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Results for “Analytic gradients”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Consequences of a chromospheric temperature gradient on the width of H-alpha in late-type giants

An analytic expression for the integrated H alpha optical depth profile is derived for a one dimensional slab geometry model chromosphere, with electron temperature increasing as a power law with height. The formula predicts H alpha opacity and profile width to be sensitive functions of the thermal gradient. Application of the model to observation reveals that broad H alpha absorption widths in G and K giant stars are consistent with a mean H alpha chromospheric optical depth of 50, while narrower widths in M stars indicate slightly lower opacities. It is proposed that differences in H alpha width between late-type giants of similar spectral type may be due, in part, to differences in their chromospheric thermal gradient, and associated H alpha opacity.

Zarro, D. M.↗
NASA NTRS1985

Least squares inversion of Stokes profiles in the presence of velocity gradients

The Auer, Heasley and House Stokes inversion procedure in use at High Altitude Observatory is based on the analytic solution of the equation of transfer for polarized light where the representation of the thermodynamic and magnetic structure of the atmosphere is assumed to have a high degree of invariance, namely, a Milne-Eddington (ME) structure with a constant magnetic field. In the presence of invariance breaking gradients the resultant Stokes profiles are represented only approximately, if at all, by analytic forms. The accuracy of the inversion parameters and their significance as measures of actual structure are explored for the ME and the Landman-Finn sunspot models under the effects of velocity gradients. The resulting field parameters are good to a few percent and prove to be insensitive to the errors committed by the use of a ME-representation, but the resulting ME parameters yield a less precise measure of thermal structure.

Skumanich, A.↗
DOE OSTI2021

Gradient sensing via cell communication

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

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

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Analytical Partial Derivatives of the Q-Law Guidance Algorithm

One method of producing low-thrust trajectories is the closed-loop Q-Law guidance algorithm. This work wraps Q-Law inside a nonlinear programming problem to search for locally optimal gain combinations and enforce nonlinear constraints on the initial state. Gradient-based trajectory optimization has been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. This paper presents the Q-Law optimization problem setup and derives the Q-Law thrust vector partial derivatives for the State Transition Matrix required by standard nonlinear optimization software.

Jackson L Shannon↗
NASA NTRS2018

Predicting Global Ground Geoelectric Field With Coupled Geospace and Three-Dimensional Geomagnetic Induction Models

We forecast the global effects of space weather on the geoelectric and geomagnetic fields using a novel combination of methods. We use a realistic three-dimensional (3-D) model of Earth's electrical conductivity and a realistic representation of magnetospheric and ionospheric current systems. Our scheme involves the following steps: (1) We run a global magnetohydrodynamic model of the magnetosphere coupled to an electrostatic model of the ionosphere. (2) We calculate a global time series of the ground magnetic field resulting from the ionospheric, field-aligned, and magnetospheric currents of the global magnetohydrodynamic model. (3) We approximate this external field by an equivalent source current flowing in a thin shell above Earth. (4) We calculate a global time series of geoelectric and geomagnetic fields from the equivalent current and a 3-D conductivity model of Earth that also takes into account the coast effect due to large horizontal conductivity gradient. We verify our implementation by comparing the results against known analytic and numeric solutions, and then apply our scheme to the geomagnetic storm of 14 and 15 December 2006. In particular, we show that accounting for 3-D structure of Earth's conductivity results in significantly enhanced geoelectric field at large lateral gradients of conductivity, especially in coastal regions, both at middle and high latitudes. In the studied geomagnetic storm the largest values of 3-D geoelectric field are detected at high latitudes reaching 2.5 volts per kilometer and the 3-D effect extends inland by a few hundred kilometers.

Honkonen, I.↗
DOE OSTI2020

Modelling and assessing the near-wake representation and turbulence behaviour of control-oriented wake models

Due to the interaction between the wake of an upstream turbine on a downstream turbine, power losses and increased fatigue loads occur. By yawing the upstream turbine with regard to the wind direction, one can potentially reduce the power losses of the downstream turbine and reduce the fatigue loads. The evolution of the wake depends on the pressure gradient within the near-wake region and the turbulent kinetic energy and must be incorporated in existing wake steering algorithms to provide an accurate estimation of the wake flow. This paper will show a first approach to implement a near-wake model and a turbulence model in the curled wake model within the controls-oriented framework FLORIS. The near-wake model is based on an analytical expression of the velocity profile to model the pressure gradient. Furthermore, two turbulence models are incorporated within the curled wake model based on a Gaussian-distribution and a mixing length formulation. The adapted curled wake model is then assessed with the measurement data acquired in the wind tunnel at ForWind – University of Oldenburg. The evaluation of the models show good agreement for the velocity deficit and representation of the near-wake region. Furthermore, the turbulent kinetic energy behaved as expected in comparison to other work, showing a ring of high turbulent kinetic energy at non-yawed condition which is deflected to a curled shape at large yaw angles with the turbulence model based on a mixing length formulation.

FLORIS↗
DOE OSTI2021

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗
DOE OSTI2020

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

We report a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ka-band linearizer for the Ultra-Compact X-ray free-electron laser at UCLA

There is a strong demand for accelerating structures able to achieve higher gradients and more compact dimensions for the next generation of linear accelerators for research, industrial and medical applications. Notably innovative technologies will permit compact and affordable advanced accelerators as the linear collider and X-ray free-electron lasers (XFELs) with accelerating gradients over twice the value achieved with current technologies. In particular XFELs are able to produce coherent X-ray pulses with peak brightness 10 orders of magnitude greater than preceding approaches, which has revolutionized numerous research fields through imaging of the nanoscopic world at the time and length scale of atom-based systems, that is of femtosecond and Angstrom. There is a strong interest for combining these two fields, to form a proper tool with the goal of producing a very compact XFEL in order to investigate multi-disciplinary topics in chemistry, biology, materials science, medicine and physics. In the framework of the Ultra-Compact XFEL project under study at the University of California, Los Angeles, a high gradient radio-frequency accelerating structure for the longitudinal phase-space linearization with an integrated voltage of at least 15 MV working on 6th harmonic of the main Linac frequency is required. We here present the electromagnetic design of a cryogenic normal-conducting 8 cm long Ka-band standing-wave linearizer working on π mode with a target accelerating gradient beyond 100 MV/m. The studies have been performed analytically and numerically to investigate the beam dynamics and electromagnetic issues.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Unveiling the dark matter of riverine dissolved organic matter and its role in molecular chemodiversity

Chemodiversity of riverine dissolved organic matter (DOM) plays a crucial role in global elemental cycles and ecosystem function. However, DOM “dark matter”—molecules without assigned specific formulae—remain unexplored in the interpretation of chemodiversity. Here, we systematically investigated the characteristics and drivers of dark matter and its impacts on DOM chemodiversity using 551 river water and sediment samples. Compared to known matter with specific formulae, dark matter exhibited lower molecular weight and diversity, but higher compositional dissimilarity, with dissolved organic carbon (DOC) as the primary driver. Including dark matter into chemodiversity analysis changed mass, diversity, and compositional dissimilarity of DOM from –10.1 to –0.04 %, –0.7 to 4.9 %, and 0.4 to 28.8 % in waters, and from –17.5 to 5.7 %, –10.5 to 19.2 %, and –22.3 to 33.1 % in sediments, respectively. DOC mediated these ecosystem-dependent effects: lower DOC amplified the effects on chemodiversity in waters, whereas in sediments, the effects shifted from negative to positive with changing DOC. Furthermore, ignoring dark matter would overestimate the regulatory role of DOC on sediment DOM chemodiversity. In conclusion, collectively, our findings clarify the influence of dark matter on DOM chemodiversity assessments across environmental gradients, improving understanding of riverine DOM and refining its analytical framework.

Chemodiversity↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented that optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗
NASA NTRS1976

Pressure and velocity in a developing coaxial jet

Determinations of static pressure, mean velocity and turbulence intensity in the developing region of coaxial jets are presented. Detailed profiles were obtained at twelve axial locations (extending from the nozzle exit for a distance of 5 diameters) downstream from a single element of the Bell Aerospace H2/O2 19-element coaxial injector. Measurements of mass-flux per unit area (using a constant temperature anemometer), total pressure and local temperature were used in the determination of local static pressure and velocity. These data show a low pressure region exists near the nozzle exit. Although this pressure reduction is small (0.34 psi), it substantially altered the flow development. Comparison of results shows that velocity near the nozzle exit decreases initially (no central velocity core) as a result of both pressure gradients and viscous mixing. These data are compared with analytical predictions made using available computer codes. Results show the need to consider pressure effects in any proposed mathematical model.

Moon, L. F.↗
NASA NTRS1977

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented which optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗
NASA NTRS1977

An information matrix approach for aircraft parameter-insensitive control

The Fisher Information Matrix provides the nucleus of a design procedure for obtaining parameter-insensitive feedback gains in Linear-Quadratic-Gaussian problems. The procedure minimizes a sum of performance and closed-loop sensitivity costs, the latter being related to the information content of the system response. Analytical expressions for the appended cost functional and its gradient with respect to the feedback gains are derived. These derivatives serve as the basis of a computationally efficient iterative algorithm that finds the optimal gains. Application of the technique is made to determine low sensitivity feedback gains for a C-5A wing loading alleviation system that has 15 states and three uncertain parameters.

Kleinman, D. L.↗
NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.

Childs, D. W.↗