The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolomogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large scale radiative hydrodynamic simulations. We reach two primary conclusions: 1. The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. 2. Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large scale modes in the deep layers are artificially reduced. Since the large scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small scale convective correlations are maintained through the bulk of the solar convection zone.Comment: 36 pages, 6 figure

The Water holes at Ijara

Volume: XXI

Evaluation of Year 1 of the Tuition Partners Programme: Impact Evaluation for Primary Schools. Evaluation Report

The National Tutoring Programme (NTP) Tuition Partners (TP) programme was designed to provide additional support to schools and teachers to supplement classroom teaching through subsidised high-quality tutoring for pupils from an approved list of tutoring organisations, the Tuition Partners. This evaluation covers the TP programme as delivered in its first year by the Education Endowment Foundation (EEF), from November 2020 to August 2021. Tuition Partners was one arm of the NTP. The NTP aimed to support teachers and schools in providing a sustained response to the Covid-19 pandemic and to provide a longer term contribution to closing the attainment gap between disadvantaged pupils and their peers. The NTP was part of a wider government response to the pandemic, funded by the Department for Education and originally developed by the EEF, Nesta, Impetus, The Sutton Trust, and Teach First, and with the support of the KPMG Foundation. The EEF appointed 33 approved ‘Tuition Partners’ that schools could select from to deliver tuition. Schools could access 15 hours of tutoring per selected pupil (with a minimum of 12 hours being considered a completed block of tuition). Tuition was provided online and/or face-to-face; and was 1:1, or in small groups (1:2 or 1:3); and available in English, maths, science, humanities and modern foreign languages. Tuition was expected to be delivered in schools (before, during and after school), in addition to usual teaching; and, in certain circumstances, at home. The programme was targeted at disadvantaged pupils attending state-maintained schools in England, including those eligible for Pupil Premium funding (PP-eligible), Free School Meals (FSM), or those identified by schools as having an equivalent need for support. Participating schools had discretion to identify which of their pupils they felt would most benefit from additional tuition support. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach 215,000 to 265,000 pupils, across 6000 state-maintained schools in England, and it was expected that approximately 20,000 tutors would be recruited by Tuition Partners. The TP programme was set up and delivered during the Covid-19 pandemic, requiring continued responsiveness to the challenges faced by schools including restricted attendance, remote teaching, and ongoing widespread staff and pupil absences. During the school closures to most pupils from January – March 2021, the EEF approved TPs to deliver online tuition at home, however many schools chose to wait to commence tutoring until schools reopened fully, and therefore started tutoring later than planned. This evaluation report covers the analysis on the impact of the TP programme on the maths and English attainment outcomes for primary school pupils (Years 1–6) using standardised classroom assessments. Separate reports relate to analysis on Year 11 pupils and an implementation and process evaluation (IPE). The evaluation findings for the TP programme are brought together in a summary and interpretation report that is available here. This evaluation uses a quasi-experimental design (QED), involving a group of intervention schools that participated in the TP programme, and a group of comparison schools that did not receive the programme. The evaluation relies on a propensity score matching and re-weighting approach to ensure that the intervention and comparison schools are similar to each other in important, observable regards. As pupils who would have received TP in comparison schools were difficult to identify, the evaluation focused on pupils eligible for Pupil Premium and on all pupils, as these groups can be identified in both TP and comparison schools. For English, the analysis is based on 165 primary schools with 7073 pupils eligible for Pupil Premium and for maths, 126 primary schools with 5102 pupils eligible for Pupil Premium3. An additional instrumental variable (IV) analysis, based on the sample of TP schools only, looked at the impact of TP in schools that signed up to the TP programme earlier (and that delivered more tutoring) compared to schools that signed up later. On average, pupils eligible for Pupil Premium in schools that received TP made similar progress in English and maths compared to pupils eligible for Pupil Premium in comparison schools (no evidence of an effect in English or in maths). This result has a low security rating. A particular challenge is that, on average, only approximately 20% of pupils eligible for Pupil Premium were selected for tutoring, meaning a large proportion of pupils eligible for Pupil Premium were included in the analysis who did not receive tutoring. Therefore, this estimated impact of TP is diluted and it is hard to detect any effect that may (or may not) be present. Similar analysis on all pupils found that pupils in schools that received TP made, on average, similar progress in English compared to all pupils in comparison schools (no evidence of an effect), and an additional one month’s progress in maths compared to pupils in comparison schools. However, there is uncertainty around these estimates, with the positive maths result being consistent with a null (0 months) or slightly larger positive effect (2 months) and the English result being consistent with small positive (1 month) or small negative effect (−1 months). Furthermore, this analysis was subject to even further dilution: on average, only 12% (for maths) and 14% (for English) of pupils in the analysed schools were selected for tutoring. Given this context, it is unlikely that any of these differences were due to TP. In the sample of TP schools, completing a 12-hour block of tutoring (compared to zero hours) was related to higher English scores amongst pupils eligible for Pupil Premium that received more tutoring due to the early sign-up of the school. An equivalent analysis for maths was not able to proceed. A different analysis within TP schools showed that pupils who received more hours of tutoring were associated with higher English scores on average than pupils who received fewer hours of tutoring. However, this was not the case for maths, where receiving more hours of tutoring was not associated with higher maths scores. These results are associations and are not necessarily causal estimates of impact; there may be other explanations for the results

Suppressing the Rayleigh-Taylor instability with a rotating magnetic field

The Rayleigh-Taylor instability of a magnetic fluid superimposed on a non-magnetic liquid of lower density may be suppressed with the help of a spatially homogeneous magnetic field rotating in the plane of the undisturbed interface. Starting from the complete set of Navier-Stokes equations for both liquids a Floquet analysis is performed which consistently takes into account the viscosities of the fluids. Using experimentally relevant values of the parameters we suggest to use this stabilization mechanism to provide controlled initial conditions for an experimental investigation of the Rayleigh-Taylor instability

Evaluation of Year 1 of the Tuition Partners Programme: Impact Evaluation Report for Year 11. Evaluation Report: An exploration of impact in Year 11

The National Tutoring Programme (NTP) Tuition Partners (TP) programme was designed to provide additional support to schools and teachers to supplement classroom teaching through subsidised, high quality tutoring for pupils from an approved list of tutoring organisations, the Tuition Partners. This evaluation covers the TP programme as delivered in its first year by the Education Endowment Foundation (EEF), from November 2020 to August 2021. Tuition Partners was one arm of the NTP. The NTP aimed to support teachers and schools in providing a sustained response to the Covid-19 pandemic and to provide a longer term contribution to closing the attainment gap between disadvantaged pupils and their peers. The NTP was part of a wider government response to the pandemic, funded by the Department for Education and originally developed by the EEF, Nesta, Impetus, The Sutton Trust, and Teach First, and with the support of the KPMG Foundation. The EEF appointed 33 approved ‘Tuition Partners’ that schools could select from to deliver tuition. Schools could access 15 hours of tutoring per selected pupil (with a minimum of 12 hours being considered a completed block of tuition). Tuition was provided online and/or face-to-face; and was 1:1, or in small groups (1:2 or 1:3); and available in English, maths, science, humanities and modern foreign languages. Tuition was expected to be delivered in schools (before, during and after school), in addition to usual teaching; and in certain circumstances, at home. The programme was targeted at disadvantaged pupils attending state-maintained schools in England, including those eligible for Pupil Premium funding (PP-eligible), Free School Meals (FSM), or those identified by schools as having an equivalent need for support. Participating schools had discretion to identify which of their pupils they felt would most benefit from additional tuition support. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach 215,000 to 265,000 pupils, across 6,000 state-maintained schools in England, and it was expected that approximately 20,000 tutors would be recruited by Tuition Partners. The TP programme was set up and delivered during the Covid-19 pandemic, requiring continued responsiveness to the challenges faced by schools including restricted attendance, remote teaching, and ongoing widespread staff and pupil absences. During school closures to most pupils from January – March 2021, the EEF approved TPs to deliver online tuition at home, however many schools chose to wait to commence tutoring until schools reopened fully, and therefore started tutoring later than planned. The usual summer exams process for Year 11 pupils could not go ahead as planned in summer 2021, and GCSEs were determined by TAGs instead. This evaluation report covers the analysis on the impact of the TP programme on the maths and English attainment outcomes for Year 11 pupils only. Separate reports relate to analysis on a sample of primary schools and an implementation and process evaluation (IPE). The evaluation findings for the TP programme are brought together in a summary and interpretation report that is available here. This evaluation uses a quasi-experimental design (QED), involving a group of intervention schools that participated in the TP programme, and a group of comparison schools that did not receive the programme. The evaluation relies on a propensity score matching approach to ensure that the intervention and comparison schools are similar to each other in important, observable regards. As pupils who would have received TP in comparison schools were difficult to identify, the evaluation focused on pupils eligible for Pupil Premium and on all pupils, as these groups can be identified in both TP and non-TP schools. The analysis is based on 1,464 secondary schools with a total of 62,024 pupils eligible for Pupil Premium. The evaluation assessed impact in English and maths using Teacher Assessed Grades (TAGs) from 2021. Year 11 pupils eligible for Pupil Premium in schools that received TP made similar progress in English and maths compared to pupils eligible for Pupil Premium in comparison schools (there was no evidence of an effect in English or maths). A particular challenge is that, on average, only 12% of pupils eligible for Pupil Premium were selected for tutoring in maths and 9% were selected for tutoring in English, meaning the vast majority of the pupils included in the analysis did not receive tutoring. Therefore, this estimated impact of TP is diluted and it is hard to detect any effect that may (or may not) be present. When looking at all pupils in Year 11, pupils in schools that received TP made, on average, similar progress in English compared to all Year 11 pupils in comparison schools (there was no evidence of an effect). In maths, Year 11 pupils in schools that received TP made slightly less progress than all Year 11 pupils in comparison schools (though this effect was very small and equivalent to zero months ’ additional progress). However, this analysis was subject to even further dilution than the PPeligible analysis: only 7% of Year 11 pupils were selected for tutoring in maths and 6% in English. Given this context, it is unlikely that any of these differences were due to TP. Additional analysis restricted the sample of schools to those that targeted higher proportions of pupils eligible for Pupil Premium to receive tutoring, to reduce the issue of dilution and bring the group of analysed pupils closer to those that were selected for the intervention. In schools that selected over 50% of pupils eligible for Pupil Premium for tutoring, pupils eligible for Pupil Premium made similar progress in TP and comparison schools in English and maths. However, when the sample was restricted to schools that selected over 70% of pupils eligible for Pupil Premium for tutoring (and reducing dilution further), the impact of TP on pupils eligible for Pupil Premium is positive. In these schools, pupils eligible for Pupil Premium made, on average, the equivalent of two months additional progress in English and two months additional progress in maths, compared to pupils eligible for Pupil Premium in comparison schools. This analysis was based on a smaller sample of schools that were rematched to a comparison sample. However, different characteristics to the rest of the TP population of schools remained (more ‘Outstanding’ schools, lower percentage of FSM students), so this finding may not necessarily be generalisable to all TP schools. Within schools that participated in TP, pupils who received more hours of tutoring in maths obtained higher maths TAGs, and pupils who received more hours of tutoring in English obtained higher English TAGs, than pupils who received fewer hours of tutoring in the respective subjects. These results are associations and are not necessarily causal estimates of impact; there may be other explanations for the higher grades among these pupils

Fluvial organic carbon flux from an eroding peatland catchment, southern Pennines, UK

This study investigates for the first time the relative importance of dissolved organic carbon (DOC) and particulate organic carbon (POC) in the fluvial carbon flux from an actively eroding peatland catchment in the southern Pennines, UK. Event scale variability in DOC and POC was examined and the annual flux of fluvial organic carbon was estimated for the catchment. At the event scale, both DOC and POC were found to increase with discharge, with event based POC export accounting for 95% of flux in only 8% of the time. On an annual cycle, exports of 35.14 t organic carbon (OC) are estimated from the catchment, which represents an areal value of 92.47 g C m<sup>−2</sup> a<sup>−1</sup>. POC was the most significant form of organic carbon export, accounting for 80% of the estimated flux. This suggests that more research is required on both the fate of POC and the rates of POC export in eroding peatland catchments

Stretching Instability of Helical Spring

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur, and propose experimental tests of our predictions.Comment: 5 pages, 4 figure

Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems

The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion, and apply this theory to the dynamics of a 1D gas of excited bosons confined in a harmonic potential and in contact with an external bath.Comment: 17 pages, 7 figures, RevTex4; few typos corrected, a figure modifie

Convection cells induced by spontaneous symmetry breaking

Ubiquitous in nature, convection cells are a clear signature of systems out-of-equilibrium. Typically, they are driven by external forces, like gravity (in combination with temperature gradients) or shear. In this article, we show the existence of such cells in possibly the simplest system, one that involves only a temperature gradient. In particular, we consider an Ising lattice gas on a square lattice, in contact with two thermal reservoirs, one at infinite temperature and another at $T$. When this system settles into a non-equilibrium stationary state, many interesting phenomena exist. One of these is the emergence of convection cells, driven by spontaneous symmetry breaking when $T$ is set below the critical temperature.Comment: published version, 2 figures, 5 page