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NASA NTRS1996

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Arian, Eyal↗

DOE OSTI2021

The soil health assessment protocol and evaluation applied to soil organic carbon

The concept of soil health has evolved over the past several decades, recognizing that dynamic soil property response to management and land use is highly dependent on site-specific factors that must be considered when interpreting soil health measurements. Initially, the Soil Management Assessment Framework (SMAF) and Comprehensive Assessment of Soil Health (CASH) were developed and used globally for scoring soil health indicators. However, both SMAF and CASH frameworks were developed using a relatively small dataset and their interpretation curves were not validated at the nationwide scale. Expanding upon these concepts, we propose the Soil Health Assessment Protocol and Evaluation (SHAPE) tool. The SHAPE was developed using 14,680 soil organic C (SOC) observations from across the United States, and accounts for edaphic and climate factors at the continental scale. Data were compiled from the literature, the Cornell Soil Health Laboratory, and the Kellogg Soil Survey Laboratory. In this approach, scoring curves are Bayesian model-based estimates of the conditional cumulative distribution function (CDF) for defined soil peer groups reflecting five soil texture and five soil suborder classes adjusted for mean annual temperature and precipitation. Specifically, SHAPE produces scores between 0 and 1 (0–100%) for measured SOC values that reflect the quantile or position within the conditional CDF along with measures of uncertainty. Herein, we focus on development of the SHAPE scoring curve for SOC with our case studies. SHAPE is a flexible, quantitative tool that provides a regionally relevant interpretation of this key soil health indicator.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

A Technique for the Quantitative Characterization of Weld Microstructure and Application to Mo Welds

The choice of weld parameters determines the size, shape, and curvature of grains in the fusion zone (FZ) and heat-affected zone (HAZ) of welds while the mechanical properties of the welds are correlated to this microstructure. Here, a new technique to quantitatively evaluate these microstructural characteristics in both zones of welds has been applied to molybdenum gas tungsten arc welds fabricated using different weld parameters. Trends in microstructural characteristics in the FZ and HAZ were evaluated and correlated with changes to heat input, weld speed, and weld technique. The use of this approach showed that a 20 pct decrease in heat input caused a 20 pct decrease in the number of FZ grains with aspect ratios ≥ 4. The orientations of the FZ grain segments as a function of distance from the FZ centerline were significantly affected by the weld speed and its effect on weld pool shape. A 50 pct increase in weld speed caused a 20 pct decrease in grain segments orientated 60 to 90 deg from the normal to the direction of welding. This technique also captured differences in grain sizes and grain size anisotropy in the FZ between welds made with a constant current, pulsed current, and use of a 4-pole-magnetic oscillator.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Electromagnetic Scattering From a Polygonal Thin Metallic Plate Using Quadrilateral Meshing

The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.

Deshpande, Manohar D.↗

NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗

DOE OSTI2024

SUNBIRD : a simulation-based model for full-shape density-split clustering

Combining galaxy clustering information from regions of different environmental densities can help break cosmological parameter degeneracies and access non-Gaussian information from the density field that is not readily captured by the standard two-point correlation function (2PCF) analyses. However, modelling these density-dependent statistics down to the non-linear regime has so far remained challenging. We present a simulation-based model that is able to capture the cosmological dependence of the full shape of the density-split clustering (DSC) statistics down to intra-halo scales. Our models are based on neural-network emulators that are trained on high-fidelity mock galaxy catalogues within an extended-ΛCDM framework, incorporating the effects of redshift-space, Alcock–Paczynski distortions, and models of the halo–galaxy connection. Our models reach sub-percent level accuracy down to $1 \, h^{-1}\text{Mpc}$ and are robust against different choices of galaxy–halo connection modelling. When combined with the galaxy 2PCF, DSC can tighten the constraints on ω cdm , σ 8 , and n s by factors of 2.9, 1.9, and 2.1, respectively, compared to a 2PCF-only analysis. DSC additionally puts strong constraints on environment-based assembly bias parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1984

The effects of dipole tilt on the structure of the magnetosphere

The structure of the magnetosphere as a function of dipole tilt was studied by using a global magnetohydrodynamics (MHD) model. We show here that the cusp current sheet in the MHD model is related to the tail current sheet and that the calculated shape and positions of the tail current sheet are consistent with observations. In addition, we discuss the difference between the MHD model and the Chapman-Ferraro type model which manifests as a function of tilt angle.

Wu, C. C.↗

NASA NTRS1989

Theoretical analysis and meteorological interpretation of the role of raindrop shape on microwave attenuation and propagation phase shifts - Implications for the radar measurement of rain

The effects of raindrop shape on the attenuation and propagation phase shift at vertical and horizontal linear polarizations is examined, focusing on the implications of these effects on rain measurements by radars. Analytic expressions for the imaginary and real components of the forward scattering amplitude function are dervied for a wavelength of 2.2 cm. It is shown that the summation attenuation rate and the rate of summation propagation phase shift are both insensitive to the shapes of raindrops.

Jameson, A. R.↗

DOE OSTI2021

Lattice Boltzmann simulation of the dissolution of slag in alkaline solution using real-shape particles

Highlights: • A dissolution numerical model was proposed to capture the real dissolution kinetics of slag in alkaline solution. • The log forward dissolution rate of Si was described as a function of NBO/T and solution pH. • A threshold solid volume fraction of 0.688 was found for a voxel in 3D, 63.8% larger than that for a pixel in 2D. • The proposed dissolution numerical model provides a reliable alternative to study the dissolution kinetics of slag. A dissolution numerical model was proposed in this study to capture the real dissolution kinetics of slag in alkaline solution. It consists of three modules, i.e. (i) simulation of the initial particle parking structure of slag in alkaline solution using real-shape particles of slag, (ii) simulation of the chemical reactions between slag and solution based on the transition state theory, and (iii) simulation of the physical transport of aqueous ions using the lattice Boltzmann method. This dissolution numerical model was verified using experimental results, showing reasonable accuracy. After verification, the dissolution numerical model was implemented to study the influences of temperature and particle shape using a proper recipe of slag in alkaline solution. This recipe was designed to avoid solid phase precipitation or gel formation via thermodynamic analysis. The simulation results showed faster dissolution kinetics of slag when using higher temperatures and more irregular particle shapes.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Self-assembly for electronics

Self-assembly, a process in which molecules, polymers, and particles are driven by local interactions to organize into patterns and functional structures, is being exploited in advancing silicon electronics and in emerging, unconventional electronics. Additionally, silicon electronics has relied on lithographic patterning of polymer resists at progressively smaller lengths to scale down device dimensions. Yet, this has become increasingly difficult and costly. Assembly of block copolymers and colloidal nanoparticles allows resolution enhancement and the definition of essential shapes to pattern circuits and memory devices. As we look to a future in which electronics are integrated at large numbers and in new forms for the Internet of Things and wearable and implantable technologies, we also explore a broader material set. Semiconductor nanoparticles and biomolecules are prized for their size-, shape-, and composition-dependent properties and for their solution-based assembly and integration into devices that are enabling unconventional manufacturing and new device functions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Energy density and spectrum of single-cycle and sub-cycle electromagnetic pulses

Based on the exact solution of the Maxwell equations in the form of a collapsing spherical vector wave specified by an arbitrary function of time, we have calculated the maximum energy density that can be achieved when focusing extremely short pulses of various shapes. It is shown that our earlier formula expressing the maximum energy density in terms of the spectrum parameters for Gaussian quasi-monochromatic pulses is approximately (with an accuracy of ±40 %) valid for the main types of extremely short pulses. (extremely short laser pulses)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Programmable Matter: The Nanoparticle Atom and DNA Bond

Colloidal crystal engineering with DNA has led to significant advances in bottom-up materials synthesis and a new way of thinking about fundamental concepts in chemistry. Here, programmable atom equivalents (PAEs), comprised of nanoparticles (the “atoms”) functionalized with DNA (the “bonding elements”), are assembled through DNA hybridization into crystalline lattices. Unlike atomic systems, the “atom” (e.g., the nanoparticle shape, size, and composition) and the “bond” (e.g., the DNA length and sequence) can be tuned independently, yielding designer materials with unique catalytic, optical, and biological properties. Here in this review, nearly three decades of work that have contributed to the evolution of this class of programmable matter is chronicled, starting from the earliest examples based on gold-core PAEs, and then delineating how advances in synthetic capabilities, DNA design, and fundamental understanding of PAE-PAE interactions have led to new classes of functional materials that, in several cases, have no natural equivalent.

36 MATERIALS SCIENCE↗

NASA NTRS1977

Three-dimensional modelling in magnetotelluric and magnetic variational sounding

The Galerkin finite-element method is used to obtain approximate solutions for the three-dimensional induction problem. A rectangular conductive prism is considered as an example, and solutions are obtained for linear and circularly polarized incident plane-wave fields. Magnetotelluric tensor impedances and magnetic transfer functions are computed. Polar diagrams of the tensor impedances and magnetic transfer functions along with their amplitude contour maps are presented. The dimensionality parameter, skew, is contoured at the surface of the earth. It is shown that the relative amplitudes and shapes of the additional and principal impedance polar diagrams can be used to determine the dimensionality of geoelectrical structures. Stations with skew values greater than 0.2 are significantly influenced by the three-dimensionality of the geoelectric structure. The amplitudes of the magnetic transfer function and the orientations of its polar diagrams exhibit large anomalies in the vicinity of the intersection of the lateral contacts.

Reddy, I. K.↗

NASA NTRS1994

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7-12 years of the cycle.

Hathaway, David H.↗

NASA NTRS2003

Active Control of Interface Shape During the Crystal Growth of Lead Bromide

A thermal model for predicting and designing the furnace temperature profile was developed and used for the crystal growth of lead bromide. The model gives the ampoule temperature as a function of the furnace temperature, thermal conductivity, heat transfer coefficients, and ampoule dimensions as variable parameters. Crystal interface curvature was derived from the model and it was compared with the predicted curvature for a particular furnace temperature and growth parameters. Large crystals of lead bromide were grown and it was observed that interface shape was in agreement with the shape predicted by this model.

Duval, W. M. B.↗

DOE OSTI2025

Joint modelling of astrophysical systematics for cosmology with LSST cosmic shear

ABSTRACT We present a novel framework for jointly modelling the weak lensing source galaxy redshift distribution and the intrinsic alignment (IA) of galaxies through a shared luminosity function (LF). In the context of a Rubin Observatory’s Legacy Survey of Space and Time (LSST) Year 1 and Year 10 cosmic shear analysis, we show that our novel approach produces cosmological parameter constraints which are comparable to standard methods, while offering more physical insight into IA and selection effects. We clarify the relationship between individual parameters of a Schechter LF and the redshift distribution of a magnitude-limited sample, showing the consequences of marginalizing over these parameters when modelling IAs in standard cosmic shear analyses. We explore the impact of the shape of the LF on the cosmic shear data vector, and we outline the potential of this method to naturally model selection functions in redshift distribution estimation. Although this work focuses on LSST cosmic shear, the proposed joint modelling framework is broadly applicable to weak lensing surveys.

Šarčević, Nikolina (ORCID:0000000173016415)↗

DOE OSTI2020

Modular repeat protein sculpting using rigid helical junctions

The ability to precisely design large proteins with diverse shapes would enable applications ranging from the design of protein binders that wrap around their target to the positioning of multiple functional sites in specified orientations. We describe a protein backbone design method for generating a wide range of rigid fusions between helix-containing proteins and use it to design 75,000 structurally unique junctions between monomeric and homo-oligomeric de novo designed and ankyrin repeat proteins (RPs). Of the junction designs that were experimentally characterized, 82% have circular dichroism and solution small-angle X-ray scattering profiles consistent with the design models and are stable at 95 °C. Crystal structures of four designed junctions were in close agreement with the design models with rmsds ranging from 0.9 to 1.6 Å. Electron microscopic images of extended tetrameric structures and ~10-nm-diameter “L” and “V” shapes generated using the junctions are close to the design models, demonstrating the control the rigid junctions provide for protein shape sculpting over multiple nanometer length scales.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Shape evolution of neutron-rich 106,108,110 Mo isotopes in the triaxial degree of freedom

Background: Neutron-rich nuclei with mass number between 100 and 110 attract much attention, since several kinds of shapes, such as spherical, prolate, oblate, and triaxial shapes, are predicted. In particular, for neutron-rich Mo isotopes, different models predict different magnitudes and rigidity of triaxial deformation. Previous interpretations of experimental results based solely on low-lying $2^+_2$ states are insufficient to distinguish between the rigid triaxial shape, $\gamma$ vibration, or $\gamma$-soft rotor. Purpose: The shape evolution of 106 Mo, 108 Mo, and 110 Mo is investigated through their $2^+_1$-state lifetimes, decay-branching ratios of the $2^+_2$ state, and energies of the low-lying collective excited states with $K^π = 0^+, 2^+$, and $4^+$. Method: $\beta$-delayed $\gamma$-ray spectroscopy was employed for neutron-rich Nb and Zr isotopes produced at the RIKEN RI Beam Factory to populate excited states in 106 Mo, 108 Mo, and 110 Mo. The EUroball-RIKEN Cluster Array was used for high-resolution $\gamma$-ray detection and lifetimes of the $2^+_1$ states were determined using the UK fast-timing array of LaBr 3 (Ce) detectors. Results: New $\gamma$-ray transitions and levels are reported, including newly assigned $0^+_2$ states in 108,110 Mo. Quadrupole deformations were obtained for 106,108,110 Mo from their $2^+_1$ energies and lifetimes. The $\beta$-delayed neutron-emission probabilities of 108 Nb and 110 Nb were determined by examining the $\gamma$ rays of their respective daughter decays. Conclusions: In this work, the even-odd energy staggering in the $2^+_2$ band was compared with typical patterns of the $\gamma$-vibrational band, rigid triaxial rotor, and $\gamma$-soft rotor. The very small even-odd staggering of 106 Mo, 108 Mo, and 110 Mo favors a $\gamma$-vibrational band assignment. The kinematic moment of inertia for the $2^+_2$ band showed a trend similar to the ground-state band, which is as expected for the $\gamma$-vibrational band. Beyond-mean-field calculations employing the constrained Hartree-Fock-Bogoliubov and local quasiparticle-random-phase approximation method using the SLy5 + T interaction reproduced the ground and $2^+_2$ bands in 106 Mo and 108 Mo. The collective wave functions are consistent with the interpretation of the $2^+_2$ band as the $\gamma$-vibrational band of the prolate shape. However, the staggering pattern observed in 110 Mo differs from the one suggested in the calculations which predict a $\gamma$-soft rotor. There was no experimental indication of the oblate shape or the $\gamma$-soft rotor predicted in these Mo isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗