The mixed problem in L^p for some two-dimensional Lipschitz domains

We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is decomposed into two disjoint sets D and N. We suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary and the Neumann data is in L^p(N). We find conditions on the domain and the sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L^p

Evaluation Of Groundwater Pathways And Travel Times From The Nevada Test Site To The Potential Yucca Mountain Repository

Yucca Mountain (YM), Nevada, has been recommended as a deep geological repository for the disposal of spent fuel and high-level radioactive waste. If YM is licensed as a repository by the Nuclear Regulatory Commission, it will be important to identify the potential for radionuclides to migrate from underground nuclear testing areas located on the Nevada Test Site (NTS) to the hydraulically downgradient repository area to ensure that monitoring does not incorrectly attribute repository failure to radionuclides originating from other sources. In this study, we use the Death Valley Regional Flow System (DVRFS) model developed by the U.S. Geological Survey to investigate potential groundwater migration pathways and associated travel times from the NTS to the proposed YM repository area. Using results from the calibrated DVRFS model and the particle tracking post-processing package MODPATH, we modeled three-dimensional groundwater advective pathways in the NTS and YM region. Our study focuses on evaluating the potential for groundwater pathways between the NTS and YM withdrawal area and whether travel times for advective flow along these pathways coincide with the prospective monitoring timeframe at the proposed repository. We include uncertainty in effective porosity, as this is a critical variable in the determination of time for radionuclides to travel from the NTS region to the YM withdrawal area. Uncertainty in porosity is quantified through evaluation of existing site data and expert judgment and is incorporated in the model through Monte Carlo simulation. Since porosity information is limited for this region, the uncertainty is quite large and this is reflected in the results as a large range in simulated groundwater travel times

The balance of power: accretion and feedback in stellar mass black holes

In this review we discuss the population of stellar-mass black holes in our galaxy and beyond, which are the extreme endpoints of massive star evolution. In particular we focus on how we can attempt to balance the available accretion energy with feedback to the environment via radiation, jets and winds, considering also possible contributions to the energy balance from black hole spin and advection. We review quantitatively the methods which are used to estimate these quantities, regardless of the details of the astrophysics close to the black hole. Once these methods have been outlined, we work through an outburst of a black hole X-ray binary system, estimating the flow of mass and energy through the different accretion rates and states. While we focus on feedback from stellar mass black holes in X-ray binary systems, we also consider the applicability of what we have learned to supermassive black holes in active galactic nuclei. As an important control sample we also review the coupling between accretion and feedback in neutron stars, and show that it is very similar to that observed in black holes, which strongly constrains how much of the astrophysics of feedback can be unique to black holes.Comment: To be published in Haardt et al. Astrophysical Black Holes. Lecture Notes in Physics. Springer 201

Abundances of the elements in the solar system

A review of the abundances and condensation temperatures of the elements and their nuclides in the solar nebula and in chondritic meteorites. Abundances of the elements in some neighboring stars are also discussed.Comment: 42 pages, 11 tables, 8 figures, chapter, In Landolt- B\"ornstein, New Series, Vol. VI/4B, Chap. 4.4, J.E. Tr\"umper (ed.), Berlin, Heidelberg, New York: Springer-Verlag, p. 560-63

Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares

The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that have utilized data from Hinode/EIS and SDO/EVE, while also providing some historical background and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the Topical Issue on Solar and Stellar Flare

The importance of long‐term experiments in agriculture: their management to ensure continued crop production and soil fertility; the Rothamsted experience

Summary Long‐term field experiments that test a range of treatments and are intended to assess the sustainability of crop production, and thus food security, must be managed actively to identify any treatment that is failing to maintain or increase yields. Once identified, carefully considered changes can be made to the treatment or management, and if they are successful yields will change. If suitable changes cannot be made to an experiment to ensure its continued relevance to sustainable crop production, then it should be stopped. Long‐term experiments have many other uses. They provide a field resource and samples for research on plant and soil processes and properties, especially those properties where change occurs slowly and affects soil fertility. Archived samples of all inputs and outputs are an invaluable source of material for future research, and data from current and archived samples can be used to develop models to describe soil and plant processes. Such changes and uses in the Rothamsted experiments are described, and demonstrate that with the appropriate crop, soil and management, acceptable yields can be maintained for many years, with either organic manure or inorganic fertilizers. Highlights Long‐term experiments demonstrate sustainability and increases in crop yield when managed to optimize soil fertility. Shifting individual response curves into coincidence increases understanding of the factors involved. Changes in inorganic and organic pollutants in archived crop and soil samples are related to inputs over time. Models describing soil processes are developed from current and archived soil data

Probabilistic solar wind and geomagnetic forecasting using an analogue ensemble or "Similar Day" approach

Effective space-weather prediction and mitigation requires accurate forecasting of near-Earth solar-wind conditions. Numerical magnetohydrodynamic models of the solar wind, driven by remote solar observations, are gaining skill at forecasting the large-scale solar-wind features that give rise to near-Earth variations over days and weeks. There remains a need for accurate short-term (hours to days) solar-wind forecasts, however. In this study we investigate the analogue ensemble (AnEn), or “similar day”, approach that was developed for atmospheric weather forecasting. The central premise of the AnEn is that past variations that are analogous or similar to current conditions can be used to provide a good estimate of future variations. By considering an ensemble of past analogues, the AnEn forecast is inherently probabilistic and provides a measure of the forecast uncertainty. We show that forecasts of solar-wind speed can be improved by considering both speed and density when determining past analogues, whereas forecasts of the out-of-ecliptic magnetic field [ BNBN ] are improved by also considering the in-ecliptic magnetic-field components. In general, the best forecasts are found by considering only the previous 6 – 12 hours of observations. Using these parameters, the AnEn provides a valuable probabilistic forecast for solar-wind speed, density, and in-ecliptic magnetic field over lead times from a few hours to around four days. For BNBN , which is central to space-weather disturbance, the AnEn only provides a valuable forecast out to around six to seven hours. As the inherent predictability of this parameter is low, this is still likely a marked improvement over other forecast methods. We also investigate the use of the AnEn in forecasting geomagnetic indices Dst and Kp. The AnEn provides a valuable probabilistic forecast of both indices out to around four days. We outline a number of future improvements to AnEn forecasts of near-Earth solar-wind and geomagnetic conditions