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The Ritz method is applied to the variation analysis of a completely free elliptical plate as an efficient alternative to a procedure using a truncated series of regular and modified Mathieu functions. It is shown that a solution as accurate as desired can be obtained with the Ritz method in solving thin plate vibration problems with difficult geometries.
Effort was dedicated to development and testing of a formal strategy for reconciling uncertain test data with physically limited computational prediction. Specific weaknesses in the logical structure of the current Power Balance Model (PBM) version are described with emphasis given to the main routing subroutines BAL and DATRED. Selected results from a variational analysis of PBM predictions are compared to Technology Test Bed (TTB) variational study results to assess PBM predictive capability. The motivation for systematic integration of uncertain test data with computational predictions based on limited physical models is provided. The theoretical foundation for the reconciliation strategy developed in this effort is presented, and results of a reconciliation analysis of the Space Shuttle Main Engine (SSME) high pressure fuel side turbopump subsystem are examined.
Exopolymers from a diverse collection of marine and freshwater bacteria were characterized by pyrolysis-mass spectrometry (Py-MS). Py-MS provides spectra of pyrolysis fragments that are characteristic of the original material. Analysis of the spectra by multivariate statistical techniques (principal component and canonical variate analysis) separated these exopolymers into distinct groups. Py-MS clearly distinguished characteristic fragments, which may be derived from components responsible for functional differences between polymers. The importance of these distinctions and the relevance of pyrolysis information to exopolysaccharide function in aquatic bacteria is discussed.
Surface winds are closely associated with the surface pressure gradient. The variational SEASAT data analysis technique was designed to improve the sea level pressure analysis in the data sparse areas. The SEASAT-derived surface wind data were compared with observations from the Joint Air Sea Interaction Experiment (JASIN) and it was found that the satellite-derived sea surface wind has an accuracy of up to + or - 2 m/s in speed and + or - 20 deg in direction. These numbers are considered characteristic of the retrieved SEASAT wind field. By combining the densely spaced SEASAT-derived wind data with the sparsely distributed sea-level pressure observation via a variational adjustment technique subject to some appropriate physical constraint(s), an improvement in the sea-level pressure analysis is expected. It is demonstrated that a simple marine boundary layer scheme in conjunction with a variational adjustment technique can be developed to help improve the sea-level pressure analysis by the SEASAT-derived wind of a limited-area domain in the ocean.
Scatterometers measure surface roughness which is empirically related either to surface stress or to the equivalent neutral stability wind. The importance of atmospheric stability effects for the analysis of these data is studied. For low wind speeds and neutral to slightly stable conditions, neutral stability wind is quite sensitive to stability. A variational analysis procedure for the scatterometer data, which adjusts both the near-surface velocity and temperature, is developed. In simulation tests, temperature analysis increments are found to be small. Also, the differences in the wind analyses due to differences in the temperature background field are small. However, if stability effects are not accounted for, there will be small systematic errors in the wind analysis.
The long range aircraft cruise problem is analyzed using a model intermediate in complexity between energy model and point mass model. It is shown that this formulation imbeds the classical steady state cruise as the central member along with several other oscillatory extremals. The oscillatory cruise trajectories are shown to exist if the Hessian of the function QD/VT with respect to altitude and airspeed is positive definite. An expression for predicting the frequency of oscillation is developed. Qualitative effects of increasing the vehicle thrust and improving the L/D are discussed. Numerical results for two fighter aircraft and a transport aircraft are given. While oscillatory cruise mode exists for the two fighter aircraft, steady state cruise at full throttle is found to be optimal for the transport aircraft. A second variation analysis to bring out the reason for fuel savings is developed. It is shown that whenever the Hessian of the function QD/VT is positive definite, the second variation will be zero along the classical steady state cruise arc, indicating that a neighboring extremal is competitive. Comparisons with the previous point mass and energy modeled results are given.
The first phase of transitioning the NASA GMAO GEOS atmospheric data assimilation capabilities to JEDI involves the replacement of the Grid-point Statistical Interpolation (GSI) with a corresponding JEDI analysis. This includes taking JEDI's Unified Observation Operator (UFO), its underlying dependencies, and the JEDI solver that enables a hybrid 4DEnVar strategy similar to what is used in the current GEOS-GSI system. Variational analysis involves at least two main components associated with the observation and background cost function terms. The first is directly related to the UFO, which is being carefully validated in a joint collaboration between GMAO and NCEP to demonstrate consistency with corresponding observations usage in GSI. The second component is the background term, which in a hybrid system involves the ability to set up both a climatologically-based term and an ensemble-based term. JEDI provides the means to implement both terms through its BUMP component. Use of BUMP would require a complete re-tune of both climatological and ensemble, which is a non-trivial exercise we would prefer to avoid. As an alternative, the work here studies the results of interfacing the GSI-background error capability (GSIBEC) into JEDI through SABER. With this, the exact same background error covariance formulation used in GSI can be employed in JEDI without need for re-tuning. This brief summary covers the work done to interface GSIBEC into JEDI and shows preliminary results where the background error covariances of the control (GEOS-GSI) and experiment (GEOS-JEDI) are identical in corresponding cycling experiments. The cycling exercise is obviously preliminary and so much can be expected from GEOS-JEDI when compared to GEOS-GSI. There is still a number of features that need closer attention and although in some cases in principle ready to cycle have been intentionally either turned off or not fully exercised (e.g., VarBC is applied but not cycled). Other features are still pending implementation, one such example is the implementation of the Tangent Linear Normal Mode Constraint. Still, results are quite encouraging as hopefully the discussion here illustrates.
The optimal trajectories in the neighborhood of an optimal intermediate-thrust arc are investigated for the minimum-fuel orbit rendezvous problem with fixed specific impulse. Since such an arc is singular, the thrust acceleration magnitude being the singular control component, a second-variation analysis leads to the identification of a field of neighboring, singular arcs in a state space of dimension four rather than six, provided that a suitable Jacobi condition is met. A given neighboring initial six-dimensional state vector does not generally lie on a neighboring singular arc, and junction onto the appropriate singular arc must be accomplished by a short period of strong variations in the acceleration. The neighboring singular arc meets the final condition in 4 dimensions, rather than 6 dimensions, and rendezvous must be completed by another, terminal short period of strong variations in the acceleration. Implications for midcourse guidance near a singular arc are discussed.
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.
Deep convection is the primary influence on weather and climate in tropical regions. However, understanding and simulating the shallow‐to‐deep (STD) convective transition has long been challenging. Here, we conduct high‐resolution numerical simulations to assess the environmental controls on the evolution of isolated convection in the Amazon during the wet season. The large‐scale forcing derived through a constrained variational analysis approach for the GoAmazon2014/5 Experiment is used in the simulations. Through sensitivity experiments, we examine the relative importance of moisture and wind shear in controlling the shallow‐to‐deep convective transition for isolated convective events. Convection exhibits the greatest sensitivity to humidity within the lowest 1.5 km, where a 4 mm reduction in column water vapor nearly suppresses ice water formation on deep convective days. In contrast, a reduction in column water vapor in the free troposphere by a factor of two or more is necessary to produce a comparable impact on convection. Increasing low‐level wind speed from 6 to 9 m s -1 enhances afternoon deep convection, raising the cloud ice mixing ratio by approximately 25%. Conversely, upper‐level wind shear reveals the weakest correlation with daytime convection in our simulations. Our results help characterize the role of moisture and wind shear on the STD transition and our understanding of the underlying mechanisms.
We present the cosmological analysis of the one-dimensional Lyman-α flux power spectrum from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We capture the dependence of the signal on cosmology and intergalactic medium physics using an emulator trained on a cosmological suite of hydrodynamical simulations, and we correct its predictions for the impact of astrophysical contaminants and systematics, many of these not considered in previous analyses. We employ this framework to constrain the amplitude and logarithmic slope of the linear matter power spectrum at k ★ = 0.009 km -1 s and redshift z = 3, obtaining Δ 2 ★ = 0.379 ± 0.032 and n ★ = -2.309 ± 0.019 https://github.com/igmhub/cobaya_lya_p1d. The robustness of these constraints is validated through the analysis of mocks and a large number of alternative data analysis variations, with cosmological parameters kept blinded throughout the validation process. We then combine our results with constraints from DESI BAO and temperature, polarization, and lensing measurements from Planck, ACT, and SPT-3G to set constraints on ΛCDM extensions. While our measurements do not significantly tighten the limits on the sum of neutrino masses from the combination of these probes, they sharpen the constraints on the effective number of relativistic species, N eff = 3.02 ± 0.10, the running of the spectral index, α s = 0.0014 ± 0.0041, and the running of the running, β s = -0.0006 ± 0.0048, by a factor of 1.18, 1.27, and 1.90, respectively. We conclude by outlining the improvements needed to fully reach the level of confidence implied by these uncertainties.
The Atmospheric Radiation Measurement (ARM) large-scale forcing data developed based on the constrained variational analysis (VARANAL) value-added product (VAP) (Zhang and Lin 1997, Zhang et al. 2001, Xie et al. 2004, Tang et al. 2019) has been widely used for single-column models (SCMs), cloud-resolving models (CRMs), and large-eddy simulation models (LESs) to understand and improve physical processes in models. Recently, the U.S. Department of Energy (DOE) ARM user facility conducted several major field campaigns using ship-based moving observational platforms. For example, the Marine ARM GPCI Investigation of Clouds (MAGIC) field campaign focused on the role of subtropical marine-boundary layer (MBL) clouds, and the Multidisciplinary Drifting Observatory for the Study of Arctic Climate (MOSAiC) field campaign aimed to improve understanding of the coupled climate systems in the Arctic. Observations from moving platforms are critical to provide a comprehensive characterization of coupled-system processes associated with all stages of the cloud and/or sea-ice life cycle. Traditional ARM large-scale forcing data have been developed at fixed locations. They need to be extended to include these moving platforms to address data needs for ship-based field campaigns or to support LES modeling in a Lagrangian framework. With these considerations in mind, we develop ARM-type Lagrangian large-scale forcing data sets based on the lagtraj framework (Boeing et al. 2020) with notable enhancements in generating forcings that are more suitable for ARM field campaigns. The lagtraj is a novel tool that generates forcings for LES and SCM simulation in both Lagrangian and Eulerian perspective. This technical report focuses on the major changes we performed on the lagtraj algorithm and provides an overview of the ARM Lagrangian Large-Scale Forcing Data (ARMLAGTRAJ) value-added products.
We investigate the Nagaoka-Thouless (NT) ferromagnetic instability in the strongly interacting t-t' Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin-polaron when the kinetic frustration t'/t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group (DMRG) simulations reveal a quantum phase transition from the NT ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite density via frustration-induced magnon band deformation.
The Amazon rainforest is a vital component of the global climate system, influencing the hydrological cycle and tropical circulation. However, understanding and modeling the evolution of convection in this region remain a scientific challenge. Here, we assess the environmental conditions associated with shallow, congestus, and isolated deep convection days during the wet season (December to April), employing measurements from the Green Ocean Amazon 2014–2015 (GoAmazon2014/5) experiment and large-scale wind fields from the constrained variational analysis. Composites of deep days show moister than average conditions below 3 km early in the morning. Analyzing the water budget at the surface through observations only, we estimated the water vapor convergence term as a residual of the water balance closure. Convergence remains nearly zero during the deep days until early afternoon (13:00 LST), when it becomes a dominant factor in the water budget. At 14:00 LST, the deep days experience a robust upward large-scale vertical velocity, especially above 4 km, which supports the shallow-to-deep convective transition occurring around 16:00–17:00 LST. In contrast, shallow and congestus days exhibit drier pre-convective conditions, along with diurnal water vapor divergence and large-scale subsidence that extend from the surface to the lower free troposphere. Moreover, afternoon precipitation exhibits the strongest linear correlation (0.6) with large-scale vertical velocity, nearly double the magnitude observed for other environmental factors, even moisture, at different levels and periods of the day. Precipitation also exhibits a moderate increase with low-level wind shear, while upper-level shear has a relatively minor negative impact on convection.
Upper atmosphere temperature variations analysis from satellite drag observations, discussing solar far UV and geomagnetic activity roles
Spectral response measurements of man-made targets and surfaces for frequency variation analysis of electromagnetic backscatter
An investigation of the isothermal wake-flow characteristics of several flame-holder shapes was carried out in a 4- by 4-inch flow chamber. The effects of flame-holder-shape changes on the characteristics of the Karman vortices and thus on the recirculation zones to which experimenters have related the combustion process were obtained for several flame holders. The results may furnish a basis of correlation, of combustion efficiency and stability for similarly shaped flame holders in combustion studies. Values of the spacing ratio-(ratio of lateral spacing to longitudinal spacing of vortices] obtained for the various shapes approximated the theoretical value of 0.36 given by the Karman stability analysis. Variations in vortex strength of more than 200 percent and in frequency of more than 60 percent were accomplished by varying flame-holder shape. A maximum increase in the recirculation parameter of 56 percent over that for a conventional V-gutter was also obtained. Varying flameholder shape and size enables the designer to select many schedules of variations in vortex strength and frequency- not obtainable by changing size only and may make it possible to approach theoretical maximum vortex strength for any given frequency.
The results of research studies on the OSO-6 zodiacal light experiment, conducted during the period from May 1976 to October 1977 are described. A discussion is included of the instrument performance and the empirical calibrations developed. Main areas of the research performed, i.e., (1) zodiacal light variation analysis; (2) integrated starlight and diffuse galactic light; and (3) earth/moon libration region counterglow, are covered. Considerable data processing was performed during these studies and it is summarized. Recommendations for future research to complete the interim results are given.