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At least 1,621 records · Page 90

Computer program for calculation of real gas turbulent boundary layers with variable edge entropy

A user's manual for a computer program which calculates real gas turbulent boundary layers with variable edge entropy on a blunt cone or flat plate at zero angle of attack is presented. An integral method is used. The method includes the effect of real gas in thermodynamic equilibrium and variable edge entropy. A modified Crocco enthalpy velocity relationship is used for the enthalpy profiles and an empirical correlation of the N-power law profile is used for the velocity profile. The skin-friction-coefficient expressions of Spalding and Chi and Van Driest are used in the solution of the momentum equation and in the heat-transfer predictions that use several modified forms of Reynolds analogy.

Boney, L. R.↗

Airfoil Theory at Supersonic Speed

A theory is developed for the airfoil of finite span at supersonic speed analogous to the Prandtl airfoil theory of 1918-1919 for incompressible flow. In addition to the profile and induced drags, account must be taken at supersonic flow of still another drag, namely, the wave drag, which is independent of the wing aspect ratio. Both wave and induced drags are proportional to the square of the lift and depend on the Mach number, that is, the ratio of flight to sound speed. In general, in the case of supersonic flow, the drag-lift ratio is considerably less favorable than is the case for incompressible flow. Among others the following examples are considered: 1) lifting line with constant lift distribution (horseshoe vortex); 2) computation of wave and induced drag and the twist of a trapezoidal wing of constant lift density; 3) computation of the lift distribution and drag of an untwisted rectangular wing.

Schlichting, H↗

Jet Aeroacoustics: Noise Generation Mechanism and Prediction

This report covers the third year research effort of the project. The research work focussed on the fine scale mixing noise of both subsonic and supersonic jets and the effects of nozzle geometry and tabs on subsonic jet noise. In publication 1, a new semi-empirical theory of jet mixing noise from fine scale turbulence is developed. By an analogy to gas kinetic theory, it is shown that the source of noise is related to the time fluctuations of the turbulence kinetic theory. On starting with the Reynolds Averaged Navier-Stokes equations, a formula for the radiated noise is derived. An empirical model of the space-time correlation function of the turbulence kinetic energy is adopted. The form of the model is in good agreement with the space-time two-point velocity correlation function measured by Davies and coworkers. The parameters of the correlation are related to the parameters of the k-epsilon turbulence model. Thus the theory is self-contained. Extensive comparisons between the computed noise spectrum of the theory and experimental measured have been carried out. The parameters include jet Mach number from 0.3 to 2.0 and temperature ratio from 1.0 to 4.8. Excellent agreements are found in the spectrum shape, noise intensity and directivity. It is envisaged that the theory would supercede all semi-empirical and totally empirical jet noise prediction methods in current use.

Tam, Christopher↗

Real-time simulation of asymmetry generation in fermion-bubble collisions

Motivated by the out-of-equilibrium dynamics during an early-Universe first-order phase transition, we perform real-time simulations of fermion-bubble scattering in 1 + 1 dimensions. This nonequilibrium process can generate a charge-conjugation C asymmetry outside the bubble wall, induced by the complex fermion mass profile. The resulting C asymmetry is the 1 + 1 -dimensional analog of the C P asymmetry in 3 + 1 dimensions, a key ingredient in baryon asymmetry generation at the electroweak scale. Using tensor network methods, we track the real-time evolution of the C asymmetry in the charge density as the fermion interacts with the bubble wall, a regime inaccessible to analytic calculations. We further introduce two observables to quantify the asymmetry in the asymptotic region where reflected particles are well separated from the scattering point: one based on the net charge outside the bubble wall, and the other on the spatial displacement between the reflected particle and antiparticle wave packets. Our study represents a first step toward nonperturbative, real-time computations of C P asymmetry in 3 + 1 dimensions for electroweak baryogenesis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Experimental study of directional solidification of aqueous ammonium chloride solution

Directional solidification experiments have been carried out using the analog casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from -31.5 C to +11.9 C. The NH4Cl concentration was 26 percent in all solutions, with a liquidus temperature of 15 C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as +11.0 C. However, when the bottom temperature was raised to +11.9 C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

Chen, C. F.↗

An Optimization Approach to Support Science Decision Making for Lunar Surface Exploration

Introduction: Scientific exploration is one of the three pillars of NASA’s Moon2Mars architecture, with crew surface extra vehicular activities (EVA) serving a critical enabling function. Development of surface EVA operational planning and execution, specifically integrating science and flight control teams (FCT), is currently being explored through analog scenarios. This integration, exercised, for example, through the Joint EVA and Hu-man Surface Mobility Test Team (JETT), allows for science input on EVA activities in near real-time through a Science Evaluation Room (SER), or Arte-mis science backroom, which integrates with the broader FCT through the Science Officer. The SER works within the FCT to support dynamic EVA planning in response to changes in operational constraints as well as science opportunities and re-prioritization, increasing the mission science return and accelerating the accomplishment of the Moon2Mars science objectives. The SER works within the FCT to provide recommendations to traverse execution in near real-time. One challenge is the requirement to deliver SER inputs to the FCT on operationally relevant timelines. Failure to do so may result in suboptimal execution of science exploration EVAs or even loss of key science objectives. To close this gap, we present a network optimization tool to allow the SER to provide rapid input to the FCT in response to changes in operational constraints or science opportunities. Inputs are predicated on approved science objectives, and clear rationale must be provided to the FCT for any requested change. Accordingly, this tool incorporates the Science Traceability Matrix (STM), SER prioritization scheme, and station characterization and action planning with operational constraints such as duration, traverse speed, and distance to maximize science objectives based on SER priorities, consistent with FCT operational requirements. Method: As a proof of concept, we used an existing linear programing software package used to simulate optimal routes through cellular metabolism. We built a Demonstrative Model with three STM objectives and four stations on a region of the Moon. The objectives were given an arbitrary prioritization and mapped to the stations through four possible crew actions. (Figs. 1 and 2). This station to STM mapping is consistent with the method used by the JETT5 Science Team to develop analog surface EVA science planning. We used a grid system with the landing site at the origin and the four stations placed across the positive x,y quadrant. Actions were assigned to each station and the accomplishment of those actions resulted in a numerical “reward” based on the ability of that action to achieve science objectives. The aggregate reward from each individual STM objective contributes to a global score (Science Yield), weighted by its priority. Operational constraints included a requirement to start and end at the landing site, 5 minutes each for initial station characterization and “clean up,” and variable total EVA time, traverse rate (fixed to 0.5 meters per second in our example), and time to perform each action (10, 5, 7, and 15 min for actions 1, 2, 3, and 4, respectively). Additional constraints and variables will be added in the future (e.g., sample mass, number of stations, traverse route constraints, illumination). Optimization. We converted the connections (arcs) between these stations (nodes) into a mixed integer linear programming optimization problem (arcs = constraints, nodes = variables) with the objective to maximize Science Yield. For any action, the Science Yield is equal to the relevance of that action to an STM objective [3, 2, and 1 point(s) for High, Med., and Low relevance, respectively], multiplied by the STM Objective Priority [3, 2, and 1 point(s) for High, Med., and Low priority, respectively]. This resulted in a model that computes the optimal station and action combination to maximize the Science Yield. These weightings can be adjusted by the SER as desired. Results: We explored three test cases for the Demonstrative Model. First, we set the maximum EVA duration to 120 minutes and computed the optimal route (Fig. 3A). The model suggested per-forming Actions 1 and 2 at Station P01, followed by Actions 1 and 2 at Station P02, and finally Actions 1 and 3 at Station P04 before returning to the Landing Site. Second, we adjusted the STM Objective Priori-ty order and computed the new optimal route (Fig. 3B). Under this situation, the model suggested per-forming all Actions at Station P02 followed by all Actions at Station P03. The previous test cases were relevant to SER planning activities. Next, we explored providing mid-EVA replanning input to the FCT. Scenario: While executing the Route in Fig. 3A the crew finishes at Station P01 and FCT decides that the EVA needs to finish in 45 minutes back at the Landing Site. FCT asks SER to recommend changes to the plan to accommodate this operation-al change. Using the model and incorporating these new constraints (start at Station P01, max. time of 45 min), the model suggested performing Actions 2 and 4 at Station P03 (Fig. 4), requiring 41 minutes to complete and return to the Landing Site. Interestingly, Station 3 was not part of the original route. Using the model, we determined the EVA would need 66 minutes, instead of 45, in order for the original Station P04 to yield a larger Science Yield than Station P03. The parametrization and simulation was per-formed in less than a minute, demonstrating the operational relevance of the approach. Future Efforts: The results from the Demonstrative Model suggest this tool can accelerate SER decision making on operationally relevant timelines. Use in analog activities, such as JETT5 or follow-ons, which have over a dozen stations for a crew to explore and over a dozen actions per station, will provide needed validation of the utility of this tool for planning EVAs, replanning mid-EVA, or planning follow-on EVAs based on previous results. Further integration with FCT execution monitoring tools may provide additional efficiency gains, al-lowing rapid and iterative exploration of operation-al and science decision space by the FCT and SER.

Science Operations↗

Linear response to nonstationary random excitation.

Development of a method for computing the mean-square response of linear systems to nonstationary random excitation of the form given by y(t) = f(t) x(t), in which x(t) = a stationary process and f(t) is deterministic. The method is suitable for application to multidegree-of-freedom systems when the mean-square response at a point due to excitation applied at another point is desired. Both the stationary process, x(t), and the modulating function, f(t), may be arbitrary. The method utilizes a fundamental component of transient response dependent only on x(t) and the system, and independent of f(t) to synthesize the total response. The role played by this component is analogous to that played by the Green's function or impulse response function in the convolution integral.

Hasselman, T.↗

Simulation as a sustainable trading zone: Aiming at intergenerational justice

The paper, drawing on the example of simulation codes used in nuclear physics and high-energy physics, seeks to call attention to the ethical implications of discontinuing support for simulation codes and the loss of knowledge embodied in them. Predicated on the concept of trading zones and actor network models, the paper addresses the problem of extinction of simulation codes and attempts to understand their evolution and development within those frameworks. We show that simulation codes of closed type develop to the level of creoles, becoming local languages and standards of scientific centers and disappearing as their few main developers leave, whereas codes of open types become universal languages, imposing problemsolving patterns on the entire community and crowding out other codes. The paper suggests that because of simulations’ reliance on tacit knowledge, practices entrenched in codes cannot be exhaustively explicated or transmitted through writing alone; on the contrary, the life cycle of a simulation code is determined by the life cycle of its trading zone. We examine the extent to which both of these phenomena pose a risk to the preservation of knowledge. Bearing upon intergenerational ethics, we draw analogies between the pure intergenerational problem (PIP) and the problem of preserving the knowledge implemented in simulation codes and transmitting it to future generations. We argue that for the complete transfer of knowledge, it is necessary to develop and maintain inhabitability and sustainability of simulation trading zones in a controllable way, at least until the demand for these codes is warranted to cease in the future.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Presentation: Evaluating scaling effects of steam condensation physics-based model for small modular reactors safety

This study focused on assessing condensation heat transfer (CHT) models for enhancing the passive safety of small modular reactors (SMRs). It also encompassed a review of the theoretical and semi-theoretical CHT models and correlations. Condensation models such as the degradation factor, heat and mass transfer analogy (HMTA), and boundary layer models are used to study advanced nuclear reactor PCCS. The previous CHT models were developed for small tube geometries, which differ from the containment of SMR. This study examined the scaled relations of a physics-based CHT model for analyzing laminar and turbulent film condensation downward flow conditions inside scaled tube geometries.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Plutonium Hybrid Materials: A Platform to Explore Assembly and Metal–Ligand Bonding

In this work, we report the synthesis of five new hybrid materials containing the [PuCl 6 ] 2- anion and charge balancing, non-covalent interaction donating 4-X-pyridinium (X = H, Cl, Br, I) cations. Single crystals of the title compounds were grown and harvested from acidic, chloride-rich, aqueous media and their structures were determined via X-ray diffraction. Compounds 1-4, (4XPyH) 2 [PuCl 6 ] and 5, (4IPyH) 4 [PuCl 6 ] · 2Cl, exhibit two distinct sheet-like structure types. Structurally relevant non-covalent interactions were tabulated from crystallographic data and verified computationally using electrostatic surface potential maps and the quantum theory of atoms in molecules (QTAIM) approach. The strength of the hydrogen and halogen bonds was quantified using Kohn-Sham density functional theory and a hierarchy of acceptor-donor pairings established. In turn, the PuIV-Cl bonds were studied using the QTAIM and natural localized molecular orbital (NLMO) approaches to delineate the underlying bond mechanism and hybrid atomic orbital contributions therein. Energy decomposition (ED) and natural ED analyses were also explored to probe the bond mechanism and, more broadly, explore the efficacy of these techniques in studying these anionic systems. The results of the PuIV-Cl bond analyses were compared across composition via analogous treatments of previously reported [PuO 2 Cl 4 ] 2- and [PuCl 3 (H 2 O) 5 ] molecular units. In summary, our study indicates that the Pu-Cl bonds are predominately ionic, yet exhibit small varying degrees of covalent character that increase from [PuCl 3 (H 2 O) 5 ], [PuO 2 Cl 4 ] 2- , to [PuCl 6 ] 2- , while the participation of the Pu based s/d and f orbitals concurrently decrease and increase, respectively.

transuranic↗

Molecular structure determination: Equilibrium structure of pyrimidine (m-C 4 H 4 N 2 ) from rotational spectroscopy (reSE) and high-level ab initio calculation (re) agree within the uncertainty of experimental measurement

The pure rotational spectrum of pyrimidine (m-C 4 H 4 N 2 ), the meta-substituted dinitrogen analog of benzene, has been studied in the millimeter-wave region from 235 GHz to 360 GHz. The rotational spectrum of the ground vibrational state has been assigned and fit to yield accurate rotational and distortion constants. Over 1700 distinct transitions were identified for the normal isotopologue in its ground vibrational state and least-squares fit to a partial sextic S-reduced Hamiltonian. Transitions for all four singly substituted 13 C and 15 N isotopologues were observed at natural abundance and were likewise fit. Deuterium-enriched samples of pyrimidine were synthesized, giving access to all eleven possible deuterium-substituted isotopologues, ten of which were previously unreported. Experimental values of rotational constants and computed values of vibration–rotation interaction constants and electron-mass corrections were used to determine semi-experimental equilibrium structures (r e SE ) of pyrimidine. The r e SE structure obtained using coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] corrections shows exceptional agreement with the re structure computed at the CCSD(T)/cc-pCV5Z level (≤0.0002 Å in bond distance and ≤0.03° in bond angle). Of the various computational methods examined, CCSD(T)/cc-pCV5Z is the only method for which the computed value of each geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The exceptionally high accuracy and precision of the structure determination is a consequence of the large number of isotopologues measured, the precision and extent of the experimental frequency measurements, and the sophisticated theoretical treatment of the effects of vibration–rotation coupling and electron mass. Taken together, these demanding experimental and computational studies establish the capabilities of modern structural analysis for a prototypical monocyclic aromatic compound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytical homogenization techniques applied to the Fickian diffusion: Effective diffusivity coefficient

For multiple applications in nuclear energy, the ability to accurately represent material behavior with a simplified model is important to facilitate practical engineering-scale simulations. In this work, we focus on the homogenized thermal response of a medium containing spherical inclusions, similar to a fuel form (compact or pebble) containing TRISO particles. An extensive survey on effective thermal conductivity modeling was performed in our previous study, considering a random distribution of mono-sized spherical inclusions in a continuous matrix. Using the analogy between heat conduction and the simplified Fickian diffusion (or fission product species conservation), we can use the same analytical homogenization methods to obtain ETC as for the effective diffusivity coefficient (EDC). We performed several numerical experiments at varying conditions to assess the validity of our hypothesis for EDC calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

MAPS of Cancer

Our goal was to produce an interactive visualization from a mathematical model that successfully predicts metastases from head and neck cancer. We met this goal early in the project. The visualization is available for the public to view. Our work appears to fill a need for more information about this deadly disease. The idea of this project was to make an easily interpretable visualization based on what we call "functional maps" of disease. A functional map is a graphic summary of medical data, where distances between parts of the body are determined by the probability of disease, not by anatomical distances. Functional maps often beat little resemblance to anatomical maps, but they can be used to predict the spread of disease. The idea of modeling the spread of disease in an abstract multidimensional space is difficult for many people. Our goal was to make the important predictions easy to see. NASA must face this problem frequently: how to help laypersons and professionals see important trends in abstract, complex data. We took advantage of concepts perfected in NASA's graphics libraries. As an analogy, consider a functional map of early America. Suppose we choose travel times, rather than miles, as our measures of inter-city distances. For Abraham Lincoln, travel times would have been the more meaningful measure of separation between cities. In such a map New Orleans would be close to Memphis because of the Mississippi River. St. Louis would be close to Portland because of the Oregon Trail. Oklahoma City would be far from Little Rock because of the Cheyenne. Such a map would look puzzling to those of us who have always seen physical maps, but the functional map would be more useful in predicting the probabilities of inter-site transit. Continuing the analogy, we could predict the spread of social diseases such as gambling along the rivers and cattle rustling along the trails. We could simply print the functional map of America, but it would be more interesting to show meaningful patterns of dispersal. We had previously published the functional map of the head and neck, but it was difficult to explain to either patients or surgeons because that view of our body did not resemble anatomy. This discrepancy between functional and physical maps is just a mathematical restatement of the well-known fact that some diseases, such as head and neck cancer, spread in complex patterns, not always to the next nearest site. We had discovered that a computer could re-arrange anatomy so that this particular disease spreads to the next nearest site. The functional map explains over 95% of the metastases in 1400 patients. In a sense, we had graphed what our body "looks like" to a tumor. The tumor readily travels between adjacent areas in the functional map. The functional map is a succinct visual display of trends that are not easily appreciated in tables of probabilities.

Gray, Lincoln↗

Crosstalk Suppression in Individually Addressed Two-Qubit Gates in a Trapped-Ion Quantum Computer

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual $X\hat{σ}_{\phi}$ interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. Finally, this scheme is widely applicable to other platforms with analogous interaction Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Recovery and Calibration of Legacy Underground Nuclear Test Seismic Data from the Leo Brady Seismic Network

The Leo Brady Seismic Network (LBSN, originally the Sandia Seismic Network) was established in 1960 by Sandia National Laboratories to monitor underground nuclear tests (UGTs) at the Nevada National Security Site (NNSS, formerly named the Nevada Test Site). The LBSN has been in various configurations throughout its existence, but it has generally been comprised of four to six stations at regional distances (~150–400 km) from the NNSS with approximately evenly spaced azimuthal coverage. Between 1962 and the end of nuclear testing in 1992, the LBSN—and a sister network operated by Lawrence Livermore National Laboratories—was the most comprehensive United States source of regional seismic data of UGTs. Approximately 75% of all UGTs performed by the United States occurred in the predigital era. At that time, LBSN data were transmitted as frequency-modulated (FM) audio over telephone lines to a central location and recorded as analog waveforms on high-fidelity magnetic audio tapes. These tapes have been in dry temperature-stable storage for decades and contain the sole record of this irreplaceable data; full waveforms of LBSN-recorded UGTs from this era were not routinely digitized or otherwise published. We have developed a process to recover and calibrate data from these tapes. First, we play back and digitize the tapes as audio. Next, we demodulate the FM “audio” into individual waveforms. We then estimate the various instrument constants through careful measurement of “weight-lift” tests performed prior to each UGT on each instrument. Finally, these coefficients allow us to scale and shape the derived instrument response of the seismographs and compute poles and zeros. Finally, the result of this process is a digital record of the recorded seismic ground motion in a modern data format, stored in a searchable database. To date, we have digitized tapes from 592 UGTs.

58 GEOSCIENCES↗

Probabilistic finite elements for transient analysis in nonlinear continua

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Liu, W. K.↗

A New Inversion Routine to Produce Vertical Electron-Density Profiles from Ionospheric Topside-Sounder Data

Two software applications have been produced specifically for the analysis of some million digital topside ionograms produced by a recent analog-to-digital conversion effort of selected analog telemetry tapes from the Alouette-2, ISIS-1 and ISIS-2 satellites. One, TOPIST (TOPside Ionogram Scalar with True-height algorithm) from the University of Massachusetts Lowell, is designed for the automatic identification of the topside-ionogram ionospheric-reflection traces and their inversion into vertical electron-density profiles Ne(h). TOPIST also has the capability of manual intervention. The other application, from the Goddard Space Flight Center based on the FORTRAN code of John E. Jackson from the 1960s, is designed as an IDL-based interactive program for the scaling of selected digital topside-sounder ionograms. The Jackson code has also been modified, with some effort, so as to run on modern computers. This modification was motivated by the need to scale selected ionograms from the millions of Alouette/ISIS topside-sounder ionograms that only exist on 35-mm film. During this modification, it became evident that it would be more efficient to design a new code, based on the capabilities of present-day computers, than to continue to modify the old code. Such a new code has been produced and here we will describe its capabilities and compare Ne(h) profiles produced from it with those produced by the Jackson code. The concept of the new code is to assume an initial Ne(h) and derive a final Ne(h) through an iteration process that makes the resulting apparent-height profile fir the scaled values within a certain error range. The new code can be used on the X-, O-, and Z-mode traces. It does not assume any predefined profile shape between two contiguous points, like the exponential rule used in Jackson s program. Instead, Monotone Piecewise Cubic Interpolation is applied in the global profile to keep the monotone nature of the profile, which also ensures better smoothness in the final profile than in Jackson s program. The new code uses the complete refractive index expression for a cold collisionless plasma and can accommodate the IGRF, T96, and other geomagnetic field models.

Wang, Yongli↗

Methods for Estimating Dose from Galactic Cosmic Rays and Jovian Radiation Belts on Reduced-Order Monte Carlo Geometries

This document outlines the methods and tools developed to estimate dose rates from galactic cosmic rays and the trapped radiation belts surrounding Jupiter using Monte Carlo particle transport software. Furthermore, the techniques described here are specific for translating high-resolution MAVRIC models to analogous but lower resolution Monte Carlo N-Particle Transport (MCNP) code models to estimate charged particle effects on models originally developed to study neutral particles only. This capability was initially developed to predict doses to various components of dynamic radioisotope power systems for spaceflight applications, but the tools and methods can be easily applied to other problem geometries and expanded to other space radiation environments.

79 ASTRONOMY AND ASTROPHYSICS↗