Loop Equations and the Topological Phase of Multi-Cut Matrix Models

We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop equations which can be expressed as Virasoro constraints on the partition function. We discover a ``pure topological" phase of the theory in which all correlation functions are determined by recursion relations. We also examine macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to dense polymers.Comment: 24p

Construction of dynamic stochastic simulation models using knowledge-based techniques

Over the past three decades, computer-based simulation models have proven themselves to be cost-effective alternatives to the more structured deterministic methods of systems analysis. During this time, many techniques, tools and languages for constructing computer-based simulation models have been developed. More recently, advances in knowledge-based system technology have led many researchers to note the similarities between knowledge-based programming and simulation technologies and to investigate the potential application of knowledge-based programming techniques to simulation modeling. The integration of conventional simulation techniques with knowledge-based programming techniques is discussed to provide a development environment for constructing knowledge-based simulation models. A comparison of the techniques used in the construction of dynamic stochastic simulation models and those used in the construction of knowledge-based systems provides the requirements for the environment. This leads to the design and implementation of a knowledge-based simulation development environment. These techniques were used in the construction of several knowledge-based simulation models including the Advanced Launch System Model (ALSYM)

Design of an Advanced Inlet Liner for the Quiet Technology Demonstrator 3

The utilization of advanced fan designs (including higher bypass ratios) and shorter engine nacelles has highlighted a need for increased fan noise reduction over a broad frequency range. Thus, improved broadband liner designs must account for these constraints and take advantage of novel liner configurations. With these observations in mind, the development and assessment of a broadband acoustic liner optimization process has been pursued through a series of design and experimental studies. In this work, an advanced inlet liner was designed for a Boeing 737MAX-7 to reduce drag and to improve the broadband noise reduction relative to conventional liners in use today. Specifically, a three layer liner was designed, fabricated, and flight tested as part of the Quiet Technology Demonstrator 3 flight test program. Initial tonal predictions captured the behavior of the measured data very well and both prediction and measurements show an increased acoustic benefit at larger observer angles, particularly at the takeoff condition. Ultimately, flight test results showed the three degree-of-freedom liner to provide a 3.2 EPNdB cumulative inlet component benefit and a 0.7 EPNdB cumulative airplane benefit over the production liner. This excellent result provides valuable validation of the broadband liner design process, as well as the enhancements made to the overall approach. It also illustrates the value of the design process in concurrently evaluating various liner designs (i.e., SDOF, MDOF, etc.) and their application to various locations. Thus, the design process may be applied with further confidence to investigate novel liner configurations in future design studies

An Investigation of Bifurcation Acoustic Treatment Effects on Aft-Fan Engine Nacelle Noise

Increasing air traffic and more stringent aircraft noise regulations continue to expand requirements on aircraft noise reduction capabilities for conventional and unconventional aircraft configurations. A major component of the overall aircraft noise is the sound associated with the propulsion system mounted in the engine nacelle. Acoustic liners mounted in the aircraft engine nacelles provide a significant portion of the current fan noise reduction. However, they must be further optimized if challenging noise reduction goals are to be achieved. One area within the aft bypass duct that may be an excellent candidate for increased attention is the acoustic treatment on the engine bifurcations (i.e., engine pylon and lower bifurcation). This paper describes a fundamental study of the effects of bifurcation treatment on simulated aft fan noise, as well as the validation of numerical tools to predict such effects. Five bifurcation configurations (four treated and one hardwall) were fabricated and tested in the NASA Langley Curved Duct Test Rig. Results show that mode scattering may occur due to both the presence of the bifurcation, as well as variable impedance distributions on the bifurcation surface. Future work will also include optimization of bifurcation treatments for testing in the Curved Duct Test Rig. These initial results are promising and this work provides valuable information for further study and improvement of the performance of bifurcation acoustic treatments

Toeplitz algebras and spectral results for the one-dimensional Heisenberg model

We determine the structure of the spectrum and obtain non-propagation estimates for a class of Toeplitz operators acting on a subset of the lattice $\Z^N$. This class contains the Hamiltonian of the one-dimensional Heisenberg model.Comment: 13 page

Assessment of Axial Wave Number and Mean Flow Uncertainty on Acoustic Liner Impedance Education

A key parameter in designing and assessing advanced broadband acoustic liners to achieve the current and future noise reduction goals is the acoustic impedance presented by the liner. This parameter, intrinsic to a specific liner configuration, is dependent on sound pressure level and grazing flow velocity. Current impedance eduction approaches have, in general, provided excellent results and continue to be employed throughout the acoustic liner community. However, some recent applications have indicated a possible dependence of the educed impedance on the direction of incident waves relative to the mean flow. The purpose of the current study is to investigate this unexpected behavior for various impedance eduction methods based on the Pridmore-Brown and convected Helmholtz equations. Specifically, the effects of flow profile and axial wavenumber uncertainties on educed impedances for upstream and downstream sources are investigated. The uniform flow results demonstrate the importance of setting a correct Mach number value in obtaining consistent educed impedances for upstream and downstream sources. In fact, the consistency of results over the two source locations was greatly improved by a slight modification of the uniform flow Mach number. In addition, uncertainty in educed axial wavenumber was also illustrated to correlate well with differences in the educed impedances, even with modified uniform flow Mach number. Finally, while less straightforward than in the uniform flow case, it appears that modification of the mean flow profile may also improve consistency of results for upstream and downstream results when shear flow is included

Robustness of the Thirty Meter Telescope Primary Mirror Control System

The primary mirror control system for the Thirty Meter Telescope (TMT) maintains the alignment of the 492 segments in the presence of both quasi-static (gravity and thermal) and dynamic disturbances due to unsteady wind loads. The latter results in a desired control bandwidth of 1Hz at high spatial frequencies. The achievable bandwidth is limited by robustness to (i) uncertain telescope structural dynamics (control-structure interaction) and (ii) small perturbations in the ill-conditioned influence matrix that relates segment edge sensor response to actuator commands. Both of these effects are considered herein using models of TMT. The former is explored through multivariable sensitivity analysis on a reduced-order Zernike-basis representation of the structural dynamics. The interaction matrix ("A-matrix") uncertainty has been analyzed theoretically elsewhere, and is examined here for realistic amplitude perturbations due to segment and sensor installation errors, and gravity and thermal induced segment motion. The primary influence of A-matrix uncertainty is on the control of "focusmode"; this is the least observable mode, measurable only through the edge-sensor (gap-dependent) sensitivity to the dihedral angle between segments. Accurately estimating focus-mode will require updating the A-matrix as a function of the measured gap. A-matrix uncertainty also results in a higher gain-margin requirement for focus-mode, and hence the A-matrix and CSI robustness need to be understood simultaneously. Based on the robustness analysis, the desired 1 Hz bandwidth is achievable in the presence of uncertainty for all except the lowest spatial-frequency response patterns of the primary mirror

The Sweet Smell of Subsidies Revisited

Agricultural and Food Policy,