Secular Coefficients and the Holomorphic Multiplicative Chaos

We study the secular coefficients of $N \times N$ random unitary matrices $U_{N}$ drawn from the Circular $\beta$-Ensemble, which are defined as the coefficients of $\{z^n\}$ in the characteristic polynomial $\det(1-zU_{N}^{*})$. When $\beta > 4$ we obtain a new class of limiting distributions that arise when both $n$ and $N$ tend to infinity simultaneously. We solve an open problem of Diaconis and Gamburd by showing that for $\beta=2$, the middle coefficient tends to zero as $N \to \infty$. We show how the theory of Gaussian multiplicative chaos (GMC) plays a prominent role in these problems and in the explicit description of the obtained limiting distributions. We extend the remarkable magic square formula of Diaconis and Gamburd for the moments of secular coefficients to all $\beta>0$ and analyse the asymptotic behaviour of the moments. We obtain estimates on the order of magnitude of the secular coefficients for all $\beta > 0,$ and these estimates are sharp when $\beta \geq 2$. These insights motivated us to introduce a new stochastic object associated with the secular coefficients, which we call Holomorphic Multiplicative Chaos (HMC). Viewing the HMC as a random distribution, we prove a sharp result about its regularity in an appropriate Sobolev space. Our proofs expose and exploit several novel connections with other areas, including random permutations, Tauberian theorems and combinatorics

Micro-macro multilevel analysis of day-to-day lifestyle and carbon emissions in UK multiple occupancy households

Far-reaching changes in daily life present a pressing need to balance energy consumption with environmental impact. Previous research on household carbon emissions generally described its contributors in disposable income, consumption pattern, and household-related lifestyle, whereas they have not fully explored how carbon emissions relate to residents' day-to-day lifestyles. Given that individual lifestyles within a household may be correlated, there is a need to disentangle the clustering effect of household members' lifestyles and their association with household carbon emissions. This study used micro-macro multilevel modelling to examine the structure of individual lifestyles and their impact on household carbon emissions for 8618 multiple occupancy households of 19,816 respondents in the UK Household Longitudinal Study dataset. The results showed that a factor capturing energy-saving lifestyle behaviours significantly reduced housing fuel use emissions and a second capturing transportation and consumption choices cut motor emissions. Interestingly, the contribution of energy-saving lifestyle in cutting down housing-fuel-using emissions becomes more pronounced when household income and household characteristics (e.g., household size, dwelling, house ownership, number of cars, urbanity, employment) were controlled for. Contrarily, the strength of green transportation and consumption lifestyle contributing to lower motor emissions was weakened after controlling for household characteristics. Findings indicated that day-to-day lifestyle not only reflects individual variability in sustainable living but also systematic household variation in carbon emissions. Knowledge of which living patterns are responsible for disproportionately high levels of carbon emissions can enhance effective targeted policy aimed at stimulating sustainable lifestyles and carbon reduction

Environmental concern over time: evidence from the longitudinal analysis of a British cohort study from 1991 to 2008

Objective We examined whether and how levels of environmental concern changed over time in the UK, from 1991 to 2008-2009, as well as how environmental concern relates to socio-economic characteristics across this same time frame. Methods Using item response theory models on the last three sweeps of the British National Child Development Study 1958, we evaluated a measure of environmental concern. Then, using latent growth curve models (LGCM) we estimated the pattern of change for environmental concern across time. Finally, theoretically relevant socio-demographic characteristics were introduced as covariates into the LGCM. Results We found a small but significant downfall of the mean level of environmental concern over time, with individual-level values displaying higher dispersion in 2008-2009 against the previous sweeps of data. We also found that political orientation has significant effects on the outcome and on its changes across time. Conclusions Hypotheses regarding the influence of interest in politics and voting choices on environmental concern are supported. The increasing variance of environmental concern over time warrants further investigation

Environmental concern over time: evidence from the longitudinal analysis of a British cohort study from 1991 to 2008

Objective We examined whether and how levels of environmental concern changed over time in the UK, from 1991 to 2008-2009, as well as how environmental concern relates to socio-economic characteristics across this same time frame. Methods Using item response theory models on the last three sweeps of the British National Child Development Study 1958, we evaluated a measure of environmental concern. Then, using latent growth curve models (LGCM) we estimated the pattern of change for environmental concern across time. Finally, theoretically relevant socio-demographic characteristics were introduced as covariates into the LGCM. Results We found a small but significant downfall of the mean level of environmental concern over time, with individual-level values displaying higher dispersion in 2008-2009 against the previous sweeps of data. We also found that political orientation has significant effects on the outcome and on its changes across time. Conclusions Hypotheses regarding the influence of interest in politics and voting choices on environmental concern are supported. The increasing variance of environmental concern over time warrants further investigation

Complex beam profiles for laser annealing of thin-film CdTe photovoltaics

Within the family of thin-film photovoltaics (PV), cadmium telluride (CdTe) has the fastest growing market share due to its high efficiencies and low cost. However, as with other PV technologies, the energy required to manufacture the panels is excessive, encompassing high environmental impact and manufacturing energy payback times of the order of 2-3 years. As part of the manufacturing process, the panels are annealed at temperatures of approximately 400°C for 30 minutes, which is inherently inefficient. Laser heating has previously been investigated as an alternative process for thin film annealing, due to its advantages with regard to its ability to localise heat treatment, anneal selectively and its short processing time. In this investigation, results focussing on improvements to the laser-based annealing process, designed to mitigate panel damage by excessive thermal gradients, are presented. Simulations of various laser beam profiles are created in COMSOL and used to demonstrate the benefit of laser beam shaping for thin film annealing processes. An enabling technology for this, the holographic optical element (HOE), is then used to experimentally demonstrate the redistribution of laser beam energy into an optimal profile for annealing, eliminating thermal concentrations

A 'design for energy minimization' approach to reduce energy consumption during the manufacturing phase

The combustion of fossil fuels for energy generation has contributed considerably to the effects of climate change. In order to reduce fossil fuel consumption, designers are increasingly seeking to reduce the energy consumption of products over their life cycle. To achieve a significant reduction in energy consumption, it is essential that energy considerations are incorporated within the design phase of a product, since the majority a product's environmental impact is determined during this phase. This work proposes a new ‘Design for Energy Minimization’ (DfEM) approach, which is intended to provide increased transparency with respect to the energy consumed during manufacture in order to help inform design decisions. An energy simulation model based on this approach is then presented to aid designers during the design phase. The application of this novel design tool is demonstrated in two cases: That of a simple product (designed by a single Original Equipment Manufacturer (OEM) through a centralized approach); and a complex product (designed by a number of designers within a supply chain using a distributed approach). The subsequent benefits to energy minimization are then discussed and conclusions drawn

Annealing of thin-film cadmium telluride photovoltaics using holographically controlled laser processing

CdTe-based thin film solar cells currently represent one of the fastest growing PV technologies, with a superior combination of efficiency, energy payback time and lifecycle environmental impact. However, the current post-deposition annealing treatment is still an energy intensive step of the manufacturing process. A novel method is presented for annealing of CdTe using a high-power diode laser (35 W, 808 nm) for thermal post-processing, combined with holographic optical elements (HOE’s) for laser beam heat flow control. The advantage of a laser for annealing lies in its ability to selectively heat only the surface of the CdTe solar cell; improving energy efficiency, process speed and energy resilience. Heat transfer simulations were used to predict the effects of different laser irradiance profiles on the annealing process thermal cycle influence the experimental design and predict optimal laser irradiance profiles. Variations in power and process speed on as-deposited and MgCl2-treated close-space sublimated (CSS) CdTe samples have been performed. The results were characterised using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). Optical properties were analysed with a spectrophotometer and ellipsometric spectroscopy (SE). The laser annealing treatment was found to be effective in promoting Chlorine diffusion and improving the optical and morphological properties of CdTe thin film device

Microchannel neural interface manufacture by stacking silicone and metal foil laminae

Objective: Microchannel neural interfaces (MNIs) overcome problems with recording from peripheral nerves by amplifying signals independent of Node of Ranvier position. Selective recording and stimulation using an MNI requires good insulation between microchannels and a high electrode density. We propose that stacking microchannel laminae will improve selectivity over single layer MNI designs due to the increase in electrode number and an improvement in microchannel sealing. Approach: This paper describes a manufacturing method for creating MNIs which overcomes limitations on electrode connectivity and microchannel sealing. Laser cut silicone – metal foil laminae were stacked using plasma bonding to create an array of microchannels containing tripolar electrodes. Electrodes were DC etched and electrode impedance and cyclic voltammetry were tested. Main results: MNIs with 100 µm and 200 µm diameter microchannels were manufactured. High electrode density MNIs are achievable with electrodes present in every microchannel. Electrode impedances of 27.2 ± 19.8 kΩ at 1kHz were achieved. Following 2 months of implantation in Lewis rat sciatic nerve, micro-fascicles were observed regenerating through the MNI microchannels. Significance: Selective microchannel neural interfaces with the peripheral nervous system may allow upper limb amputees to control prostheses intuitively

Use of laser beam diffraction for non-invasive characterisation of CdTe thin film growth structure

Characterisation of Cadmium Telluride (CdTe) thin films commonly requires the use of invasive techniques for the identification of their structural growth and the detection of defects which occur during the deposition process. Structural growth and the presence of defects can affect the performance of the final device. A non-invasive inspection system for CdTe films has been developed to identify the structural properties of this material, comparing two different deposition techniques, Close Space Sublimation (CSS) and Magnetron Sputtering (MS). The proposed system utilises a 1 μm diode laser which passes through the CdTe layer, originating detectable diffraction patterns, which are characterised using image processing techniques and assessed using a neural network-based cognitive decision-making support system. Results are found to be consistent with the conventional microscopic techniques (SEM and TEM) used to analyse morphological and structural properties of thin-film CdTe solar cells

Physical Activity, Mental Health and Wellbeing During the First COVID-19 Containment in New Zealand: A Cross-Sectional Study.

Strategies implemented worldwide to contain COVID-19 outbreaks varied in severity across different countries, and established a new normal for work and school life (i.e., from home) for many people, reducing opportunities for physical activity. Positive relationships of physical activity with both mental and physical health are well recognised, and therefore the aim was to ascertain how New Zealand’s lockdown restrictions impacted physical activity, mental health and wellbeing. Participants (n = 4007; mean ± SD: age 46.5 ± 14.7 years, 72% female, 80.7% New Zealand European) completed (10–26 April 2020) an online amalgamated survey (Qualtrics): International Physical Activity Questionnaire: Short Form; Depression, Anxiety and Stress Scale-9; World Health Organisation-Five Well-Being Index; Stages of Change Scale. Positive dose–response relationships between physical activity levels and wellbeing scores were demonstrated for estimates that were unadjusted (moderate activity OR 3.79, CI 2.88–4.92; high activity OR 8.04, CI 6.07–10.7) and adjusted (confounding variables: age, gender, socioeconomic status, time sitting and co-morbidities) (moderate activity 1.57, CI 1.11–2.52; high activity 2.85, CI 1.97–4.14). The study results support previous research demonstrating beneficial effects of regular physical activity on mental health and wellbeing. Governments may use these results to promote meeting physical activity guidelines in order to protect mental health and wellbeing during the ongoing COVID-19 restrictions and future pandemics