Modelling and prototyping the conceptual design of 3D CMM micro-probe

This paper details the prototyping of a novel three axial micro probe based on utilisation of piezoelectric sensors and actuators for true three dimensional metrology and measurements at micro- and nanometre scale. Computational mechanics is used first to model and simulate the performance of the conceptual design of the micro-probe. Piezoelectric analysis is conducted to understand performance of three different materials - silicon, glassy carbon, and nickel - and the effect of load parameters (amplitude, frequency, phase angle) on the magnitude of vibrations. Simulations are also used to compare several design options for layout of the lead zirconium titanate (PZT) sensors and to identify the most feasible from fabrication point of view design. The material options for the realisation of the device have been also tested. Direct laser machining was selected as the primary means of production. It is found that a Yb MOPA based fiber laser was capable of providing the necessary precision on glassy carbon (GC), although machining trials on Si and Ni were less successful due to residual thermal effects.To provide the active and sensing elements on the flexures of the probe, PZT thick films are developed and deposited at low temperatures (Lt720 degC) allowing a high quality functional ceramic to be directly integrated with selected materials. Characterisation of the materials has shown that the film has a homogenous and small pore microstructure.

BSHM meetings: British Mathematics Colloquium

Report on the British Mathematics Colloquium, which took place in York, 25-28 March 2008. Also includes abstracts of the individual talks.

Design, modeling and characterization of a microinductor for future DC-DC power converters

Experimental, analytical and simulated data are presented in this article to assess the performance of electrodeposited nickel-iron within a novel solenoid microinductor. A design flowchart highlights the primary design principles when developing a microscale magnetic component for DC-DC power converters. Thermal modeling is used to predict the operational conditions that generate undesirable thermal generation within the component. Operating at 0.5MHz, the microinductor achieves an efficiency and power density of 78% and 7.8 W/cm3, respectively.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

Reviews: making mathematics with needlework

Review of Making Mathematics with Needlework, edited by Sarah-Marie Belcastro and Carolyn Yackel, published by AK Peters Ltd, 2007 (ISBN 978-1-56881-331-8).

[Book review] Collaborative learning in mathematics

Review of: Collaborative Learning in Mathematics: A challenge to our beliefs and practices by Malcolm Swan, National Institute of Adult Continuing Education, paperback £24.95, ISBN 981-1-86201-311-7; hardback £44.95, ISBN 978-1-86201-316-2.

Effects of magnetic fields on crystal growth

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using a two-dimensional enthalpy based numerical model. Using an approximation for three-dimensional unconstricted growth, the resulting Lorentz forces generate a circulating flow influencing the solidification pattern. Under the presence of a strong magnetic field secondary growth on the clockwise side of the primary arm of the dendrite was encouraged, whereas the anticlockwise side is suppressed due to a reduction in local free energy. The preferred direction of growth rotated in the clockwise sense under an anticlockwise flow. The tip velocity is significantly increased compared with growth in stagnant flow. This is due to a small recirculation at the tip of the dendrite; bringing in colder liquid and lowering the concentration of solute.

Some issues on assessment methods and learning in mathematics and statistics

This paper looks at the application of some of the assessment methods in practice with the view to enhance students’ learning in mathematics and statistics. It explores the effective application of assessment methods and highlights the issues or problems, and ways of avoiding them, related to some of the common methods of assessing mathematical and statistical learning. Some observations made by the author on good assessment practice and useful approaches employed at his institution in designing and applying assessment methods are discussed. Successful strategies in implementing assessment methods at different levels are described.

Thermoelectric MHD in dendritic solidification

The effects of a constant uniform magnetic field on dendritic solidification were investigated using an enthalpy based numerical model. The interaction between thermoelectric currents on a growing crystal and the magnetic field generates a Lorentz force that creates flow. The need for very high resolution at the liquid-solid boundary where the thermoelectric source originates plus the need to accommodate multiple grains for a realistic simulation, make this a very demanding computational problem. For practical simulations, a quasi 3-dimensional approximation is proposed which nevertheless retains essential elements of transport in the third dimension. A magnetic field normal to the plane of growth leads to general flow circulation around an equiaxed dendrite, with secondary recirculations between the arms. The heat/solute advection by the flow is shown to cause a change in the morphology of the dendrite; secondary growth is promoted preferentially on one side of the dendrite arm and the tip velocity of the primary arm is increased. The degree of approximation introduced is quantified by extending the model into 3-dimensions, where the full Navier-Stokes equation is solved, and compared against the 2-dimensional solution.

Primary Production In A Turbid Estuary

The primary production in the Bristol Channel, U.K., was studied from 1973 to 1977: in this estuary, the euphotic zone extends from less than 0.5 m to greater than 10m and there is a large riverine input of inorganic nutrients. The standing stock of phytoplankton chlorophyll a was measured in 1973 and 1974 and was similar throughout the Bristol Channel but the rate of primary production was much greater where the water was less turbid. The estimated primary production was 6.8g C m−2 for the most turbid region and 164.9g C m−2 for the Outer Bristol Channel. A larger proportion of the annual primary production occurred in the spring in the Outer Channel than in the most turbid regions. Phaeocystis developed into blooms in some, but not all, years and exhibited a different light saturation curve to other phytoplankton populations. Serial incubations of short duration gave higher fixation rates than day-long incubations and it is argued that photoinhibition is probably insignificant in a mixed water column. Excretion rates of dissolved organic carbon by phytoplankton were always low.

Primary Production In An Estuarine Environment - Comparison Of Insitu And Simulated Insitu C-14 Techniques

A simulated in situ incubation box has been compared with in situ exposure for 14C production measurements in an estuarine environment. Measurements were made over the course of 14 months, mainly in the Tamar estuary; production rates ranged from less than 1 mg C m−2h−1 to 350 mg C m−2h−1 and there was no significant difference between results from the two methods. In the estuarine waters investigated, the simulated in situ incubator with neutral density filters, used with a Secchi disc to determine sampling depths, gives a satisfactory estimate of in situ primary production.