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At least 955 records · Page 53

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Wigton, Larry↗

Aerodynamic Design of the Hybrid Wing Body Propulsion-Airframe Integration

A hybrid wingbody (HWB) concept is being considered by NASA as a potential subsonic transport aircraft that meets aerodynamic, fuel, emission, and noise goals in the time frame of the 2030s. While the concept promises advantages over conventional wing-and-tube aircraft, it poses unknowns and risks, thus requiring in-depth and broad assessments. Specifically, the configuration entails a tight integration of the airframe and propulsion geometries; the aerodynamic impact has to be carefully evaluated. With the propulsion nacelle installed on the (upper) body, the lift and drag are affected by the mutual interference effects between the airframe and nacelle. The static margin for longitudinal stability is also adversely changed. We develop a design approach in which the integrated geometry of airframe (HWB) and propulsion is accounted for simultaneously in a simple algebraic manner, via parameterization of the planform and airfoils at control sections of the wingbody. In this paper, we present the design of a 300-passenger transport that employs distributed electric fans for propulsion. The trim for stability is achieved through the use of the wingtip twist angle. The geometric shape variables are determined through the adjoint optimization method by minimizing the drag while subject to lift, pitch moment, and geometry constraints. The design results clearly show the influence on the aerodynamic characteristics of the installed nacelle and trimming for stability. A drag minimization with the trim constraint yields a reduction of 10 counts in the drag coefficient.

hybrid wing↗

Expedited Model Building Method for Rocket Nozzle Side Loading

Statistical analysis of test data is currently the preferred method of creating models for uncharacterized side loading in rocket nozzles. However, statistical analysis requires multiple data sets to be reliable; getting these sets requires building and testing multiple rocket motors, which is not feasible given the incredible time and cost required to do so. By using a combination of geometry, simplified finite element analysis (FEA) analogs, and algebra we can create a limited predictive model from only one test data set. Once created, the model requires only the input from one strain gauge located at each yaw and pitch attachment bracket for the actuation system. This process is not computationally intensive, therefore saving an abundance of time and budget over using full 3D FEA models to develop a similar predictive model. To develop the model, conversion factors between the strain at the gauge locations and corresponding actuator load is derived from the data. These conversion factors are used to create a “conversion ellipse” that bounds the constitutive properties of the nozzle as one lumped factor. Using a 2D cross-sectional analog of the nozzle exit plane, we create a function that allows us to determine the azimuthal location of the unexpected load based on the ratio between yaw and pitch strain readings. Combining this with the “conversion ellipse” yields a function that given the strain reading outputs an induced actuator load, regardless of the azimuthal location of the unexpected load. As previously mentioned, this predictive model is limited in its application as there is inaccuracy introduced by the use of data by only one test as well as simplifying assumptions. This approach makes a useful tool to quickly determine whether uncharacterized actuator loading events can damage actuation systems or induce loading that exceeds design limits.

Seetha A Kolli↗

An approach to simultaneous system design. I - Semialgebraic geometric methods

This paper introduces semialgebraic parameterization as an approach to analyze simultaneous stabilization and pole placement problems. Rational families of plants of a given McMillan degree, that are simultaneously stabilizable by a fixed family of compensators, are parameterized. For a discrete family of plants, the parameterization problem reduces to the simultaneous stabilization or the pole placement problem of a r-tuple of multi input multi output plants by a nonswitching compensator. It is shown that by removing a semialgebraic subset of a proper algebraic set, the 'space of plants' can be decomposed into components that are either simultaneously stabilizable or simultaneously unstabilizable. Under special cases, explicit parameterization of the semialgebraic set is obtained. Finally a necessary condition for the simultaneous stabilization of single input or single output plants is obtained.

Ghosh, B. K.↗

Finite difference grid generation by multivariate blending function interpolation

The General Interpolants Method (GIM) code which solves the multidimensional Navier-Stokes equations for arbitrary geometric domains is described. The geometry module in the GIM code generates two and three dimensional grids over specified flow regimes, establishes boundary condition information and computes finite difference analogs for use in the GIM code numerical solution module. The technique can be classified as an algebraic equation approach. The geometry package uses multivariate blending function interpolation of vector-values functions which define the shapes of the edges and surfaces bounding the flow domain. By employing blending functions which conform to the cardinality conditions the flow domain may be mapped onto a unit square (2-D) or unit cube (3-D), thus producing an intrinsic coordinate system for the region of interest. The intrinsic coordinate system facilitates grid spacing control to allow for optimum distribution of nodes in the flow domain.

Anderson, P. G.↗

Three dimensional flow field inside compressor rotor, including blade boundary layers

The Reynolds stress equation, pressure strain correlation, and dissipative terms and diffusion are discussed in relation to turbulence modelling using the Reynolds stress model. Algebraic modeling of Reynolds stresses and calculation of the boundary layer over an axial cylinder are examined with regards to the kinetic energy model for turbulence modelling. The numerical analysis of blade and hub wall boundary layers, and an experimental study of rotor blade boundary layer in an axial flow compressor rotor are discussed. The Patankar-Spalding numerical method for two dimensional boundary layers is included.

Galmes, J. M.↗

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.

Gorski, Krzysztof M.↗

Synthesis of Greedy Algorithms Using Dominance Relations

Greedy algorithms exploit problem structure and constraints to achieve linear-time performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a matroid, but the existence of such a translation can be as hard to determine as the existence of a greedy algorithm itself. An alternative characterization of greedy algorithms is in terms of dominance relations, a well-known algorithmic technique used to prune search spaces. We demonstrate a process by which dominance relations can be methodically derived for a number of greedy algorithms, including activity selection, and prefix-free codes. By incorporating our approach into an existing framework for algorithm synthesis, we demonstrate that it could be the basis for an effective engineering method for greedy algorithms. We also compare our approach with other characterizations of greedy algorithms.

Nedunuri, Srinivas↗

Flow field analysis for a class of waverider configurations

A package of computer codes for analysis of flow fields for waverider configurations is described. The package consists of a surface/volume grid generator and a finite-volume flow solver. The grid generator defines body geometries and computational grids by an algebraic homotopy procedure. The algebraic procedure is versatile in its application and can readily generate configurations in the class of blended wing-body geometries. This code has the ability to produce a wide variety of geometries in the given class with varying geometrical attributes. The flow solver employs a finite-volume formation and solves the explicit, Runge-Kutta integration technique. The method or flow simulation incorporates several techniques for acceleration of the convergence of the interaction process and an entropy corrected enthalpy damping procedure for efficient computation of high Mach number flows.

Moitra, Anutosh↗

TOA Lightning Location Retrieval on Spherical and Oblate Spheroidal Earth Geometries

A simple linear algebraic solution is introduced for retrieving the location and time-of-occurrence of lightning ground strikes on a spherical Earth from a network of four or more time-of-arrival (TOA) sensors. Since the solution accounts for Earth curvature, it represents an extension to earlier planar model results described by Koshak et al. A test of the retrieval method is provided using computer-simulated data sets. The method is easy to comprehend and completely avoids reference to the mathematics of spherical hyperbolas such as discussed by Lewis. A quasi-analytic extension to the spherical Earth solution is provided for an oblate spheroidal Earth geometry, and the importance/relevance of oblate effects are discussed. Future application of these methods in support of the North American National Lightning Detection Network (NALDN) described by Cummins et al. is desirable, but additional theoretical investigations are required to incorporate magnetic bearing information into the present solution process.

Koshak, W. J.↗

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Summary We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.

Barker, Andrew T.↗

Development of the general interpolants method for the CYBER 200 series of supercomputers

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

Stalnaker, J. F.↗

Heat transfer predictions for two turbine nozzle geometries at high Reynolds and Mach numbers

Predictions of turbine vane and endwall heat transfer and pressure distributions are compared with experimental measurements for two vane geometries. The differences in geometries were due to differences in the hub profile, and both geometries were derived from the design of a high rim speed turbine (HRST). The experiments were conducted in the Isentropic Light Piston Facility (ILPF) at Pyestock at a Reynolds number of 5.3 x 10(exp 6), a Mach number of 1.2, and a wall-to-gas temperature ratio of 0.66. Predictions are given for two different steady-state three-dimensional Navier-Stokes computational analyses. C-type meshes were used, and algebraic models were employed to calculate the turbulent eddy viscosity. The effects of different turbulence modeling assumptions on the predicted results are examined. Comparisons are also given between predicted and measured total pressure distributions behind the vane. The combination of realistic engine geometries and flow conditions proved to be quite demanding in terms of the convergence of the CFD solutions. An appropriate method of grid generation, which resulted in consistently converged CFD solutions, was identified.

Boyle, R. J.↗

A phase transition model and temporal logic specifications for smart energy systems - revisited

In this paper, we revisit the method of a phase transition model for representing hybrid systems and temporal logic specifications (TLSs) for specifying desired behaviors of systems, and discuss their usefulness for smart energy systems. On the one hand, the phase transition model incorporates the continuous model of the relay device action with a particular structural form that allows for the construction of a single, global differential-algebraic equation for hybrid systems (thus smoothed hybrid systems). On the other hand, the TLS allows sophisticated descriptions of control specifications addressing both magnitude and time simultaneously, which has recently been applied to the control strategy of several types of continuous and hybrid systems. We provide high-level descriptions of each of the two techniques and present simulation results in the context of smart energy systems.

Park, Byungkwon↗

Universal time scalings of sensitivity in Markovian quantum metrology

Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear, and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Surface Analysis Insight Note: Observations relating to photoemission peak shapes, oxidation state, and chemistry of titanium oxide films

It is common practice to describe the coordination of metal atoms in a binding configuration with their nearest neighbors in terms of oxidation state, a measure by which the number of electrons redistributed between atoms forming chemical bonds. In XPS terms, change to an oxidation state is commonly inferred by correlating photoemission signal with binding energy. The assumption, when classifying photoemission signals into distinct spectral shapes, is that a distribution of intensities shifted to lower binding energy is evidence of a reduction in oxidation state. In this Insight note, we raise the prospect that changes in photoemission peak shape may occur without obvious changes, determined by XPS in stoichiometry for a material. It is well known that TiO 2 measured by XPS yields reproducible Ti 2p photoemission peaks. However, on exposing TiO 2 to ion beams, Ti 2p photoemission evolves to complex distributions in intensity, which are particularly difficult to analyze by traditional fitting of bell-shaped curves to these data. For these reasons, in this Insight note, a thin film of TiO 2 deposited on a silicon substrate is chosen for analysis by XPS and linear algebraic techniques. Alterations in spectral shapes created from modified TiO 2 , which might be interpreted as the change in oxidation state, are assessed in terms of relative proportions of titanium to oxygen. It is found through detailed analysis of spectra that quantification by XPS, using procedures routinely used in practice, is not in accord with the typical interpretations of photoemission shapes. The data processing methods used and results presented in this work are of particular relevance to elucidating fundamental phenomena governing the surface evolution of materials-enabled energy processes where cyclic/non-steady usage changes the nature of bonding, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Path integrals, complex probabilities and the discrete Weyl representation

Abstract A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Physics↗

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗