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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Ejecta from large craters on the moon - Comments on the geometric model of McGetchin et al
Amendments to a quantitative scheme developed by T. R. McGetchin et al. (1973) for predicting the distribution of ejecta from lunar basins yield substantially thicker estimates of ejecta, deposited at the basin rim-crest and at varying ranges beyond, than does the original model. Estimates of the total volume of material ejected from a basin, illustrated by Imbrium, also are much greater. Because many uncertainties affect any geometric model developed primarily from terrestrial analogs of lunar craters, predictions of ejecta thickness and volume on the moon may range within at least an order of magnitude. These problems are exemplified by the variability of T, thickness of ejecta at the rim-crest of terrestrial experimental craters. The proportion of T to crater rim-height depends critically upon scaled depth-of-burst and whether the explosive is nuclear or chemical.
Pike, R. J.↗
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↗
Absolute spatial registration of Skylab S192 conical scanner imagery by means of dynamic geometrical modeling
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Malhotra, R. C.↗
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↗
Common radiation analysis model for 75,000 pound thrust NERVA engine (1137400E)
The mathematical model and sources of radiation used for the radiation analysis and shielding activities in support of the design of the 1137400E version of the 75,000 lbs thrust NERVA engine are presented. The nuclear subsystem (NSS) and non-nuclear components are discussed. The geometrical model for the NSS is two dimensional as required for the DOT discrete ordinates computer code or for an azimuthally symetrical three dimensional Point Kernel or Monte Carlo code. The geometrical model for the non-nuclear components is three dimensional in the FASTER geometry format. This geometry routine is inherent in the ANSC versions of the QAD and GGG Point Kernal programs and the COHORT Monte Carlo program. Data are included pertaining to a pressure vessel surface radiation source data tape which has been used as the basis for starting ANSC analyses with the DASH code to bridge into the COHORT Monte Carlo code using the WANL supplied DOT angular flux leakage data. In addition to the model descriptions and sources of radiation, the methods of analyses are briefly described.
Warman, E. A.↗
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↗
The Computerized Anatomical Man (CAM) model
A computerized anatomical man (CAM) model, representing the most detailed and anatomically correct geometrical model of the human body yet prepared, has been developed for use in analyzing radiation dose distribution in man. This model of a 50-percentile standing USAF man comprises some 1100 unique geometric surfaces and some 2450 solid regions. Internal body geometry such as organs, voids, bones, and bone marrow are explicitly modeled. A computer program called CAMERA has also been developed for performing analyses with the model. Such analyses include tracing rays through the CAM geometry, placing results on magnetic tape in various forms, collapsing areal density data from ray tracing information to areal density distributions, preparing cross section views, etc. Numerous computer drawn cross sections through the CAM model are presented.
Billings, M. P.↗
Computerized anatomical model man for analyses of radiation doses
Computerized human body anatomical geometrical model with life size skeleton and organs scaling for radiation dosage analyses in space missions
Kase, P. G.↗
An analysis of the light curve of Pluto.
The light curve of Pluto is analyzed in terms of a geometrical model consisting of bright and dark areas which are assumed to exhibit either a diffuse or a geometrical type of reflectivity. A Fourier analysis method is used to invert the observed light curve to obtain the longitudinal distribution of bright and dark areas for any combination of albedos selected for the two types of terrain. The analysis indicates that the light curve of Pluto can be readily understood in terms of a surface consisting of bright and dark areas. However, on the basis of the presently available photometric data, the existence or absence of limb-darkened material cannot be established.
Lacis, A. A.↗
<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↗
Assessment of jets as acoustic shields by comparison of single- and multitube suppressor nozzle data
Recent 1/4 scale and engine size nozzle acoustic data, for both 37-tube and single nozzles, were used to test the jet-shielding principle. At low jet velocities the multitube nozzle total sound power approaches the equivalent of 37 single tubes (no shielding), while near-sonic and above, the small equivalent number of single tubes compares well with a geometric model of lateral radiation from only about a third of the circumference of the outer jets (nearly complete shielding). At high jet velocities, the geometric shielding hypothesis is in excellent agreement with acoustic data from which the downstream coalesced jet noise is excluded. Present results are compared with an existing correlation for single jets, and with previous publications on multijet shielding.
Gray, V. H.↗
Assessment of jets as acoustic shields by comparison of single- and multitube suppressor nozzle data
Recent 1/4 scale and engine size nozzle acoustic data, for both 37-tube and single nozzles, are used to test the jet-shielding principle. At low jet velocities the multitube nozzle total sound power approaches the equivalent of 37 single tubes (no shielding), while near-sonic and above, the small equivalent number of single tubes compares well with a geometric model of lateral radiation from only about a third of the circumference of the outer jets (nearly complete shielding). At high jet velocities, the geometric shielding hypothesis is in excellent agreement with acoustic data from which the downstream coalesced jet-noise is excluded. Present results are compared with an existing correlation for single jets, and with previous publications on multijet shielding.
Gray, V. H.↗
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↗