Fractionated crystallisation in a polydisperse mixture of hard spheres

We consider the nature of the fluid-solid phase transition in a polydisperse mixture of hard spheres. For a sufficiently polydisperse mixture crystallisation occurs with simultaneous fractionation. At the fluid-solid boundary, a broad fluid diameter distribution is split into a number of narrower fractions, each of which then crystallises. The number of crystalline phases increases with the overall level of polydispersity. At high densities, freezing is followed by a sequence of demixing transitions in the polydisperse crystal.Comment: 10 pages, 4 figures to appear in J. Chem. Phy

Secret objectives: promoting inquiry and tackling preconceptions in teaching laboratories

In its most general form, a `secret objective' is any inconsistency between the experimental reality and the information provided to students prior to starting work on an experiment. Students are challenged to identify the secret objectives and then given freedom to explore and understand the experiment, thus encouraging and facilitating genuine inquiry elements in introductory laboratory courses. Damping of a simple pendulum is used as a concrete example to demonstrate how secret objectives can be included. We also discuss the implications of the secret objectives method and how this can provide a link between the concepts of problem based learning and inquiry style labs

Bounding Embeddings of VC Classes into Maximum Classes

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving the conjecture is by embedding general VC classes into maximum classes without super-linear increase to their VC dimensions, as such embeddings would extend the known compression schemes to all VC classes. We show that maximum classes can be characterised by a local-connectivity property of the graph obtained by viewing the class as a cubical complex. This geometric characterisation of maximum VC classes is applied to prove a negative embedding result which demonstrates VC-d classes that cannot be embedded in any maximum class of VC dimension lower than 2d. On the other hand, we show that every VC-d class C embeds in a VC-(d+D) maximum class where D is the deficiency of C, i.e., the difference between the cardinalities of a maximum VC-d class and of C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible results on embedding into maximum classes. For some special classes of Boolean functions, relationships with maximum classes are investigated. Finally we give a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum classes for smallest k.Comment: 22 pages, 2 figure

The EET Horizontal Tails Investigation and the EET Lateral Controls Investigation

In the energy efficient transport (EET) Horizontal Tails Investigation, aerodynamic data were measured for five different horizontal tails on a full span model with a wide body fuselage. Three of the horizontal tails were low tail configurations and two were T tail configurations. All tails were tested in conjunction with two wings, a current wide body wing and a high aspect ratio supercritical wing. Local downwash angles and dynamic pressures in the vicinity of the tails were measured using a yaw head rake. The results provide a comparison of the aerodynamic characteristics of the two wing configurations at trimmed conditions for Mach numbers between 0.60 and 0.90. In the EET Lateral Controls Investigation, the control effectiveness of a conventional set of lateral controls was measured over a Mach number range from 0.60 to 0.90 on a high aspect ratio supercritical wing semispan model. The conventional controls included a high speed aileron, a low speed aileron, and six spoiler segments. The wing was designed so that the last 25% of the chord is removable to facilitate testing of various control systems. The current status and an indication of the data obtained in these investigations are presented

Fractionation effects in phase equilibria of polydisperse hard sphere colloids

The equilibrium phase behaviour of hard spheres with size polydispersity is studied theoretically. We solve numerically the exact phase equilibrium equations that result from accurate free energy expressions for the fluid and solid phases, while accounting fully for size fractionation between coexisting phases. Fluids up to the largest polydispersities that we can study (around 14%) can phase separate by splitting off a solid with a much narrower size distribution. This shows that experimentally observed terminal polydispersities above which phase separation no longer occurs must be due to non-equilibrium effects. We find no evidence of re-entrant melting; instead, sufficiently compressed solids phase separate into two or more solid phases. Under appropriate conditions, coexistence of multiple solids with a fluid phase is also predicted. The solids have smaller polydispersities than the parent phase as expected, while the reverse is true for the fluid phase, which contains predominantly smaller particles but also residual amounts of the larger ones. The properties of the coexisting phases are studied in detail; mean diameter, polydispersity and volume fraction of the phases all reveal marked fractionation. We also propose a method for constructing quantities that optimally distinguish between the coexisting phases, using Principal Component Analysis in the space of density distributions. We conclude by comparing our predictions to perturbative theories for near-monodisperse systems and to Monte Carlo simulations at imposed chemical potential distribution, and find excellent agreement.Comment: 21 pages, 23 figures, 2 table

The High Energy Emission of the Crab Nebula from 20 keV to 6 MeV with INTEGRAL

The SPI spectrometer aboard the INTEGRAL mission observes regularly the Crab Nebula since 2003. We report on observations distributed over 5.5 years and investigate the variability of the intensity and spectral shape of this remarkable source in the hard X-rays domain up to a few MeV. While single power law models give a good description in the X-ray domain (mean photon index ~ 2.05) and MeV domain (photon index ~ 2.23), crucial information are contained in the evolution of the slope with energy between these two values. This study has been carried out trough individual observations and long duration (~ 400 ks) averaged spectra. The stability of the emission is remarkable and excludes a single power law model. The slopes measured below and above 100 keV agree perfectly with the last values reported in the X-ray and MeV regions respectively, but without indication of a localized break point. This suggests a gradual softening in the emission around 100 keV and thus a continuous evolution rather than an actual change in the mechanism parameters. In the MeV region, no significant deviation from the proposed power law model is visible up to 5-6 MeV. Finally, we take advantage of the spectroscopic capability of the instrument to seek for previously reported spectral features in the covered energy range with negative results for any significant cyclotron or annihilation emission on 400 ks timescales. Beyond the scientific results, the performance and reliability of the SPI instrument is explicitly demonstrated, with some details about the most appropriate analysis method.Comment: accepted for publication in ApJ; 4 figures, 2 table

An increase in N-Ras expression is associated with development of hormone refractory prostate cancer in a subset of patients

Protein expression of H, K and N-Ras was assessed in hormone sensitive and hormone refractory prostate tumour pairs from 61 patients by immunohistochemistry. Expression of H-Ras and K- Ras was not associated with any known clinical parameters. In contrast an increase in N-Ras membrane expression in the transition from hormone sensitive to hormone refractory prostate cancer was associated with shorter time to relapse (p=0.01) and shorter disease specific survival (p=0.008). In addition, patients with an increase in N-Ras membrane expression had lower levels of PSA at relapse (p=0.02) and expression correlated with phosphorylated MAP kinase (p=0.010) and proliferation index (Ki67, p=0.02). These results suggest that in a subgroup patients N-Ras expression is associated with development of hormone refractory prostate cancer via activation of the MAP kinase cascade

Can lay-led walking programmes increase physical activity in middle aged adults? : a randomised controlled trial

Study objective: To compare health walks, a community based lay-led walking scheme versus advice only on physical activity and cardiovascular health status in middle aged adults. Design: Randomised controlled trial with one year follow up. Physical activity was measured by questionnaire. Other measures included attitudes to exercise, body mass index, cholesterol, aerobic capacity, and blood pressure. Setting: Primary care and community. Participants: 260 men and women aged 40–70 years, taking less than 120 minutes of moderate intensity activity per week. Main results: Seventy three per cent of people completed the trial. Of these, the proportion increasing their activity above 120 minutes of moderate intensity activity per week was 22.6% in the advice only and 35.7% in the health walks group at 12 months (between group difference =13% (95% CI 0.003% to 25.9%) p=0.05). Intention to treat analysis, using the last known value for missing cases, demonstrated smaller differences between the groups (between group difference =6% (95% CI -5% to 16.4%)) with the trend in favour of health walks. There were improvements in the total time spent and number of occasions of moderate intensity activity, and aerobic capacity, but no statistically significant differences between the groups. Other cardiovascular risk factors remained unchanged. Conclusions: There were no significant between group differences in self reported physical activity at 12 month follow up when the analysis was by intention to treat. In people who completed the trial, health walks was more effective than giving advice only in increasing moderate intensity activity above 120 minutes per week