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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Equivalence of quantum barren plateaus to cost concentration and narrow gorges

Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus (BPs)), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minima (called narrow gorges). Here we analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose BPs via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results could be interesting from a quantum foundations perspective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

A defect stream function formulation for compressible turbulent boundary layers

Progress to date on the development of a method for turbulent, wall-bounded flow which uses the defect stream function formulation in the outer layer and an analytic law of the wall and wake formulation in the inner region is reviewed. This two-formulation approach avoids the need to computationally resolve the high-gradient inner layer. One of the most appealing recent developments is the transformation of the compressible governing equation for the defect stream function into a linear, second-order differential equation which has analytic solutions for many problems of practical interest. Numerical and analytic results for incompressible and compressible flows are shown to be in excellent agreement with experimental results. In this paper the two-formulation approach is applied to primitive-variable computations. Excellent comparisons with experiment are presented for two compressible flat plate flows.

Barnwell, Richard W.↗
DOE OSTI2026

Comparative analysis of plasticity-based GND density estimation methods in crystal plasticity finite element models

In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.

Crystal plasticity↗
NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗
DOE OSTI2022

Kinetic Model for Moisture-Controlled CO 2 Sorption

The understanding of the sorption/desorption kinetics is essential for practical applications of moisture-controlled CO 2 sorption. We introduce an analytic model of the kinetics of moisture-controlled CO 2 sorption and its interpretation in two limiting cases. In one case, chemical reaction kinetics on pore surfaces dominates, in the other case, diffusive transport through the sorbent defines the kinetics. Here, we show that reaction kinetics, which is dominant in the first case, can be expressed as a linear combination of 1st and 2nd order kinetics in agreement with the static isotherm equation derived and validated in a previous paper. The interior transport kinetics can be described by non-linear diffusion equations. By combining all carbon species into a single equation, we can eliminate — in certain limits — the source terms associated with chemical reactions. In this case, the governing equation is ∂θ/∂t = –∇ · (–D eff ∇ θ ). For a sorbent in a form of a flat sheet or a membrane, one can maintain the same functional form of a diffusion equation by introducing a generalized effective diffusivity D M that combines contributions from both surface chemical reaction kinetics and interior diffusive transport kinetics. Experimental data of transient CO 2 flux in a preconditioned commercial anion exchange membrane fit well to the 1st order model as long as very dry states are avoided, validating the theory. The observed DM for a preconditioned commercial anion exchange membrane ranges from 6.6× 10 -14 to 7.1× 10 -14 m 2 s -1 at 35°C. These small values compared to typical ionic diffusivities imply a very slow kinetics, which will be the largest issue that needs to be addressed for practical application. The collected transient CO 2 flux data are used to predict the magnitude of a continuous CO 2 pumping flux in an active membrane that transports CO 2 against a CO 2 concentration gradient. The pumped CO 2 flux is supported by water flux due to a water concentration gradient.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The effect of saturated thermal conduction on clouds in a hot plasma

We numerically investigate the internal evolution of multiphase clouds, which are at rest with respect to an ambient, highly ionized medium (HIM) representing the hot component of the circumgalactic medium. Time-dependent saturated thermal conduction and its implications like condensation rates and mixing efficiency are assessed in multiphase clouds. Our simulations are carried out by using the adaptive mesh refinement code FLASH. The model clouds are initially in both hydrostatic and thermal equilibrium and are in pressure balance with the HIM. Thus, they have steep gradients in both temperature and density at the interface to HIM leading to non-negligible thermal conduction. Several physical processes are considered numerically or semi-analytically: thermal conduction, radiative cooling and external heating of gas, self-gravity, mass diffusion, and dissociation of molecules and ionization of atoms. It turns out that saturated thermal conduction triggers a continuous condensation irrespective of cloud mass. Dynamical interactions with ambient HIM all relate to the radial density gradient in the clouds: (1) mass flux due to condensation is the higher the more homogeneous the clouds are; (2) mixing of condensed gas with cloud gas is easier in low-mass clouds, because of their shallower radial density gradient; and thus (3) accreted gas is distributed more efficiently. A distinct and sub-structured transition zone forms at the interface between cloud and HIM, which starts at smaller radii and is much narrower as deduced from analytical theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models

Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g.,having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound [1]. However, the approach in [1] requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES)combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.

Zhang, Jiaxin↗
DOE OSTI2023

Computational diagnostics for flame acceleration and transition to detonation in a hydrogen/air mixture

A new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The new method is validated for the study of detonation development during the deflagration-to-detonation transition (DDT) process. The flame characteristics are identified through the quantification of individual CEM contributions of chemical reaction, diffusion, and pressure-induced compressibility. Numerical simulations are performed to investigate the DDT processes in a stoichiometric hydrogen-air mixture. A Godunov algorithm, fifth-order in space, and third-order in time are used to solve the fully compressible Navier-Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model (CDM) described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The new diagnostic method is first applied to onedimensional (1D) canonical flame configurations followed by two-dimensional (2D) simulations of DDT in an obstructed channel where different detonation initiation scenarios are examined using the new CEMA projection formulation. Detailed examinations of the idealized configuration of detonation initiation through shock focusing mechanism at a flame front are also studied using the new formulation. A comparison of the currently proposed CEMA projection and the original formulation by the authors suggests that including the pressure-induced compressibility is essential for the use of CEMA in DDT process. The results also show that the new formulation of CEMA projection can successively capture the detonation initiation through either a gradient mechanism or a direct initiation mechanism, and therefore can be used as an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. It was found that detonation development is characterized by a strong contribution of chemistry role to the CEM which is pivotal to the initiation of detonation. The role of compressibility is found enhanced at the edge of the detonation front where diffusion was found to have minimal effects on detonation development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Hyperspectral Detection of the Fluorescence Shift between Chirality-Sorted Empty and Water-Filled Single-Wall Carbon Nanotube Enantiomers

Single-wall carbon nanotubes (SWCNTs) have extraordinary electronic and optical properties that depend strongly on their exact chiral structure and their interaction with their inner and outer environment. The fluorescence (PL) of semiconducting SWCNTs, for instance, will shift depending on the molecules with which the SWCNT’s hollow core is filled. These interaction-induced shifts are challenging to resolve on the ensemble level in samples containing a mixture of different filling contents due to the relatively large inhomogeneous line width of the ensemble SWCNT PL compared to the size of these shifts. To circumvent this inhomogeneous broadening, single-tube spectroscopy and hyperspectral imaging are often applied, which until now required time-consuming statistical studies. Here, we present hyperspectral PL microscopy combined with automated SWCNT segmenting based on either principal component analysis or a convolutional neural network, capable of both spatially and spectrally resolving the PL along the length of many individual SWCNTs at the same time and automatically fitting peak positions and line widths of individual SWCNTs. The methodology is demonstrated by accurately determining the emission shifts and line widths of thousands of left- and right-handed empty and water-filled SWCNTs coated with a chiral surfactant, resulting in four statistical distributions which cannot be resolved in ensemble spectroscopy of unsorted samples. The results demonstrate a robust method to quickly probe ensemble properties with single-enantiomer spectral resolution. Moreover, it promises to be an absolute quantitative method to characterize the relative abundances of SWCNTs with different handedness or filling content in macroscopic samples, simply by counting individual species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Domain wall diode based on functionally graded Dzyaloshinskii–Moriya interaction

In this work, we present a general approach for studying the dynamics of domain walls in biaxial ferromagnetic stripes with functionally graded Dzyaloshinskii–Moriya interaction (DMI). By engineering the spatial profile of the DMI parameter we propose the concept of a diode, which implements filtering of domain walls of certain topological charge and helicity. We base our study on phenomenological Landau–Lifshitz–Gilbert equations with additional Zhang–Li spin-transfer terms using a collective variable approach. In the effective equations of motion the gradients of DMI play the role of a driving force which competes with current driving. All analytical predictions are confirmed by numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Verification of local electrostatic gyrokinetic simulation of driftwave instability in field-reversed configuration

Local linear simulations of ion temperature gradient (ITG) instabilities using a gyrokinetic particle code GKD1D have been verified by comparing with the analytic dispersion relation in the slab geometry and by benchmarking with a global gyrokinetic code GTC-X in a realistic field-reversed configuration (FRC). Results of ITG simulations using either adiabatic or kinetic electrons exhibit excellent agreements between the two codes for linear frequencies, growth rates, and mode structures. The ITG modes in the FRC scrape-off layer region are mostly dominated by the poloidal m = 1 harmonic. Kinetic electrons enhance the subdominant m = 2 harmonic and the even parity dominates the ITG mode structure. Kinetic electrons increase the growth rates for the low-n modes, but decrease the growth rates for the high-n modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

Marangoni bubble motion in zero gravity

It was shown experimentally that the Marangoni phenomenon is a primary mechanism for the movement of a gas bubble in a nonisothermal liquid in a low gravity environment. A mathematical model consisting of the Navier-Stokes and thermal energy equations, together with the appropriate boundary conditions for both media, is presented. Parameter perturbation theory is used to solve this boundary value problem; the expansion parameter is the Marangoni number. The zeroth, first, and second order approximations for the velocity, temperature and pressure distributions in the liquid and in the bubble, and the deformation and terminal velocity of the bubble are determined. Experimental zero gravity data for a nitrogen bubble in ethylene glycol, ethanol, and silicone oil subjected to a linear temperature gradient were obtained using the NASA Lewis zero gravity drop tower. Comparison of the zeroth order analytical results for the bubble terminal velocity showed good agreement with the experimental measurements. The first and second order solutions for the bubble deformation and bubble terminal velocity are valid for liquids having Prandtl numbers on the order of one, but there is a lack of appropriate data to test the theory fully.

Thompson, R. L.↗
NASA NTRS1990

A mathematical model of the structure and evolution of small scale discrete auroral arcs

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Seyler, C. E.↗
NASA NTRS2005

The Derivation of the Gradient of the Acoustic Pressure on a Moving Surface for Application to the Fast Scattering Code (FSC)

In this paper we develop an analytic expression for calculation of the the acoustic pressure from a rotating blade on a moving surface for application to the Fast Scattering Code (FSC). The analytic result is intended to be used in the helicopter noise prediction code PSU-WOPWOP. One of the goals of the derivation is obtaining a result that will not use any more information than are needed for the prediction of the thickness and loading noise. The result derived here achieves this goal and its incorporation in PSU-WOPWOP is straight forward and attainable.

Farassat, F.↗
DOE OSTI2021

Ascending Columns, WTG, and Convective Aggregation

Analytic solutions are derived for a convecting atmosphere with mean ascent using a zero-buoyancy bulk-plume approximation for moist convection. It has been suggested that such solutions should serve as a model for the relationship between humidity, instability, and precipitation in the tropics, but it is shown here that this interpretation is incompatible with the observed weak temperature gradient (WTG). Instead, the solutions can be used to understand the atmospheric state averaged over all tropical convecting regions. Further, using the analytic solutions in this way, they predict the changes in humidity, instability, and precipitation as a function of the size of the moist patch in a convectively aggregated state.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2020

Structural Model Tuning Tool: User's Reference Manual

This report presents an efficient approach for tuning finite element models to match the measured ground vibration test and static test data. Frequencies, mode shapes, total weight, location of the center of gravity, and static deformation computed from the finite element model are matched to the measured data. The model tuning procedure used in this work is based on solving an optimization problem in which the errors for the considered metrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values of performance indices are computed using the NASTRAN-generated sensitivity values together with the in-house computer codes, which allow for faster computational time and the use of gradient-based optimizers. The method is applied to the Aerostructures Test Wing IV model. The study shows that the military standard and the National Aeronautics and Space Administration standard for comparing analytical and experimental modal data are all satisfied. The final finite element model correlates well with the test data. The flutter speed decreases by 8.91 percent after model tuning compared with the original Aerostructures Test Wing IV design.

Chan-gi Pak↗
NASA NTRS1987

Fluid dynamics of unsteady separated flow. II - Lifting surfaces

An analytic method is described which uses static experimental data to predict the separated flow effect on rigid and elastic vehicle dynamics. Key parameters in the analytic relationship between steady and nonsteady aerodynamics are: the time lag occurring before a change of flow conditions can affect the separation-induced aerodynamic loads; the accelerated flow effect (i.e., the pressure gradient lag relative to the static aerodynamic characteristics); and the moving wall effect (i.e., the effect of the nonsteady boundary condition at the vehicle surface). Using the existing experimental data base, an analytic theory is formulated that can predict the separation-induced unsteady aerodynamics if the static characteristics are known from theory or experiment. Reference is made to increased-maneuverability advanced aircraft and to Space Shuttle Orbiter aerodynamics.

Ericsson, L. E.↗
NASA NTRS1979

Effects of refraction by means flow velocity gradients on the standing wave pattern in three-dimensional, rectangular waveguides

The influence of a mean vortical flow on the connection between the standing wave pattern in a rectangular three dimensional waveguide and the corresponding duct axial impedance was determined analytically. The solution was derived using a perturbation scheme valid for low mean flow Mach numbers and plane wave sound frequencies. The results show that deviations of the standing wave pattern due to refraction by the mean flow gradients are small.

Hersh, A. S.↗