8,224 research outputs found
On 3rd and 4th moments of finite upper half plane graphs
AbstractTerras [A. Terras, Fourier Analysis on Finite Groups and Applications, Cambridge Univ. Press, 1999] gave a conjecture on the distribution of the eigenvalues of finite upper half plane graphs. This is known as a finite analogue of Sato–Tate conjecture. There are several modified versions of them. In this paper, we show that this conjecture is not correct in its original form (i.e., Conjecture 1.1). This is shown for the calculations of the 3rd and 4th moments of the distribution of the eigenvalues. We remark that a weaker version of the conjecture (i.e., Conjecture 1.2) may still hold
Tensile buckling of advanced turboprops
Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present
Z(3) Interfaces in Lattice Gauge Theory
A study is made of properties of the Z(3) interface which forms between the
different ordered phases of pure SU(3) gauge theory above a critical
temperature. The theory is simulated on a (2+1)-D lattice at various
temperatures above this critical point. At high temperatures, the interface
tension is shown to agree well with the prediction of perturbation theory. Near
the critical temperature, the interface behaviour is characterised by various
displacement moments, and modelled by an interacting scalar field theory. This
thesis is provided for reference, as it gives full details of the computational
and statistical methods outlined only briefly in preprints hep-lat/9605040 and
hep-lat/9607005.Comment: TeX, 143 pages, 52 figure
Systematic Study of Accuracy of Wall-Modeled Large Eddy Simulation using Uncertainty Quantification Techniques
The predictive accuracy of wall-modeled large eddy simulation is studied by
systematic simulation campaigns of turbulent channel flow. The effect of wall
model, grid resolution and anisotropy, numerical convective scheme and
subgrid-scale modeling is investigated. All of these factors affect the
resulting accuracy, and their action is to a large extent intertwined. The wall
model is of the wall-stress type, and its sensitivity to location of velocity
sampling, as well as law of the wall's parameters is assessed. For efficient
exploration of the model parameter space (anisotropic grid resolution and wall
model parameter values), generalized polynomial chaos expansions are used to
construct metamodels for the responses which are taken to be measures of the
predictive error in quantities of interest (QoIs). The QoIs include the mean
wall shear stress and profiles of the mean velocity, the turbulent kinetic
energy, and the Reynolds shear stress. DNS data is used as reference. Within
the tested framework, a particular second-order accurate CFD code (OpenFOAM),
the results provide ample support for grid and method parameters
recommendations which are proposed in the present paper, and which provide good
results for the QoIs. Notably, good results are obtained with a grid with
isotropic (cubic) hexahedral cells, with cells per , where
is the channel half-height (or thickness of the turbulent boundary
layer). The importance of providing enough numerical dissipation to obtain
accurate QoIs is demonstrated. The main channel flow case investigated is , but extension to a wide range of -numbers is
considered. Use of other numerical methods and software would likely modify
these recommendations, at least slightly, but the proposed framework is fully
applicable to investigate this as well
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
Conceptual design of an airborne laser Doppler velocimeter system for studying wind fields associated with severe local storms
An airborne laser Doppler velocimeter was evaluated for diagnostics of the wind field associated with an isolated severe thunderstorm. Two scanning configurations were identified, one a long-range (out to 10-20 km) roughly horizontal plane mode intended to allow probing of the velocity field around the storm at the higher altitudes (4-10 km). The other is a shorter range (out to 1-3 km) mode in which a vertical or horizontal plane is scanned for velocity (and possibly turbulence), and is intended for diagnostics of the lower altitude region below the storm and in the out-flow region. It was concluded that aircraft flight velocities are high enough and severe storm lifetimes are long enough that a single airborne Doppler system, operating at a range of less than about 20 km, can view the storm area from two or more different aspects before the storm characteristics change appreciably
Confocal Laser Induced Fluorescence with Comparable Spatial Localization to the Conventional Method
We present measurements of ion velocity distributions obtained by laser induced fluorescence (LIF) using a single viewport in an argon plasma. A patent pending design, which we refer to as the confocal fluorescence telescope, combines large objective lenses with a large central obscuration and a spatial filter to achieve high spatial localization along the laser injection direction. Models of the injection and collection optics of the two assemblies are used to provide a theoretical estimate of the spatial localization of the confocal arrangement, which is taken to be the full width at half maximum of the spatial optical response. The new design achieves approximately 1.4 mm localization at a focal length of 148.7 mm, improving on previously published designs by an order of magnitude and approaching the localization achieved by the conventional method. The confocal method, however, does so without requiring a pair of separated, perpendicular optical paths. The confocal technique therefore eases the two window access requirement of the conventional method, extending the application of LIF to experiments where conventional LIF measurements have been impossible or difficult, or where multiple viewports are scarce
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