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At least 1,315 records · Page 73

Theory and implementation of high-order adaptive hp methods for analysis of incompressible viscous flows

An account is given of 'smart' algorithms for CFD which change in structure and performance with during flow calculations to accommodate changing properties of the solution. Such algorithms prominently include adaptive FEM methods, which are designed to adjust mesh parameters for the control of numerical error; attention is presently given to those which change the mesh size h and the local spectral order p in order to achieve high accuracies with minimal numbers of degrees of freedom. These 'hp methods' produce exponentially convergent approximations through which flow features are resolved by automatically distributing element sizes and spectral orders. This leads to calculation of the local (elementwise) error in the approximation.

Oden, J. T.↗

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Jacquotte, Olivier P.↗

Processes of Equatorial Thermal Structure: An Analysis of Galileo Temperature Profile with 3-D Model

The Jupiter Thermosphere General Circulation Model (JTGCM) calculates the global dynamical structure of Jupiter's thermosphere self-consistently with its global thermal structure and composition. The main heat source that drives the thermospheric flow is high-latitude Joule heating. A secondary source of heating is the auroral process of particle precipitation. Global simulations of Jovian thermospheric dynamics indicate strong neutral outflows from the auroral ovals with velocities up to approximately 2 kilometers per second and subsequent convergence and downwelling at the Jovian equator. Such circulation is shown to be an important process for transporting significant amounts of auroral energy to equatorial latitudes and for regulating the global heat budget in a manner consistent with the high thermospheric temperatures observed by the Galileo probe. Adiabatic compression of the neutral atmosphere resulting from downward motion is an important source of equatorial heating (less than 0.06 microbar). The adiabatic heating continues to dominate between 0.06 and 0.2 microbar, but with an addition of comparable heating due to horizontal advection induced by the meridional flow. Thermal conduction plays an important role in transporting heat down to lower altitudes (greater than 0.2microbar) where it is balanced by the cooling associated with the wind transport processes. Interestingly, we find that radiative cooling caused by H3(+), CH4, and C2H2 emissions does not play a significant role in interpreting the Galileo temperature profile.

Majeed, T.↗

Characterization and Detailed Analysis of Regression Behavior for HTPB Solid Fuels Containing High Aluminum Loadings

NASA Marshall Space Flight Center's Materials and Processes Department, with support from the Propulsion Systems Department, has renewed the development and maintenance of a hybrid test bed for exposing ablative thermal protection materials to an environment similar to that seen in solid rocket motors (SRM). The Solid Fuel Torch (SFT), operated during the Space Shuttle program, utilized gaseous oxygen for oxidizer and an aluminized hydroxyl-terminated polybutadiene (HTPB) fuel grain to expose a converging section of phenolic material to a 400 psi, 2-phase flow combustion environment. The configuration allows for up to a 2 foot long, 5 inch diameter fuel grain cartridge. Wanting to now test rubber insulation materials with a turn-back feature to mimic the geometry of an aft dome being impinged by alumina particles, the throat area has now been increased by several times to afford flow similarity. Combined with the desire to maintain a higher operating pressure, the oxidizer flow rate is being increased by a factor of 10. Out of these changes has arisen the need to characterize the fuel/oxidizer combination in a higher mass flux condition than has been previously tested at MSFC, and at which the literature has little to no reporting as well. For (especially) metalized fuels, hybrid references have pointed out possible dependence of fuel regression rate on a number of variables: mass flux, G - oxidizer only (G0), or - total mass flux (Gtot), Length, L, Pressure, P, and Diameter, D.

Kibbey, Timothy P.↗

Cross-national analysis of food security drivers: comparing results based on the Food Insecurity Experience Scale and Global Food Security Index

Abstract The second UN Sustainable Development Goal establishes food security as a priority for governments, multilateral organizations, and NGOs. These institutions track national-level food security performance with an array of metrics and weigh intervention options considering the leverage of many possible drivers. We studied the relationships between several candidate drivers and two response variables based on prominent measures of national food security: the 2019 Global Food Security Index (GFSI) and the Food Insecurity Experience Scale’s (FIES) estimate of the percentage of a nation’s population experiencing food security or mild food insecurity (FI ). We compared the contributions of explanatory variables in regressions predicting both response variables, and we further tested the stability of our results to changes in explanatory variable selection and in the countries included in regression model training and testing. At the cross-national level, the quantity and quality of a nation’s agricultural land were not predictive of either food security metric. We found mixed evidence that per-capita cereal production, per-hectare cereal yield, an aggregate governance metric, logistics performance, and extent of paid employment work were predictive of national food security. Household spending as measured by per-capita final consumption expenditure (HFCE) was consistently the strongest driver among those studied, alone explaining a median of 92% and 70% of variation (based on out-of-sample R 2 ) in GFSI and FI , respectively. The relative strength of HFCE as a predictor was observed for both response variables and was independent of the countries used for model training, the transformations applied to the explanatory variables prior to model training, and the variable selection technique used to specify multivariate regressions. The results of this cross-national analysis reinforce previous research supportive of a causal mechanism where, in the absence of exceptional local factors, an increase in income drives increase in food security. However, the strength of this effect varies depending on the countries included in regression model fitting. We demonstrate that using multiple response metrics, repeated random sampling of input data, and iterative variable selection facilitates a convergence of evidence approach to analyzing food security drivers.

42 ENGINEERING↗

“Freedom of design” in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure–property/property–property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space—the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS—our analysis reveals that one has a substantial degree of flexibility or “freedom of design” when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO–LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quasi-Lindblad pseudomode theory for open quantum systems

Here, we introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nozzle flow of laser-heated radiating hydrogen with application to a laser-heated rocket

This paper presents a model for the steady heating of flowing hydrogen by a CW 10.6 micron laser, to consider the feasibility of a laser-heated rocket. The hydrogen flow and the laser beam are parallel, and move into a converging-diverging nozzle. The absorption of laser energy is initiated by a laser-supported combustion wave. The hydrogen is in chemical equilibrium, absorbs laser energy by inverse Bremsstrahlung, and loses energy by radiation. The hydrogen flow was calculated from the rear of the LSC wave to the throat. Estimates of convective heat losses were made using a hydrogen boundary layer analysis. Specific impulse, obtained by expanding isentropically from the throat to 1 atm or a vacuum, varies from 1400 to 3000 s. Radiation losses are 5 to 20%, though the energy fluxes to the walls are quite high. Convective loss estimates are high enough to indicate that coupling to the hot gas flow is required for a 10 kW engine, but not for a 5 MW engine.

Kemp, N. H.↗

Stress-intensity factors for two symmetric corner cracks

This paper presents stress-intensity factors, calculated by a three-dimensional finite-element analysis, for shallow or deep quarter-elliptical corner cracks at the edge of a hole in a finite-thickness plate. The plate was subjected to remote uniform tension, remote bending, or simulated pin loading in the hole; a wide range of configuration parameters was investigated. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the numbers of degrees of freedom. The stress-intensity factor variations along the crack front are compared with solutions from the literature.

Raju, I. S.↗

Efficient computation of the stability of three-dimensional compressible boundary layers

Methods for the computer analysis of the stability of three-dimensional compressible boundary layers are discussed and the user-oriented Compressible Stability Analysis (COSAL) computer code is described. The COSAL code uses a matrix finite-difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, M. R.↗

Unsteady transonic algorithm improvements for realistic aircraft applications

Improvements to a time-accurate approximate factorization (AF) algorithm have been implemented for steady and unsteady transonic analysis of realistic aircraft configurations. The algorithm improvements include: an Engquist-Osher (E-O) type-dependent switch to more accurately and efficiently treat regions of supersonic flow, extension of the E-O switch for second-order spatial accuracy in these regions, nonreflecting far field boundary conditions for more accurate unsteady applications, and several modifications which accelerate convergence to steady-state. Calculations are presented for several configurations to evaluate the algorithm modifications. The modifications have significantly improved the stability of the AF algorithm and hence the reliability of the CAP-TSD code in general.

Batina, John T.↗

The effect of horizontal resolution on systematic errors of the GLA forecast model

Systematic prediction errors of the Goddard Laboratory for Atmospheres (GLA) forecast system are reduced when the higher-resolution (2 x 2.5 deg) model version is used. Based on a budget analysis of the 200-mb eddy streamfunction, the improvement of stationary eddy forecasting is seen to be caused by the following mechanism: by increasing the horizontal spatial resolution of the forecast model, atmospheric diabatic heating over the three tropical continents is changed in a way that intensifies the planetary-scale divergent circulations associated with the three pairs of divergent-convergent centers over these continents. The intensified divergent circulation results in an enhancement of vorticity sources in the Northern Hemisphere. The additional vorticity is advected eastward by a stationary wave train along 30 deg N, thereby reducing systematic errors in the lower-resolution (4 x 5 deg) GLA model.

Chen, Tsing-Chang↗

Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis

There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.

Foye, R. L.↗

The Climate Signal in Regional Moisture Fluxes: A Comparison of Three Global Data Assimilation Products

This study assesses the quality of estimates of climate variability in moisture flux and convergence from three assimilated data sets: two are reanalysis products generated at the Goddard Data Assimilation Office (DAO) and the National Centers for Environmental Prediction/National Centers for Atmospheric Research (NCEPJNCAR), and the third consists of the operational analyses generated at the European Center for Medium Range Forecasts (ECMWF). The regions under study (the United States Great Plains, the Indian monsoon region, and Argentina east of the Andes) are characterized by frequent low level jets (LLJs) and other interannual low level wind variations tied to the large-scale flow. While the emphasis is on the reanalysis products, the comparison with the operational product is provided to help assess the improvements gained from a fixed analysis system. All three analyses capture the main moisture flux anomalies associated with selected extreme climate (drought and flood) events during the period 1985-93. The correspondence is strongest over the Great Plains and weakest over the Indian monsoon region reflecting differences in the observational coverage. For the reanalysis products, the uncertainties in the lower tropospheric winds is by far the dominant source of the discrepancies in the moisture flux anomalies in the middle latitude regions. Only in the Indian Monsoon region, where interannual variability in the low level winds is comparatively small, does the moisture bias play a substantial role. In contrast, the comparisons with the operational product show differences in moisture which are comparable torhe differences in the wind in all three regions. Compared with the fluxes, the anomalous moisture convergences show substantially larger differences among the three products. The best agreement occurs over the Great Plains region where all three products show vertically-integrated moisture convergence during the floods and divergence during the drought with differences in magnitude of about 25%. The reanalysis products, in particular, show good agreement in depicting the different roles of the mean flow and transients during the flood and drought periods. Differences between the three products in the other two regions exceed 100% reflecting differences in the low level jets and the large scale circulation patterns. The operational product tends to have locally larger amplitude convergence fields which average out in area-mean budgets: this appears to be at least in part due to errors in the surface pressure fields and aliasing from the higher resolution of the original ECMWF fields. On average, the reanalysis products show higher coherence with each other than with the operational product in the estimates of interannual variability. This result is less clear in the Indian monsoon region where differences in the input observations appears to be an important factor. The agreement in the anomalous convergence patterns is, however, still rather poor even over relatively data dense regions such as the United States Great Plains. These differences are attributed to deficiencies in the assimilating GCM's representations of the planetary boundary layer and orography, and a global observing system incapable of resolving the highly confined low level winds associated with the climate anomalies.

Min, Wei↗

Grid resolution and solution convergence for Mars Pathfinder forebody

As part of the Discovery Program, NASA Plans to launch a series of probes to Mars. The Mars Pathfinder project is the first of this series with a scheduled Mars arrival in July 1997. The entry vehicle will perform a direct entry into the atmosphere and deliver a lander to the surface. Predicting the entry vehicle's flight performance and designing the forebody heatshield requires knowledge of the expected aerothermodynamic environment. Much of this knowledge can be obtained through computational fluid dynamic (CFD) analysis.

Nettelhorst, Heather L.↗

Designing the Protocols for Programmable Ammonia Catalysis

Programmable catalysis can provide a more energy-efficient and cost-effective route to enhancing commercial ammonia production, a key process in the advancement of renewable energy technologies and the manufacture of fertilizers and basic chemicals. This work explores the computational discovery of optimal forcing protocols to drive such dynamic catalysis models. By employing matrix-free time-stepper methods, coupled with an optimization approach, that integrates Bayesian optimization with a Bayesian continuation strategy to efficiently discover the periodic steady states of such periodically forced systems, we enable the discovery of complex optimal catalyst strain waveforms, while ensuring robust solver convergence. We demonstrate the flexibility of our approach to discover optimized forcing protocols under varying physical constraints on strain modulation or other catalyst operating parameters. We show that these can have a temporal structure more complex than simple step functions. In order to detect undesirable catalytic loops that may correlate with overall reduced performance, we perform a study using graph-theoretical analysis to investigate the dynamics of catalytic kinetic networks formed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Use of machine learning to analyze chemistry card sort tasks

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student’s organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student’s strategy. Here in this work, we propose new machine learning strategies that leverage a potentially richer source of student thinking: free-form written language justifications associated with student sorts. Using data from a university chemistry card sort task, we use vectorized representations of language and unsupervised learning techniques to generate qualitatively interpretable clusters, which can provide unique insight in how students organize their knowledge. We compared these to machine learning analysis of the students’ sorts themselves. Machine learning-generated clusters revealed different organizational strategies than those built into the task; for example, sorts by difficulty or even discipline. There were also many more categories generated by machine learning for what we would identify as more novice-like sorts and justifications than originally built into the task, suggesting students’ organizational strategies converge when they become more expert-like. Finally, we learned that categories generated by machine learning for students’ justifications did not always match the categories for their sorts, and these cases highlight the need for future research on students’ organizational strategies, both manually and aided by machine learning. In sum, the use of machine learning to analyze results from a card sort task has helped us gain a more nuanced understanding of students’ expertise, and demonstrates a promising tool to add to existing analytic methods for card sorts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗