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This file contains a compilation of BHT data from oil wells in southwestern New Mexico. Surface temperature is calculated using the collar elevation. An estimate of geothermal gradient is calculated using the estimated surface temperature and the uncorrected BHT data.
Abstract not provided.
The development of high-speed volumetric laser-induced fluorescence measurements of formaldehyde (CH 2 O-LIF) using a pulse-burst laser operated at a repetition rate of 100 kHz is presented here. A novel laser scanning system employing an acousto-optic deflector (AOD) enables quasi-4D CH 2 O-LIF imaging at a scan frequency of 10 kHz. The diagnostic capability of time-resolved volumetric imaging is demonstrated in a partially premixed DME/air lifted turbulent jet flame near the flame base. Simultaneous imaging of laser beam profiles is performed to account for the laser pulse energy fluctuation and laser sheet inhomogeneity. With the accurate registration of laser sheet positions, the volumetric reconstruction of CH 2 O-LIF signals is performed within a detection volume of 17.3 × 11.9 × 2.3 mm 3 with an average out-of-plane spatial resolution of 250μm. A surface detection algorithm with adaptive thresholding is used to determine the global maximum intensity gradient by calculating gradient percentiles. The flame topology characteristics are investigated by evaluating the 3D curvatures of CH 2 O surfaces. Curvatures calculated using 2D data systematically underestimate the full 3D curvature due to the lack of out-of-plane information. The inner surfaces near the turbulent fuel jet exhibit higher probabilities of large mean curvature than the outer surfaces. The saddle and cylindrical structures are dominant on both the inner and outer surfaces and the elliptic structures occur with lower probability. The results suggest that the damping of turbulent fluctuations by the temperature increase through the CH 2 O region reduces the curvature, but the local structure topology remains self-similar.
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient technique for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is introduced. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of $O(N)$ , where $N$ is the number of parameters used to describe the outer flux surface or coil shapes.
The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Here, two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w = (0.298, 0.284, 0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β = (0.5, 0.7, 0.99), somewhat higher than the w = 0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w = 1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w = 0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.
The public release of WRF has two options for calculating horizontal gradients in the horizontal diffusion scheme. When the default option (diff_opt = 1) is used, horizontal gradients are calculated along coordinate surfaces, which roughly follow the terrain surface due to WRF’s terrain-conforming grid (i.e. along a sloping line in Fig. 1). Over steeply sloping terrain, horizontal gradients calculated in this way become inaccurate because they do not capture horizontal variation correctly. Therefore, another option exists (diff_opt = 2), for which Taylor series are used to approximate the derivative along a truly horizontal line. During WFIP2, HRRR forecasts switched from using diff_opt = 1 to diff_opt =2, and this was shown to improve velocity predictions, especially within observed cold pools (Olson et al., 2019).
Yamaguchi and Feingold (2012) note that the cloud fields in their Weather Research and Forecasting (WRF) large-eddy simulations (LESs) of marine stratocumulus exhibit a strong sensitivity to time stepping choices. In this study, we reproduce and analyze this sensitivity issue using two stratocumulus cases, one marine and one continental. Results show that (1) the sensitivity is associated with spurious motions near the moisture jump between the boundary layer and the free atmosphere, and (2) these spurious motions appear to arise from neglecting small variations in water vapor mixing ratio (qv) in the pressure gradient calculation in the acoustic substepping portion of the integration procedure. We show that this issue is remedied in the WRF dynamical core by replacing the prognostic equation for the potential temperature θ with one for the moist potential temperature θm=θ(1+1.61qv), which allows consistent treatment of moisture in the calculation of pressure during the acoustic substeps. With this modification, the spurious motions and the sensitivity to the time stepping settings (i.e., the dynamic time step length and number of acoustic substeps) are eliminated in both of the example stratocumulus cases. This modification improves the applicability of WRF for LES applications, and possibly other models using similar dynamical core formulations, and also permits the use of longer time steps than in the original code.
We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional grain boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.
We have implemented the unrestricted DFT approach with one-electron spin–orbit operators in the massively parallel NWChem program. Also implemented is the analytic gradient in the DFT approach with spin–orbit interactions. The current capabilities include single-point calculations and geometry optimization. Vibrational frequencies can be calculated numerically from the analytically calculated gradients. The implementation is based on the spin–orbit interaction operator derived from the effective core potential approach. The exchange functionals used in the implementation are functionals derived for non-spin–orbit calculations, including GGA as well as hybrid functionals. Spin–orbit Hartree–Fock calculations can also be carried out. We have applied the spin–orbit DFT methods to the Uranyl aqua complexes. We have optimized the structures and calculated the vibrational frequencies of both (UO2 2+)aq and (UO2 +)aq with and without spin–orbit effects. The effects of the spin–orbit interaction on the structures and frequencies of these two complexes are discussed. We also carried out calculations for Th2, and several low-lying electronic states are calculated. Our results indicate that, for open-shell systems, there are significant effects due to the spin–orbit effects and the electronic configurations with and without spin–orbit interactions could change due to the occupation of orbitals of larger spin–orbit interactions.
Gas-phase abundances in H ii regions of two spiral galaxies, NGC 7793 and NGC 4945, have been studied to determine their radial metallicity gradients. We used the strong-line method to derive oxygen abundances from spectra acquired with GMOS-S, the multi-object spectrograph on the 8 m Gemini South telescope. We found that NGC 7793 has a well-defined gas-phase radial oxygen gradient of −0.321 ± 0.112 dex R{sub 25}{sup −1} (or −0.054 ± 0.019 dex kpc{sup −1}) in the galactocentric range 0.17 < R{sub G}/R{sub 25} < 0.82, not dissimilar from gradients calculated with direct abundance methods in galaxies of similar mass and morphology. We also determined a shallow radial oxygen gradient in NGC 4945, −0.253 ± 0.149 dex R{sub 25}{sup −1} (or −0.019 ± 0.011 dex kpc{sup −1}) for 0.04 < R{sub G}/R{sub 25} < 0.51, where the larger relative uncertainty derives mostly from the larger inclination of this galaxy. NGC 7793 and NGC 4945 have been selected for this study because they are similar, in mass and morphology, to M33 and the Milky Way, respectively. Since at zeroth order we expect the radial metallicity gradients to depend on mass and galaxy type, we compared our galaxies in the framework of radial metallicity models best suited for M33 and the Galaxy. We found a good agreement between M33 and NGC 7793, pointing toward similar evolution for the two galaxies. We notice instead differences between NGC 4945 and the radial metallicity gradient model that best fits the Milky Way. We found that these differences are likely related to the presence of an active galactic nucleus combined with a bar in the central regions of NGC 4945, and to its interacting environment.
Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.
The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.
Analyzing the experimental data from L-2M stellarator and performing appropriate theoretical analysis, the authors affirmatively answer the question raised in the title of the article. The external peeling mode is proposed as the instability triggering the transition. Peeling mode stability in magnetic-hill Mercierstable plasmas is analyzed analytically. It is shown that correctly taking into account vacuum region forbids internal peeling modes, while the external peeling mode has a threshold with respect to the plasma pressure gradient. Calculations and experimental data are in reasonable agreement.
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.
Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors < 0.1 cm -1 as compared to results based on an analytic Hessian. For very small frequencies corresponding to nonbonded vibrations in noncovalent complexes (for which the harmonic approximation is questionable anyway), the finite-difference error can be larger, but even in these cases the errors can be reduced below 0.1 cm -1 by judicious choice of the displacement step size and a higher-order finite-difference approach. Finally, the surprising accuracy and robustness of the finite-difference results suggests that availability of the analytic Hessian is not so important in today's era of commodity processors that are readily available in large numbers.
This study evaluated the influence of diameter and grain size on the initiation and continuation phase of piping erosion. Twelve tests were performed in a laboratory setting in which sand was fluidized in a controlled setting and hydraulic gradients within the sand, flow rates through the sand, and expansion of the sand columns were measured as the sand was fluidized. This study was conducted to improve the understanding of the resistance a vertical column of sand offers to piping erosion. From the fluidization tests conducted in two permeameters with different diameters, it cannot be concluded that permeameter diameter has a significant influence on a specimen’s resistance to piping erosion. Although one test conducted in the smaller diameter permeameter did record hydraulic gradients lower than those recorded in tests conducted in the larger diameter permeameter, this was not a consistent observation for all tests run in the smaller diameter permeameter. Further analysis ought to involve more tests run in each permeameter as well as incorporating additional permeameters with both larger and smaller diameters than those used in this study. From the fluidization tests conducted using the well-graded, coarse-, medium-, and fine-grained sands, it appears that resistance to piping is dependent on grain size and grain size distribution. The coarse-grained sand offered the most resistance to piping, the fine-grained sand offered the least, and the medium-grained and well-graded sands offered similar resistances between those of the coarse-grained and fine-grained sands. Gradients at which sand boils were observed, maximum gradients reached before the sand fluidized, and the minimum gradients reached at the conclusion of each test also appear to be influenced by grain size and grain size distribution. Tests conducted on the coarse-grained sand recorded the highest and most closely spaced sand boil, maximum, and minimum gradients, indicating that it offered the highest and most constant resistance to piping, while the fine-grained sand tests recorded the lowest sand boil, maximum, and minimum gradients, indicating that it offered the least resistance to piping and that resistance decreased as the tests progressed. The medium-grained sand tests recorded sand boil, maximum, and minimum gradients between those of the coarse-grained and fine-grained sands. The well-graded sand tests recorded the lowest sand boil gradient, which could be indicative of the occurrence of suffusion erosion occurring in conjunction with piping erosion, whereby the finer particles were washed out of the sand matrix at relatively low gradients, forming sand boils while the relatively coarser matrix remained resistant to piping. All tests recorded maximum gradients that were lower than the theoretical critical gradients calculated using Equation 4. This is likely due to the changes in the internal configuration of the sand as the piping process 33 initiates. In order to better understand the influence of gradation on resistance to piping, more sand gradations should be tested in future work. Measured hydraulic gradients in the lower portion of the fluidized sands were higher than those measured in higher portions. This could be explained if the density of the fluidized sand was not uniform, with more material near the base of the column than near the top, which is contrary to the findings of Sellmeijer. Furthermore, the tests were terminated when the maximum height of the upstream reservoir was reached but did not give any evidence that gradients had leveled off to a uniform “final gradient”. It is likely that gradients would have continued to dissipate had more hydraulic head been applied to the upstream reservoir. In order to better understand this, additional testing should be conducted using an upstream reservoir capable of simulating higher hydraulic heads.
Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.
Parameter estimation using observables is a fundamental concept in the experimental sciences. Mathematical models that represent the physical processes can enable reconstructions of the experimental observables and greatly assist in parameter estimation by turning it into an optimization problem which can be solved by gradient-free or gradient-based methods. In this work, the recent rise in flexible frameworks for developing differentiable scientific computing programs is leveraged in order to dramatically accelerate data analysis of a common experimental diagnostic relevant to laser–plasma and inertial fusion experiments, Thomson scattering. A differentiable Thomson-scattering data analysis tool is developed that uses reverse-mode automatic differentiation (AD) to calculate gradients. By switching from finite differencing to reverse-mode AD, three distinct outcomes are achieved. First, gradient descent is accelerated dramatically to the extent that it enables near real-time usage in laser–plasma experiments. Second, qualitatively novel quantities which require $\mathcal{O}(10^3)$ parameters can now be included in the analysis of data which enables unprecedented measurements of small-scale laser–plasma phenomena. Third, uncertainty estimation approaches that leverage the value of the Hessian become accurate and efficient because reverse-mode AD can be used for calculating the Hessian.