An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations

We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations

A fixed-base simulation study of two STOL aircraft flying curved, descending instrument approach paths

A real-time, fixed-base simulation study has been conducted to determine the curved, descending approach paths (within passenger-comfort limits) that would be acceptable to pilots, the flight-director-system logic requirements for curved-flight-path guidance, and the paths which can be flown within proposed microwave landing system (MLS) coverage angles. Two STOL aircraft configurations were used in the study. Generally, no differences in the results between the two STOL configurations were found. The investigation showed that paths with a 1828.8 meter turn radius and a 1828.8 meter final-approach distance were acceptable without winds and with winds up to at least 15 knots for airspeeds from 75 to 100 knots. The altitude at roll-out from the final turn determined which final-approach distances were acceptable. Pilots preferred to have an initial straight leg of about 1 n. mi. after MLS guidance acquisition before turn intercept. The size of the azimuth coverage angle necessary to meet passenger and pilot criteria depends on the size of the turn angle: plus or minus 60 deg was adequate to cover all paths execpt ones with a 180 deg turn

Heat driven pulse pump

A heat driven pulse pump includes a chamber having an inlet port, an outlet port, two check valves, a wick, and a heater. The chamber may include a plurality of grooves inside wall of the chamber. When heated within the chamber, a liquid to be pumped vaporizes and creates pressure head that expels the liquid through the outlet port. As liquid separating means, the wick, disposed within the chamber, is to allow, when saturated with the liquid, the passage of only liquid being forced by the pressure head in the chamber, preventing the vapor from exiting from the chamber through the outlet port. A plurality of grooves along the inside surface wall of the chamber can sustain the liquid, which is amount enough to produce vapor for the pressure head in the chamber. With only two simple moving parts, two check valves, the heat driven pulse pump can effectively function over the long lifetimes without maintenance or replacement. For continuous flow of the liquid to be pumped a plurality of pumps may be connected in parallel

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

A flight investigation with a STOL airplane flying curved, descending instrument approach paths

A flight investigation using a De Havilland Twin Otter airplane was conducted to determine the configurations of curved, 6 deg descending approach paths which would provide minimum airspace usage within the requirements for acceptable commercial STOL airplane operations. Path configurations with turns of 90 deg, 135 deg, and 180 deg were studied; the approach airspeed was 75 knots. The length of the segment prior to turn, the turn radius, and the length of the final approach segment were varied. The relationship of the acceptable path configurations to the proposed microwave landing system azimuth coverage requirements was examined

Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Electron-hole correlation effects in the emission of light from quantum wires

We present a self-consistent treatment of the electron-hole correlations in optically excited quantum wires within the ladder approximation, and using a contact potential interaction. The limitations of the ladder approximation to the excitonic low-density region are largely overcome by the introduction of higher order correlations through self consistency. We show relevance of these correlations in the low-temperature emission, even for high density relevant in lasing, when large gain replaces excitonic absorption.Comment: 4 paes 3 figure

Assessment of Ground-Based and Aerial Cloud Seeding Using Trace Chemistry

Targeting seedable clouds with silver iodide in complex terrain adds considerable uncertainty in weather modification studies. This study explores the geographic and temporal distribution of silver iodide associated with an active cloud seeding program in central Idaho snowpack using trace chemistry. Over 4,000 snow samples were analyzed for the presence of a cloud seeding silver iodide (AgI) signature over two winter seasons. The results indicate the following. (1) At sites within 70 km of AgI sources, silver enrichments were detected at 88% of cases involving seeding efforts from ground generators, but none from aircraft seeded cases. (2) Real-time snow collection methods were replicable within 0.41 ppt and confirmed seeding signatures for the entire duration of a seeded storm (n=3). (3) Sites sampled beyond 70 km of AgI sources (n=13) lacked detectable seeding signatures in snow. The results of this study demonstrate some of the strengths and limitations of chemical tracers to evaluate cloud seeding operations and provide observational data that can inform numerical simulations of these processes. The results also indicate that this chemical approach can be used to help constrain the spatiotemporal distribution of silver from cloud seeding efforts