying remaining technical challenges related to standardization, performance optimization, and kernel integration.
42 ENGINEERING↗
Prevention of resistive wall tearing mode major disruptions with feedback
Resistive wall tearing modes (RWTMs) can cause major disruptions. A signature of RWTMs is that the rational surface is sufficiently close to the wall to interact with it. For (m,n) = (2,1) modes, a RWTM requires normalized minor radius of the rational surface ρ q2 ≥ 0.75, which can also be expressed as q 75 ≤ 2. Major disruptions can occur when the criterion is satisfied. This is confirmed in simulations and theory and in a DIII-D locked mode disruption database. The q 75 < 2 criterion is valid at high β as well as at low β. A very important feature of RWTMs is that they can be feedback stabilized. If the ρ q2 criterion is not satisfied, or if the wall is ideally conducting, then the mode does not produce a major disruption, although it can produce a minor disruption. Feedback, or rotation of the mode at the wall by complex feedback, can emulate an ideal wall, preventing major disruptions. The ρ q2 criterion depends weakly on the wall radius. A simple geometric model of its dependence on wall radius is given.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Gamma Decay of the 154 Sm Isovector Giant Dipole Resonance: Smekal-Raman Scattering as a Novel Probe of Nuclear Ground-State Deformation
𝛾 decays of the isovector giant dipole resonance (IVGDR) of the deformed nucleus 154 Sm were measured using 2$^{+}_{1}$-Smekal-Raman and elastic scattering of linearly polarized, quasimonochromatic photon beams. The two scattering processes were disentangled through their distinct angular distributions. Their branching ratio and cross sections were determined at six excitation energies covering the 154 Sm IVGDR. Both agree with the predictions of the geometrical model for the IVGDR and confirm 𝛾 decay as an observable sensitive to the structure of the resonance. Consequently, the data place strong constraints on the nuclear shape, including the degree of triaxiality. The derived 154 Sm shape parameters 𝛽 = 0.2925(25) and 𝛾 = 5.0(15)° agree well with other measurements and recent Monte Carlo shell-model calculations.
150 ≤ A ≤ 189↗
Optimization of midcourse velocity corrections
Optimum time to apply single midcourse velocity correction and optimum schedule for corrections in variable time-of-arrival guidance - geometrical model
MATHEMATICAL MODEL↗
Crater effects on full moon directionality of lunar thermal radiation
Local lunar crater density calculated from geometrical model of crater effects on full moon directionality of lunar thermal radiation
Doty, J. P.↗
High-Order Methods in NASA’s Next Generation of Computational Fluid Dynamics Tools
The missions of the National Aeronautics and Space Administration (NASA) routinely produce unique requirements and challenges for development and application of Computational Fluid Dynamics (CFD) methods. NASA presently embodies four distinct Mission Directorates: Aeronautics Research, Exploration Systems, Science, and Space Operations. These missions generate requirements for systems that operate in a wide variety of environments. They range from the high-speed flight of aerodynamically optimized vehicles operating in the earth’s atmosphere to spacecraft designed for missions that don’t favor aerodynamic optimization, some operating in the atmosphere of planets and planetary moons such as Mars and Venus or Saturn’s moon Titan. Systems supporting these vehicles, such as rocket and jet propulsion, reaction control systems, fluid and thermal transfer systems, etc. can also generate their own unique set of flow phenomena that challenge today’s CFD methodology. Through the NASA Engineering and Safety Center (NESC), NASA annually conducts state-of-the-discipline assessments in fifteen distinct engineering disciplines. These assessments are performed by the NASA Technical Fellows that lead Technical Discipline Teams (TDT) of recognized experts in these fifteen areas. In the Aerosciences discipline, three topics have been identified as the top challenges for the discipline: aero-plume interaction prediction, unsteady separated flows, and aerothermodynamic prediction. These challenge areas are defined by the Agency’s high-risk projects and problems on which the NESC is requested to perform independent testing, analysis, and assessments. When viewed as a whole, these tests, analyses, and assessments provide a clear view of the recurring technical challenges facing Agency engineers and researchers and can be used to guide future research and technology development. The present state-of-the-art in the application of CFD at NASA is the use of Reynolds-Averaged Navier- Stokes (RANS) solvers, primarily executed in a steady-state mode of operation. In isolated cases, Unsteady RANS (URANS) solvers have been employed when steady RANS solutions produce poorly converging or oscillating results or in cases, such as aeroelastic analysis, which require unsteady aerodynamic simulation. For most traditional external and internal aerodynamic flows, structured overset grids or unstructured grids are employed to minimize geometric modeling and grid generation times. Grid adaptation, primarily as a series of coarse-grain intermediate processing steps is also seeing use on particularly complex flow problems and configurations. In the case of aerothermodynamic flows, engineers have been forced to continue to employ structured grid techniques as the present unstructured grid methodology has proven inadequate in the prediction of surface heating. In the area of aero-plume interaction modeling, two-gas, frozen chemistry simulation is generally the state-of-the- art, with some production solvers capable of predicting flows with only a single gas component. Prediction of flows falling into the afore-mentioned top Aerosciences technical challenges have severely stressed the present state-of-the-art in CFD prediction and for some problems, such as unsteady separated flows and aero-plume interaction cases, engineers have begun employing Large Eddy Simulation (LES) and Hybrid RANS/LES techniques. In some isolated aero-propulsion interaction cases, chemically reacting flow simulations have been applied. These methods are highly evolutionary and engineers have little experience in their application, so they cannot be heavily relied upon in today’s application environment. Therefore, this leads one to muse over which numerical technologies will be included in the CFD tools that will be employed 30 years in the future. This presentation will describe specific technical problems that have stressed NASA’s traditional CFD methods to their breaking point and will link these issues to the Agency’s top Aerosciences technical challenges. The discussion will then shift to the characteristics of future CFD solvers that will be required to attack these challenges and how these characteristics differ from the present state-of-the- art. High-order methods certainly appear to have a place in the development of future CFD tools and some of the physical characteristics of our most challenging problems suggest that high-order methods are the only way to effectively solve them. But there are some relatively severe implementation issues that face these methods, particularly in the area of general applicability and robust operation as an engineering tool. Desired characteristics of next-generation CFD solvers will be discussed and the author’s view of which emerging numerical technologies might be employed to address these attributes will also be presented
David M Schuster↗
Quantum quench dynamics of geometrically frustrated Ising models
Not provided.
Science & Technology - Other Topics↗