A new approach to perturbation theory for a Dirac particle in a central field

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the Dirac equation is developed. Avoiding disadvantages of the standard approach in the description of exited states, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Yukawa potential containing the vector part as well as the scalar component are considered.Comment: 12 pages, LaTe

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward-traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward- and downward-traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an alpha-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.Comment: 23 pages, 5 figures. Accepted for publication in Solar Physic

Pulse Dynamics in a Chain of Granules With Friction

We study the dynamics of a pulse in a chain of granules with friction. We present theories for chains of cylindrical granules (Hertz potential with exponent $n=2$) and of granules with other geometries ($n>2$). Our results are supported via numerical simulations for cylindrical and for spherical granules ($n=5/2$).Comment: Submitted to PR

Phase Transition in the 1d Random Field ising model with long range interaction

We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent identically distributed random variables, subgaussian with mean zero. We show that for temperature and strength of the randomness (variance) small enough with P=1 with respect to the distribution of the random fields there are at least two distinct extremal Gibbs measures

Evaluation of a microplate spectrophotometer for soil organic carbon determination in south-central Idaho

Soil organic carbon (SOC) is traditionally measured through dry combustion of soil but is inaccurate in soils recently limed or containing carbonates. Soils of south central Idaho contain carbonates therefore 3 alternative methods are typically used. Walkley-Black titration (WBTIT) has an extensive history but generates a large volume of hazardous waste for each sample analyzed. Low temperature loss on ignition (LOI360°C) may be utilized but requires frequent sample manipulation and is therefore prone to human error. A pressure calcimeter (Pcal) may be used, however the sample container may leak leading to inaccurate results. Therefore, a new method of SOC determination (WBSPEC) utilizing a microplate spectrophotometer was compared to LOI360°C, Pcal, and WBTIT in 75 south central Idaho soils and 10 standard soils. First, it was confirmed that soils of south central Idaho contain carbonates leading to inaccurate SOC determination by dry combustion. During the alternative method comparison, the WBSPEC method reduced waste production over the traditional WBTIT method by 89% while reducing sample handling over LOI360°C. The LOI360°C and WBTIT methods were most similar, however, the WBSPEC method performed adequately; the Pcal method often overestimated SOC compared to each other method. As the low SOC soils of south central Idaho were of particular interest, the methods were compared a second time on low SOC (<13.11 g kg-1) soils. Here, SOC determination was challenging however the WBSPEC method followed other methods well. It was determined that WBSPEC allows for accurate SOC determination in low SOC soils containing carbonates while reducing hazardous waste production and sample handling

Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets

In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation $$\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,$$ where $K$ is a p.c.f. set and $\Delta$ its Laplacian given by a regular harmonic structure. In particular, we prove the existence of nontangential limits of the corresponding Poisson integrals, and the analogous results of the classical Fatou theorems for bounded and nontangentially bounded harmonic functions.Comment: 22 page

The impact of deep-sea fisheries and implementation of the UNGA Resolutions 61/105 and 64/72. Report of an international scientific workshop

The scientific workshop to review fisheries management, held in Lisbon in May 2011, brought together 22 scientists and fisheries experts from around the world to consider the United Nations General Assembly (UNGA) resolutions on high seas bottom fisheries: what progress has been made and what the outstanding issues are. This report summarises the workshop conclusions, identifying examples of good practice and making recommendations in areas where it was agreed that the current management measures fall short of their target

Comparison of nutrient management recommendations and soil health indicators in southern Idaho

Advanced soil tests are being developed to help improve the estimation of plant available nutrients in order to better match fertilizer additions with plant needs as well as provide a measure of soil health, in some instances. The Soil Health Tool (SHT) has been developed with both goals in mind, yet it has not been tested for use in semi-arid regions such as southern Idaho. In the present study, we compared the use of the SHT for making fertilizer recommendations vs. using the standard regional method as well as evaluated the SHT soil health score (SHS) relative to crop yields and quality. The SHT was designed to analyze samples for 0-15 cm depth and regional guidelines call for deeper soil sampling (0-30 cm or 0-60 cm). In order to determine N fertilizer applications, use of the tool without accounting for depth, would recommend greater N application (~138 kg/ha) than the current regional methodology. However, it does appear that by accounting for depth in the SHT can provide similar available N estimates for the top 30 cm of soil. While N mineralization was not well predicted utilizing the method included in the SHT or from the regional methodology, the average estimated available N for these soils (47 kg/ha) was similar to the N mineralization value used in the current regional methodology (50 kg/ha). The P fertilizer recommendations were more similar between the two methodologies with the SHT recommending, on average 4.7 kg/ha less P than the regional method. The lower P recommendation are likely due to a lack of accounting for the effects of high calcium carbonate levels on the P availability from fertilizers in this region. The SHS was highly correlated with measures of soil C but was not positively correlated to crop yield. In some instances, increasing SHS resulted in decreases in crop quality as the addition of manure increased soil C but also created other potential problems such as high salt contents and release of late season N. With modification to more accurately represent irrigation conditions and including sampling to greater soil depths, this test may be tailored to better estimate soil nutrient status and provide better fertilizer recommendations for the region

Structured machine learning tools for modelling characteristics of guided waves

The use of ultrasonic guided waves to probe the materials/structures for damage continues to increase in popularity for non-destructive evaluation (NDE) and structural health monitoring (SHM). The use of high-frequency waves such as these offers an advantage over low-frequency methods from their ability to detect damage on a smaller scale. However, in order to assess damage in a structure, and implement any NDE or SHM tool, knowledge of the behaviour of a guided wave throughout the material/structure is important (especially when designing sensor placement for SHM systems). Determining this behaviour is extremely difficult in complex materials, such as fibre–matrix composites, where unique phenomena such as continuous mode conversion takes place. This paper introduces a novel method for modelling the feature-space of guided waves in a composite material. This technique is based on a data-driven model, where prior physical knowledge can be used to create structured machine learning tools; where constraints are applied to provide said structure. The method shown makes use of Gaussian processes, a full Bayesian analysis tool, and in this paper it is shown how physical knowledge of the guided waves can be utilised in modelling using an ML tool. This paper shows that through careful consideration when applying machine learning techniques, more robust models can be generated which offer advantages such as extrapolation ability and physical interpretation