Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Turbulence model performance in continuous casting simulations

This paper concerns the development and validation (using an oil/water system) of a finite volume computer model of the continuous casting process for steel flat products. The emphasis is on hydrodynamic aspects and in particular the dynamic behaviour of the metal/slag interface. Instability and wave action encourage the entrainment of inclusions into the melt affecting product quality. To track the interface between oil and water a new implicit algorithm was developed, called the Counter Diffusion Method. To prevent excessive damping, a time-filtered version of the k-e model, was found necessary, with appropriate density stratification terms representing interface turbulence damping.

Time-dependent modelling and experimental validation of the metal/flux interface in a continuous casting mould

A finite volume computer model of the continuous casting process for steel flat products has been developed. In this first stage, the model concentrates on the hydrodynamic aspects of the process and in particular the dynamic behavior of the metal/slag interface. The model was validated against experimental measurements obtained in a water model apparatus.

Singular stresses at the tip of a crack terminating at frictional interface of fibre reinforced composites

The stress singularities at the tip of a crack that terminates at a frictional interface between two layers in anisotropic composites are investigated. The order of stress singularities is determined by solving the characteristic equations obtained from the boundary conditions and the frictional interface conditions for the cases concerned. The interface is assumed to be governed by Coulomb's law of friction. Numerical results are presented for the cases with a crack terminating at a frictional interface of a fibre reinforced composite, and it is shown that there is a big difference of stress singularities between cases with and without considering friction along the interface.

Molecular analysis of Continuous Plankton Recorder samples, an examination of echinoderm larvae in the North Sea

Analysis of the biological time series of plankton samples collected by the Continuous Plankton Recorder (CPR) in the North Atlantic and North Sea has shown a regime shift in the plankton in this region. Both the distributions of planktonic organisms and their timing of occurrence in the seasonal cycle have changed and these changes appear to ref lect global warming. In the North Sea the planktonic larvae of echinoderms have shown a recent dramatic increase in both relative and absolute abundance and their seasonal peak of occurrence has advanced by 47 days. The identity of the echinoderm larvae involved in this change has, however, remained equivocal. The small size of many organisms like echinoderm larvae combined with incomplete taxonomic keys hinders their visual identification and their fragility often means that useful morphological features are damaged during sampling by the CPR. Here, using new molecular methods applied to CPR samples, we show that planktonic larvae of the benthic Echinocardium cordatum dominate the North Sea plankton. We argue that since this species benefits from mild winters and warmer waters their numerical increase in the plankton is consistent with recent climatic changes that appear to be affecting the wider ecology of this region.

Use of Continuous Plankton Recorder information in support of marine management: applications in fisheries, environmental protection, and in the study of ecosystem response to environmental change

The Continuous Plankton Recorder (CPR) survey was conceived from the outset as a programme of applied research designed to assist the fishing industry. Its survival and continuing vigour after 70 years is a testament to its utility, which has been achieved in spite of great changes in our understanding of the marine environment and in our concerns over how to manage it. The CPR has been superseded in several respects by other technologies, such as acoustics and remote sensing, but it continues to provide unrivalled seasonal and geographic information about a wide range of zooplankton and phytoplankton taxa. The value of this coverage increases with time and provides the basis for placing recent observations into the context of long-term, large-scale variability and thus suggesting what the causes are likely to be. Information from the CPR is used extensively in judging environmental impacts and producing quality status reports (QSR); it has shown the distributions of fish stocks, which had not previously been exploited; it has pointed to the extent of ungrazed phytoplankton production in the North Atlantic, which was a vital element in establishing the importance of carbon sequestration by phytoplankton. The CPR continues to be the principal source of large-scale, long-term information about the plankton ecosystem of the North Atlantic. It has recently provided extensive information about the biodiversity of the plankton and about the distribution of introduced species. It serves as a valuable example for the design of future monitoring of the marine environment and it has been essential to the design and implementation of most North Atlantic plankton research.

How well does the Continuous Plankton Recorder (CPR) sample zooplankton? A comparison with the Longhurst Hardy Plankton Recorder (LHPR) in the northeast Atlantic

The Continuous Plankton Recorder (CPR) survey has collected data on basin- scale zooplankton abundance in the North Atlantic since the 1930s. These data have been used in many studies to elucidate seasonal patterns and long-term change in plankton populations, as well as more recently to validate ecosystem models. There has, however, been relatively little comparison of the data from the CPR with that from other samplers. In this study we compare zooplankton abundance estimated from the CPR in the northeast Atlantic with near-surface samples collected by a Longhurst-Hardy Plankton Recorder (LHPR) at Ocean Weather Station India (59 degree N, 19 degree W) between 1971 and 1975. Comparisons were made for six common copepods in the region: Acartia clausi, Calanus finmarchicus, Euchaeta norvegica, Metridia lucens, Oithona sp. and Pleuromamma robusta. Seasonal cycles based on CPR data were similar to those recorded by the LHPR. Differences in absolute abundances were apparent, however, with the CPR underestimating abundances by a factor of between 5 and 40, with the exception of A. clausi. Active avoidance by zooplankton is thought to be responsible. This avoidance is species specific, so that care must be taken describing communities, as the CPR emphasises those species that are preferentially caught, a problem common to many plankton samplers.

Using continuous plankton recorder data

The continuous plankton recorder (CPR) survey is the largest multi-decadal plankton monitoring programme in the world. It was initiated in 1931 and by the end of 2004 had counted 207,619 samples and identified 437 phyto- and zooplankton taxa throughout the North Atlantic. CPR data are used extensively by the research community and in recent years have been used increasingly to underpin marine management. Here, we take a critical look at how best to use CPR data. We first describe the CPR itself, CPR sampling, and plankton counting procedures. We discuss the spatial and temporal biases in the Survey, summarise environmental data that have not previously been available, and describe the new data access policy. We supply information essential to using CPR data, including descriptions of each CPR taxonomic entity, the idiosyncrasies associated with counting many of the taxa, the logic behind taxonomic changes in the Survey, the semi-quantitative nature of CPR sampling, and recommendations on choosing the spatial and temporal scale of study. This forms the basis for a broader discussion on how to use CPR data for deriving ecologically meaningful indices based on size, functional groups and biomass that can be used to support research and management. This contribution should be useful for plankton ecologists, modellers and policy makers that actively use CPR data.

Distribution and abundance of sardine (Sardina pilchardus) eggs in the English Channel from Continuous Plankton Recorder sampling

Continuous Plankton Recorder (CPR) samples from the English Channel and adjacent Celtic shelf, taken over the period 1958-1980, were analysed for sardine (Sardina pilchardus) eggs. Results showed the progression of sardine spawning along the English Channel from west to east from March to August and a return from east to west from September to November. This corresponds with the two seasonal peaks of sardine egg abundance in the western Channel: the main summer peak being in May/June, with a smaller autumn peak in October/November. Long-term changes in sardine egg abundance in CPR samples showed a decline in summer spawning from the late 1960s, but no clear trend in autumn-spawned egg abundance. Similar patterns were observed in the numbers of sardine eggs sampled by conventional plankton net tows at the time-series Station L5 off Plymouth. This supports the use of the longer time-series of sardine egg data at L5 as being representative of a wider area and emphasizes the importance in continuation of the L5 time-series.