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DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗

DOE OSTI2021

Guest-Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2 and H2S in (H2O)20 Cages

We present benchmark binding energies of naturally occurring gas molecules CH4, CO2, and H2S in the small cage, namely the pentagonal dodecahedron (512) (H2O)20, which is one of the constituent cages of the 3 major lattices (structures I, II and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with increasing basis set to the Complete Basis Set (CBS) limit, necessitating the use of large basis sets up to the augcc- pV5Z and subsequent correction for Basis Set Superposition Error (BSSE). For the host hollow (H2O)20 cages we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Moller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H2O)20 cage of -4.3 ± 0.1 for CH4@(H2O)20, -6.6 ± 0.1 for CO2@(H2O)20 and -8.5 ± 0.1 kcal/mol for H2S@(H2O)20, respectively. For CH4@(H2O)20, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH4@(H2O)20 is the largest one reported to date (168 valence electrons, 1978 basis functions and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350208 cores) of the “Cori” supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 minutes (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path towards parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as Density Functional Theory (DFT) and MP2 including its spin-biased variants.

Heindel, Joseph↗

DOE OSTI2019

Renormalization group computation of likelihood functions for cosmological data sets

I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian fields, where the method allows arbitrarily close to exact computation of the likelihood function in order N time, even for problems with no symmetry, compared to N 3 for brute force linear algebra (where N is the number of data points - to be fair, methods already exist to solve the Gaussian problem in at worst N log N time, and this method will not necessarily be faster in practice). The method requires no sampling or other Monte Carlo (random) element. Nonlinearity/non-Gaussianity can be accounted for to the extent that terms generated by integrating out small scale modes can be projected onto a sufficient basis, e.g., at least in the sufficiently perturbative regime. The formulas to evaluate are straightforward and require no understanding of quantum field theory, but this paper may also serve as a pedagogical introduction to Wilsonian RG for astronomers.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2021

Patched Local Lunar Gravity Solutions using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into twelve regions and two polar caps, with a resolution of 0.15˚ x 0.15˚ (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Sander Goossens↗

DOE OSTI2026

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗

DOE OSTI2015

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

The effect of interstellar absorption on measurements of the baryon acoustic peak in the Lyman α forest

In recent years, the autocorrelation of the hydrogen Lyman α forest has been used to observe the baryon acoustic peak at redshift 2 < z < 3.5 using tens of thousands of QSO spectra from the BOSS survey. However, the interstellar medium of the Milky Way introduces absorption lines into the spectrum of any extragalactic source. These lines, while weak and undetectable in a single BOSS spectrum, could potentially bias the cosmological signal. In order to examine this, we generate absorption line maps by stacking over a million spectra of galaxies and QSOs. Here, we find that the systematics introduced are too small to affect the current accuracy of the baryon acoustic peak, but might be relevant to future surveys such as the Dark Energy Spectroscopic Instrument (DESI). We outline a method to account for this with future data sets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

CMB-S4: Iterative Internal Delensing and r Constraints

Abstract The tightest constraints on the tensor-to-scalar ratio r can only be obtained after removing a substantial fraction of the lensing B -mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment ( cmb-s4.org ) will remove the lensing B -mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power on r , including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component separation of the high-resolution maps, followed by the construction of lensing B -mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood for r . We find that the lensing reconstruction and framework achieve the expected performance, compatible with the target σ ( r ) ≃ 5 · 10 −4 in the absence of a tensor signal, after an effective removal of 92%–93% of the lensing B -mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests, we also demonstrate the joint optimal reconstruction of the lensing potential with the lensing curl potential mode at second order in the density fluctuations.

Astronomy & Astrophysics↗

NASA NTRS2004

The Space Technology 5 Avionics System

The Space Technology 5 (ST5) mission is a NASA New Millennium Program project that will validate new technologies for future space science missions and demonstrate the feasibility of building launching and operating multiple, miniature spacecraft that can collect research-quality in-situ science measurements. The three satellites in the ST5 constellation will be launched into a sun-synchronous Earth orbit in early 2006. ST5 fits into the 25-kilogram and 24-watt class of very small but fully capable spacecraft. The new technologies and design concepts for a compact power and command and data handling (C&DH) avionics system are presented. The 2-card ST5 avionics design incorporates new technology components while being tightly constrained in mass, power and volume. In order to hold down the mass and volume, and quali& new technologies for fUture use in space, high efficiency triple-junction solar cells and a lithium-ion battery were baselined into the power system design. The flight computer is co-located with the power system electronics in an integral spacecraft structural enclosure called the card cage assembly. The flight computer has a full set of uplink, downlink and solid-state recording capabilities, and it implements a new CMOS Ultra-Low Power Radiation Tolerant logic technology. There were a number of challenges imposed by the ST5 mission. Specifically, designing a micro-sat class spacecraft demanded that minimizing mass, volume and power dissipation would drive the overall design. The result is a very streamlined approach, while striving to maintain a high level of capability, The mission's radiation requirements, along with the low voltage DC power distribution, limited the selection of analog parts that can operate within these constraints. The challenge of qualifying new technology components for the space environment within a short development schedule was another hurdle. The mission requirements also demanded magnetic cleanliness in order to reduce the effect of stray (spacecraft-generated) magnetic fields on the science-grade magnetometer.

Speer, Dave↗

DOE OSTI2018

Sodium Pumping via Condensation within a Non-Wetting Porous Structure

In a sodium thermal electrochemical converter (Na-TEC), the transfer of liquid sodium from a low-pressure condenser to a high-pressure evaporator is necessary to complete the thermodynamic cycle. This pumping can be typically achieved via capillary action. A unique capillary pump is explored in this work, whereby low-pressure sodium vapor is condensed within a non-wetting (i.e. contact angle > π/2) stainless steel porous structure. Due to the curvature of the non-wetting liquid-vapor interface, the liquid adjacent to the interface is at a higher pressure than the vapor. This is in contrast to traditional wicks, where the liquid adjacent to the interface has a lower pressure. Conjugate heat transfer techniques are required to model the coupled momentum and thermal transport processes within this porous structure. Due to the low mass flowrates in the Na-TEC (< 0.1 mg/s), higher order friction terms are neglected and the classical Darcy’s law is applied for the non-isothermal, compressible vapor flow. At lower temperatures, the sodium vapor density becomes sufficiently small and there is a transition from classic Poiseuille flow (Kn < 0.1) to Knudsen flow (Kn > 10). The permeability of the porous structure is modeled using the Blaze-Kozeny expression, with an additional factor that accounts for this change in Kn. Initial modeling results showing expected mass flowrates, temperature profiles, and liquid-vapor interface locations are presented. The design of an experiment to validate the results from this modeling effort is also described. The main design features of the experimental set-up are presented, and the method used to measure the low sodium mass flowrates is discussed. Initial experimental results demonstrating sodium pumping for a range of temperatures (850K – 1150K) will be presented and compared against the model predictions. A number of challenges affecting the successful completion of this experiment will also be discussed. Primarily, the sodium vapor must be superheated to prevent condensation anywhere except within the porous structure. Other challenges include the requirement to keep the condensation interface above ~ 675K to prevent transition to a wetting regime, and the control of the transient heating rate so that vapor flows slower than the quasi steady-state mass flowrate, which would otherwise lead to a flooding condition that prevents pumping. Specific strategies used to address these challenges are presented, and the experimental procedures used to gather data are discussed.

14 SOLAR ENERGY↗

DOE OSTI2019

Deep Learning for Semantic Segmentation of Defects in Advanced STEM Images of Steels

Crystalline materials exhibit long-range ordered lattice unit, within which resides nonperiodic structural features called defects. These crystallographic defects play a vital role in determining the physical and mechanical properties of a wide range of material systems. While computer vision has demonstrated success in recognizing feature patterns in images with well defined contrast, automated identification of nanometer scale crystallographic defects in electron micrographs governed by complex contrast mechanism is still a challenging task. Here, building upon an advanced defect imaging mode that offers high feature clarity, we introduce DefectSegNet - a new convolutional neural network (CNN) architecture that performs semantic segmentation of three common crystallographic defects in structural alloys: dislocation lines, precipitates and voids. Results from supervised training of a small set of high-quality defect images of steels show high pixel-wise accuracy across all three types of defects: 91.60 ± 1.77% on dislocations, 93.39 ± 1.00% on precipitates, and 98.85 ± 0.56% on voids. We discuss the sources of uncertainties in CNN prediction, and the training data in terms of feature density, representation and homogeneity and their effects on deep learning performance. Further defect quantification using DefectSegNet prediction outperforms human expert average, presenting a promising new workflow for fast and statistically meaningful quantification of materials defects.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Acoustic Mode Measurements in the Inlet of a Model Turbofan Using a Continuously Rotating Rake

Comprehensive measurements of the spinning acoustic mode structure in the inlet of the Advanced Ducted Propeller (ADP) have been completed. These measurements were taken using a unique and previously untried method which was first proposed by T.G. Sofrin. A continuously rotating microphone system was employed. The ADP model was designed and built by Pratt & Whitney and tested in the NASA Lewis 9- by 15-foot Anechoic Wind Tunnel. Three inlet configurations were tested with cut-on and cutoff stator vane sets. The cutoff stator was designed to suppress all modes at the blade passing frequency. Rotating rake measurements indicate that several extraneous circumferential modes were active. The mode orders suggest that their source was an interaction between the rotor and small interruptions in the casing tip treatment. The cut-on stator produced the expected circumferential modes plus higher levels of the unexpected modes seen with the cutoff stator.

Heidelberg, Laurence J.↗

NASA NTRS1993

Acoustic mode measurements in the inlet of a model turbofan using a continuously rotating rake

Heidelberg, Laurence J.↗

NASA NTRS2000

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗

NASA NTRS2013

NASA Software Engineering Benchmarking Study

To identify best practices for the improvement of software engineering on projects, NASA's Offices of Chief Engineer (OCE) and Safety and Mission Assurance (OSMA) formed a team led by Heather Rarick and Sally Godfrey to conduct this benchmarking study. The primary goals of the study are to identify best practices that: Improve the management and technical development of software intensive systems; Have a track record of successful deployment by aerospace industries, universities [including research and development (R&D) laboratories], and defense services, as well as NASA's own component Centers; and Identify candidate solutions for NASA's software issues. Beginning in the late fall of 2010, focus topics were chosen and interview questions were developed, based on the NASA top software challenges. Between February 2011 and November 2011, the Benchmark Team interviewed a total of 18 organizations, consisting of five NASA Centers, five industry organizations, four defense services organizations, and four university or university R and D laboratory organizations. A software assurance representative also participated in each of the interviews to focus on assurance and software safety best practices. Interviewees provided a wealth of information on each topic area that included: software policy, software acquisition, software assurance, testing, training, maintaining rigor in small projects, metrics, and use of the Capability Maturity Model Integration (CMMI) framework, as well as a number of special topics that came up in the discussions. NASA's software engineering practices compared favorably with the external organizations in most benchmark areas, but in every topic, there were ways in which NASA could improve its practices. Compared to defense services organizations and some of the industry organizations, one of NASA's notable weaknesses involved communication with contractors regarding its policies and requirements for acquired software. One of NASA's strengths was its software assurance practices, which seemed to rate well in comparison to the other organizational groups and also seemed to include a larger scope of activities. An unexpected benefit of the software benchmarking study was the identification of many opportunities for collaboration in areas including metrics, training, sharing of CMMI experiences and resources such as instructors and CMMI Lead Appraisers, and even sharing of assets such as documented processes. A further unexpected benefit of the study was the feedback on NASA practices that was received from some of the organizations interviewed. From that feedback, other potential areas where NASA could improve were highlighted, such as accuracy of software cost estimation and budgetary practices. The detailed report contains discussion of the practices noted in each of the topic areas, as well as a summary of observations and recommendations from each of the topic areas. The resulting 24 recommendations from the topic areas were then consolidated to eliminate duplication and culled into a set of 14 suggested actionable recommendations. This final set of actionable recommendations, listed below, are items that can be implemented to improve NASA's software engineering practices and to help address many of the items that were listed in the NASA top software engineering issues. 1. Develop and implement standard contract language for software procurements. 2. Advance accurate and trusted software cost estimates for both procured and in-house software and improve the capture of actual cost data to facilitate further improvements. 3. Establish a consistent set of objectives and expectations, specifically types of metrics at the Agency level, so key trends and models can be identified and used to continuously improve software processes and each software development effort. 4. Maintain the CMMI Maturity Level requirement for critical NASA projects and use CMMI to measure organizations developing software for NASA. 5.onsolidate, collect and, if needed, develop common processes principles and other assets across the Agency in order to provide more consistency in software development and acquisition practices and to reduce the overall cost of maintaining or increasing current NASA CMMI maturity levels. 6. Provide additional support for small projects that includes: (a) guidance for appropriate tailoring of requirements for small projects, (b) availability of suitable tools, including support tool set-up and training, and (c) training for small project personnel, assurance personnel and technical authorities on the acceptable options for tailoring requirements and performing assurance on small projects. 7. Develop software training classes for the more experienced software engineers using on-line training, videos, or small separate modules of training that can be accommodated as needed throughout a project. 8. Create guidelines to structure non-classroom training opportunities such as mentoring, peer reviews, lessons learned sessions, and on-the-job training. 9. Develop a set of predictive software defect data and a process for assessing software testing metric data against it. 10. Assess Agency-wide licenses for commonly used software tools. 11. Fill the knowledge gap in common software engineering practices for new hires and co-ops.12. Work through the Science, Technology, Engineering and Mathematics (STEM) program with universities in strengthening education in the use of common software engineering practices and standards. 13. Follow up this benchmark study with a deeper look into what both internal and external organizations perceive as the scope of software assurance, the value they expect to obtain from it, and the shortcomings they experience in the current practice. 14. Continue interactions with external software engineering environment through collaborations, knowledge sharing, and benchmarking.

Rarick, Heather L.↗

DOE OSTI2018

Electronic Energies Are Not Enough: An Ion Mobility-Aided, Quantum Chemical Benchmark Analysis of H + GPGG Conformers

Peptides and proteins exist not as single, lowest energy structures but as ensembles of states separated by small barriers. In order to study these species we must be able to correctly identify their gas phase conformational distributions, and ion mobility spectrometry (IMS) has arisen as an experimental method for assessing the gas phase energetics of flexible peptides. Here, we present a thorough exploration and benchmarking of the low energy conformers of the small, hairpin peptide H+ GPGG with the aid of ion mobility spectrometry against a wide swath of density functionals (35 dispersion-corrected and uncorrected functionals represented by 21 unique exchange–correlation functionals) and wave function theory methods (15 total levels of theory). The three experimentally resolved IMS peaks were found to correspond to three distinct pairs of conformers, each pair composed of species differing only by the chair or boat configuration of the proline. Two of the H+ GPGG conformer pairs possess a cis configuration about the Pro–Gly1 peptide bond while the other adopts a trans configuration. While the experimental spectrum reports a higher intensity for the cis-1 conformer than the trans conformer, 13 WFT levels of theory, including a complete basis set CCSD(T) extrapolation, obtain trans to be favored in terms of the electronic energy. This same effect is seen in 14 of the 18 dispersion-corrected density functionals studied, whereas the remaining 17 functionals show more variety. Only when Gibbs free energies are considered do the WFT methods and dispersion-corrected functionals reflect the experimental distribution. CAM-B3LYP-D3BJ emerges as the best-performing density functional, matching the experimental distribution and the CCSD(T)/CBS relative energies within 6%. Further analysis reveals the trans conformer to be favored electronically, but entropically disfavored, leading to the experimental preference of the cis-1 conformer. Furthermore, these results highlight the danger in considering only the electronic energies, which is common practice in electronic structure theory predictions of conformational energy distributions. Additionally, the effects of temperature and scaling of the frequencies used in obtaining the Gibbs free energies are explored.

Energy↗

DOE OSTI2015

Detecting vortices in superconductors: Extracting one-dimensional topological singularities from a discretized complex scalar field

In type II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise positions and motion from discretized numerical simulation data is an important, but challenging, task. In the past, vortices have mostly been detected by analyzing the magnitude of the complex scalar field representing the order parameter and visualized by corresponding contour plots and isosurfaces. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. In this paper, we present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. Finally, by representing the field as the set of vortices, this method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1987

The mechanisms of temporal inference

The properties of a temporal language are determined by its constituent elements: the temporal objects which it can represent, the attributes of those objects, the relationships between them, the axioms which define the default relationships, and the rules which define the statements that can be formulated. The methods of inference which can be applied to a temporal language are derived in part from a small number of axioms which define the meaning of equality and order and how those relationships can be propagated. More complex inferences involve detailed analysis of the stated relationships. Perhaps the most challenging area of temporal inference is reasoning over disjunctive temporal constraints. Simple forms of disjunction do not sufficiently increase the expressive power of a language while unrestricted use of disjunction makes the analysis NP-hard. In many cases a set of disjunctive constraints can be converted to disjunctive normal form and familiar methods of inference can be applied to the conjunctive sub-expressions. This process itself is NP-hard but it is made more tractable by careful expansion of a tree-structured search space.

Fox, B. R.↗