A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations

Split-screen single-camera stereoscopic PIV application to a turbulent confined swirling layer with free surface

An annular liquid wall jet, or vortex tube, generated by helical injection inside a tube is studied experimentally as a possible means of fusion reactor shielding. The hollow confined vortex/swirling layer exhibits simultaneously all the complexities of swirling turbulence, free surface, droplet formation, bubble entrapment; all posing challenging diagnostic issues. The construction of flow apparatus and the choice of working liquid and seeding particles facilitate unimpeded optical access to the flow field. A split-screen, single-camera stereoscopic particle image velocimetry (SPIV) scheme is employed for flow field characterization. Image calibration and free surface identification issues are discussed. The interference in measurements of laser beam reflection at the interface are identified and discussed. Selected velocity measurements and turbulence statistics are presented at Re_λ = 70 (Re = 3500 based on mean layer thickness)

Modeling Arsenic Behavior During Artificial Aquifer Recharge

Increased variability in precipitation coupled with increases in population across the large portions of the western United States has resulted in greater demand being placed on this region's water resources. As a result, water conservation and storage methods are being explored to mitigate the impact that potential drought may have on these expanding population centers. Aquifer storage and recovery projects (ASR) in which excess surface water is captured and injected in local aquifers for storage, are becoming more widespread and important. As part of these programs, the use of highly treated wastewater or reclaimed water as a potential source for groundwater injection is becoming more feasible. This wastewater stream is typically underutilized if utilized at all. A hurdle in “traditional” ASR projects and particularly in reclaimed water ASR projects is understanding how these injected water’s chemistries will interact with the native groundwater and geology of the aquifer into which they are being introduced. This study looks to identify how a numerical geochemical model framework can be used to identify potential compatibility issues between injected and native groundwaters in which degradation to overall water quality may occur. This framework is tested by looking at a case study in Reno, Nevada in which a small-scale aquifer injection test was conducted utilizing highly treated reclaimed water. In this case study, unanticipated changes in arsenic levels were observed in the aquifer during the injection test. A geochemical model was created utilizing the USGS PHREEQC modeling software to replicate batch experiments performed utilizing mineralogy collected from the Reno-Stead site. This model was used to confirm the mechanism of arsenic release at the site as well as demonstrate its ability to understand potential mitigation measures or investigate other potential contaminants. The results were matched with the lab and field observations and iron-oxide sorption was identified as the source and driver of arsenic mobility at the site. The developed geochemical model was able to match the observed arsenic variability at the Reno-Stead site in response to changes to injection pH values. Injection pH values in the range of 6.7-7.2 were shown to decrease arsenic concentrations below background levels. At pH values in the range of 7.1-7.4 which correspond to the actual pH values of the injection water at the site, arsenic concentrations remained relatively stable or increased slightly in response to desorption from iron-oxide surfaces caused by shifts in pH. Models run without the inclusion of iron-oxide surfaces showed no arsenic concentration changes in response to changes in injected pH and did not match the field observations from the site. This validates the hypothesis that iron-oxide sorption and desorption was the primary driver of arsenic variability observed at the Reno-Stead site. The ability of this relatively simple geochemical framework to accurately identify and replicate observed chemistry changes at this test site proves its viability as a potential method to identify and test future sites for any compatibility issues between injected and native groundwater before significant investments of time and resources occur. While further work is needed to create a more rounded and widely applicable model, this modeling pathway allows for better understanding of the geochemical mechanisms present at recharge sites and helps direct future investigations

The Liquefaction Sand Boils in the San Francisco Marina District During the 1989 Loma Prieta Earthquake

The paper presents and analyzes the observations of the sand boils that emerged in the Marina District after the Loma Prieta Earthquake of October 17, 1989. The sand boils left behind by liquefaction revealed an old lagoon, the periphery of which had experienced severe damage in the 1906 San Francisco earthquake. The buildings in the Marina District were damaged primarily as the liquefied ground spread laterally along the shoreline of the 1906 lagoon that was filled to host the 1915 Panama-Pacific International Exposition in San Francisco. The present work infers that the sand boils are not random phenomena but instrumental sensors to understand the ground failure induced by liquefaction

In-flight measurements of energetic radiation from lightning and thunderclouds

In the certification procedure aircraft builders carry out so-called icing tests flights, where the zero degree Celsius altitude is deliberately sought and crossed in or under thunderstorms. Airbus also used these flights to test ILDAS, a system aimed to determine lightning severity and attachment points during flight from high speed data on the electric and magnetic field at the aircraft surface. We used this unique opportunity to enhance the ILDAS systems with two x-ray detectors coupled to high speed data recorders in an attempt to determine the x-rays produced by lightning in-situ, with synchronous determination of the lightning current distribution and electric field at the aircraft. Such data are of interest in a study of lightning physics. In addition, the data may provide clues to the x-ray dose for personnel and equipment during flights. The icing campaign ran in April 2014; in six flights we collected data of 61 lightning strikes on an Airbus test aircraft. In this communication we briefly describe ILDAS and present selected results on three strikes, two aircraft initiated and one intercepted. Most of the x-rays have been observed synchronous with initiating negative leader steps, and as bursts immediately preceding the current of the recoil process. Those processes include the return stroke. The bursts last one to four micro-second and attain x-ray energies up to 10 MeV. Intensity and spectral distribution of the x-rays and the association with the current distribution are discussed. ILDAS also continuously records x-rays at low resolution in time and amplitude.Comment: 28 pages, 9 figure

Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

Permeability and compressibility of wax-coated sands

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