Reports on a Course for Prospective High School Mathematics Teachers

The author describes his design for a course entitled Secondary School Mathematics from an Advanced Viewpoint. He adds subjective comments on how his design has worked in practice

An assessment of nitrogen fixation in 'organically managed' spring-sown lupins and leaching under a following winter cereal

Three spring-sown species of lupins (Bora, Prima and Wodjil) and peas were compared in terms of N fixation and subsequent leaching under a following winter cereal crop. Although peas out-yielded lupins (5.4 t compared with ca 3.5 t grain, respectively), the yellow lupin (Wodjil) fixed more N than peas (180 compared with 120 kg N ha-1) and all three lupins contained more protein (> 30%) than the peas (22%). Wodjil was the most effective at suppressing weeds, carrying only 12% of the weed burden found in fallow plots, followed by peas (19%). Winter leaching amounted to > 50 kg nitrate-N ha-1 from under the winter cereal, regardless of whether the previous treatment was a legume crop or was left fallow. There were no significant differences in leaching between the three species of lupin. Leachate in the first 350 mm of drainage under the winter cereal exceeded the EU limit on nitrate in drinking water in all treatments. This work is part of a wider collaborative study supported by Defra which covers a range of UK sites

Rapid design of LCC current-output resonant converters with reduced electrical stresses

The paper presents and validates a straightforward design methodology for realising LCC current-output resonant converters, with the aim of reducing tank currents, and hence, electrical stresses on resonant components. The scheme is ideally suited for inclusion in a rapid iterative design environment e.g. part of a graphical user interfac

Resonance Lineshapes in Quasi-One-Dimensional Scattering

An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in microstructures or transmission resonances in waveguide junctions. The generic resonance is shown to have the asymmetric Fano lineshape. The asymmetry parameter q is independent of coupling to the quasi-bound level implying a scaling property of the resonances which can be tested in transport experiments.Comment: 4 pages, Revtex 3.0, Figure available in Postscrip

Hidden Black: Coherent Enhancement of Absorption in Strongly-scattering Media

We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random matrix theory imply that the reflectivity of the medium can be suppressed by a factor ~(l_a/lN^2), where N is the number of incident channels and l,l_a are the elastic and absorption mean free paths respectively. It is thus possible to increase absorption from a few percent to > 99%. For a localized weak absorber buried in a non-absorbing scattering medium, we find a large but bounded enhancement.Comment: 4 pages, 4 figure

Model wall and recovery temperature effects on experimental heat transfer data analysis

Basic analytical procedures are used to illustrate, both qualitatively and quantitatively, the relative impact upon heat transfer data analysis of certain factors which may affect the accuracy of experimental heat transfer data. Inaccurate knowledge of adiabatic wall conditions results in a corresponding inaccuracy in the measured heat transfer coefficient. The magnitude of the resulting error is extreme for data obtained at wall temperatures approaching the adiabatic condition. High model wall temperatures and wall temperature gradients affect the level and distribution of heat transfer to an experimental model. The significance of each of these factors is examined and its impact upon heat transfer data analysis is assessed

Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures

We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT-symmetry and of PT-symmetry breaking transitions. The uniqueness of PT-symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.Comment: 10 pages, 10 figure

On-line multiobjective automatic control system generation by evolutionary algorithms

Evolutionary algorithms are applied to the on- line generation of servo-motor control systems. In this paper, the evolving population of controllers is evaluated at run-time via hardware in the loop, rather than on a simulated model. Disturbances are also introduced at run-time in order to pro- duce robust performance. Multiobjective optimisation of both PI and Fuzzy Logic controllers is considered. Finally an on-line implementation of Genetic Programming is presented based around the Simulink standard blockset. The on-line designed controllers are shown to be robust to both system noise and ex- ternal disturbances while still demonstrating excellent steady- state and dvnamic characteristics