Study of fluid transients in closed conduits progress report no. 64-5, 1-30 nov. 1964

Fluid transients in closed conduit

Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes

Rindler's acceleration-induced partitioning of spacetime leads to a nature-given interferometer. It accomodates quantum mechanical and wave mechanical processes in spacetime which in (Euclidean) optics correspond to wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting, reflection, and interference. These processes are described in terms of amplitudes which behave smoothly across the event horizons of all four Rindler sectors. In this context there arises quite naturally a complete set of orthonormal wave packet histories, one of whose key properties is their "explosivity index". In the limit of low index values the wave packets trace out fuzzy world lines. By contrast, in the asymptotic limit of high index values, there are no world lines, not even fuzzy ones. Instead, the wave packet histories are those of entities with non-trivial internal collapse and explosion dynamics. Their details are described by the wave processes in the above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit interference process. These wave processes are applied to elucidate the amplification of waves in an accelerated inhomogeneous dielectric. Also discussed are the properties and relationships among the transition amplitudes of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version of the figures and of related papers available at http://www.math.ohio-state.edu/~gerlac

Quantum Mechanical Carrier of the Imprints of Gravitation

We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic system a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of gravitation. This carrier consists of the phase and amplitude correlations of waves in oppositely accelerating frames. These correlations are expressed as a Klein-Gordon-equation-determined vector field whose components are the ``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The imprints themselves are deviations away from this vector field.Comment: 8 pages, RevTex. Html version of this and related papers on accelerated frames available at http://www.math.ohio-state.edu/~gerlac

Charge carrier interaction with a purely electronic collective mode: Plasmarons and the infrared response of elemental bismuth

We present a detailed optical study of single crystal bismuth using infrared reflectivity and ellipsometry. Colossal changes in the plasmon frequency are observed as a function of temperature due to charge transfer between hole and electron Fermi pockets. In the optical conductivity, an anomalous temperature dependent mid-infrared absorption feature is observed. An extended Drude model analysis reveals that it can be connected to a sharp upturn in the scattering rate, the frequency of which exactly tracks the temperature dependent plasmon frequency. We interpret this absorption and increased scattering as the first direct optical evidence for a charge carrier interaction with a collective mode of purely electronic origin; here electron-plasmon scattering. The observation of a \emph{plasmaron} as such is made possible only by the unique coincidence of various energy scales and exceptional properties of semi-metal bismuth.Comment: 4 pages, 4 figure

High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schroedinger equation

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schroedinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS - a hotly debated subject in current scientific literature.Comment: 5 Figures, Physics Letters A (accepted

Small Displacement, Long Life On-Orbit Compressor Design and Fabrication

The focus is the generation of technology and fabrication of prototype hardware applicable to seven Space Station compressor system applications. The compressors are of the single acting reciprocating piston type and, in general, may be termed miniature in size compared with normal commercially available equipment. The initial technology development is focused on improved valve designs, and the control of pulsations and heating effects in order to increase compressor efficiency and reduce cycle temperatures, thus permitting significantly increased stage pressure ratios. The initial test compressor was successfully operated at pressure ratios of up to 50:1, and this significant extension of allowable pressure ratio will result in a reduction of the number of required stages and, hence, total hardware thereby reducing system weight and volume. These experiments have also identified the need to employ low shaft speeds, on the order of 250 to 500 rpm, to enhance heat transfer and increase life. The prototype compressor currently being designed, is to be driven by a low-speed brushless dc motor sealed in a case common to the compressor drive mechanism case. The compressor and motor case will communicate with stage suction pressure so that any minor gas leakage past the piston rings will be returned to the suction. Emphasis in this prototype design is being placed on simplicity, durability, commonality of components, and high efficiency

Bellows flow-induced vibrations

Results of theoretical and experimental investigations of bellows typical of those found in space shuttle external tanks are presented. Correlation parameters are identified which generalize the alternating stress calculations cited in an earlier study. Alternating stress amplitudes and mean stress levels form the basis of a fatigue analysis incorporating seven ordinate charts for 347 stainless steel, alloy 21 6-9, and Inco 718. A crack propagation model is included with a program for computing bellows fatigue life. Two phase flow and material hardness properties are discussed

Efficient integration of the variational equations of multi-dimensional Hamiltonian systems: Application to the Fermi-Pasta-Ulam lattice

We study the problem of efficient integration of variational equations in multi-dimensional Hamiltonian systems. For this purpose, we consider a Runge-Kutta-type integrator, a Taylor series expansion method and the so-called `Tangent Map' (TM) technique based on symplectic integration schemes, and apply them to the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice of $N$ nonlinearly coupled oscillators, with $N$ ranging from 4 to 20. The fast and accurate reproduction of well-known behaviors of the Generalized Alignment Index (GALI) chaos detection technique is used as an indicator for the efficiency of the tested integration schemes. Implementing the TM technique--which shows the best performance among the tested algorithms--and exploiting the advantages of the GALI method, we successfully trace the location of low-dimensional tori.Comment: 14 pages, 6 figure