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FireCat performs multiscale simulations by coupling ab initio microkinetic simulations from CatMAP with two-dimensional continuum transport simulations from EchemFEM (Firedrake). This coupling is performed in an iterative fashion. The examples provided here are specific to electrochemical CO2 reduction to CO on Au electrodes.
A low speed wind tunnel equipped with a axial gust generator to simulate the aerodynamic environment of a helicopter rotor was used to study the dynamic stall of a pitching blade in an effort to ascertain to what extent harmonic velocity perturbations in the freestream affect dynamic stall. The aerodynamic moment on a two dimensional, pitching blade model in both constant and pulsating airstream was measured. An operational analog computer was used to perform on-line data reduction and plots of moment versus angle of attack and work done by the moment were obtained. The data taken in the varying freestream were then compared to constant freestream data and to the results of two analytical methods. These comparisons show that the velocity perturbations have a significant effect on the pitching moment which can not be consistently predicted by the analytical methods, but had no drastic effect on the blade stability.
An improved system for measuring aerodynamic skin friction which uses a dual-laser-beam oil-film interferometer was developed. Improvements in the optical hardware provided equal signal characteristics for each beam and reduced the cost and complexity of the system by replacing polarization rotation by a mirrored prism for separation of the two signals. An automated, objective, data-reduction procedure was implemented to eliminate tedious manual manipulation of the interferometry data records. The present system was intended for use in two-dimensional, incompressible flows over a smooth, level surface without pressure gradient, but the improvements discussed are not limited to this application.
The problem of flow past bluff bodies was studied extensively in the past. The problem of drag reduction is very important in many high speed flow applications. Considerable work has been done in this subject area in case of circular cylinders. The present study attempts to investigate the feasibility of drag reduction on a rectangular cylinder by flow injection by flow injection from the rear stagnation region. The physical problem is modeled as two-dimensional body and numerical analysis is carried out with and without trailing jets. A commercial code is used for this purpose. Unsteady computation is performed in case of rectangular cylinders with no trailing jets where as steady state computation is performed when jet is introduced. It is found that drag can be reduced by introducing jets with small intensity in rear stagnation region of the rectangular cylinders.
In this paper, we summarize the results of the sensitivity analysis and data reduction carried out to determine the information content of AIRS and IASI channels. The analysis and data reduction was based on the use of subset selection techniques developed in the linear algebra and statistical community to study linear dependencies in high dimensional data sets. We applied the subset selection method to study dependency among channels by studying the dependency among their weighting functions. Also, we applied the technique to study the information provided by the different levels in which the atmosphere is discretized for retrievals and analysis. Results from the method correlate well with intuition in many respects and point out to possible modifications for band selection in sensor design and number and location of levels in the analysis process.
The initiation and propagation of damage mechanisms such as cracks and delaminations generate acoustic waves, which propagate through a structure. These waves can be detected and analyzed to provide the location and severity of damage as part of a structural health monitoring (SHM) system. This methodology of damage detection is commonly known as acoustic emission (AE) monitoring, and is widely used on a variety of applications on civil structures. AE has been widely considered for SHM of aerospace vehicles. Numerous successful ground and flight test demonstrations have been performed, which show the viability of the technology for damage monitoring in aerospace structures. However, one significant current limitation for application of AE techniques on aerospace vehicles is the large size, mass, and power requirements for the necessary monitoring instrumentation. To address this issue, a prototype multiplexing approach has been developed and demonstrated in this study, which reduces the amount of AE monitoring instrumentation required. Typical time division multiplexing techniques that are commonly used to monitor strain, pressure and temperature sensors are not applicable to AE monitoring because of the asynchronous and widely varying rates of AE signal occurrence. Thus, an event based multiplexing technique was developed. In the initial prototype circuit, inputs from eight sensors in a linear array were multiplexed into two data acquisition channels. The multiplexer rapidly switches, in less than one microsecond, allowing the signals from two sensors to be acquired by a digitizer. The two acquired signals are from the sensors on either side of the trigger sensor. This enables the capture of the first arrival of the waves, which cannot be accomplished with the signal from the trigger sensor. The propagation delay to the slightly more distant neighboring sensors makes this possible. The arrival time from this first arrival provides a more accurate source location determination. The multiplexer also identifies which channels are acquired by encoding TTL logic pulses onto the latter portion of the signals. This prototype system was demonstrated using pencil lead break (Hsu-Neilsen) sources on an aluminum plate. It performed as designed providing rapid low noise trigger based switching with encoded channel identification. this multiplexing approach is not limited to linear arrays, but can be easily extended to monitor sensors in planar ot three dimensional arrays. A 32 channel multiplexing system is under development that will allow arbitrary sensor placement. Another benefit of this multiplexing system is the reduction in the expense of data acquisition hardware. In addition, the reduced weight and power requirements are of extreme importance for proposed AE systems on aerospace vehicles.
This report summarizes FY16 progress towards enabling uncertainty quantification for compressible cavity simulations using model order reduction (MOR). The targeted application is the quantification of the captive-carry environment for the design and qualification of nuclear weapons systems. To accurately simulate this scenario, Large Eddy Simulations (LES) require very fine meshes and long run times, which lead to week-long runs even on parallel state-of-the-art super- computers. MOR can reduce substantially the CPU-time requirement for these simulations. We describe two approaches for model order reduction for nonlinear systems, which can yield significant speed-ups when combined with hyper-reduction: the Proper Orthogonal Decomposition (POD)/Galerkin approach and the POD/Least-Squares Petrov Galerkin (LSPG) approach. The implementation of these methods within the in-house compressible flow solver SPARC is discussed. Next, a method for stabilizing and enhancing low-dimensional reduced bases that was developed as a part of this project is detailed. This approach is based on a premise termed "minimal subspace rotation", and has the advantage of yielding ROMs that are more stable and accurate for long-time compressible cavity simulations. Numerical results for some laminar cavity problems aimed at gauging the viability of the proposed model reduction methodologies are presented and discussed.
In the calculation of turbulent boundary layers, a large number of mesh points are required to adequately resolve the intense variation in the velocity and enthalpy in the near-wall region. A substantial reduction in computational effort may be realized by representing the velocity and enthalpy profiles in the wall layer by analytical embedded functions. The effectively inviscid flow in the outer part of the boundary layer may then be resolved by employing a relatively coarser mesh. To obtain complete profiles, the outer numerical solution is matched asymptotically to the inner wall-layer analytical solution. To date, this approach has been restricted to two-dimensional flows; in the present study, a method which may be utilized for turbulent boundary layers with heat transfer in a plane of symmetry is developed as a first step in the application of the embedded-function method to full three-dimensional flows. The present method uses only about half as many mesh points as that required in a conventional procedure, which calculates the flow all the way to the wall, but there is no degradation in accuracy of the computed results.
Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.
The reduction of the asymmetry in the plasma sheath voltages of a cylindrical coaxial capacitively coupled plasma is crucial for efficient surface modification of the inner surfaces of concave three-dimensional structures, including superconducting radio frequency cavities. One critical asymmetry effect is the negative dc self-bias, formed across the inner electrode plasma sheath due to its lower surface area compared to the outer electrode. The effect on the self-bias potential with the surface enhancement by geometric modification on the inner electrode structure is studied. The shapes of the inner electrodes are chosen as cylindrical tube, large and small pitch bellows, and disc-loaded corrugated structure (DLCS). The dc self-bias measurements for all these shapes were taken at different process parameters in Ar/Cl 2 discharge. Lastly, the reversal of the negative dc self-bias potential to become positive for a DLCS inner electrode was observed and the best etch rate is achieved due to the reduction in plasma asymmetry.
The Bloch equation in the Heisenberg–Weyl group is considered. A λ-representation of the Lie algebra of a Heisenberg–Weyl group of arbitrary dimensionality is constructed, and an expression for the statistical sum in the Heisenberg–Weyl group is obtained. Expressions for the statistical sum of the Heisenberg–Weyl group and other thermodynamic quantities are analyzed.
In an effort to secure, refine, and supplement the relation between central supermassive black hole masses, M {sub •}, and the bulge luminosities of their host galaxies, L {sub bul}, we obtained deep, high spatial resolution K-band images of 35 nearby galaxies with securely measured M {sub •}, using the wide-field WIRCam imager at the Canada-France-Hawaii-Telescope. A dedicated data reduction and sky subtraction strategy was adopted to estimate the brightness and structure of the sky, a critical step when tracing the light distribution of extended objects in the near-infrared. From the final image product, bulge and total magnitudes were extracted via two-dimensional profile fitting. As a first order approximation, all galaxies were modeled using a simple Sérsic-bulge+exponential-disk decomposition. However, we found that such models did not adequately describe the structure that we observed in a large fraction of our sample galaxies which often include cores, bars, nuclei, inner disks, spiral arms, rings, and envelopes. In such cases, we adopted profile modifications and/or more complex models with additional components. The derived bulge magnitudes are very sensitive to the details and number of components used in the models, although total magnitudes remain almost unaffected. Usually, but not always, the luminosities and sizes of the bulges are overestimated when a simple bulge+disk decomposition is adopted in lieu of a more complex model. Furthermore, we found that some spheroids are not well fit when the ellipticity of the Sérsic model is held fixed. This paper presents the details of the image processing and analysis, while we discuss how model-induced biases and systematics in bulge magnitudes impact the M {sub •}-L {sub bul} relation in a companion paper.
Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.
We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.
Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.
The propagation of orographic gravity waves into an atmosphere with exponentially decreasing density is simulated with a two-dimensional, nonlinear, time-dependent numerical model. After the stationary wave is established over the mountain, the model predicts that wave breaking causes a large reduction of the vertical momentum flux in the flow, not only at levels where wave breaking is present, but also far below the lowest occurrence of overturning. More than half of the decrease in momentum flux is explained by the presence of large amplitude, downward propagating waves, which are generated in regions of wave breaking. The downward propagating waves appear almost simultaneously with overturning, and have nonzero phase speeds, suggesting a strongly nonlinear generation mechanism that depends on local wave properties. The generation of these downward propagating waves is a robust process, insensitive to mountain height, mountain width, or density scale height. These results have important implications for observational studies of orographically generated waves as well as for schemes that seek to parameterize the effects of orogoraphy in large-scale models.