An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Plasma surface dynamics and smoothing in the relativistic few-cycle regime

Efficient production of coherent harmonic radiation from solid targets relies critically on the formation of smooth, short density scalelength plasmas. Recent experimental results (Dromey et al 2009 Nat. Phys. 5 146) suggest, however, that the target roughness on the scale of the emitted harmonic wavelength does not result in diffuse reflection-in apparent contradiction to the Rayleigh criterion for coherent reflection. In this paper we show, for the first time, using analytic theory and 2D PIC simulations, that the interaction of relativistically strong laser pulses with corrugated target surfaces results in a highly effective smoothing of the interaction surface and consequently the generation of highly collimated and temporally confined XUV pulses from rough targets, in excellent agreement with experimental observations.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.

Investigating erythemal UV exposure and vitamin D production in the urban canyon

Exposure to ultraviolet radiation (UV) results in both damaging and beneficial health outcomes. Excessive UV exposure has been linked to many skin and eye problems, but moderate exposure induces vitamin D production. It has been reported that humans receive 90-95% of their vitamin D from production that starts after UV exposure. Although it is possible to acquire vitamin D through dietary supplementation, the average person receives very little in this manner. Therefore, since most people acquire their vitamin D from synthesis after exposure to UV from sunlight, it is very important to understand the different environments in which people encounter UV. This project measured UV radiation and in-vitro vitamin D production in the urban canyon and at a nearby suburban location. The urban canyon is an environment consisting of tall buildings and tropospheric air pollution, which have an attenuating effect on UV. Typically, UV measurements are collected in areas outside the urban canyon, meaning that at times studies and public recommendations do not accurately represent the amount of UV reaching street-level in highly urbanized areas. Understanding of UV exposure in urban canyons becomes increasingly important as the number of people working and living in large cities steadily increases worldwide. This study was conducted in the central business district (CBD) of Brisbane, Australia, which models the urban canyons of large cities around the world in that it boasts a great number of tall buildings, including many skyscrapers, meaning that most areas only see a small amount of direct sunlight each day. During the winter of 2007 measurements of UV radiation and in-vitro vitamin D production were collected in the CBD and at a suburban site approximately 2.5km outside the CBD. Air pollution data was obtained from a central CBD measurement site. Data analysis showed that urban canyon measurements of both UV radiation and in-vitro vitamin D production were significantly lower than those collected at the suburban site. These results will aid both future researchers and policy makers in better understanding human UV exposure in Brisbane’s CBD and other urban canyons around the world.