Full PIC simulation of a first ACHIP experiment @ SINBAD

In laser illuminated dielectric accelerators (DLA) high acceleration gradients can be achieved due to high damage thresholds of the materials at optical frequencies. This is a necessity for developing more compact particle accelerator technologies. The Accelerator on a CHip International Program (ACHIP) funded by the Gordon and Betty Moore Foundation is researching such devices. DESY Hamburg is part of the collaboration. The dedicated accelerator research facility SINBAD is particularly well suited for DLA experiments at relativistic electron energies. High quality beams and short bunch lengths are anticipated from the ARES linac which is currently under construction at SINBAD. The aim of the experiment is the injection of a short electron bunch from the ARES linac into a DLA. In this study the results of one of the first possible experiments at the facility are estimated via a combination of particle-in-cell (PIC) and tracking simulations. ASTRA is used to simulate an electron bunch from the ARES linac at a suitable working point. The dielectric part of the setup will be simulated using the PIC code from CST Particle Studio incorporating the retrieved bunch from the ASTRA simulation. The energy spectra of the electron bunches are calculated as would be measured from a spectrometer dipole with and without the laser fields

Woolworths Holdings Limited's (WHL) strategic business positioning in the South African clothing and food industry

The South African food and clothing retail industry is highly sophisticated and dominated by a few large competitors. The market is unique and has been shaped by abnormal political influences that have created a polarised society. The market holds a high potential owing to the burgeoning young middle class that is also attracting global attention. This necessitates an increase in economies of scale through expansion and acquisition strategies. Woolworths Holdings Limited has experienced significant growth in tough trading conditions whilst many competitors have lost ground. The Woolworths’ brand is primarily aimed at the high-income groupings but also appeals to the burgeoning middle class with their private-label products. The clothing and food divisions also provide a unique appeal that concentrates on the strong brand name to cater to the polarised nature of the market. The Woolworths Holding Limited (WHL) business model aims to offer superior quality at a lower cost than competitors which competitors find difficult to imitate. The apparent paradox is solved through tightly-knit supplier relationships and a culture demanding continuous improvement. The company is uniquely positioned to service the Living Standards Measure (LSM) 8-10 niche market whilst improving efficiencies. The company drives its competitive advantage over competitors through the key competencies of a reputable brand name, a strong sustainability programme, a strong operation and supply chain network, all of which are crucially-supported by superior and innovative technology utilisation. The study analysed the strategic brand positioning with a focus on the introduction of the supermarket concept. The study indicated that the supermarket concept was a reaction from WHL to consumer’s requirements for a one-stop shop aimed at increasing existing customers’ basket spend and drawing similar new clients. An increase in spend is potentially lucrative to WHL, and the strategy is a viable option as long as the company remains focussed on the core principles of the business model

On the measurement of the proton-air cross section using cosmic ray data

Cosmic ray data may allow the determination of the proton-air cross section at ultra-high energy. For example, the distribution of the first interaction point in air showers reflects the particle production cross section. As it is not possible to observe the point of the first interaction $X_{\rm 1}$ of a cosmic ray primary particle directly, other air shower observables must be linked to $X_{\rm 1}$. This introduces an inherent dependence of the derived cross section on the general understanding and modeling of air showers and, therfore, on the hadronic interaction model used for the Monte Carlo simulation. We quantify the uncertainties arising from the model dependence by varying some characteristic features of high-energy hadron production.Comment: Conference proceedings for the Blois07/EDS07 (12th International Conference on Elastic and Diffractive Scattering) Workshop DESY Hambur

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.delayed differential equations, delayed optimal control, numerical optimization, time-to-build

Martin Hofmann’s case for non-strictly positive data types

We describe the breadth-first traversal algorithm by Martin Hofmann that usesa non-strictly positive data type and carry out a simple verification in anextensional setting. Termination is shown by implementing the algorithm inthe strongly normalising extension of system F by Mendler-style recursion.We then analyze the same algorithm by alternative verifications in anintensional setting, in a setting with non-strictly positive inductivedefinitions (not just non-strictly positive data types), and one by algebraicreduction. The verification approaches are compared in terms of notions ofsimulation and should elucidate the somewhat mysterious algorithm and thusmake a case for other uses of non-strictly positive data types. Except forthe termination proof, which cannot be formalised in Coq, all proofs wereformalised in Coq and some of the algorithms were implemented in Agda andHaskell