Torsional rigidity for cylinders with a Brownian fracture

We obtain bounds for the expected loss of torsional rigidity of a cylinder $\Omega_L=(-L/2,L/2) \times \Omega\subset \R^3$ of length $L$ due to a Brownian fracture that starts at a random point in $\Omega_L,$ and runs until the first time it exits $\Omega_L$. These bounds are expressed in terms of the geometry of the cross-section $\Omega \subset \R^2$. It is shown that if $\Omega$ is a disc with radius $R$, then in the limit as $L \rightarrow \infty$ the expected loss of torsional rigidity equals $cR^5$ for some $c\in (0,\infty)$. We derive bounds for $c$ in terms of the expected Newtonian capacity of the trace of a Brownian path that starts at the centre of a ball in $\R^3$ with radius $1,$ and runs until the first time it exits this ball.Comment: 18 page

Heat content and inradius for regions with a Brownian boundary

In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$ of $\mathbb R^m\setminus \beta[0; s]$ for fixed $s$ and $m = 2,3$ in the limit $t \downarrow 0$, when $\beta[0; s]$ is kept at temperature 1 for all $t > 0$ and $\mathbb R^m\setminus \beta[0; s]$ has initial temperature 0, and (ii) the inradius of $\mathbb R^m\setminus \beta[0; s]$ for $m = 2,3,\cdots$ in the limit $s \rightarrow \infty$.Comment: 13 page

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity

We present some open problems and obtain some partial results for spectral optimization problems involving measure, torsional rigidity and first Dirichlet eigenvalue.Comment: 18 pages, 4 figure

Stiffening while drying

We present two models for the drying of waterborne paints, which consist of non-volatile latex particles suspended in water. One model considers the water and latex density in a layer as a function of time. Water evaporation at the surface represents the drying. This model results in a one-dimensional free boundary problem, which is solved numerically. Extensions to the model are given that describe the stiffening of the paint. A second model is a particle based dynamical simulation where latex particles form a network through which water particles move. A thin slab of the suspension in a three-dimensional box is studied. Water particles escaping the slab at the surface represent the drying, progressing network formation the stiffening of the paint. Both models allow for validation with material properties as determined experimentally on real coatings

Moral imagination as the foundation of ethics

Floris van den Berg (1973) studeerde filosofie in Leiden en Utrecht en Japanologie. Naast zijn baan als programmamaker bij Studium Generale van de UU werkt hij aan een proefschrift in de moderne politieke filosofie. Hij is actief als vrijdenker en humanist. Ook heeft hij een academisch weblog: www.florismontis.nl.Universeel subjectivisme is een – tegen de tijdgeest in – universele ethische theorie. Door het vergroten van het domein van het Rawlsiaanse procedurele model van rechtvaardigheid ontwikkel ik een theorie die afwijkt van Rawls omdat het de notie van de Original Position oprekt en zodoende het model van rechtvaardigheid koppelt aan thema’s uit de toegepaste ethiek vanuit utilitaristisch perspectief zoals vooral ontwikkeld door Peter Singer. Universeel subjectivisme is gebaseerd op het idee dat vanuit de Original Position alle mogelijke vormen van leven kunnen worden gerealiseerd. Het vermogen tot lijden is het criterium voor ethische consideratie in dit model. Universeel subjectivisme is een gedachtenexperiment om de wereld te beleven vanuit elk mogelijk levend wezen. Het is een methode om de verschillende belangen met elkaar te harmoniseren. Universeel subjectivisme is een optimaliseringtheorie van de belangen van alle (in ieder geval zoveel mogelijk) levende wezens. Het model maakt het mogelijk om de belangen van diverse groepen te incorporeren in een coherente theorie, zoals de belangen van dieren, toekomstige generaties, internationale relaties, gehandicapten, immigranten etcetera. Zodoende komt tot uiting waar onrecht is en hoe het, in theorie althans, kan worden verworpen. Universeel subjectivisme is een niet-transcendente fundering van de ethiek en het doet geen beroep op noties van altruïsme

Evaluating load balancing policies for performance and energy-efficiency

Nowadays, more and more increasingly hard computations are performed in challenging fields like weather forecasting, oil and gas exploration, and cryptanalysis. Many of such computations can be implemented using a computer cluster with a large number of servers. Incoming computation requests are then, via a so-called load balancing policy, distributed over the servers to ensure optimal performance. Additionally, being able to switch-off some servers during low period of workload, gives potential to reduced energy consumption. Therefore, load balancing forms, albeit indirectly, a trade-off between performance and energy consumption. In this paper, we introduce a syntax for load-balancing policies to dynamically select a server for each request based on relevant criteria, including the number of jobs queued in servers, power states of servers, and transition delays between power states of servers. To evaluate many policies, we implement two load balancers in: (i) iDSL, a language and tool-chain for evaluating service-oriented systems, and (ii) a simulation framework in AnyLogic. Both implementations are successfully validated by comparison of the results.Comment: In Proceedings QAPL'16, arXiv:1610.0769

A systems approach to the process dynamics of interpersonal selling in the financial services industry

The Financial Services Industry (FSI) in South Africa is currently under severe criticism for the quality of service it provides to its customer base. Customer dissatisfaction expressed through individuals, (See Appendix A) consumer bodies and members of parliament has resulted in the draft and approval of three new bills in parliament, which will protect the rights of customer

Dose and number of applications that maximise fungicide effective life exemplified by Zymoseptoria tritici on wheat - a model analysis

Two key decisions that need to be taken about a fungicide treatment programme are (i) the number of applications that should be used per crop growing season, and (ii) the dosage that should be used in each application. There are two opposing considerations, with control efficacy improved by a higher number of applications and higher dose, and resistance management improved by a lower number of applications and lower dose. Resistance management aims to prolong the effective life of the fungicide, defined as the time between its introduction onto the market for use on the target pathogen, and the moment when effective control is lost due to a build-up of fungicide resistance. Thus, the question is whether there are optimal combinations of dose rate and number of applications that both provide effective control and lead to a longer effective life. In this paper, it is shown how a range of spray programmes can be compared and optimal programmes selected. This is explored with Zymoseptoria tritici on wheat and a quinone outside inhibitor (QoI) fungicide. For this pathogen-fungicide combination, a single treatment provided effective control under the simulated disease pressure, but only if the application timing was optimal and the dose was close to the maximum permitted. Programmes with three applications were generally not optimal as they exerted too much selection for resistance. Two-application fungicide programmes balanced effective control with reasonable flexibility of dose and application timing, and low resistance selection, leading to long effective lives of the fungicide

Quantifying the hidden costs of imperfect detection for early detection surveillance

The global spread of pathogens poses an increasing threat to health, ecosystems, and agriculture worldwide. As early detection of new incursions is key to effective control, new diagnostic tests which can detect pathogen presence shortly after initial infection hold great potential for detection of infection in individual hosts. However, these tests may be too expensive to be implemented at the sampling intensities required for early detection of a new epidemic at the population level. To evaluate the trade-off between earlier and/or more reliable detection and higher deployment costs, we need to consider the impacts of test performance, test cost, and pathogen epidemiology. Regarding test performance, the period before new infections can be first detected and the probability of detecting them are of particular importance. We propose a generic framework which can be easily used to evaluate a variety of different detection methods and identify important characteristics of the pathogen and the detection method to consider when planning early detection surveillance. We demonstrate the application of our method using the plant pathogen Phytophthora ramorum in the UK, and find that visual inspection for this pathogen is a more cost effective strategy for early detection surveillance than an early detection diagnostic test