The azimuth structure of nuclear collisions -- I

We describe azimuth structure commonly associated with elliptic and directed flow in the context of 2D angular autocorrelations for the purpose of precise separation of so-called nonflow (mainly minijets) from flow. We extend the Fourier-transform description of azimuth structure to include power spectra and autocorrelations related by the Wiener-Khintchine theorem. We analyze several examples of conventional flow analysis in that context and question the relevance of reaction plane estimation to flow analysis. We introduce the 2D angular autocorrelation with examples from data analysis and describe a simulation exercise which demonstrates precise separation of flow and nonflow using the 2D autocorrelation method. We show that an alternative correlation measure based on Pearson's normalized covariance provides a more intuitive measure of azimuth structure.Comment: 27 pages, 12 figure

Analysis and Measurement of Thermophysical Properties by Temperature Oscilation

The problem of determining the thermophysical properties of material has been of great interest to scientists and engineers for more than hundred years. The thermophysical study of material has gained much importance recently with the vast development of newer materials. The development, specification, and quality control of materials used in semiconductor devices and thermal management often require the measurement of thermophysical properties where these data can be critical to a successful design........ The experimental results of the thermal diffusivity of the four liquid samples are obtained along with their uncertainties. The total uncertainty assessment has been used for plotting the error bar in the measurement of thermal diffusivity. The reliability of such is evident from its results as compared with the reported values. The deviation from the reported values in literatures are, 6.38%, 9.77%, 10.82%, and 2.74% for the respective samples of ethylene glycol..

Two Simple Approximate Methods of Laplace Transform Inversion for Viscoelastic Stress Analysis

Two approximate methods of Laplace transform inversion are given which are simple to use and are particularly applicable to stress analysis problems in quasi-static linear viscoelasticity. Once an associated elastic solution is known numerically or analytically, the time-dependent viscoelastic response can be easily calculated using realistic material properties, regardless of how complex the property dependence of the elastic solution may be. The new feature of these methods is that it is necessary to know only 1) an elastic solution numerically for certain ranges of elastic constants and 2) numerical values of the operational moduli or compliances for real, positive values of the transform parameter. One method utilizes a mathematical property of the Laplace transform, while the other is based on some results obtained from Irreversible Thermodynamics and variational principles. Because of this, they are quite general and can be used with anisotropic and inhomogeneous materials. Two numerical examples are given: As the first one, we calculate the time-dependent strain in a long, internally. pressurized cylinder with an elastic case. The second example consists of inverting a transform which was derived by Muki and Sternberg in the thermo-viscoelastic analysis of a slab and a sphere(1). Both methods were found to provide results which are within the usual engineering requirements of accuracy. Application of the approximate methods to problems in dynamic viscoelasticity is discussed briefly. Supplementing the stress analysis, two techniques for calculating operational moduli and compliances from experimental stress-strain data are discussed and applied. Both can be used with creep, relaxation, and steady-state oscillation data. The most direct one consists of numerically integrating experimental data, while the other is a model-fitting scheme. With this latter method finite-element spring and dashpot models are readily found which fit the entire response.curves. In using these methods to calculate the operational functions employed in the stress analysis examples, we found that model-fitting was the fastest of the two, yet was very accurate

Determining cluster-cluster aggregation rate kernals using inverse methods

We investigate the potential of inverse methods for retrieving adequate information about the rate kernel functions of cluster-cluster aggregation processes from mass density distribution data. Since many of the classical physical kernels have fractional order exponents the ability of an inverse method to appropriately represent such functions is a key concern. In early chapters, the properties of the Smoluchowski Coagulation Equation and its simulation using Monte Carlo techniques are introduced. Two key discoveries made using the Monte Carlo simulations are briefly reported. First, that for a range of nonlocal solutions of finite mass spectrum aggregation systems with a source of mass injection, collective oscillations of the solution can persist indefinitely despite the presence of significant noise. Second, that for similar finite mass spectrum systems with (deterministic) stable, but sensitive, nonlocal stationary solutions, the presence of noise in the system can give rise to behaviour indicative of phase-remembering, noise-driven quasicycles. The main research material on inverse methods is then presented in two subsequent chapters. The first of these chapters investigates the capacity of an existing inverse method in respect of the concerns about fractional order exponents in homogeneous kernels. The second chapter then introduces a new more powerful nonlinear inverse method, based upon a novel factorisation of homogeneous kernels, whose properties are assessed in respect of both stationary and scaling mass distribution data inputs

Computationally Efficient Steady--State Simulation Algorithms for Finite-Element Models of Electric Machines.

The finite element method is a powerful tool for analyzing the magnetic characteristics of electric machines, taking account of both complex geometry and nonlinear material properties. When efficiency is the main quantity of interest, loss calculations can be affected significantly due to the development of eddy currents as a result of Faraday’s law. These effects are captured by the periodic steady-state solution of the magnetic diffusion equation. A typical strategy for calculating this solution is to analyze an initial value problem over a time window of sufficient length so that the transient part of the solution becomes negligible. Unfortunately, because the time constants of electric machines are much smaller than their excitation period at peak power, the transient analysis strategy requires simulating the device over many periods to obtain an accurate steady-state solution. Two other categories of algorithms exist for directly calculating the steady-state solution of the magnetic diffusion equation; shooting methods and the harmonic balance method. Shooting methods search for the steady-state solution by solving a periodic boundary value problem. These methods have only been investigated using first order numerical integration techniques. The harmonic balance method is a Fourier spectral method applied in the time dimension. The standard iterative procedures used for the harmonic balance method do not work well for electric machine simulations due to the rotational motion of the rotor. This dissertation proposes several modifications of these steady-state algorithms which improve their overall performance. First, we demonstrate how shooting methods may be implemented efficiently using Runge-Kutta numerical integration methods with mild coefficient restrictions. Second, we develop a preconditioning strategy for the harmonic balance equations which is robust against large time constants, strong nonlinearities, and rotational motion. Third, we present an adaptive framework for refining the solutions based on a local error criterion which further reduces simulation time. Finally, we compare the performance of the algorithms on a practical model problem. This comparison demonstrates the superiority of the improved steady-state analysis methods, and the harmonic balance method in particular, over transient analysis.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113322/1/pries_1.pd