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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

An Optical Differentiator Based on a Three-Layer Structure with a W-Shaped Refractive Index Profile

An optical differentiator based on a three-layer resonant structure with a W-shaped refractive index profile is proposed. The differentiation operation is performed in reflection and is associated with the resonant excitation of an eigenmode of the structure localized in the central layer. The presented results of numerical simulations demonstrate the possibility of spatial differentiation of the transverse profile of an incident optical beam, temporal differentiation of the envelope of an incident optical beam, and simultaneous spatial and temporal differentiation with a high quality. The proposed structure can find applications in designing analog optical computing and optical information processing systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Differentiable Quantum Programming with Unbounded Loops

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

Computer Science↗
DOE OSTI2019

Analysis of Differential Financial Impacts of LWR Load-Following Operations. Revision 1

This document reports the application of HERON (Holistic Energy Resource Optimization Network), a newly-developed RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization, to a case study conducted in collaboration with Arizona Public Service (APS). The study is a work in progress; this report presents a description of current models and corresponding results for a particular consideration. APS is anticipating several operational challenges. The first is rapid growth of Variable Renewable Energy (VRE) sources such as wind and solar power providing energy to the grid in the APS service region. This creates challenges for baseload operation of the Palo Verde Generating Station (PVGS), a nuclear power plant co-owned and operated by APS. The second challenge for APS is a change in the cooling water acquisition contract with the Sub Regional Operating Group (SROG). The existing contract is expiring soon, and a renewal is only available for a significantly higher price of water. These two challenges represent a difficulty in maintaining profitability for PVGS as local area demand is highly fluctuant and water prices may increase. Furthermore, excess production at PVGS is currently traded on the Palo Verde energy Hub (PVH), which occasionally offers very low or negative locational marginal prices (LMP) for electricity. This analysis considers the potential benefits of occasional curtailment of PVGS as a method to mitigate unprofitable production hours. Similar to load following, optional daily curtailment would allow APS to elect curtailment of PVGS as low as 70% of its nominal operating level between the hours of 08:00 and 16:00 provided local area demand is met and it is profitable to do so. This document reports a stochastic differential analysis of the Net Present Value (NPV) of PVGS as operated by NPS as a result of optional curtailment operation. To model this differential case, HERON has been designed from previous efforts in this study as a generic tool to accelerate the design and execution of RAVEN workflows for technoeconomic analysis of grid energy systems. HERON leverages both RAVEN and the CashFlow plugin for RAVEN to stochastically explore or optimize a response surface with energy grid system production capacities as inputs and mean NPV as a goal function. HERON performs these evaluations by stochastically sampling market, weather, and demand events using RAVEN’s ARMA reduced-order model capability to generate boundary conditions for dispatch optimization. The algorithm performs the dispatch optimization for each of the synthetic scenarios. For this case, HERON designs workflows to simulate behavior of the PVH, wind, solar, and APS local area demand, and use these synthetic scenarios to stochastically evaluate the differential benefit of optional curtailment for each scenario. While this study finds optional curtailment to be a potential source of revenue, the magnitude of the differential NPV is sufficiently small that it is unlikely a priority for increasing the profitability of PVGS. Further, the differential NPV shrinks throughout the simulated years, suggesting the long-term benefit of such operation given current assumptions is negligible.

14 SOLAR ENERGY↗
DOE OSTI2021

Double-differential Measurements of Mesonless Charged-current Muon Neutrino Interactions on Argon with Final-State Protons using the MicroBooNE Detector

This note reports the first double-differential measurements of charged-current $ν_µ$ scattering on argon leading to final states containing zero mesons and one or more protons. This event topology (hereafter abbreviated as CC0$πNp$) is the most common at the neutrino energies typically produced by the Fermilab Booster Neutrino Beam. A detailed understanding of neutrino-argon scattering in the CC0$πNp$ channel is therefore crucial for the success of the precision neutrino oscillation analyses planned for the Short-Baseline Neutrino (SBN) program. This remains true for the upcoming Deep Underground Neutrino Experiment (DUNE), but the higher mean neutrino energy used there will ensure that more inelastic reaction modes, such as single pion production, will also play a major role. The analysis described in this note builds on a previous MicroBooNE study of the CC0$πNp$ channel which obtained the first single-differential cross-section measurements on an argon target. Since that foundational work, significant improvements have been made to MicroBooNE’s simulation software, event reconstruction algorithms, and procedure for calculating systematic uncertainties. When combined with a larger dataset (corresponding to a beam exposure of 6.79 × 10 20 protons-on-target versus 1.60 × 10 20 in Ref. [3]), these enhancements allow the important CC0$πNp$ channel to be studied in more detail. This note begins with a description of the data and simulation samples used as input to the analysis. Section 3 then defines the CC0$πNp$ signal event topology, and Section 4 describes a set of selection criteria designed to identify these events in MicroBooNE data. Binning schemes are then defined in Section 5 for two double-differential measurements of event rates. The first of these considers the momentum and scattering cosine of the outgoing muon, while the second reports the same observables for the leading proton, i.e., the final-state proton with the largest momentum. After a discussion of systematic uncertainties in Section 6, the note concludes by comparing the predictions of MicroBooNE Monte Carlo (MC) simulations to the measured double-differential distributions. These results will form the basis for a future extraction of flux-averaged double-differential CC0$πNp$ cross sections that will be immediately comparable to the theoretical predictions of multiple neutrino event generators. The selection described herein may also be used to study various other observables in CC0$πNp$ events, including those which are sensitive to correlations between leptonic and hadronic kinematics in the final state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
NASA NTRS1972

On the detection of differentially encoded polyphase signals.

Consideration of the transmission and detection of differentially encoded multiple phase-shift-keyed (MPSK) signals, paying particular attention to the ambiguity resolution problem resulting from suppression of the transmitted carrier. A study is made of the coherent detection of differentially encoded MPSK signals, and the performance of a differentially encoded MPSK system is compared with that of a system which transmits absolutely encoded polyphase signals and performs perfect ambiguity resolution. Both the perfect and noisy reference signal cases are treated. Also, the performance of coherent detection of differentially encoded MPSK signals is compared with that of differentially coherent reception of the same signal set.

Lindsey, W. C.↗
NASA NTRS1974

Classical seventh-, sixth-, and fifth-order Runge-Kutta-Nystrom formulas with stepsize control for general second-order differential equations

Runge-Kutta-Nystrom formulas of the seventh, sixth, and fifth order were derived for the general second order (vector) differential equation written as the second derivative of x = f(t, x, the first derivative of x). The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the local truncation error in x, and they require no more evaluations per step than the earlier Runge-Kutta formulas for the first derivative of x = f(t, x). The developed formulas are expected to be time saving in comparison to the Runge-Kutta formulas for first-order differential equations, since it is not necessary to convert the second-order differential equations into twice as many first-order differential equations. The examples shown saved from 25 percent to 60 percent more computer time than the earlier formulas for first-order differential equations, and are comparable in accuracy.

Fehlberg, E.↗
NASA NTRS1983

Legendre-Tau approximations for functional differential equations

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Ito, K.↗
NASA NTRS1986

Differential stiffness effects

Differential stiffness as developed in NASTRAN is a linear change in stiffness caused by applied loads. Examples of differential stiffness are the stiffening effects of gravity forces in a pendulum, centrifugal forces in rotor blades and pressure loading of shell structures. In cases wherein this stiffness caused by a load is destabilizing, the differential stiffness concept lends itself to nonlinear structural analysis. Rigid Formats 4 (static analysis with differential stiffness) and 13 (normal modes with differential stiffness) are specifically designed to account for such stiffness changes. How pressure loading may be treated in these rigid formats is clarified. This clarification results from modal correlation of Ground Vibration Test (GVT) results from the empty and pressurized Filament Wound Case (FWC) quarter-scale Space Shuttle solid rocket booster (QSSRB). A sketch of the QSSRB cantilevered to the floor by its external tank attachments is shown.

Ujihara, B. H.↗
NASA NTRS1985

Helicopter flight test demonstration of differential GPS

An off-line post-mission processing facility is being established by NASA Ames Research Center to analyze differential GPS flight tests. The current and future differential systems are described, comprising an airborne segment in an SH-3 helicopter, a GPS ground reference station, and a tracking system. The post-mission processing system provides for extensive measurement analysis and differential computation. Both differential range residual corrections and navigation corrections are possible. Some preliminary flight tests were conducted in a landing approach scenario and statically. Initial findings indicate the possible need for filter matching between airborne and ground systems (if used in a navigation correction technique), the advisability of correction smoothing before airborne incorporation, and the insensitivity of accuracy to either of the differential techniques or to update rates.

Denaro, R. P.↗
NASA NTRS1986

Legendre-tau approximations for functional differential equations

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Ito, K.↗
NASA NTRS1989

Multiple symbol differential detection of uncoded and trellis coded MPSK

A differential detection for MPSK, which uses a multiple symbol observation interval, is presented and its performance analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. As such the performance of this multiple symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases, M, and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded and trellis coded MPSK.

Divsalar, Dariush↗
NASA NTRS1990

Multiple-symbol differential detection of MPSK

A differential detection technique for MPSK (multiple-phase shift keying), which uses a multiple-symbol observation interval, is presented, and its performance is analyzed and simulated. The technique makes use of maximum-likelihood sequence estimation of the transmitted phases rather than symbol-by-symbol detection as in conventional differential detection. Thus, the performance of this multiple-symbol detection scheme fills the gap between conventional (two-symbol observation) differentially coherent detection of MPSK and ideal coherent of MPSK with differential encoding. The amount of improvement gained over conventional differential detection depends on the number of phases M and the number of additional symbol intervals added to the observation. What is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation. The analysis and simulation results presented are for uncoded MPSK.

Divsalar, Dariush↗
NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗
NASA NTRS1991

The application of differential roughness to mitigate friction and wear

By definition, differential roughness occurs where the surface roughness of one region is distinctly different from that of an adjacent region. Differential roughness may occur on a sliding surface when the structure of an area of the surface is modified relative to the original material. Differential roughness may be used to effect a film thickness change so as to cause hydrodynamic or hydrostatic lubrication effects just as if the surfaces were machined. The advantage of differential roughness is that the effective offset of film thickness continues to exist even if there is gross wear. One can effect film thickness changes which are smaller than can be made directly. Furthermore, asperity tip load support is the same over both the high roughness and small roughness regions. The potential uses for differential roughness are seals, bearings, and pumps. Some examples are presented.

Lebeck, Alan O.↗
NASA NTRS1992

Differential GPS/inertial navigation approach/landing flight test results

In November of 1990 a joint Honeywell/NASA-Langley differential GPS/inertial flight test was conducted at Wallops Island, Virginia. The test objective was to acquire a system performance database and demonstrate automatic landing using an integrated differential GPS/INS (Global Positioning System/inertial navigation system) with barometric and radar altimeters. The flight test effort exceeded program objectives with over 120 landings, 36 of which were fully automatic differential GPS/inertial landings. Flight test results obtained from post-flight data analysis are discussed. These results include characteristics of differential GPS/inertial error, using the Wallops Island Laser Tracker as a reference. Data on the magnitude of the differential corrections and vertical channel performance with and without radar altimeter augmentation are provided.

Snyder, Scott↗
NASA NTRS1992

Differential shear wave attenuation and its lateral variation in the North Atlantic region

A digital data base of over 150 seismograms and a spectral radio technique are used to measure SS-S differential attenuation in the North Atlantic region. Differential attenuation is positively correlated with SS-S travel time residual, and both differential attentuation and travel time residual decrease with increasing seafloor age. Models are developed for seismic Q in which lateral variations include contributions from the asthenospheric low-Q zone as well as from lithospheric cooling. The Q models obtained under this assumption are in good agreement with those obtained from surface wave studies and are therefore preferred over those models with lateral variations confined to the upper 125 km. Systematic long-wavelength (1000-7000 km) variations in differential attenuation, corrected for seafloor age, are evident along the axis of the Mid-Atlantic Ridge. These variations can be qualitatively correlated with long-wavelength variations in SS-S differential travel time residuals and are attributed to along-axis differences in upper mantle temperature.

Sheehan, Anne F.↗
NASA NTRS1993

Power-law confusion: You say incremental, I say differential

Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.

Colwell, Joshua E.↗