Evidence for Short Temporal Atmospheric Variations Observed by Infrasonic Signals: 1. The Troposphere

Infrasound monitoring is used in the forensic analysis of events, studying the physical processes of sources of interest, and probing the atmosphere. The dynamical nature of the atmosphere and the use of infrasound as a forensic tool lead to the following questions; (1) what is the timescale of atmospheric variability that affects infrasonic signals? (2) how do infrasound signals vary as a function of time? This study addresses these questions by monitoring a repetitive infrasound source and its corresponding tropospheric returns 54 km away. Source-receiver empirical Green\u27s functions are obtained every 20 s and used to demonstrate the effect of atmospheric temporal variability on infrasound propagation. In addition, observations are compared to predicted simulated signals based on realistic atmospheric conditions. Based on 127 events over 3 days, it is shown that infrasound properties change within tens of seconds. Particularly, phases can appear and disappear, the propagation time varies, and the signals\u27 energy fluctuates. Such variations are attributed to changes in temperatures and winds. Furthermore, atmospheric models can partly explain the observed changes. Therefore, this study highlights the potential of high temporal infrasound-based atmospheric sounding

Comparison of Horizontal, Vertical and Diagonal Smooth Pursuit Eye Movements in Normal Human Subjects

AbstractWe compared horizontal and vertical smooth pursuit eye movements in five healthy human subjects. When maintenance of pursuit was tested using predictable waveforms (sinusoidal or triangular target motion), the gain of horizontal pursuit was greater, in all subjects, than that of vertical pursuit; this was also the case for the horizontal and vertical components of diagonal and circular tracking. When initiation of pursuit was tested, four subjects tended to show larger eye accelerations for vertical as opposed to horizontal pursuit; this trend became a consistent finding during diagonal tracking. These findings support the view that different mechanisms govern the onset of smooth pursuit, and its subsequent maintenance when the target moves in a predictable waveform. Since the properties of these two aspects of pursuit differ for horizontal and vertical movements, our findings also point to separate control of horizontal and vertical pursuit. Copyright © 1996 Elsevier Science Ltd

Universality of low-energy scattering in (2+1) dimensions

We prove that, in (2+1) dimensions, the S-wave phase shift, $\delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled.Comment: 23 pages, Late

Re: "Comparison of antipseudomonal betalactams for febrile neutropenia empiric therapy: systematic review and network metaanalysis" by Horita et al

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High-dimensional wave atoms and compression of seismic datasets

Wave atoms are a low-redundancy alternative to curvelets, suitable for high-dimensional seismic data processing. This abstract extends the wave atom orthobasis construction to 3D, 4D, and 5D Cartesian arrays, and parallelizes it in a shared-memory environment. An implementation of the algorithm for NVIDIA CUDA capable graphics processing units (GPU) is also developed to accelerate computation for 2D and 3D data. The new transforms are benchmarked against the Fourier transform for compression of data generated from synthetic 2D and 3D acoustic models.National Science Foundation (U.S.); Alfred P. Sloan Foundatio

Asymptotic Fourier Coefficients for a C ∞ Bell (Smoothed-“Top-Hat”) & the Fourier Extension Problem

In constructing local Fourier bases and in solving differential equations with nonperiodic solutions through Fourier spectral algorithms, it is necessary to solve the Fourier Extension Problem. This is the task of extending a nonperiodic function, defined on an interval , to a function which is periodic on the larger interval . We derive the asymptotic Fourier coefficients for an infinitely differentiable function which is one on an interval , identically zero for , and varies smoothly in between. Such smoothed “top-hat” functions are “bells” in wavelet theory. Our bell is (for x ≥ 0) where where . By applying steepest descents to approximate the coefficient integrals in the limit of large degree j , we show that when the width L is fixed, the Fourier cosine coefficients a j of on are proportional to where Λ( j ) is an oscillatory factor of degree given in the text. We also show that to minimize error in a Fourier series truncated after the N th term, the width should be chosen to increase with N as . We derive similar asymptotics for the function f ( x )= x as extended by a more sophisticated scheme with overlapping bells; this gives an even faster rate of Fourier convergencePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43417/1/10915_2005_Article_9010.pd

Scattering in flatland: Efficient representations via wave atoms

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by thresholding the small coefficients to zero. This phenomenon was perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context of local Fourier bases \cite{BCG}. Their results have since then been extended in various ways. The purpose of this paper is to bridge a theoretical gap and prove that a well-chosen fixed expansion, the nonstandard wave atom form, provides a compression of the acoustic single and double layer potentials with wave number $k$ as $O(k)$-by-$O(k)$ matrices with $O(k^{1+1/\infty})$ nonnegligible entries, with a constant that depends on the relative $\ell_2$ accuracy \eps in an acceptable way. The argument assumes smooth, separated, and not necessarily convex scatterers in two dimensions. The essential features of wave atoms that enable to write this result as a theorem is a sharp time-frequency localization that wavelet packets do not obey, and a parabolic scaling wavelength $\sim$ (essential diameter)${}^2$. Numerical experiments support the estimate and show that this wave atom representation may be of interest for applications where the same scattering problem needs to be solved for many boundary conditions, for example, the computation of radar cross sections.Comment: 39 page