Scaling Properties of Paths on Graphs

Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of places along the way. For each path, sum the weights of its edges, and then list the path weights in increasing order. The asymptotic behaviour of this sequence is described, in terms of the structure and type of strongly connected components on the graph. As a special case, for a Markov chain the asymptotic probability of paths obeys either a power law scaling or a weaker type of scaling, depending on the structure of the transition matrix. This generalizes previous work by Mandelbrot and others, who established asymptotic power law scaling for special classes of Markov chains.Comment: 23 pages, 2 figure

Investigation of aeroelastic stability phenomena of a helicopter by in-flight shake test

The analytical capability of the helicopter stability program is discussed. The parameters which are found to be critical to the air resonance characteristics of the soft in-plane hingeless rotor systems are detailed. A summary of two model test programs, a 1/13.8 Froude-scaled BO-105 model and a 1.67 meter (5.5 foot) diameter Froude-scaled YUH-61A model, are presented with emphasis on the selection of the final parameters which were incorporated in the full scale YUH-61A helicopter. Model test data for this configuration are shown. The actual test results of the YUH-61A air resonance in-flight shake test stability are presented. Included are a concise description of the test setup, which employs the Grumman Automated Telemetry System (ATS), the test technique for recording in-flight stability, and the test procedure used to demonstrate favorable stability characteristics with no in-plane damping augmentation (lag damper removed). The data illustrating the stability trend of air resonance with forward speed and the stability trend of ground resonance for percent airborne are presented

Are Topological Charge Fluctuations in QCD Instanton Dominated?

We consider a recent proposal by Horv\'ath {\em et al.} to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD.Comment: LaTeX, 15 pages, 8 postscript figures, minor improvements, version to appear in PR

Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories

We compute the low lying spectrum of the overlap Dirac operator in the deconfined phase of finite-temperature quenched gauge theory. It suggests the existence of a chiral condensate which we confirm with a direct stochastic estimate. We show that the part of the spectrum responsible for the chiral condensate can be understood as arising from a dilute gas of instantons and anti-instantons.Comment: Revtex, 16 pages, 3 postscript figure

Statistical Mechanics of Vibration-Induced Compaction of Powders

We propose a theory which describes the density relaxation of loosely packed, cohesionless granular material under mechanical tapping. Using the compactivity concept we develope a formalism of statistical mechanics which allows us to calculate the density of a powder as a function of time and compactivity. A simple fluctuation-dissipation relation which relates compactivity to the amplitude and frequency of a tapping is proposed. Experimental data of E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of initially deposited in a fluffy state powder evolves under carefully controlled tapping towards a random close packing (RCP) density. Ramping the vibration amplitude repeatedly up and back down again reveals the existence of reversible and irreversible branches in the response. In the framework of our approach the reversible branch (along which the RCP density is obtained) corresponds to the steady state solution of the Fokker-Planck equation whereas the irreversible one is represented by a superposition of "excited states" eigenfunctions. These two regimes of response are analyzed theoretically and a qualitative explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex

Participatory assessment of the South African abalone resource and its impact on predicted population trajectories

Illegal harvesting is a cause for concern in many of the world's fisheries. Over the last decade, the abalone resource in South Africa has come under severe fishing pressure, largely because of increased and unmitigated levels of poaching. The unquantified illegal exploitation of this resource is a major impediment to management, because understanding of abalone population dynamics is affected. Incorrect assessments of population abundance could lead to inadequate attempts by management to stem the decline. Here, population trends along the west coast of South Africa are investigated. A simple discrete-time logistic model was used to estimate parameters within a maximum likelihood statistical framework by fitting to available catch rate data. To address the problem of unknown levels of illegal catch, interview data were collected on non-commercial catch trends and the model was structured to allow this catch to be estimated during the fitting process. The results show that such a participatory approach to stock assessment can lead to an improved understanding of resource dynamics, illustrating the benefit this approach may have for management

An analysis for high speed propeller-nacelle aerodynamic performance prediction. Volume 1: Theory and application

A computer program, the Propeller Nacelle Aerodynamic Performance Prediction Analysis (PANPER), was developed for the prediction and analysis of the performance and airflow of propeller-nacelle configurations operating over a forward speed range inclusive of high speed flight typical of recent propfan designs. A propeller lifting line, wake program was combined with a compressible, viscous center body interaction program, originally developed for diffusers, to compute the propeller-nacelle flow field, blade loading distribution, propeller performance, and the nacelle forebody pressure and viscous drag distributions. The computer analysis is applicable to single and coaxial counterrotating propellers. The blade geometries can include spanwise variations in sweep, droop, taper, thickness, and airfoil section type. In the coaxial mode of operation the analysis can treat both equal and unequal blade number and rotational speeds on the propeller disks. The nacelle portion of the analysis can treat both free air and tunnel wall configurations including wall bleed. The analysis was applied to many different sets of flight conditions using selected aerodynamic modeling options. The influence of different propeller nacelle-tunnel wall configurations was studied. Comparisons with available test data for both single and coaxial propeller configurations are presented along with a discussion of the results

An analysis for high speed propeller-nacelle aerodynamic performance prediction. Volume 2: User's manual

A user's manual for the computer program developed for the prediction of propeller-nacelle aerodynamic performance reported in, An Analysis for High Speed Propeller-Nacelle Aerodynamic Performance Prediction: Volume 1 -- Theory and Application, is presented. The manual describes the computer program mode of operation requirements, input structure, input data requirements and the program output. In addition, it provides the user with documentation of the internal program structure and the software used in the computer program as it relates to the theory presented in Volume 1. Sample input data setups are provided along with selected printout of the program output for one of the sample setups

Variable Conductance Heat Pipe Technology

A research and development program in variable conductance heat pipe technology is reported. The project involved: (1) theoretical and/or experimental studies in hydrostatics, (2) hydrodynamics, (3) heat transfer into and out of the pipe, (4) fluid selection, and (5) materials compatibility. The development, fabrication, and test of the space hardware resulted in a successful flight of the heat pipe experiment on the OAO-3 satellite. A summary of the program is provided and a guide to the location of publications on the project is included