IEPs in mainstream secondary schools: an agenda for research

Providing children with special educational needs with individual education plans (IEPs) was advocated in the 1994 code of practice for SEN, and retained in the 2000 code. Specifically as it relates to mainstream secondary schools, this has proved highly controversial: many SENCos report that the writing and implementing of IEPs is a bureaucratic encumbrance, whilst others, going about the process of writing IEPs in very different ways, report that the process is both manageable and beneficial to the children concerned. Given this contradictory evidence, there is an urgent need for research into this area. Having looked at three case-studies of schools using very different methods to write IEPs in ways with which they feel comfortable, a research agenda is set out with a view to informing policies which ensure that resources spent on SEN are used as productively as possible.

Observations of ice multiplication in a weakly convective cell embedded in supercooled mid-level stratus

Simultaneous observations of cloud microphysical properties were obtained by in-situ aircraft measurements and ground based Radar/Lidar. Widespread mid-level stratus cloud was present below a temperature inversion (~5 °C magnitude) at 3.6 km altitude. Localised convection (peak updraft 1.5 m s−1) was observed 20 km west of the Radar station. This was associated with convergence at 2.5 km altitude. The convection was unable to penetrate the inversion capping the mid-level stratus. The mid-level stratus cloud was vertically thin (~400 m), horizontally extensive (covering 100 s of km) and persisted for more than 24 h. The cloud consisted of supercooled water droplets and small concentrations of large (~1 mm) stellar/plate like ice which slowly precipitated out. This ice was nucleated at temperatures greater than −12.2 °C and less than −10.0 °C, (cloud top and cloud base temperatures, respectively). No ice seeding from above the cloud layer was observed. This ice was formed by primary nucleation, either through the entrainment of efficient ice nuclei from above/below cloud, or by the slow stochastic activation of immersion freezing ice nuclei contained within the supercooled drops. Above cloud top significant concentrations of sub-micron aerosol were observed and consisted of a mixture of sulphate and carbonaceous material, a potential source of ice nuclei. Particle number concentrations (in the size range 0.1of ~25 cm−3. Ice crystal concentrations in the cloud were constant at around 0.2 L−1. It is estimated that entrainment of aerosol particles into cloud cannot replenish the loss of ice nuclei from the cloud layer via precipitation. Precipitation from the mid-level stratus evaporated before reaching the surface, whereas rates of up to 1 mm h−1 were observed below the convective feature. There is strong evidence for the Hallett-Mossop (HM) process of secondary ice particle production leading to the formation of the precipitation observed. This includes (1) Ice concentrations in the convective feature were more than an order of magnitude greater than the concentration of primary ice in the overlaying stratus, (2) Large concentrations of small pristine columns were observed at the ~−5 °C level together with liquid water droplets and a few rimed ice particles, (3) Columns were larger and increasingly rimed at colder temperatures. Calculated ice splinter production rates are consistent with observed concentrations if the condition that only droplets greater than 24 μm are capable of generating secondary ice splinters is relaxed. This case demonstrates the importance of understanding the formation of ice at slightly supercooled temperatures, as it can lead to secondary ice production and the formation of precipitation in clouds which may not otherwise be considered as significant precipitation sources.

The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

The effect of the magnetic field of the secondary star in dwarf novae

We investigate the effect of a secondary star magnetic field on the accretion disc dynamics of dwarf novae. Simulations have been carried out with a particle code and a dipolar magnetic field structure. The magnetic field acts to remove angular momentum from the disc material, increasing the inward mass flow. This makes the accretion disc more centrally condensed, causing a reduction in the recurrence time for dwarf nova outbursts. We have produced Doppler tomograms and light curves which may be compared with observations. These tomograms are significantly different from those produced in the absence of a magnetic field on the secondary. We derive an upper limit to the magnetic moment of the secondary star in UGem of mu_2<2x10^32 A m^2. The magnetic truncation of the accretion disc produces resonance phenomena similar to those seen in the superoutbursts of SUUMa systems. While these have not been observed for systems like UGem, observations of the SUUMa systems provide us with a useful diagnostic of the disc-field interaction. We are able to place an upper limit on the magnetic moment of the secondary in ZCha of mu_2<1x10^30 A m^2.