Nonlinear Stability Analyses for Variable Viscosity and Compressible Convection Problems

In this thesis we present nonlinear energy stability analyses of a variety of convection problems, specifically concentrating on compressible convection and convection where the viscosity of the fluid depends on the temperature. To begin we introduce the energy method, which we shall employ in later chapters in order to derive nonlinear stability criteria, and illustrate its effectiveness with a simple one-dimensional example. We then study the stability of a system containing a generalized incompressible fluid, employing linear theory, the energy method and an asymptotic analysis. Next we study a variable viscosity fluid, first establishing continuous dependence of the solution to the Oberbeck-Boussinesq equations, both forward and backward in time, on the viscosity. We then look at convection where the viscosity is first a linear function of the temperature and then a quadratic one. In both cases we employ a generalized energy in order to derive a nonlinear stability boundary. To conclude our analysis of a variable viscosity fluid we also introduce a temperature dependent conductivity and carry out both linear and heuristic nonlinear analyses. We then turn our attention to the phenomenon of convection within a porous medium, concentrating first on penetrative convection. We examine the stability of convection in a porous medium containing an internal heat source and a salt field, using linear theory, the energy method and a weighted energy. Then, returning to the topic of variable viscosity, we demonstrate that, in a porous medium, the solution to the equations of motion depends continuously on the viscosity both forward and backward in time. Finally we study a porous medium saturated with a variable viscosity fluid, employing the Brinkman equation, coupled with the energy method, in order to derive a nonlinear stability boundary

Optomechanical lasers for inertial sensing

We have developed an inertially sensitive optomechanical laser by combining a Vertical-External-Cavity Surface-Emitting Laser with a monolithic fused silica resonator. By placing the external cavity mirror of the VECSEL onto the optomechanical resonator test mass, we create a sensor where external accelerations are directly transcribed onto the lasing frequency. We developed a proof-of-principle laboratory prototype and observe test mass oscillations at the resonance frequency of the sensor through the VECSEL lasing frequency, 4.18 +/- .03 Hz. In addition, we set up an ancillary heterodyne interferometer to track the motion of the mechanical oscillator's test mass, observing a resonance of 4.194 +/- 0.004 Hz. The interferometer measurements validate the VECSEL results, confirming the feasibility of using optomechanical lasers for inertial sensing

Quantum Test of the Universality of Free Fall

We simultaneously measure the gravitationally-induced phase shift in two Raman-type matter-wave interferometers operated with laser-cooled ensembles of $^{87}$Rb and $^{39}$K atoms. Our measurement yields an E\"otv\"os ratio of $\eta_{\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}$. We briefly estimate possible bias effects and present strategies for future improvements

Non-pharmacological interventions for ADHD in school settings: an overarching synthesis of systematic reviews

OBJECTIVE: This overarching synthesis brings together the findings of four systematic reviews including 138 studies focused on non-pharmacological interventions for ADHD used in school settings. These reviews considered the effectiveness of school-based interventions for ADHD, attitudes toward and experience of school-based interventions for ADHD, and the experience of ADHD in school settings. METHOD: We developed novel methods to compare the findings across these reviews inductively and deductively. RESULTS: Key contextual issues that may influence the effectiveness and implementation of interventions include the relationships that pupils with ADHD have with their teachers and peers, the attributions individuals make about the etiology of ADHD, and stigma related to ADHD or intervention attendance. CONCLUSION: Although we found some positive effects for some outcomes and intervention categories, heterogeneity in effect size estimates and research evidence suggests a range of diverse contextual factors potentially moderate the implementation and effectiveness of school-based interventions for ADHD.National Institute for Health Research Health Technology Assessment (NIHR HTA) programNIHR Collaboration for Leadership in Applied HealthResearch and Care South West Peninsula (PenCLAHRC

Interventions to improve continence for children and young people with neurodisability: a national survey of practitioner and family perspectives and experiences.

Objective Describe families’ experiences of interventions to improve continence in children and young people with neurodisability, and health professionals’ and school and social care staff’s perspectives regarding factors affecting intervention use. Design Four online surveys were developed and advertised to parent carers, young people with neurodisability, health professionals and school and social care staff, via societies, charities, professional contacts, schools, local authorities, and national parent carer and family forums, who shared invitations with their networks. Survey questions explored: difficulties helping children and young people use interventions; acceptability of interventions and waiting times; ease of use and availability of interventions, and facilitators and barriers to improving continence. Results 1028 parent carers, 26 young people, 352 health professionals and 202 school and social care staff registered to participate. Completed surveys were received from 579 (56.3%) parent carers, 20 (77%) young people, 193 (54.8%) health professionals, and 119 (58.9%) school and social care staff. Common parent carer-reported difficulties in using interventions to help their children and young people to learn to use the toilet included their child’s lack of understanding about what was required (reported by 337 of 556 (60.6%) parent carers who completed question) and their child’s lack of willingness (343 of 556, 61.7%). Almost all (142 of 156, 91%) health professionals reported lack of funding and resources as barriers to provision of continence services. Many young people (14 of 19, 74%) were unhappy using toilet facilities while out and about. Conclusions Perceptions that children lack understanding and willingness, and inadequate facilities impact the implementation of toileting interventions for children and young people with neurodisability. Greater understanding is needed for children to learn developmentally appropriate toileting skills. Further research is recommended around availability and acceptability of interventions to ensure quality of life is unaffected

Decomposing reflectance spectra to track gross primary production in a subalpine evergreen forest

Photosynthesis by terrestrial plants represents the majority of CO₂ uptake on Earth, yet it is difficult to measure directly from space. Estimation of gross primary production (GPP) from remote sensing indices represents a primary source of uncertainty, in particular for observing seasonal variations in evergreen forests. Recent vegetation remote sensing techniques have highlighted spectral regions sensitive to dynamic changes in leaf/needle carotenoid composition, showing promise for tracking seasonal changes in photosynthesis of evergreen forests. However, these have mostly been investigated with intermittent field campaigns or with narrow-band spectrometers in these ecosystems. To investigate this potential, we continuously measured vegetation reflectance (400–900 nm) using a canopy spectrometer system, PhotoSpec, mounted on top of an eddy-covariance flux tower in a subalpine evergreen forest at Niwot Ridge, Colorado, USA. We analyzed driving spectral components in the measured canopy reflectance using both statistical and process-based approaches. The decomposed spectral components co-varied with carotenoid content and GPP, supporting the interpretation of the photochemical reflectance index (PRI) and the chlorophyll/carotenoid index (CCI). Although the entire 400–900 nm range showed additional spectral changes near the red edge, it did not provide significant improvements in GPP predictions. We found little seasonal variation in both normalized difference vegetation index (NDVI) and the near-infrared vegetation index (NIRv) in this ecosystem. In addition, we quantitatively determined needle-scale chlorophyll-to-carotenoid ratios as well as anthocyanin contents using full-spectrum inversions, both of which were tightly correlated with seasonal GPP changes. Reconstructing GPP from vegetation reflectance using partial least-squares regression (PLSR) explained approximately 87 % of the variability in observed GPP. Our results linked the seasonal variation in reflectance to the pool size of photoprotective pigments, highlighting all spectral locations within 400–900 nm associated with GPP seasonality in evergreen forests