Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Analysis of wall plasters and natural sediments from the Neolithic town of Çatalhöyük (Turkey) by a range of analytical techniques

Wall plaster sequences from the Neolithic town of Çatalhöyük have been analysed and compared to three types of natural sediment found in the vicinity of the site, using a range of analytical techniques. Block samples containing the plaster sequences were removed from the walls of several different buildings on the East Mound. Sub-samples were examined by IR spectroscopy, X-ray diffraction and X-ray fluorescence to determine the overall mineralogical and elemental composition, whilst thin sections were studied using optical polarising microscopy, IR Microscopy and Environmental Scanning Electron Microscopy with Energy Dispersive X-ray analysis. The results of this study have shown that there are two types of wall plaster found in the sequences and that the sediments used to produce these were obtained from at least two distinct sources. In particular, the presence of clay, calcite and magnesian calcite in the foundation plasters suggested that these were prepared predominantly from a marl source. On the other hand, the finishing plasters were found to contain dolomite with a small amount of clay and no calcite, revealing that softlime was used in their preparation. Whilst marl is located directly below and around Çatalhöyük, the nearest source of softlime is 6.5 km away, an indication that the latter was important to the Neolithic people, possibly due to the whiter colour (5Y 8/1) of this sediment. Furthermore, the same two plaster types were found on each wall of Building 49, the main building studied in this research, and in all five buildings investigated, suggesting that the use of these sources was an established practice for the inhabitants of several different households across the site.

Sample preparation: a crucial factor for the analytical performance of rationally designed MALDI matrices

Evidence is presented that the performance of the rationally designed MALDI matrix 4-chloro-α-cyanocinnamic acid (ClCCA) in comparison to its well-established predecessor α-cyano-4-hydroxycinnamic acid (CHCA) is significantly dependent on the sample preparation, such as the choice of the target plate. In this context, it becomes clear that any rational designs of MALDI matrices and their successful employment have to consider a larger set of physicochemical parameters, including sample crystallization and morphology/topology, in addition to parameters of basic (solution and/or gas-phase) chemistry.

High Royds: an integrated, analytical approach for mapping the unmarked burials of a pauper cemetery

Applying geophysical techniques to detect and map the physical extent of individual unmarked graves proves difficult in many cases. The success of individual geophysical techniques for detecting unmarked graves may be due to a poor understanding of the nature of the graves themselves, the context in which they lie in, and temporal changes to the burial state. Given the unpredictability of these variables, it is surprising that grave prospection is often undertaken using only a single method. This paper presents a multi-methodological survey strategy for detecting unmarked burials and utilises an analytical approach for visualising and evaluating survey results.

Still searching for graves: an analytical strategy for interpreting geophysical data used in the search for “unmarked” graves

Searching for and mapping the physical extent of unmarked graves using geophysical techniques has proven difficult in many cases. The success of individual geophysical techniques for detecting graves depends on a site-by-site basis. Significantly, detection of graves often results from measured contrasts that are linked to the background soils rather than the type of archaeological feature associated with the grave. It is evident that investigation of buried remains should be considered within a 3D space as the variation in burial environment can be extremely varied through the grave. Within this paper, we demonstrate the need for a multi-method survey strategy to investigate unmarked graves, as applied at a “planned” but unmarked pauper’s cemetery. The outcome from this case study provides new insights into the strategy that is required at such sites. Perhaps the most significant conclusion is that unmarked graves are best understood in terms of characterization rather than identification. In this paper, we argue for a methodological approach that, while following the current trends to use multiple techniques, is fundamentally dependent on a structured approach to the analysis of the data. The ramifications of this case study illustrate the necessity of an integrated strategy to provide a more holistic understanding of unmarked graves that may help aid in management of these unseen but important aspects of our heritage. It is concluded that the search for graves is still a current debate and one that will be solved by methodological rather than technique-based arguments.