Abstract We present a method for analyzing supernova remnants (SNRs) by diagnosing the drivers responsible for structure at different angular scales. First, we perform a suite of hydrodynamic models of the Rayleigh–Taylor instability (RTI) as a supernova (SN) collides with its surrounding medium. Using these models we demonstrate how power spectral analysis can be used to attribute which scales in an SNR are driven by RTI and which must be caused by intrinsic asymmetries in the initial explosion. We predict the power spectrum of turbulence driven by RTI and identify a dominant angular mode that represents the largest scale that efficiently grows via RTI. We find that this dominant mode relates to the density scale height in the ejecta, and therefore reveals the density profile of the SN ejecta. If there is significant structure in an SNR on angular scales larger than this mode, then it is likely caused by anisotropies in the explosion. Structure on angular scales smaller than the dominant mode exhibits a steep scaling with wavenumber, possibly too steep to be consistent with a turbulent cascade, and therefore might be determined by the saturation of RTI at different length scales (although systematic 3D studies are needed to investigate this). We also demonstrate, consistent with previous studies, that this power spectrum is independent of the magnitude and length scales of perturbations in the surrounding medium and therefore this diagnostic is unaffected by “clumpiness” in the circumstellar medium.
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Wavelet Tree Parsing with Freeform Lensing
We propose an architecture for adaptive sensing of images by progressively measuring its wavelet coefficients. Our approach, commonly referred to as wavelet tree parsing, adaptively selects the specific wavelet coefficients to be sensed by modeling the children of dominant coefficients to be dominant themselves. A key challenge for practical implementation of this technique is that the wavelet patterns, especially at finer scales, occupy a tiny portion of the field of view and, hence, the resulting measurements have very poor light levels and signal-to-noise ratios (SNR). To address this, we propose a novel imaging architecture that uses a phase-only spatial light modulator as a freeform lens to concentrate a light source and create the wavelet patterns. This ensures that the SNR of measurements remain constant across different spatial scales. Using a lab prototype, we demonstrate successful reconstruction on a wide range of real scenes and show that concentrating illumination enables us to outperform non-adaptive techniques as well as adaptive techniques based on traditional projectors.
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- NSF-PAR ID:
- 10106207
- Date Published:
- Journal Name:
- IEEE International Conference on Computational Photography
- Page Range / eLocation ID:
- 1 to 10
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Feature extraction from wideband radio-frequency (RF) signals, such as spectral activity, interferer energy and type, or direction- of-arrival, finds use in a growing number of applications. Compressive sensing (CS)-based analog-to-information (A2I) converters enable the design of inexpensive and energy-efficient wideband RF sensing solutions for such applications. However, most A2I architectures suffer from a variety of real-world impairments. We propose a novel A2I architecture, referred to as non-uniform wavelet bandpass sampling (NUWBS). Our architecture extracts a carefully-tuned subset of wavelet coefficients directly in the RF domain, which mitigates the main issues of most existing A2I converters. We use simulations to show that NUWBS approaches the performance limits of l1-norm-based sparse signal recovery.more » « less
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Summary Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. Motivated by the facts that the wavelet transform decomposes a time series into coefficients that are associated with different scales and that the variance of these coefficients (the so-called wavelet variance) decomposes the variance of the time series across scales, the paper proposes a definition for characteristic scale in terms of peaks in plots of the wavelet variance versus scale. After presenting basic theory for wavelet-based characteristic scales, a natural estimator for these scales is considered. Large sample theory for this estimator permits the construction of confidence intervals for a true unknown characteristic scale. Computer experiments are presented that demonstrate the efficacy of the large sample theory for finite sample sizes. Characteristic scale estimates are calculated for medium multiyear Arctic sea ice, global temperature records, coherent structures in river flows and the Madden–Julian oscillation in an atmospheric time series.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICCPHOT.2019.8747327
