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Results for “SRB measure gradient”

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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4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Trajectory-Driven Algorithm for Differentiating SRB Measures on Unstable Manifolds

Sinai-Ruelle-Bowen (SRB) measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on unstable manifolds are critical in the sensitivity analysis of hyperbolic chaos. These derivatives, known as the SRB density gradients, are by-products of the regularization of Lebesgue integrals appearing in the original linear response expression. In this paper, we propose a novel trajectory- driven algorithm for computing the SRB density gradient defined for systems with high-dimensional unstable manifolds. We apply the concept of measure preservation together with the chain rule on smooth manifolds. Due to the recursive one-step nature of our derivations, the proposed procedure is memory-efficient and can be naturally integrated with existing Monte Carlo schemes widely used in computational chaotic dynamics. Here, we numerically show the exponential convergence of our scheme, analyze the computational cost, and present its use in the context of Monte Carlo integration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Hot wire anemometer measurements in the unheated air flow tests of the SRB nozzle-to-case joint

Hot-Wire Anemometer measurements made in the Solid Rocket Booster (SRB) nozzle-to-case joint are discussed. The study was undertaken to glean additional information on the circumferential flow induced in the SRB nozzle joint and the effect of this flow on the insulation bonding flaws. The tests were conducted on a full-scale, 2-D representation of a 65-in long segment of the SRB nozzle joint, with unheated air as the working fluid. Both the flight Mach number and Reynolds number were matched simultaneously and different pressure gradients imposed along the joint face were investigated. Hot-wire anemometers were used to obtain velocity data for different joint gaps and debond configurations. The procedure adopted for hot-wire calibration and use is outlined and the results from the tests summarized.

Ramachandran, N.↗
DOE OSTI2021

Nutrient Inputs Stimulate Mercury Methylation by Syntrophs in a Subarctic Peatland

Climate change dramatically impacts Arctic and subarctic regions, inducing shifts in wetland nutrient regimes as a consequence of thawing permafrost. Altered hydrological regimes may drive changes in the dynamics of microbial mercury (Hg) methylation and bioavailability. Important knowledge gaps remain on the contribution of specific microbial groups to methylmercury (MeHg) production in wetlands of various trophic status. Here, we measured aqueous chemistry, potential methylation rates (k meth ), volatile fatty acid (VFA) dynamics in peat-soil incubations, and genetic potential for Hg methylation across a groundwater-driven nutrient gradient in an interior Alaskan fen. We tested the hypotheses that (1) nutrient inputs will result in increased methylation potentials, and (2) syntrophic interactions contribute to methylation in subarctic wetlands. We observed that concentrations of nutrients, total Hg, and MeHg, abundance of hgcA genes, and rates of methylation in peat incubations (k meth ) were highest near the groundwater input and declined downgradient. hgcA sequences near the input were closely related to those from sulfate-reducing bacteria (SRB), methanogens, and syntrophs. Hg methylation in peat incubations collected near the input source (FPF2) were impacted by the addition of sulfate and some metabolic inhibitors while those down-gradient (FPF5) were not. Sulfate amendment to FPF2 incubations had higher k meth relative to unamended controls despite no effect on k meth from addition of the sulfate reduction inhibitor molybdate. The addition of the methanogenic inhibitor BES (25 mM) led to the accumulation of VFAs, but unlike molybdate, it did not affect Hg methylation rates. Rather, the concurrent additions of BES and molybdate significantly decreased k meth , suggesting a role for interactions between SRB and methanogens in Hg methylation. The reduction in k meth with combined addition of BES and molybdate, and accumulation of VFA in peat incubations containing BES, and a high abundance of syntroph-related hgcAsequences in peat metagenomes provide evidence for MeHg production by microorganisms growing in syntrophy. Collectively the results suggest that wetland nutrient regimes influence the activity of Hg methylating microorganisms and, consequently, Hg methylation rates. Our results provide key information about microbial Hg methylation and methylating communities under nutrient conditions that are expected to become more common as permafrost soils thaw.

59 BASIC BIOLOGICAL SCIENCES↗