Fluid mechanics experiments in oscillatory flow. Volume 2: Tabulated data

Results of a fluid mechanics measurement program in oscillating flow within a circular duct are presented. The program began with a survey of transition behavior over a range of oscillation frequency and magnitude and continued with a detailed study at a single operating point. Such measurements were made in support of Stirling engine development. Values of three dimensionless parameters, Re sub max, Re sub w, and A sub R, embody the velocity amplitude, frequency of oscillation, and mean fluid displacement of the cycle, respectively. Measurements were first made over a range of these parameters that are representative of the heat exchanger tubes in the heater section of NASA's Stirling cycle Space Power Research Engine (SPRE). Measurements were taken of the axial and radial components of ensemble-averaged velocity and rms velocity fluctuation and the dominant Reynolds shear stress, at various radial positions for each of four axial stations. In each run, transition from laminar to turbulent flow, and its reverse, were identified and sufficient data was gathered to propose the transition mechanism. Volume 2 contains data reduction program listings and tabulated data (including its graphics)

Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity

We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems with continuous symmetries. We then show that for a fermionic system with a spin gap, it is possible to insert $\pi$-flux into a cylinder with only exponentially small change in the energy of the system, a scenario which covers several physically interesting cases such as an s-wave superconductor or a resonating valence bond state.Comment: 19 pages, 2 figures, final version in press at JSTA

Role of geometrical symmetry in thermally activated processes in clusters of interacting dipolar moments

Thermally activated magnetization decay is studied in ensembles of clusters of interacting dipolar moments by applying the master-equation formalism, as a model of thermal relaxation in systems of interacting single-domain ferromagnetic particles. Solving the associated master-equation reveals a breakdown of the energy barrier picture depending on the geometrical symmetry of structures. Deviations are most pronounced for reduced symmetry and result in a strong interaction dependence of relaxation rates on the memory of system initialization. A simple two-state system description of an ensemble of clusters is developed which accounts for the observed anomalies. These results follow from a semi-analytical treatment, and are fully supported by kinetic Monte-Carlo simulations.Comment: 9 pages, 6 figure

Fluid mechanics experiments in oscillatory flow. Volume 1: Report

Results of a fluid mechanics measurement program in oscillating flow within a circular duct are presented. The program began with a survey of transition behavior over a range of oscillation frequency and magnitude and continued with a detailed study at a single operating point. Such measurements were made in support of Stirling engine development. Values of three dimensionless parameters, Re(sub max), Re(sub w), and A(sub R), embody the velocity amplitude, frequency of oscillation and mean fluid displacement of the cycle, respectively. Measurements were first made over a range of these parameters which included operating points of all Stirling engines. Next, a case was studied with values of these parameters that are representative of the heat exchanger tubes in the heater section of NASA's Stirling cycle Space Power Research Engine (SPRE). Measurements were taken of the axial and radial components of ensemble-averaged velocity and rms-velocity fluctuation and the dominant Reynolds shear stress, at various radial positions for each of four axial stations. In each run, transition from laminar to turbulent flow, and its reverse, were identified and sufficient data was gathered to propose the transition mechanism. Models of laminar and turbulent boundary layers were used to process the data into wall coordinates and to evaluate skin friction coefficients. Such data aids in validating computational models and is useful in comparing oscillatory flow characteristics to those of fully-developed steady flow. Data were taken with a contoured entry to each end of the test section and with flush square inlets so that the effects of test section inlet geometry on transition and turbulence are documented. Volume 1 contains the text of the report including figures and supporting appendices. Volume 2 contains data reduction program listings and tabulated data (including its graphical presentation)

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Noise data from tests of a 1.83 meter (6-ft-) diameter variable-pitch 1.2-pressure-ratio fan (QF-9)

Acoustic and aerodynamic data for a 1.83-meter (6-ft.) diameter fan suitable for a quiet engine for short-takeoff-and-landing (STOL) aircraft are documented. The QF-9 rotor blades had an adjustable pitch feature which provided a means for testing at several rotor blade setting angles, including one for reverse thrust. The fan stage incorporated features for low noise. Far-field noise around the fan was measured without acoustic suppression over a range of operating conditions for six different rotor blade setting angles in the forward thrust configuration, and for one in the reverse configuration. Complete results of one-third-octave band analysis of the data are presented in tabular form. Also included are power spectra, data referred to the source, and sideline perceived noise levels

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem