Analysis of the extreme wave elevation due to second-order diffraction around a vertical cylinder

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics.     

Statistics for Twenty-first Century Astrometry

H. K. Eichhorn had a lively interest in statistics during his entire scientific career, and made a number of significant contributions to the statistical treatment of astrometric problems. In the past decade, a strong movement has taken place for the reintroduction of Bayesian methods of statistics into astronomy, driven by new understandings of the power of these methods as well as by the adoption of computationally-intensive simulation methods to the practical solution of Bayesian problems. In this paper I will discuss how Bayesian methods may be applied to the statistical discussion of astrometric data, with special reference to several problems that were of interest to Eichhorn.     

The local environment of H ii galaxies

We have carried out an investigation of the environments of low redshift H  ii galaxies by cross-correlating their positions on the sky with those of faint field galaxies in the Automatic Plate Measuring Machine (APM) catalogues. We address the question of whether violent star formation in H  ii galaxies is induced by low-mass companions by statistically estimating the mean space density of galaxies around them. We argue that even if low-mass companions were mainly intergalactic H  i clouds, their optical counterparts should be detectable at faint limits of the APM scans.
A significantly positive signal is detected for the H  ii galaxy–APM galaxy angular cross-correlation function, but the amplitude is poorly determined. The projected cross-correlation function has a higher signal-to-noise ratio, and suggests that the amplitude is slightly lower than for normal field galaxies. This implies that these bursting dwarf galaxies inhabit slightly lower density environments than those of normal field galaxies, consistent with other studies of emission-line galaxies. This suggests that in these dwarf starburst galaxies, star formation is not always triggered by tidal interactions, and a significant fraction must have a different origin.     

Environmental dependence of stellar mass,SFR, and SSFR for the Luminous Red Galaxy (LRG) sample of the SDSS DR7

Using the Luminous Red Galaxy (LRG) sample of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we investigate the environmental dependence of stellar mass, star formation rate (SFR) and specific star formation rate (SSFR) of LRGs. It is found that stellar mass of LRGs nearly is independent of local environments, and that the environmental dependence of SFR and SSFR in the LRG sample is much weaker than the one in the Main galaxy sample. One possible explanation is that galaxy color and morphology are a pair of galaxy properties most predictive of local environments, while LRGs are a group of galaxies that are likely to be luminous, red and of early types (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

中国大陆余震活动深度分布及其流变学机制

本文研究了中国大陆１９６６年以来发生的５次大地震（Ｍｓ≥７．０）的余震活动深度与地热流的关系。研究表明，地热流较高的震源区，余震活动深度分布较浅，并且得出余震深度分布受地壳内部岩石脆性－韧性转变深度的流变学特征控制的推论。     

An application of the Kerr black hole fly-wheel model to statistical properties of QSOs/AGNs

The aim of this work is to demonstrate the properties of the magnetospheric model around Kerr black holes (BHs), the so-called fly-wheel (rotation driven) model. The fly-wheel engine of the BH–accretion disc system is applied to the statistics of QSOs/AGNs. In the model, the central BH is assumed to be formed at z ∼10² and obtains nearly maximum but finite rotation energy (∼extreme Kerr BH) at the formation stage. The inherently obtained rotation energy of the Kerr BH is released through a magnetohydrodynamic process. This model naturally leads to a finite lifetime of AGN activity.
Nitta, Takahashi & Tomimatsu clarified the individual evolution of the Kerr BH fly-wheel engine, which is parametrized by BH mass, initial Kerr parameter, magnetic field near the horizon and a dimensionless small parameter. We impose a statistical model for the initial mass function (IMF) of an ensemble of BHs using the Press–Schechter formalism. With the help of additional assumptions, we can discuss the evolution of the luminosity function and the spatial number density of QSOs/AGNs.
By comparing with observations , it is found that a somewhat flat IMF and weak dependence of the magnetic field on the BH mass are preferred. The result explains well the decrease of very bright QSOs and decrease of population after z ∼2.     

Effect of agricultural land use on the chemistry of groundwater from basaltic aquifers, Jeju Island, South Korea

Geochemical processes were identified as controlling factors of groundwater chemistry, including chemical weathering, salinization from seawater and dry sea-salt deposition, nitrate contamination, and rainfall recharge. These geochemical processes were identified using principal component analysis of major element chemistry of groundwater from basaltic aquifers in Jeju Island, South Korea, a volcanic island with intense agricultural activities. The contribution of the geochemical processes to groundwater chemistry was quantified by a simple mass-balance approach. The geochemical effects due to seawater were considered based on Cl contributions, whereas the effects due to natural chemical weathering were based on alkalinity. Nitrogenous fertilizers, and especially the associated nitrification processes, appear to significantly affect groundwater chemistry. A strong correlation was observed between Na, Mg, Ca, SO₄ and Cl, and nitrate concentrations in groundwater. Correspondingly, the total major cations, Cl, and SO₄ in groundwater were assessed to estimate relative effect of N-fertilizer use on groundwater chemistry. Cl originates more from nitrate sources than from seawater, whereas SO₄ originates mostly from rainwater. N-fertilizer use has shown the greatest effect on groundwater chemistry, particularly when nitrate concentrations exceed 6–7 mg/L NO₃–N. Nitrate contamination significantly affects groundwater quality and 18% of groundwater samples have contamination-dominated chemistry.