Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice

Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behaviour of a system under parameter variation can differ significantly from the familiar Hermitian case in the presence of exceptional points. Here we analytically derive the probability of a non-adiabatic transition in a two-level system driven through two consecutive exceptional points at finite speed. The system is Hermitian far away from the exceptional points. In the adiabatic limit an equal redistribution between the states coalescing in the exceptional point is observed, which can be interpreted as a loss of information when passing through the exceptional point. For finite parameter variation this gets modified. We demonstrate how the transition through the exceptional points can be experimentally addressed in a PT-symmetric lattice using Bloch oscillations

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs

Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.Comment: 12 pages, 9 figure

Modelling uncertainty associated with comparative coordinate measurement through analysis of variance techniques

Over the last few years, various techniques and metrological instruments have been proposed to achieve accurate process control on the shop floor at low cost. An efficient solution that has been recently adopted for this complex task is to perform coordinate measurement in comparator mode in order to eliminate the influence of systematic effects associated with the measurement system. In this way, more challenging parts can be inspected in the shop floor environment and higher quality products can be produced while also enabling feedback to the production loop. This paper is concerned with the development of a statistical model for uncertainty associated with comparative coordinate measurement through analysis of variance (ANOVA) techniques. It employs the Renishaw Equator comparative gauging system and a production part with thirteen circular features of three different diameters. An experimental design is applied to investigate the influence of two key factors and their interaction on the comparator measurement uncertainty. The factors of interest are the scanning speed and the sampling point density. In particular, three different scanning speeds and two different sampling point densities are considered. The measurands of interest are the circularity of each circular feature. The present experimental design is meant to be representative of the actual working conditions in which the automated flexible gauge is used. The Equator has been designed for high speed comparative gauging on the shop floor with possibly wide temperature variation. Therefore, two replicates are used at different temperature conditions to decouple the influence of environmental effects and thus drawing more refined conclusions on the statistical significance

Evaluation of automated flexible gauge performance using experimental designs

An essential part of assessing whether a measurement or gauging system meets its intended purpose is to estimate the measurement uncertainties. This paper employs the design of experiments (DOE) approach to implement a practical analysis of measurement uncertainty of Renishaw Equator automated flexible gauge. The factors of interest are measurement strategy, part location, and environmental effects. The experimental results show the ability of the versatile gauge to effectively meet its measurement capability in both discrete-point probing and scanning measuring modes within its whole measuring volume and, in particular, at high scanning speeds and under workshop conditions

Developments in automated flexible gauging and the uncertainty associated with comparative coordinate measurement

Traditional manufacturing uses coordinate measuring machines (CMMs) or component-specific gauging for in-process and post-process inspection. In assessing the fitness for purpose of these measuring systems, it is necessary to evaluate the uncertainty associated with CMM measurement. However, this is not straightforward since the measurement results are subject to a large range of factors including systematic and environmental effects that are difficult to quantify. In addition, machine tool errors and thermal effects of the machine and component can have a significant impact on the comparison between on-machine measurement, in-process measurement and post-process inspection. Coordinate measurements can also be made in a gauging/comparator mode in which measurements of a work piece are compared with those of a calibrated master artefact, and many of the difficulties associated with evaluating the measurement uncertainties are avoided since many of the systematic effects cancel out. Therefore, the use of flexible gauging either as part of an automated or manually-served workflow is particularly beneficial

Seagrass habitats of northeast Australia: models of key processes and controls

An extensive and diverse assemblage of seagrass habitats exists along the tropical and subtropical coastline of north east Australia and the associated Great Barrier Reef. In their natural state, these habitats are characterised by very low nutrient concentrations and are primarily nitrogen limited. Summer rainfall and tropical storms/cyclones lead to large flows of sediment-laden fresh water. Macro grazers, dugongs (Dugong dugon) and green sea turtles (Chelonia mydas) are an important feature in structuring tropical Australian seagrass communities. In general, all seagrass habitats in north east Australia are influenced by high disturbance and are both spatially and temporally variable. This paper classifies the diversity into four habitat types and proposes the main limiting factor for each habitat. The major processes that categorise each habitat are described and significant threats or gaps in understanding are identified. Four broad categories of seagrass habitat are defined as 'River estuaries', 'Coastal', 'Deep water' and 'Reef', and the dominant controlling factors are terrigenous runoff, physical disturbance, low light and low nutrients, respectively. Generic concepts of seagrass ecology and habitat function have often been found inappropriate to the diverse range of seagrass habitats in north east Australian waters. The classification and models developed here explain differences in habitats by identifying ecological functions and potential response to impacts in each habitat. This understanding will help to better focus seagrass management and research in tropical habitats

Local density approximations from finite systems

The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slablike systems of one, two, and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow