Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Distributed educated throat stability bypass to increase the stable airflow range of a Mach 2.5 inlet with 60-percent internal contraction

The results of an experimental investigation to increase the stable airflow operating range of a supersonic mixed-compression inlet are presented. A distributed educated throat stability-bypass entrance configuration was tested. In terms of diffuser-exit corrected airflow, a large inlet stable airflow range of about 16.1 percent was obtained if a constant pressure was maintained in the bypass plenum. Limited unstart angle of attack data are presented

Shock temperatures in anorthite glass

Temperatures of CaAl2Si2O8 (anorthite glass) shocked to pressures between 48 and 117 GPa were measured in the range from 2500 to 5600 K, using optical pyrometry techniques. The pressure dependence of the shock temperatures deviates significantly from predictions based on a single high pressure phase. At least three phase transitions, at pressures of about 55, 85, and 100 GPa and with transition energies of about 0.5 MJ/kg each (approximately 1.5 MJ/kg total) are required to explain the shock temperature data. The phase transition at 100 GPa can possibly be identified with the stishovite melting transition. Theoretical models of the time dependence of the thermal radiation from the shocked anorthite based on the geometry of the experiment and the absorptive properties of the shocked material yields good agreement with observations, indicating that it is not necessary to invoke intrinsic time dependences to explain the data in many cases

Distributed porous throat stability bypass to increase the stable airflow range of a Mach 2.5 inlet with 60 percent internal contraction

The results of an experimental investigation to increase the stable airflow operating range of a supersonic, mixed-compression inlet with 60-percent internal contraction are presented. Various distributed-porous, throat stability-bypass entrance configurations were tested. In terms of diffuser-exit corrected airflow, a large inlet stable airflow range of about 25 percent was obtained with the optimum configuration if a constant pressure was maintained in the by-pass plenum. The location of the centerbody bleed region had a decided effect on the overall inlet performance. Limited unstart angle-of-attack data are presented

Global Dimension of Polynomial Rings in Partially Commuting Variables

For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.Comment: 11 pages, 2 figure

Transmission Efficiency Measurements and Correlations with Physical Characteristics of the Lubricant

Data from helicopter transmission efficiency tests were compared to physical properties of the eleven lubricants used in those tests. The tests were conducted with the OH-58 helicopter main rotor transmission. Efficiencies ranged from 98.3 to 98.8 percent. The data was examined for correlation of physical properties with efficiency. There was a reasonable correlation of efficiency with absolute viscosity if the viscosity was first corrected for temperature and pressure in the lubricated contact. Between lubricants, efficiency did not correlate well with viscosity at atmospheric pressure. Between lubricants, efficiency did not correlate well with calculated lubricant film forming capacity. Bench type sliding friction and wear measurements could not be correlated to transmission efficiency and component wear

Controlling the uncontrolled: Are there incidental experimenter effects on physiologic responding?

The degree to which experimenters shape participant behavior has long been of interest in experimental social science research. Here, we extend this question to the domain of peripheral psychophysiology, where experimenters often have direct, physical contact with participants, yet researchers do not consistently test for their influence. We describe analytic tools for examining experimenter effects in peripheral physiology. Using these tools, we investigate nine data sets totaling 1,341 participants and 160 experimenters across different roles (e.g., lead research assistants, evaluators, confederates) to demonstrate how researchers can test for experimenter effects in participant autonomic nervous system activity during baseline recordings and reactivity to study tasks. Our results showed (a) little to no significant variance in participants' physiological reactivity due to their experimenters, and (b) little to no evidence that three characteristics of experimenters that are well known to shape interpersonal interactions-status (using five studies with 682 total participants), gender (using two studies with 359 total participants), and race (in two studies with 554 total participants)-influenced participants' physiology. We highlight several reasons that experimenter effects in physiological data are still cause for concern, including the fact that experimenters in these studies were already restricted on a number of characteristics (e.g., age, education). We present recommendations for examining and reducing experimenter effects in physiological data and discuss implications for replication

Direction-Dependent Polarised Primary Beams in Wide-Field Synthesis Imaging

The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionisation experiments. These experiments seek to detect weak signatures from redshifted 21cm emission in deep residual datasets, after suppression and subtraction of foreground emission. Many subtraction algorithms benefit from low side-lobes and polarisation leakage at the outset, and both of these are intimately linked to how the polarised primary beams are handled. Building on previous contributions from a number of authors, in which direction-dependent corrections are incorporated into visibility gridding kernels, we consider the special characteristics of arrays of fixed dipole antennas operating around 100-200 MHz, looking towards instruments such as the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Arrays (HERA). We show that integrating snapshots in the image domain can help to produce compact gridding kernels, and also reduce the need to make complicated polarised leakage corrections during gridding. We also investigate an alternative form for the gridding kernel that can suppress variations in the direction-dependent weighting of gridded visibilities by 10s of dB, while maintaining compact support.Comment: 15 pages, 4 figures. Accepted for publication in JA

Throat stability-by pass systems to increase the stable airflow range of a Mach 2.5 inlet with 60-percent internal contraction

The results of an experimental investigation to increase the stable airflow range (without unstart) of a supersonic mixed-compression inlet are presented. Various stability bypass entrances were located on the cowl side of the inlet throat. The types of entrance were distributed porous (normal holes), forward-slanted slot, and distributed educated slots. A large stable airflow range was obtained for each entrance type if a constant pressure was maintained in the stability bypass plenum. The distributed porous entrance provided the largest stable airflow range. Inlet unstart angle of attack was unaffected by the entrances