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At least 1,621 records · Page 90

Standardized development of computer software. Part 1: Methods

This work is a two-volume set on standards for modern software engineering methodology. This volume presents a tutorial and practical guide to the efficient development of reliable computer software, a unified and coordinated discipline for design, coding, testing, documentation, and project organization and management. The aim of the monograph is to provide formal disciplines for increasing the probability of securing software that is characterized by high degrees of initial correctness, readability, and maintainability, and to promote practices which aid in the consistent and orderly development of a total software system within schedule and budgetary constraints. These disciplines are set forth as a set of rules to be applied during software development to drastically reduce the time traditionally spent in debugging, to increase documentation quality, to foster understandability among those who must come in contact with it, and to facilitate operations and alterations of the program as requirements on the program environment change.

Tausworthe, R. C.↗

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

We consider a quantum mechanical system represented in phase space (referred to hereafter as “Wigner space”), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Source size of x rays from self-modulated laser wakefield accelerators

A comparative study of x-ray sources generated with different mechanisms from self-modulated laser wakefield acceleration (SM-LWFA) electrons was performed to compare the source size or spatial resolution for use in high energy density science applications. We examine the source size of betatron, inverse Compton scattering, and bremsstrahlung radiation with a Fresnel diffraction based formalism and a modified x-ray ray tracing model. We observe the dependence of source size on the radiation generation process, laser parameters, and compare to what is possible in other regimes of LWFA, as well as current methods. This information is significant as we begin to explore the use of light sources driven by SM-LWFA for use as a diagnostic at large-scale laser facilities where blowout regime LWFA is not possible.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermal conductivity in large-J two-dimensional antiferromagnets: Role of phonon scattering

Motivated by the recent heat transport experiments in 2D antiferromagnets, such as La 2 CuO 4 , where the exchange coupling J is larger than the Debye energy Θ D , we discuss different types of relaxation processes for magnon heat current with a particular focus on coupling to 3D phonons. In this work, we study thermal conductivity by these in-plane magnetic excitations using two distinct techniques, Boltzmann formalism within the relaxation-time approximation and memory-function approach. Within these approaches, a close consideration is given to the scattering of magnons by both acoustic and optical branches of phonons. A remarkable accord between the two methods with regards to the asymptotic behavior of the effective relaxation rates is demonstrated. Additional scattering mechanisms, due to grain boundaries, impurities, and finite correlation length in the paramagnetic phase, are discussed and included in the calculations of the thermal conductivity κ(T). Again, we demonstrate a close similarity of the results from the two techniques of calculating κ(T). Our complementary approach strongly suggests that scattering from optical or zone-boundary phonons is important for magnon heat current relaxation in a high temperature window of Θ D ≲T$\ll$J.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Convolution Lagrangian perturbation theory for biased tracers beyond general relativity

We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian perturbation theory approaches against those from state of the art N-body simulations in f(R) Hu-Sawicki and the nDGP braneworld modified gravity theories. We show that the novel physics of gravitational collapse in scalar tensor theories with the chameleon or the Vainshtein screening mechanism can be effectively factored in with bias parameters analytically predicted using the peak-background split formalism when updated to include the environmental sensitivity of modified gravity theories as well as changes to the halo mass function. Here, we demonstrate that convolution Lagrangian perturbation theory (CLPT) and standard perturbation theory (SPT) approaches provide accurate analytic methods to predict the correlation function and power spectra, respectively, for biased tracers in modified gravity models and are able to characterize both the baryon acoustic oscillation, power-law, and small scale regimes needed for upcoming galaxy surveys such as DESI, Euclid, LSST and WFIRST.

79 ASTRONOMY AND ASTROPHYSICS↗

Summary of LANL Critical Benchmark Comparison Study and Revisions for Cases Involving HEU, LEU, MIX, and Pu

This report documents results obtained for revisions made to cases involving Highly Enriched Uranium (HEU), Intermediate Enriched Uranium (IEU), a mixture of Pu and Uranium (MIX), as well as Pu cases. A previous summary of revisions for HEU an Pu cases was reported and additional investigations into four cases originally presented therein uncovered further revisions which led to better agreement with other transport codes, those cases are updated in this report. The summary of all cases reported in Reference 2 is updated in this report. In addition, a previous summary of revisions for LEU and MIX was reported, a summary of those revisions in reproduced in this report for a comprehensive summary of changes to benchmarks beginning in fiscal year 2020 to current date. The report focuses on the changes made to LANL benchmarks modeled with MCNP6 using ENDF/B-VII.1 nuclear data that appeared to have discrepant results when compared with results of other codes. Feedback was used to pinpoint review of benchmark input files and to revise them when necessary. This report documents the results of review and revision of specific benchmarks highlighted as possibly discrepant in the comparison study. In addition, there is an effort tied to this work involving collaboration between LANL XCP and NCS Divisions in the development of a shared review/revision procedure and use of a new benchmark repository. LANL has a benchmark library of critical experiments from the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook modeled for use with MCNP. This collection is now over 1100 benchmarks, referred to as the Whisper-1.1 library because it is used with the sensitivity/uncertainty package, Whisper, which supports nuclear criticality safety validation and is released with MCNP6.2. The collection, originally created several decades ago, is a combination of smaller collections, which has been revised and expanded, by various groups at LANL over the years. The original authors are no longer at the laboratory and little formal documentation of review and revision of these benchmarks exists today. A branch of the benchmark collection was already the subject of a formal review undertaken by the LANL NCS Division and expanded to include XCP Division.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Radiative transfer in spherical atmospheres

A method for defining spherical model atmospheres in radiative/convective and hydrostatic equilibrium is presented. A finite difference form is found for the transfer equation and a matrix operator is developed as the discrete space analog (in curvilinear coordinates) of a formal integral in plane geometry. Pressure is treated as a function of temperature. Flux conservation is maintained within the energy equation, although the correct luminosity transport must be assigned for any given level of the atmosphere. A perturbed integral operator is used in a complete linearization of the transfer and constraint equations. Finally, techniques for generating stable solutions in economical computer time are discussed.

Kalkofen, W.↗

Operations planning and analysis handbook for NASA/MSFC phase B development projects

Current operations planning and analysis practices on NASA/MSFC Phase B projects were investigated with the objectives of (1) formalizing these practices into a handbook and (2) suggesting improvements. The study focused on how Science and Engineering (S&E) Operational Personnel support Program Development (PD) Task Teams. The intimate relationship between systems engineering and operations analysis was examined. Methods identified for use by operations analysts during Phase B include functional analysis, interface analysis methods to calculate/allocate such criteria as reliability, Maintainability, and operations and support cost.

Batson, Robert C.↗

An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses

The problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane is considered and a formal expression is derived for the joint probability density of finding shear and convergence at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. This method is applied to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses.

Lee, Man Hoi↗

Probabilistic structural analysis: Introductory remarks

The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra models, (2) computational probabilistic structural analysis methods, and (3) probabilistic constitutive relationships. The development of the probabilistic structural analysis methodology is a joint program of NASA Lewis in-house and sponsored research. The objective of this session is to illustrate recent progress on the application of this methodology to determine the reliability of structural components for rocket propulsion systems. The session contains descriptions of and progress reports on the following specific activities: (1) The NESSUS computer code, (2) approximate methods, (3) advanced methods, (4) composite load spectra applications, (5) probabilistic fracture mechanisms, and (6) probability of failure and risk analysis. Collectively, the progress to date demonstrates that the structural durability of hot engine structural components can be effectively evaluated in a formal probabilistic/reliability framework.

Chamis, Christos C.↗

Design and evaluation of executable assertions for concurrent error detection

System level concurrent detection of errors due to hardware faults can be accomplished by introducing software redundancy in the form of executable assertions into a program to monitor the correct operation of the system during its execution. This paper attempts to formalize the use of executable assertions for the purpose of concurrent error detection, and discusses a transformation approach to the design of assertion statements. The second part deals with the effectiveness of the error detection technique. A fault simulation method for the evaluation of the reliability of the assertion statements is described. This scheme was used to study the effectiveness of a nontrivial program in providing protection against faults in the underlying system. The experimental results shows that the use of executable assertions provides an effective approach to achieve concurrent error detection.

Hua, Kien A.↗

Integrated topology and shape optimization in structural design

Structural optimization procedures usually start from a given design topology and vary its proportions or boundary shapes to achieve optimality under various constraints. Two different categories of structural optimization are distinguished in the literature, namely sizing and shape optimization. A major restriction in both cases is that the design topology is considered fixed and given. Questions concerning the general layout of a design (such as whether a truss or a solid structure should be used) as well as more detailed topology features (e.g., the number and connectivities of bars in a truss or the number of holes in a solid) have to be resolved by design experience before formulating the structural optimization model. Design quality of an optimized structure still depends strongly on engineering intuition. This article presents a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated in addition to selecting shape and size dimensions. A three-phase design process is discussed: an optimal initial topology is created by a homogenization method as a gray level image, which is then transformed to a realizable design using computer vision techniques; this design is then parameterized and treated in detail by sizing and shape optimization. A fully automated process is described for trusses. Optimization of two dimensional solid structures is also discussed. Several application-oriented examples illustrate the usefulness of the proposed methodology.

Bremicker, M.↗

Provably Correct Floating-Point Implementation of a Point-In-Polygon Algorithm

The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating- point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in- polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source- to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).

Moscato, Mariano M.↗

Orbital interactions - A new geometrical formalism

The geometry of encounters between two bodies on independent Keplerian orbits around a third body is considered by a novel analysis, which avoids approximations made in previous studies. For the case of most of the applications considered, the formulas for collision frequencies and orbital element rates of change due to close approaches which comprise the method agree with past results. It is shown that the method can be extended to such other applications as the consideration of oscillations in orbital elements due to secular perturbations, and the computation of probabilities of escape from the system.

Greenberg, R.↗

Effect of Impurities on the Formation Energy of Point Defects in the γ-TiAl Alloy

The projector augmented-wave method within density functional theory is used to study the effect of 4d elements and Group IIIA and IVA elements on the energetics of point defect formation and elastic moduli of the γ-TiAl alloy. To calculate the point defect formation energy, the grand canonical formalism was used. It is shown that the formation energy of aluminum vacancies decreases by approximately 1.3 eV with increasing its content in the series of alloys Ti{sub 3}Al–TiAl–TiAl{sub 3}, whereas the formation energy of titanium vacancies changes insignificantly. In general, the formation of titanium vacancies in these alloys is preferred to the formation of aluminum vacancies. It has been found that Nb, Mo, Tc, Ru, Rh, and Pd impurities on the aluminum sublattice contribute to an increase in the formation energy of an aluminum vacancies, and Mo and Tc also lead to an increase in the formation energy of titanium vacancies. All 4d impurities, if they substitute for titanium, reduce the formation energy of aluminum vacancies, and Nb and Mo are favorable for increasing the formation energy of titanium vacancies. The influence of impurities on the chemical bond in the γ-TiAl alloy and its elastic moduli and characteristics based on them is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy

We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the free energy, atomic forces, and pressure, in conjunction with a linear regression model between the internal and free energies to compute the internal energy, with all training data generated from Kohn–Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that Kohn–Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗

Few-Body Bound States and Resonances in Finite Volume

Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with more constituents. This work is relevant not only for nuclear physics, where lattice methods are now able to calculate few- and many-nucleon states, but also for other fields such as simulations of cold atoms. This article discusses recent progress regarding the extraction of few-body bound-state and resonance properties from finite-volume calculations of systems with an arbitrary number of constituents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗