On the acoustical theory of the trumpet : is it sound? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, New Zealand

Newton's Second Law of Motion for one-dimensional inviscid flow of an incompressible fluid, in the absence of external forces, is often expressed in a form known as Bernoulli's equation: There are two distinct forms of Bernoulli's equation used in the system of equations which is commonly considered to describe sound production in a trumpet. The flow between the trumpeter's lips is, in the literature, assumed to be quasi-steady. From this assumption, the first term of the above Bernoulli equation is omitted, since it is then small in comparison to the other two terms. The flow within the trumpet itself is considered to consist of small fluctuations about some mean velocity and pressure. A linearized version of Bernoulli's equation (as used in the equations of linear acoustics) is then adequate to describe the flow. In this case it is the second term of the above equation which is neglected, and the first term is retained. Given that the flow between the trumpeter's lips is that same flow which enters the trumpet itself, a newcomer to the field of trumpet modelling might wonder whether the accepted model is really correct when these two distinct versions of the Bernoulli Equation are used side by side. This thesis addresses this question, and raises others that arise from a review of the standard theory of trumpet physics. The investigation comprises analytical and experimental components, as well as computational simulations. No evidence has been found to support the assumption of quasi-steady flow between the lips of a trumpeter. An alternative flow equation is proposed, and conditions given for its applicability. [NB: Mathematical/chemical formulae or equations have been omitted from the abstract due to website limitations. Please read the full text PDF file for a complete abstract.

Quantifying the effectiveness of agri-environment schemes for a grassland butterfly using individual-based models

The intensification of agricultural practices throughout the twentieth century has had large detrimental effects on biodiversity and these are likely to increase as the human population rises, with consequent pressure on land. To offset these negative impacts, agri-environment schemes have been widely implemented, offering financial incentives for land-owners to create or maintain favourable habitats that enhance or maintain biodiversity. While some evidence is available on the resulting species richness and abundance for groups such as natural predators, pollinating insects including butterflies and moths, this is costly to obtain and it is difficult to predict the effects of specific habitat designs. To alleviate this problem we here develop an individual-based model (IBM), modelling the detailed movement behaviour, foraging, and energy budget of a grassland butterfly Maniola jurtina Linn. in patches of varying dimensions and quality. The IBM is successfully validated against data on M. jurtina densities, movement behaviour, resource use, fecundity and lifespan in habitats of varying quality. We use the IBM to quantify the benefits for life-history outcomes of M. jurtina of increasing the quantity and the quality of field margins within agricultural landscapes. We find that increasing the quantity of field margin habitat from 1 to 3 ha per 100 ha, as recommended in agri-environment schemes, increases the average number of eggs laid across a two-week period by 60% and adds an extra day to the average lifespan. Similar effects are reported for variation in the quality of field margins. We discuss the implications of the result for modelling butterfly responses to management scenarios

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead