Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary

In 1965, Armstrong and Head (Acta Metall. 13(7):759–764, 1965) explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall-Petch relationship. More recently, Voskoboinikov et al. (Phil. Mag. Lett. 87(9):669-676, 2007) used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface.\ud \ud In this paper, we extend the work of Voskoboinikov et al. to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small

Asymptotic analysis of a pile-up of edge dislocation

The idealised problem of a pile-up of dislocation walls (that is, of planes each containing an infinite number of parallel and identical dislocations) was presented by Roy et al. (Mater. Sci. Eng. A 486:653-661, 2008) as a proto-type for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of screw dislocation walls, but that numerical methods seem to be necessary for investigating edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up

On approaches to modelling lattice dislocations

By proposing a sinusoidal relationship between slip discontinuity and the associated mismatch force, Peierls and Nabarro famously developed a dislocation model that eliminates the stress singularity from the Volterra dislocation model. Recently, Lubarda and Markenscoff (Appl. Phys. Lett. 89:151923, 2006) developed a model in which the Burgers vector of the dislocation is applied over some finite distance, , described as the ‘core radius’. They found that the shear stress on the glide-plane predicted in the Lubarda-Markenscoff model is identical to that predicted by the Peierls-Nabarro model. In this paper, we investigate generalisations of both the Lubarda-Markenscoff and Peierls-Nabarro models, demonstrating that different distributions of infinitesimal dislocations in a generalised Lubarda-Markenscoff model can be associated with different expressions for the misalignment force in a generalised Peierls-Nabarro model. Our results indicate that the generalised Lubarda-Markenscoff framework is a versatile and useful method for modelling the core of a dislocation that neatly complements the well established Peierls-Nabarro framework

Status of ultrachemical analysis for semiconductors

Status of ultratrace chemical analyses of materials for semiconductors was studied. This study covered atomic absorption spectroscopy, emission spectroscopy, and activation analyses. It makes recommendations to improve sensitivity, reliability and versatility for ultratrace chemical analysis

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

APPLICATION OF THE ECONOMIC THRESHOLD FOR INTERSEASONAL PEST CONTROL

We show how an interseasonal pest control problem can be simplified to enable an intraseasonal model to be empirically applied, extending the range of application of the intraseasonal model. Three alternative economic thresholds are compared. The optimal solution requires repeated computations by the farmer to compute the profit maximizing dose, with a corresponding threshold, for each pest infestation. Two alternative decision rules require a single computation by the farmer for the threshold and dosage rate. An empirical illustration shows that, relative to the optimal solution which is computationally burdensome to the farmer, little net revenue is lost by using one of the thresholds based upon a simpler decision rule.Farm Management,

Biomass production and nitrogen dynamics in an integrated aquaculture/agriculture system

A combined aquaculture/agriculture system that brings together the three major components of a Controlled Ecological Life Support System (CELSS) - biomass production, biomass processing, and waste recycling - was developed to evaluate ecological processes and hardware requirements necessary to assess the feasibility of and define design criteria for integration into the Kennedy Space Center (KSC) Breadboard Project. The system consists of a 1 square meter plant growth area, a 500 liter fish culture tank, and computerized monitoring and control hardware. Nutrients in the hydrophonic solution were derived from fish metabolites and fish food leachate. In five months of continuous operation, 27.0 kg of lettuce tops, 39.9 kg of roots and biofilm, and 6.6 kg of fish (wet weights) were produced with 12.7 kg of fish food input. Based on dry weights, a biomass conversion index of 0.52 was achieved. A nitrogen budget was derived to determine partitioning of nitrogen within various compartments of the system. Accumulating nitrogen in the hypoponic solution indicated a need to enlarge the plant growth area, potentially increasing the biomass production and improving the biomass conversion index

Sensing of Fluctuating Nanoscale Magnetic Fields Using NV Centres in Diamond

New magnetometry techniques based on Nitrogen-Vacancy (NV) defects in diamond allow for the imaging of static (DC) and oscillatory (AC) nanoscopic magnetic systems. However, these techniques require accurate knowledge and control of the sample dynamics, and are thus limited in their ability to image fields arising from rapidly fluctuating (FC) environments. We show here that FC fields place restrictions on the DC field sensitivity of an NV qubit magnetometer, and that by probing the dephasing rate of the qubit in a magnetic FC environment, we are able to measure fluctuation rates and RMS field strengths that would be otherwise inaccessible with the use of DC and AC magnetometry techniques. FC sensitivities are shown to be comparable to those of AC fields, whilst requiring no additional experimental overheads or control over the sample.Comment: 5 pages, 4 figure

Asymptotic analysis of a system of algebraic equations arising in dislocation theory

The system of algebraic equations given by\ud \ud $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$\ud \ud appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole.\ud \ud We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n -> ∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment but, up to corrections of logarithmic order, it also leads to a differential equation.\ud \ud The continuum approximation is only valid for i not too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem

Study of behavioral modifications resulting from exposure to high let radiation

Animal irradiations, behavioral studies, neurological studies, and nuclear medicine studies are discussed