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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Solving PDEs in Irregular Geometries with Multiresolution Methods I: Embedded Dirichlet Boundary Conditions

In this work, we develop and analyze a formalism for solving boundary value problems in arbitrarily-shaped domains using the MADNESS (multiresolution adaptive numerical environment for scientific simulation) package for adaptive computation with multiresolution algorithms. We begin by implementing a previously-reported diffuse domain approximation for embedding the domain of interest into a larger domain (Li et al., 2009 [1]). Numerical and analytical tests both demonstrate that this approximation yields non-physical solutions with zero first and second derivatives at the boundary. This excessive smoothness leads to large numerical cancellation and confounds the dynamically-adaptive, multiresolution algorithms inside MADNESS. We thus generalize the diffuse domain approximation, producing a formalism that demonstrates first-order convergence in both near- and far-field errors. We finally apply our formalism to an electrostatics problem from nanoscience with characteristic length scales ranging from 0.0001 to 300 nm.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2015

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. I.

Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.

Baxley, J. V.↗
NASA NTRS1979

An 'adding' algorithm for the Markov chain formalism for radiation transfer

An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.

Esposito, L. W.↗
NASA NTRS1985

Optimization methods applied to the aerodynamic design of helicopter rotor blades

This paper describes a formal optimization procedure for helicopter rotor blade designs which minimizes hover horsepower while assuring satisfactory forward flight performance. The approach is to couple hover and forward flight analysis programs with a general purpose optimization procedure. The resulting optimization system provides a systematic evaluation of the rotor blade design variables and their interaction, thus reducing the time and cost of designing advanced rotor blades. The paper discusses the basis for and details of the overall procedure, describes the generation of advanced blade designs for representative Army helicopters, and compares designs and design effort with those from the conventional approach which is based on parametric studies and extensive cross-plots.

Walsh, J. L.↗
DOE OSTI2011

Calibration of the Gamma Knife Perfexion using TG-21 and the solid water Leksell dosimetry phantom

Purpose: To calibrate a Gamma Knife (GK) Perfexion using TG-21 with updated chamber-dependent values for modern microionization chambers in the new solid water Leksell dosimetry phantom. This work illustrates a calibration method using commercially available equipment, instruments, and an established dosimetry protocol that may be adopted at any GK center, thus reducing the interinstitutional variation in GK calibration. The calibration was verified by three third-party dosimetry checks. In addition, measurements of the relative output factors are presented and compared to available data and the new manufacturer-provided relative output factors yet to be released. Methods: An absolute dose calibration based on the TG-21 formalism, utilizing recently reported phantom material and chamber-dependent factors, was performed using a microionization chamber in a spherical solid water phantom. The result was compared to other calibration protocols based on TG-51. Independent verification of the machine output was conducted through M.D. Anderson Dosimetry Services (MDADS), using thermoluminescent dosimeters (TLDs) in an anthropomorphic head phantom; the Radiological Physics Center (RPC), using TLDs in the standard Elekta ABS plastic calibration phantom (gray phantom), included with the GK; and through a collaborative international calibration survey by the University of Pittsburgh Medical Center (UPMC) using alanine dosimeters, also in the gray phantom. The alanine dosimeters were read by the National Institute of Standards and Technology. Finally, Gafchromic EBT film was used to measure relative output factors and these factors were compared to values reported in the literature as well as new values announced for release by Elekta. The films were exposed in the solid water phantom using an included film insert accessory. Results: Compared to the TG-21 protocol in the solid water phantom, the modified and unmodified TG-51 calibrations resulted in dose rates which were 1.8% and 1.3% lower, respectively. Ratios of the doses measured by third parties to the dose reported showed excellent agreement. MDADS returned ratios of 1.00 and 0.98 for the two TLDs irradiated. The RPC returned a mean ratio of 0.98 of the dose reported and the UPMC alanine study returned a mean ratio of 1.008. Relative output factors were found to be 0.817{+-}0.009 and 0.897{+-}0.008 for the 4 and 8 mm collimators, respectively, which are in excellent agreement with revised Monte Carlo-derived relative output factors Elekta is expected to recommend with the next version of the GK treatment planning software (GAMMAPLAN version 10). Conclusions: The TG-21 dosimetry protocol, performed in a solid water phantom in conjunction with modern dosimeters and phantom material and chamber-dependent factors, can yield an accurate dose measurement in the unique GK treatment geometry. The technique described here can be easily adopted by institutions worldwide since all equipment and instruments used are commercially available, thus reducing the existing interinstitutional variation in GK calibration techniques. Relative output factor measurements made in this same solid water phantom were used to verify the relative output factors provided by Elekta and agreed excellently with output factors expected to be released in conjunction with GAMMAPLAN version 10.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2010

Formal analysis of device authentication applications in ubiquitous computing.

Authentication between mobile devices in ad-hoc computing environments is a challenging problem. Without pre-shared knowledge, existing applications rely on additional communication methods, such as out-of-band or location-limited channels for device authentication. However, no formal analysis has been conducted to determine whether out-of-band channels are actually necessary. We answer this question through formal analysis, and use BAN logic to show that device authentication using a single channel is not possible.

99 GENERAL AND MISCELLANEOUS↗
NASA NTRS1985

Projection and quasi-projection operators for electron impact resonances on many-electron atomic targets

A framework is established for deriving true projection operators in electron resonance calculations involving many electron targets (ions and atoms). The analytical approach is based on Feshbach's formalism the true and quasi-projection operators (QPO) one-electron systems. In the case of QPOs, the formalism is explicitly generalized to treat autoionization states lying in the region of inelastic scattering. In order to illustrate the analytical method, a recent calculation of the lowest 2P0 resonance in He is described. The application of the modified Feshbach formalism to calculation of nonresonant phase shifts in many electron systems is also discussed.

Temkin, A.↗
NASA NTRSDate not supplied

Guiding Integration of Formal Verification in Assurance Cases

Assurance cases are being increasingly acknowledged as away to build trust in complex systems with autonomous capabilities. An assurance case is a comprehensive, defensible, and valid justification that a system will function as intended for a specific mission and operating environment. Formal verification is often reserved for the most critical components of such systems. However, formal verification tools are often complex, and their usage is subject to many constraints and contextual dependencies. This can raise challenges both for performing the verification as well as reflecting the verification results appropriately in the assurance case, especially for non-expert users of the verification tool. To address these challenges, we present a tool-supported methodology for integrating formal verification results in an assurance case by capturing key verification method information in a rigorously constructed assurance case. In particular, we capture the tool specification in terms of its inputs, outputs, and assurance constraints as assumptions over inputs and guarantees provided over its outputs. The tool specification is parametrized over the inputs and outputs to both guide the intended application of the tool, as well as to check that the tool has been applied following the stated assumptions and that the guarantees hold. We define a generic tool assurance argument pattern that enables integration of the verification results in the assurance case by allowing custom refinement and automated instantiation for each tool use. We demonstrate our methodology on two formal verification tools and their applications to the verification of neural network properties for the aircraft domain.

Assurance Cases↗
DOE OSTI2023

Four‐Electron Oxidative Addition of an N=N Double Bond at a Chromium Metallocyclopropene**

Abstract This report describes the synthesis of a pseudo‐tetrahedral chromium alkyne complex supported by a bidentate phosphinimide ligand and its reactivity with an azobenzene derivative. Characterization of the former by structural and computational methods reveals an unprecedented extent of alkyne activation by a formal chromium(II) center, suggesting that this complex is best described as a chromium(IV)‐metallocyclopropene. Exposure of this compound to 4,4′‐difluoroazobenzene results in the formation of a chromium(VI) diimido complex, which constitutes a rare 4‐electron oxidative addition of an N=N double bond. The isolation of a chromium(IV)‐hydrazido intermediate enabled mechanistic investigations of this challenging bond cleavage process. This work substantiates the notion that terminal phosphinimide ligands can engender first‐row transition metal ions with exceptional reactivity.

Chemistry↗
DOE OSTI2020

Optimized recursion relation for the computation of partition functions in the superconfiguration approach

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this work, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Electron ionization of open/closed chain isocarbonic molecules relevant in plasma processing: Theoretical cross sections

In this paper, we report theoretical electron impact ionization cross sections from threshold to 2000 eV for isocarbonic open chain molecules C{sub 4}H{sub 6}, C{sub 4}H{sub 8}, C{sub 4}F{sub 6} including their isomers, and closed chain molecules c-C{sub 4}H{sub 8} and c-C{sub 4}F{sub 8}. Theoretical formalism employed presently, viz., Complex Scattering Potential-ionization contribution method has been used successfully for a variety of polyatomic molecules. The present ionization calculations are very important since results available for the studied targets are either scarce or none. Our work affords comparison of C{sub 4} containing hydrocarbon versus fluorocarbon molecules. Comparisons of the present ionization cross sections are made wherever possible, and new ionization data are also presented.

2-METHYLPROPENE↗
DOE OSTI2011

BAYESIAN INFERENCE OF SOLAR AND STELLAR MAGNETIC FIELDS IN THE WEAK-FIELD APPROXIMATION

The weak-field approximation is one of the simplest models that allows us to relate the observed polarization induced by the Zeeman effect with the magnetic field vector present on the plasma of interest. It is usually applied for diagnosing magnetic fields in the solar and stellar atmospheres. A fully Bayesian approach to the inference of magnetic properties in unresolved structures is presented. The analytical expression for the marginal posterior distribution is obtained, from which we can obtain statistically relevant information about the model parameters. The role of a priori information is discussed and a hierarchical procedure is presented that gives robust results that are almost insensitive to the precise election of the prior. The strength of the formalism is demonstrated through an application to IMaX data. Bayesian methods can optimally exploit data from filter polarimeters given the scarcity of spectral information as compared with spectro-polarimeters. The effect of noise and how it degrades our ability to extract information from the Stokes profiles is analyzed in detail.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR

We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation-modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10{sup -4}-10{sup 4}. Across most of the parameter space, we find that the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve the accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find that the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SU-F-BRD-15: Quality Correction Factors in Scanned Or Broad Proton Therapy Beams Are Indistinguishable

Purpose: The IAEA TRS-398 code of practice details the reference conditions for reference dosimetry of proton beams using ionization chambers and the required beam quality correction factors (kQ). Pencil beam scanning (PBS) requires multiple spots to reproduce the reference conditions. The objective is to demonstrate, using Monte Carlo (MC) calculations, that kQ factors for broad beams can be used for scanned beams under the same reference conditions with no significant additional uncertainty. We consider hereafter the general Alfonso formalism (Alfonso et al, 2008) for non-standard beam. Methods: To approach the reference conditions and the associated dose distributions, PBS must combine many pencil beams with range modulation and shaping techniques different than those used in passive systems (broad beams). This might lead to a different energy spectrum at the measurement point. In order to evaluate the impact of these differences on kQ factors, ion chamber responses are computed with MC (Geant4 9.6) in a dedicated scanned pencil beam (Q-pcsr) producing a 10×10cm2 composite field with a flat dose distribution from 10 to 16 cm depth. Ion chamber responses are also computed by MC in a broad beam with quality Q-ds (double scattering). The dose distribution of Q -pcsr matches the dose distribution of Q-ds. k-(Q-pcsr,Q-ds) is computed for a 2×2×0.2cm{sup 3} idealized air cavity and a realistic plane-parallel ion chamber (IC). Results: Under reference conditions, quality correction factors for a scanned composite field versus a broad beam are the same for air cavity dose response, k-(Q-pcsr,Q-ds) =1.001±0.001 and for a Roos IC, k-(Q-pcsr,Q-ds) =0.999±0.005. Conclusion: Quality correction factors for ion chamber response in scanned and broad proton therapy beams are identical under reference conditions within the calculation uncertainties. The results indicate that quality correction factors published in IAEA TRS-398 can be used for scanned beams in the SOBP of a high-energy proton beam. Jefferson Sorriaux is financed by the Walloon Region under the convention 1217662. Jefferson Sorriaux is sponsored by a public-private partnership IBA - Walloon Region.

60 APPLIED LIFE SCIENCES↗