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At least 289 records · Page 16

Mathematical Analysis of Space Radiator Segmenting for Increased Reliability and Reduced Mass

Spacecraft for long duration deep space missions will need to be designed to survive micrometeoroid bombardment of their surfaces some of which may actually be punctured. To avoid loss of the entire mission the damage due to such punctures must be limited to small, localized areas. This is especially true for power system radiators, which necessarily feature large surface areas to reject heat at relatively low temperature to the space environment by thermal radiation. It may be intuitively obvious that if a space radiator is composed of a large number of independently operating segments, such as heat pipes, a random micrometeoroid puncture will result only in the loss of the punctured segment, and not the entire radiator. Due to the redundancy achieved by independently operating segments, the wall thickness and consequently the weight of such segments can be drastically reduced. Probability theory is used to estimate the magnitude of such weight reductions as the number of segments is increased. An analysis of relevant parameter values required for minimum mass segmented radiators is also included.

Juhasz, Albert J.↗

Uncertainty-aware Continuous Implicit Neural Representations for Remote Sensing Object Counting

Many existing object counting methods rely on density map estimation (DME) of the discrete grid representation by decoding extracted image semantic features from designed convolutional neural networks (CNNs). Relying on discrete density maps not only leads to information loss dependent on the original image resolution, but also has a scalability issue when analyzing high-resolution images with cubically increasing memory complexity. Furthermore, none of the existing methods can offer reliable uncertainty quantification (UQ) for the derived count estimates. To overcome these limitations, we design UNcertainty-aware, hypernetwork-based Implicit neural representations for Counting (UNIC) to assign probabilities and the corresponding counting confidence over continuous spatial coordinates. We derive a sampling-based Bayesian counting loss function and develop the corresponding model training algorithm. UNIC outperforms existing methods on the Remote Sensing Object Counting (RSOC) dataset with reliable UQ and improved interpretability of the derived count estimates. Our code is available at https://github.com/SiyuanXu-tamu/UNIC.

97 MATHEMATICS AND COMPUTING↗

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), walk moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

97 MATHEMATICS AND COMPUTING↗

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Saatchi, Sasan S.↗

Possible effects of protracted exposure on the additivity of risks from space radiations

Conventional radiation risk assessments are presently based on the additivity assumption. This assumption states that risks from individual components of a complex radiation field involving many different types of radiation can be added to yield the total risk of the complex radiation field. If the assumption is not correct, the summations and integrations performed to obtain the presently quoted risk estimates are not appropriate. This problem is particularly important in the area of space radiation risk evaluation because of the many different types of high- and low-LET radiation present in the galactic cosmic ray environment. For both low- and high-LET radiations at low enough dose rates, the present convention is that the addivity assumption holds. Mathematically, the total risk, Rtot is assumed to be Rtot = summation (i) Ri where the summation runs over the different types of radiation present. If the total dose (or fluence) from each component is such that the interaction between biological lesions caused by separate single track traversals is negligible within a given cell, it is presently considered to be reasonable to accept the additivity assumption. However, when the exposure is protracted over many cell doubling times (as will be the case for extended missions to the moon or Mars), the possibility exists that radiation effects that depend on multiple cellular events over a long time period, such as is probably the case in radiation-induced carcinogenesis, may not be additive in the above sense and the exposure interval may have to be included in the evaluation procedure. It is shown, however, that "inverse" dose-rate effects are not expected from intermediate LET radiations arising from the galactic cosmic ray environment due to the "sensitive-window-in-the-cell-cycle" hypothesis.

NASA Discipline Number 45-10↗

Performance and Reliability of Solid Tantalum Capacitors at Cryogenic Conditions

Performance of different types of solid tantalum capacitors was evaluated at room and low temperatures, down to 15 K. The effect of temperature on frequency dependencies of capacitance, effective series resistances (ESR), leakage currents, and breakdown voltages has been investigated and analyzed. To assess thermo-mechanical robustness of the parts, several groups of loose capacitors and those soldered on FR4 boards were subjected to multiple (up to 500) temperature cycles between room temperature and 77 K. Experiments and mathematical modeling have shown that degradation in tantalum capacitors at low temperatures is mostly due to increasing resistance of the manganese cathode layer, resulting in substantial decrease of the roll-off frequency. Absorption currents follow a power law, I approximately t(sup -m), with the exponent m varying from 0.8 to 1.1. These currents do not change significantly at cryogenic conditions and the value of the exponent remains the same down to 15 K. Variations of leakage currents with voltage can be described by Pool-Frenkel and Schottky mechanisms of conductivity, with the Schottky mechanism prevailing at cryogenic conditions. Breakdown voltages of tantalum capacitors increase and the probability of scintillations decreases at cryogenic temperatures. However, breakdown voltages measured during surge current testing decrease at liquid nitrogen (LN) compared to room-temperature conditions. Results of temperature cycling suggest that tantalum capacitors are capable of withstanding multiple exposures to cryogenic conditions, but the probability of failures varies for different part types.

Teverovsky, Alexander↗

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗

Growth of Hexagonal Boron Nitride from Molten Nickel Solutions: A Reactive Molecular Dynamics Study

Metal flux methods are excellent for synthesizing high-quality hexagonal boron nitride (hBN) crystals, but the atomic mechanisms of hBN nucleation and growth in these systems are poorly understood and difficult to probe experimentally. Here, we harness classical reactive molecular dynamics (ReaxFF) to unravel the mechanisms of hBN synthesis from liquid nickel solvent over time scales up to 30 ns. These simulations mimic experimental conditions by including relatively large liquid nickel slabs containing dissolved boron and a molecular nitrogen gas phase. Overall, the reaction takes place almost exclusively on the surface of the liquid nickel, owing to the low solubility of nitrogen in bulk nickel and the intermediate species’ preference for the metal–gas interface. The formation of hBN invariably begins by reaction of dinitrogen with nickel-solvated boron atoms at the surface, forming intermediate N–N–B species, which typically evolve into B–N–B units through a short-lived intermediate where a single nitrogen atom is coordinated by one nitrogen and two boron atoms. The resulting B–N–B units, in turn, coalesce with growing hBN nuclei and carry nitrogen between hBN nanocrystals in an Ostwald ripening process. The amount of hBN produced on the tens of nanosecond time scale depends critically on the boron concentration, while having a much weaker dependence on the N 2 pressure for the regime considered (N 2 pressures of 2.5–10 MPa, Ni–B solutions with 6–12% boron by atom fraction). The highest rate of hBN formation occurs at the lowest temperature considered (1750 K, just above the melting point of nickel), while no hBN sheets are formed at 2000 K or above. An analysis of the transition pathways for nitrogen atoms shows that the final step, incorporation of small B–N motifs into larger hBN sheets, is the rate-limiting step in the regimes considered. While raising the temperature from 1750 to 2000 K has little effect on the formation of intermediates (N–N–B, B–N–B, etc.), the lack of large hBN sheets at temperatures >1900 K is explained by decreased probability of the final step and increased probability of breakup of hBN into B–N motifs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Management of SSME hardware life utilization

Statistical and probabilistic reliability methodologies were developed for the determination of hardware life limits for the Space Shuttle Main Engine (SSME). Both methodologies require that a mathematical reliability model of the engine (system) performance be developed as a function of the reliabilities of the components and parts. The system reliability model should be developed from the Failute Modes and Effects Analysis/Critical Items List. The statistical reliability methodology establishes hardware life limits directly from the failure distributions of the components and parts obtained from statistically-designed testing. The probabilistic reliability methodology establishes hardware life limits from a decision analysis methodology which incorporates the component/part reliabilities obtained from a probabilistic structural analysis, a calibrated maintenance program, inspection techniques, and fabrication procedures. Probilistic structural analysis is recommended as a tool to prioritize upgrading of the components and parts. The Weibull probability distribution is presently being investigated by NASA/MSFC to characterize the failure distribution of the SSME hardware from a limited data base of failures.

Pauschke, J. M.↗

Collision-induced squeezing in a harmonic oscillator

The concept of squeezing has so far been applied mainly to light, as is evidenced by the number of research works on the subject of squeezed light. Since, in quantum mechanics, both light and the simple harmonic oscillator are described within the same mathematical framework, there is of course no difficulty in applying the concept to the simple harmonic oscillator as well. In fact, the theoretical development of squeezed states and squeezed light owes much to the physical insights that one obtains as the analogy between light and the harmonic oscillator is exploited. The example presented shows clearly that two states with different phases in general have different degrees of squeezing, even if they have the same state distribution. This means that, even if one considers collision processes that produce the same state distribution, the degree of squeezing obtained during and after the collisions can be quite different, depending on how the phases phi(sub n) of the probability amplitudes develop in time as the collisions proceed. It is therefore evident that, for a detailed study of collision-induced squeezing, further study on the time development of the phases in collisions and its relation to collision parameters such as potential energy surfaces and collision energy is needed.

Lee, Hai-Woong↗

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

Crystallization of amorphous water ice in the solar system

Electron diffraction studies of vapor-deposited water ice have characterized the dynamical structural changes during crystallization that affect volatile retention in cometary materials. Crystallization is found to occur by nucleation of small domains, while leaving a significant part of the amorphous material in a slightly more relaxed amorphous state that coexists metastably with cubic crystalline ice. The onset of the amorphous relaxation is prior to crystallization and coincides with the glass transition. Above the glass transition temperature, the crystallization kinetics are consistent with the amorphous solid becoming a "strong" viscous liquid. The amorphous component can effectively retain volatiles during crystallization if the volatile concentration is approximately 10% or less. For higher initial impurity concentrations, a significant amount of impurities is released during crystallization, probably because the impurities are trapped on the surfaces of micropores. A model for crystallization over long timescales is described that can be applied to a wide range of impure water ices under typical astrophysical conditions if the fragility factor D, which describes the viscosity behavior, can be estimated.

NASA Center ARC↗

Certification of ICI 1012 optical data storage tape

ICI has developed a unique and novel method of certifying a Terabyte optical tape. The tape quality is guaranteed as a statistical upper limit on the probability of uncorrectable errors. This is called the Corrected Byte Error Rate or CBER. We developed this probabilistic method because of two reasons why error rate cannot be measured directly. Firstly, written data is indelible, so one cannot employ write/read tests such as used for magnetic tape. Secondly, the anticipated error rates need impractically large samples to measure accurately. For example, a rate of 1E-12 implies only one byte in error per tape. The archivability of ICI 1012 Data Storage Tape in general is well characterized and understood. Nevertheless, customers expect performance guarantees to be supported by test results on individual tapes. In particular, they need assurance that data is retrievable after decades in archive. This paper describes the mathematical basis, measurement apparatus and applicability of the certification method.

Howell, J. M.↗

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Hard and Soft Constraints in Reliability-Based Design Optimization

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

Crespo, L.uis G.↗

Natural Hazard Forecast Alert Grid Risk System

Weather events cause most power outages. Often, we even get notifications on our phones to take cover or be prepared for an imminent event. If electric grid utilities had a similar warning that also included probable scenarios and the equipment involved, they could prepare and minimize the effects. Idaho National Laboratory had a project with the U.S. Department of Energy’s Cybersecurity, Energy Security, and Emergency Response program to develop a grid alert application that receives messages from the existing emergency alert system, filters and determines components possibly affected by the emergency event, calculates probable scenarios using MASTERRI (Modeling And Simulation for Targeted Reliability and Resilience Improvement). For high-risk events, the application can then send alert links to subscribed electric distribution utility operations staff to allow them to see and evaluate the scenarios and the impact in a web based interactive map tool. This proof of concept application used data from utilities and organizations, such as the international regulatory body North American Electric Reliability Corporation, which have complied historical failure data of elements that comprise the U.S. electric grid. Nominal failure rates are obtained from this data. To make this tool possible, estimated failure rates were calculated for different component types given the alert type, severity, and location. Historic weather-related grid element failures were correlated with historic weather events from the Integrated Public Alert & Warning System. These correlated events and failures are used along with Bayesian updates from the historical norms to provide a modified failure rate for grid elements in the alert areas and calculate probable scenarios. Working with an industry collaborator, actual grid models and data were used for demonstration cases. This report outlines the work performed for this project.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DNA Repair Domain Modeling Can Predict Cell Death and Mutation Frequency for Wide Range Spectrum of Radiation

Exploration missions to Mars and other destinations raise many questions about the health of astronauts. The continuous exposure of astronauts to galactic cosmic rays is one of the main concerns for long-term missions. Cosmic ionizing radiations are composed of different ions of various charges and energies notably, highly charged energy (HZE) particles. The HZE particles have been shown to be more carcinogenic than low-LET radiation, suggesting the severity of chromosomal aberrations induced by HZE particles is one possible explanation. However, most mathematical models predicting cell death and mutation frequency are based on directly fitting various HZE dose response and are in essence empirical approaches. In this work, we assume a simple biological mechanism to model DNA repair and use it to simultaneously explain the low- and high-LET response using the exact same fitting parameters. Our work shows that the geometrical position of DNA repair along tracks of heavy ions are sufficient to explain why high-LET particles can induce more death and mutations. Our model is based on assuming DNA double strand breaks (DSBs) are repaired within repair domain, and that any DSBs located within the same repair domain cluster into one repair unit, facilitating chromosomal rearrangements and increasing the probability of cell death. We introduced this model in 2014 using simplified microdosimetry profiles to predict cell death. In this work, we collaborated with NASA Johnson Space Center to generate more accurate microdosimetry profiles derived by Monte Carlo techniques, taking into account track structure of HZE particles and simulating DSBs in realistic cell geometry. We simulated 224 data points (D, A, Z, E) with the BDSTRACKS model, leading to a large coverage of LET from ~10 to 2,400 keV/μm. This model was used to generate theoretical RBE for various particles and energies for both cell death and mutation frequencies. The RBE LET dependence is in agreement with experimental data known in human and murine cells. It suggests that cell shape and its orientation with respect to the HZE particle beam can modify the biological response to radiation. Such discovery will be tested experimentally and, if proven accurate, will be another strong supporting evidence for DNA repair domains and their critical role in interpreting cosmic radiation sensitivity.

Viger, Louise↗

Correlation Between Weather Alerts and Grid Component Failures for Grid Alert

Weather events cause most grid failures. Often, we even get notifications on our phones to take cover or be prepared for an imminent event. If electric grid utilities had a similar warning that also included probable scenarios and the equipment involved, they could prepare and minimize the effects. Recent research at Idaho National Laboratory into electric grid risk analysis methods resulted in a tool that allows for the development of the most likely scenarios given failure probabilities of grid components. INL has a project with the U.S. Department of Energy’s Cybersecurity, Energy Security, and Emergency Response (CESER) program to develop a Grid Alert application that receives messages from the existing emergency alert system, filters and determines components possibly affected by the emergency event, calculates probable scenarios uses MASTERRI and then notifies the utility if there is significant risk. Historical failure data of elements that comprise the U.S. electric grid have been compiled by utilities and organizations such as the international regulatory body North American Electric Reliability Corporation (NERC). Nominal failure rates are obtained from this data. To make this tool possible, estimated failure rates are needed for different component types given the alert type, severity, and location. Historic weather-related grid element failures are correlated with historic weather events from Integrated Public Alert & Warning System (IPAWS). These correlated events and failures are used along with Bayesian updates from the historical norms to provide a modified failure rate for grid elements in the alert areas and calculate probable scenarios. This discusses the Grid Alert project plan but focuses on the data gathered and process used in determining failure rates for possible grid failure scenarios.

24 - POWER TRANSMISSION AND DISTRIBUTION↗