Cercles De Remplissage for Entire Functions

It is shown that every transcendental entire function f growstranscendentally in a sequence of cercles de remplissage. Anexample shows that if then there may be no sequence of cercles de remplissage theunion of which contains infinitely many zeros of f. It is alsoshown that every transcendental entire function f has a Haymandirection, that is, a direction such that, in every open sectorcontaining , either f assumes all complex values infinitelyoften, or else every derivative of f assumes all complex values,except possibly zero, infinitely often. 1991 Mathematics SubjectClassification 30D20.     

Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation

Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized. (c)1998 American Institute of Physics.     

Model-based detection of synthetic bat echolocation calls using an energy threshold detector for initialization

Detection of echolocation calls is fundamental to quantitative analysis of bat acoustic signals. Automated methods of detection reduce the subjectivity of hand labeling of calls and speed up the detection process in an accurate and repeatable manner. A model-based detector was initialized using a baseline energy threshold detector, removing the need for hand labels to train the model, and shown to be superior to the baseline detector using synthetic calls in two experiments: (1) an artificial environment and (2) a field playback setting. Synthetic calls using a piecewise exponential frequency modulation function from five hypothetical species were employed to control the signal-to-noise ratio (SNR) in each experiment and to provide an absolute ground truth to judge detector performance. The model-based detector outperformed the baseline detector by 2.5 dB SNR in the artificial environment and 1.5 dB SNR in the field playback setting. Atmospheric absorption was measured for the synthetic calls, and 1.5 dB increased the effective detection radius by between 1 and 7 m depending on species. The results demonstrate that hand labels are not necessary for training detection models and that model-based detectors significantly increase the range of detection for a recording system.     

Flow of a particulate suspension in the wake of a circular cylinder

Measurements are reported for the average local particulate velocity and concentration distributions in the wake of a cylinder immersed in a stream containing a polydisperse aerosol. The wake centerline defects and transverse distributions were determined for both parameters. It was found that the particulate centerline defect persists a considerable distance downstream of the cylinder before fully developed conditions are satisfied. Transverse particulates and gaseous velocity distributions assume a Gaussian profile at the same point downstream. The charge-to-mass ratio throughout the wake region was equal to the free stream value for all experimental conditions and was of such a magnitude to permit the electrostatic effects to be neglected in the governing equations. Gaseous and particulate transport properties were identified in the wake.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.