Abstract:
We study the non-equilibrium version of the fluctuation dissipation (FD) relation in the glass phase of a trap model that is driven into a non-equilibrium steady state by external ``shear''. This extends our recent study of ageing FD relations in the same model, where we found limiting, observable independent FD relations for ``neutral'' observables that are uncorrelated with the system's average energy. In this work, for such neutral observables, we find the FD relation for a stationary weakly driven system to be the same, to within small corrections, as for an infinitely aged system. We analyse the robustness of this correspondence with respect to non-neutrality of the observable, and with respect to changes in the driving mechanism.

Abstract:
We study the non-equilibrium version of the fluctuation-dissipation theorem (FDT) within the glass phase of Bouchaud's trap model. We incorporate into the model an arbitrary observable m and obtain its correlation and response functions in closed form. A limiting non-equilibrium FDT plot (of correlator vs response) is approached at long times for most choices of m, with energy-temperature FDT a notable exception. In contrast to standard mean field models, however, the shape of the plot depends nontrivially on the observable, and its slope varies continuously even though there is a single scaling of relaxation times with age. Non-equilibrium FDT plots can therefore not be used to define a meaningful effective temperature T_eff in this model. Consequences for the wider applicability of an FDT-derived T_eff are discussed.

Abstract:
We study a simple model of shear banding in which the flow-induced phase is destabilised by coupling between flow and microstructure (wormlike micellar length). By varying the strength of the instability and the applied shear rate, we find a rich variety of oscillatory and rheochaotic shear banded flows. At low shear and weak instability, the induced phase pulsates in width next to one wall of the flow cell. For stronger instability, single or multiple high shear pulses ricochet across the cell. At high shear rates we observe oscillating bands on either side of a defect. In some cases, multiple such defects exist and propagate across the cell to interact with each other. We discuss our results in the context of recent observations of oscillating and fluctuating shear banded flows.

Abstract:
Many countries use national-level surveys to capture student opinions about their university experiences. It is necessary to interpret survey results in an appropriate context to inform decision-making at many levels. To provide context to national survey outcomes, we describe patterns in the ratings of science and engineering subjects from the UK’s National Student Survey (NSS). New, robust statistical models describe relationships between the Overall Satisfaction’ rating and the preceding 21 core survey questions. Subjects exhibited consistent differences and ratings of “Teaching”, “Organisation” and “Support” were thematic predictors of “Overall Satisfaction” and the best single predictor was “The course was well designed and running smoothly”. General levels of satisfaction with feedback were low, but questions about feedback were ultimately the weakest predictors of “Overall Satisfaction”. The UK’s universities affiliated groupings revealed that more traditional “1994” and “Russell” groups over-performed in a model using the core 21 survey questions to predict “Overall Satisfaction”, in contrast to the under-performing newer universities in the Million+ and Alliance groups. Findings contribute to the debate about “level playing fields” for the interpretation of survey outcomes worldwide in terms of differences between subjects, institutional types and the questionnaire items.

Abstract:
After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant solutions, we present flow phase diagrams spanned by shear stress (or strain-rate) and concentration in the two-fluid, non-local Johnson-Segalman (d-JS-phi) model. We also present macroscopic flow curves for a range of (average) concentrations. For any concentration high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence ``plateau'' that slopes upwards. As the concentration is reduced, the width of the coexistence regime diminishes, then terminates at a non-equilibrium critical point. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves measured for several different average concentrations. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-phi model contains two spatial gradient terms describing the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length, l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length, xi, for equilibrium concentration-fluctuations. We show that the phase diagrams depend on the ratio r=l/xi, with loss of unique state selection at r=0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width at the critical point.

Abstract:
We study the early stages of the shear banding instability in semidilute wormlike micelles using the non-local Johnson-Segalman model with a two-fluid coupling of the concentration (phi) to the shear rate (gamma_dot) and micellar strain (tensor{W}). We calculate the ``spinodal'' limit of stability for sweeps along the homogeneous intrinsic flow curve. For startup ``quenches'' into the unstable region, the instability in general occurs before the homogeneous startup flow can attain the intrinsic flow curve. We predict the selected time and length scales at which inhomogeneity first emerges. In the ``infinite drag'' limit, fluctuations in the mechanical variables (gamma_dot and \tensor{W}) are independent of those in phi, and are unstable when the slope of the intrinsic flow curve is negative; but no length scale is selected. For finite drag, the mechanical instability is enhanced by coupling to phi and a length scale is selected, in qualitative agreement with recent experiments. For systems far from an underlying zero-shear demixing instability this enhancement is slight, while close to demixing the instability sets in at low shear rates and is essentially demixing triggered by flow.

Abstract:
Motivated by experiments on wormlike micelles, we study the early stages of the shear banding instability using a two-fluid Johnson-Segalman model. We perform a linear stability analysis for coupled fluctuations in shear rate, micellar strain and concentration about an initially homogeneous state. First we calculate the ``spinodal'' onset of instability in sweeps along the intrinsic constitutive curve. For startup ``quenches'' into the unstable region, the instability usually occurs before the intrinsic constitutive curve can be attained so we analyse the fluctuations with respect to the homogeneous startup flow to find the selected length and time scales at which inhomogeneity first emerges. In the uncoupled limit, fluctuations in shear rate and micellar strain are independent of those in concentration, and are unstable when the intrinsic constitutive curve has negative slope; but no length scale is selected. When coupled to concentration, this instability is enhanced at short length scales; a length scale is selected, as seen experimentally. The unstable region is then broadened. Far from an underlying (zero-shear) demixing instability, the broadening is slight and the instability is still dominated by shear rate and micellar strain. Close to demixing, instability sets in at very low shear rate, where it is demixing triggered by flow.

Abstract:
We study numerically the nonlinear dynamics of a shear banding interface in two dimensional planar shear flow, within the non-local Johnson Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for sufficiently small ratio of the interfacial width $\ell$ to cell length $L_x$. The instability saturates in finite amplitude interfacial fluctuations. For decreasing $\ell/L_x$ these undergo a non equilibrium transition from simple travelling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.

Abstract:
The Paediatric Observation Priority Score (POPS) is a bespoke assessment tool for use in Paediatric
Emergency Departments incorporating traditional physiological parameters alongside more
subjective observational criteria. Initial performance characteristics of POPS were analysed in a
convenience sample of 936 presentations to ED. Triage on the basis of gut instinct parameters
identified an additional 261 patients deemed of lowest acuity compared to analysis by physiology
scores. Resource consumption increased with increasing acuity on presentation. POPS shows
promise in assisting in the assessment process of children presenting to Emergency Departments.
Inclusion of subjective triage criteria helps contextualise the physiological parameter scoring by
using the experience of staff conducting triage. Initial interpretation of presenting physiology
gives a more informed assessment of initial acuity, and thus is better able to identify a child who
can be safely managed in the community. The system also allows for rapid detection of those most
unwell.

Abstract:
Five clinical trial datasets that employed a reminder system at follow-up were used. Some quality of life questionnaires were initially missing, but later recovered through reminders. Four methods of determining the missing data mechanism were applied. Two response data scenarios were considered. Firstly, immediate data only; secondly, all observed responses (including reminder-response).In three of five trials the hypothesis tests found evidence against the MCAR assumption. Logistic regression suggested MAR, but was able to use the reminder-collected data to highlight potential MNAR data in two trials.The four methods were consistent in determining the missingness mechanism. One hypothesis test was preferred as it is applicable with intermittent missingness. Some inconsistencies between the two data scenarios were found. Ignoring the reminder data could potentially give a distorted view of the missingness mechanism. Utilising reminder data allowed the possibility of MNAR to be considered.Missing data are a major issue during the analysis of any study. The absence of data can be informative, and should not be disregarded; ignoring the pattern of missingness may bias the results obtained. In particular, for health-related quality of life (QoL) outcomes, the fact that data are missing may be informative. Patients who feel unwell are perhaps likely to be less able to complete and return questionnaires.Patterns of missingness are described as either monotone (terminal), intermittent or mixed. Monotone missingness occurs when data are available at every assessment until a time the patient drops out and provides no further assessments. Intermittent missingness occurs if there is a missing observation in between observed assessments. A mixed pattern occurs when a period of intermittent missingness is followed by monotone missingness. The three mechanisms of missing data are missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR) [1]. D