A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

Ab-initio simulation of high-temperature liquid selenium

Ab initio molecular dynamics simulation is used to investigate the structure and dynamics of liquid Se at temperatures of 870 and 1370~K. The calculated static structure factor is in excellent agreement with experimental data. The calculated radial distribution function gives a mean coordination number close to 2, but we find a significant fraction of one-fold and three-fold atoms, particularly at 1370~K, so that the chain structure is considerably disrupted. The self-diffusion coefficient has values ($\sim 1 \times 10^{-8}$~m~s$^{-1}$) typical of liquid metals.Comment: 10 pages, 4 Poscript figures, uses REVTE

Effect of interface bonding on spin-dependent tunneling from the oxidized Co surface

We demonstrate that the factorization of the tunneling transmission into the product of two surface transmission functions and a vacuum decay factor allows one to generalize Julliere's formula and explain the meaning of the ``tunneling density of states'' in some limiting cases. Using this factorization we calculate spin-dependent tunneling from clean and oxidized fcc Co surfaces through vacuum into Al using the principal-layer Green's function approach. We demonstrate that a monolayer of oxygen on the Co (111) surface creates a spin-filter effect due to the Co-O bonding which produces an additional tunneling barrier in the minority-spin channel. This changes the minority-spin dominated conductance for the clean Co surface into a majority spin dominated conductance for the oxidized Co surface.Comment: 7 pages, revtex4, 4 embedded eps figure

Naturally fractured tight gas - gas reservoir detection optimization. Quarterly report, June 1, 1996--September 30, 1996

This document contains the status report for the Naturally Fractured Tight Gas-Gas Reservoir Detection Optimization project for the contract period 9/30/93 to 3/31/97. Data from seismic surveys are analyzed for structural imaging of reflector units. The data were stacked using the new, improved statics and normal moveout velocities. The 3-D basin modeling effort is continuing with code development. The main activities of this quarter were analysis of fluid pressure data, improved sedimentary history, lithologic unit geometry reconstruction algorithm and computer module, and further improvement, verification, and debugging of the basin stress and multi-phase reaction transport module

Randomized controlled field trial comparing quarter and cow level selective dry cow treatment using the California Mastitis Test

Selective use of antibiotic dry cow treatment can be implemented at the cow or quarter level, with the latter having the potential to further reduce antibiotic use. Our objective was to compare these 2 approaches in 6 herds in the United Kingdom in which environmental mastitis predominated. Eight hundred seven cows were enrolled and categorized as having a high cell count (n = 401) or low cell count (n = 406) in the last 3 mo of lactation and clinical mastitis history. All quarters of all enrolled cows received an internal teat sealant. Within each category, cows were randomly allocated to 1 of 3 groups; in one group antibiotic treatment was allocated at cow level (i.e., all 4 quarters received antibiotic), whereas in the 2 remaining groups antibiotic treatment was allocated at quarter level, based on California Mastitis Test (CMT) findings. Two different thresholds, score 1 and 2, were used to determine likely infection status. Quarter milk samples were collected at dry off and postcalving for bacteriological culture and somatic cell count (SCC). Cows were monitored for clinical mastitis from dry off until 100 d in milk. Cow level SCC and milk yield data were collated from farm records. Within each category, the 2 quarter level treatment groups were compared with cow level treatment at dry off. Leaving quarters untreated with intramammary antibiotic in cows in the high cell count group, with a CM

Impact of simulated nitrogen pollution on heathland microfauna, mesofauna and plants

Deposition of reactive nitrogen derived from intensive agriculture and industrial processes is a major threat to biodiversity and ecosystem services around the world; however our knowledge of the impacts of nitrogen is restricted to a very limited range of organisms. Here we examine the response of groups of microfauna (testate amoebae), mesofauna (enchytraeid worms) and plants to ammonium nitrate application in the Ruabon heathland long-term experiment. Plant data showed significant differences between treatments, particularly characterised by a loss of bryophytes in nitrogen-treated plots, by contrast enchytraeids showed a non-significant increase in abundance in response to treatment. Testate amoebae showed no significant changes in abundance or inferred biomass but significant changes in community structure with a reduced abundance of Corythion dubium, interpreted as a response to the loss of bryophytes. Our results suggest that simple indices of plant community may have value for bioindication while the bioindication value of testate amoebae and enchytraeids is not clearly demonstrated

Gravitational waves from rapidly rotating neutron stars

Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced and magnetically sustained mountains in the crust. In general magnetic mountains are likely to be detectable only if the buried magnetic field of the star is of the order of $B\approx 10^{12}$ G. In the thermal mountain case we find that gravitational wave emission from persistent systems may be detected by ground based interferometers. Finally we re-asses the idea that gravitational wave emission may be balancing the accretion torque in these systems, and show that in most cases the disc/magnetosphere interaction can account for the observed spin periods.Comment: To appear in 'Gravitational Waves Astrophysics: 3rd Session of the Sant Cugat Forum on Astrophysics, 2014', Editor: Carlos F. Sopuert

Pentagonal nanowires: a first-principles study of atomic and electronic structure

We performed an extensive first-principles study of nanowires in various pentagonal structures by using pseudopotential plane wave method within the density functional theory. Our results show that nanowires of different types of elements, such as alkali, simple, transition and noble metals and inert gas atoms, have a stable structure made from staggered pentagons with a linear chain perpendicular to the planes of the pentagons and passing through their centers. This structure exhibits bond angles close to those in the icosahedral structure. However, silicon is found to be energetically more favorable in the eclipsed pentagonal structure. These quasi one dimensional pentagonal nanowires have higher cohesive energies than many other one dimensional structures and hence may be realized experimentally. The effect of magnetic state are examined by spin-polarized calculations. The origin of the stability are discussed by examining optimized structural parameters, charge density and electronic band structure, and by using analysis based on the empirical Lennard-Jones type interaction. Electronic band structure of pentagonal wires of different elements are discussed and their effects on quantum ballistic conductance are mentioned. It is found that the pentagonal wire of silicon exhibits metallic band structure.Comment: 4 figures, accepted for publication in Phys. Rev.

Structure and Dynamics of Liquid Iron under Earth's Core Conditions

First-principles molecular dynamics simulations based on density-functional theory and the projector augmented wave (PAW) technique have been used to study the structural and dynamical properties of liquid iron under Earth's core conditions. As evidence for the accuracy of the techniques, we present PAW results for a range of solid-state properties of low- and high-pressure iron, and compare them with experimental values and the results of other first-principles calculations. In the liquid-state simulations, we address particular effort to the study of finite-size effects, Brillouin-zone sampling and other sources of technical error. Results for the radial distribution function, the diffusion coefficient and the shear viscosity are presented for a wide range of thermodynamic states relevant to the Earth's core. Throughout this range, liquid iron is a close-packed simple liquid with a diffusion coefficient and viscosity similar to those of typical simple liquids under ambient conditions.Comment: 13 pages, 8 figure