Experimental model of the interfacial instability in aluminium reduction cells

A solution has been found to the long-standing problem of experimental modelling of the interfacial instability in aluminium reduction cells. The idea is to replace the electrolyte overlaying molten aluminium with a mesh of thin rods supplying current down directly into the liquid metal layer. This eliminates electrolysis altogether and all the problems associated with it, such as high temperature, chemical aggressiveness of media, products of electrolysis, the necessity for electrolyte renewal, high power demands, etc. The result is a room temperature, versatile laboratory model which simulates Sele-type, rolling pad interfacial instability. Our new, safe laboratory model enables detailed experimental investigations to test the existing theoretical models for the first time

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Retail price optimisation from sparse demand data

It will be shown how the retailer can use economic theory to exploit the sparse information available to him to set the price of each item he is selling close to its profit-maximizing level. The variability of the maximum price acceptable to each customer is modeled using a probability density for demand, which provides an alternative to the conventional demand curve often employed. This alternative way of interpreting retail demand data provides insights into the optimal price as a central measure of a demand distribution. Modeling individuals’ variability in their maximum acceptable price using a near-exhaustive set of “demand densities”, it will be established that the optimal price will be close both to the mean of the underlying demand density and to the mean of the Rectangular distribution fitted to the underlying distribution. An algorithm will then be derived that produces a near-optimal price, whatever the market conditions prevailing, monopoly, oligopoly, monopolistic competition or, in the limiting case, perfect competition, based on the minimum of market testing. The algorithm given for optimizing the retail price, even when demand data are sparse, is shown in worked examples to be accurate and thus of practical use to retail businesses

Testing the validity of the “value of a prevented fatality” (VPF) used to assess UK safety measures

AbstractThe “value of a prevented fatality” (VPF), the maximum amount that it is notionally reasonable to pay for a safety measure that will reduce by one the expected number of preventable premature deaths in a large population, is published by the UK Department for Transport (DfT). The figure, updated for changes in GDP per head, is used by the DfT, the Health and Safety Executive and other UK regulatory bodies as well as very widely in the process, nuclear and other industries as the standard by which to judge how much to spend to reduce harm to humans. The paper tests the validity of the 1999 study on which the VPF is based and finds that that study fails numerous tests of its validity. It is concluded that there is no evidential base for the VPF that has been used for many years in the UK and is still in standard use today. Given the difficulties evident in the interpretation of survey results, an urgent re-appraisal is needed of alternative statistical methodologies that can allow robust regulatory and industry safety decision making and, vitally, give adequate protection to the UK public and to those working in the UK's transport, process, nuclear and other industries

Green functions of the spectral ball and symmetrized polydisk

The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic (non-derogatory) matrix. When the pole is derogatory, the inequality is always strict, and the difference between the two functions depends on the order of nilpotence of the strictly upper triangular blocks that appear in the Jordan decomposition of the pole. In particular, the Green function of the spectral ball is not symmetric in its arguments. Additionally, some estimates are given for invariant functions in the symmetrized polydisc, e.g. (infinitesimal versions of) the Carath\'eodory distance and the Green function, that show that they are distinct in dimension greater or equal to $3$.Comment: 12 page

Possible role of fungi in negatively affecting fruit-set in avocados

Poor fruit set continues to be a major problem in the avocado industry in South Africa. In the past this was estimated to have caused a loss of income of millions of rands. In this investigation the role of fungi on the pistils of avocado cultivars after pollination was examined. Pollinated pistils of avocado cultivars ‘Pinkerton’, ‘Ryan’, ‘Hass’, ‘Fuerte’ and ‘Nabal’ were removed twenty-four hours after the first anthesis (female stage), for detection and isolation of fungi. Germinating conidia were seen on the surface of stigma adjacent to the germinated pollen grains. A number of dematiaceous fungi were isolated from the pistils and the most important species were identified.When a drop of the spore suspension of the most frequently isolated fungi was inoculated on the stigmas of emasculated flowers after hand pollination, a high rate of abscission was observed. Thus some of these fungi appear to have played a significant role which resulted in greater abscission of flowers

A deterministic detector for vector vortex states

Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom. We demonstrate our detection system with vector vortex modes from the |[Formula: see text]| = 1 and |[Formula: see text]| = 10 subspaces using classical and weak coherent states and find excellent detection fidelities for both pure and superposition vector states. This work opens the possibility to increase the dimensionality of the state-space used for encoding information while maintaining deterministic detection and will be invaluable for long distance classical and quantum communication

Considerations in relation to off-site emergency procedures and response for nuclear accidents

The operation of nuclear facilities has, fortunately, not led to many accidents with off-site consequences. However, it is well-recognised that should a large release of radioactivity occur, the effects in the surrounding area and population will be significant. These effects can be mitigated by developing emergency preparedness and response plans prior to the operation of the nuclear facility that can be exercised regularly and implemented if an accident occurs. This review paper details the various stages of a nuclear accident and the corresponding aspects of an emergency preparedness plan that are relevant to these stages, both from a UK and international perspective. The paper also details how certain aspects of emergency preparedness have been affected by the accident at Fukushima Dai-ichi and as a point of comparison how emergency management plans were implemented following the accidents at Three Mile Island 2 and Chernobyl. In addition, the UK’s economic costing model for nuclear accidents COCO-2, and the UK’s Level-3 Probabilistic Safety Assessment code “PACE” are introduced. Finally, the factors that affect the economic impact of a nuclear accident, especially from a UK standpoint, are described