A rigorous proof of the Landau-Peierls formula and much more

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.Comment: 30 pages - Accepted for publication in A.H.

Collective waves in dense and confined microfluidic droplet arrays

Excitation mechanisms for collective waves in confined dense one-dimensional microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. Excited longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets. Transversely excited modes obey the dispersion relation of microfluidic phonons and induce a coupling between longitudinal and transverse modes, whose origin is the hydrodynamic interaction of the droplets with the confining walls. Moreover, we investigate the long-time behaviour of the oscillations and discuss possible mechanisms for the onset of instabilities. Our findings demonstrate that the collective dynamics of microfluidic droplet ensembles can be studied particularly well in dense and confined systems. Experimentally, the ability to control microfluidic droplets may allow to modulate the refractive index of optofluidic crystals which is a promising approach for the production of dynamically programmable metamaterials.Comment: 13 pages, 17 figure

On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

Gemini Planet Imager Observational Calibrations III: Empirical Measurement Methods and Applications of High-Resolution Microlens PSFs

The newly commissioned Gemini Planet Imager (GPI) combines extreme adaptive optics, an advanced coronagraph, precision wavefront control and a lenslet-based integral field spectrograph (IFS) to measure the spectra of young extrasolar giant planets between 0.9-2.5 um. Each GPI detector image, when in spectral model, consists of ~37,000 microspectra which are under or critically sampled in the spatial direction. This paper demonstrates how to obtain high-resolution microlens PSFs and discusses their use in enhancing the wavelength calibration, flexure compensation and spectral extraction. This method is generally applicable to any lenslet-based integral field spectrograph including proposed future instrument concepts for space missions.Comment: 10 pages, 6 figures. Proceedings of the SPIE, 9147-282 v2: reference adde

A Bayesian spatio-temporal study of the association between meteorological factors and the spread of COVID-19

BACKGROUND: The spread of COVID-19 has brought challenges to health, social and economic systems around the world. With little to no prior immunity in the global population, transmission has been driven primarily by human interaction. However, as with common respiratory illnesses such as influenza some authors have suggested COVID-19 may become seasonal as immunity grows. Despite this, the effects of meteorological conditions on the spread of COVID-19 are poorly understood. Previous studies have produced contrasting results, due in part to limited and inconsistent study designs. METHODS: This study investigates the effects of meteorological conditions on COVID-19 infections in England using a Bayesian conditional auto-regressive spatio-temporal model. Our data consists of daily case counts from local authorities in England during the first lockdown from March-May 2020. During this period, legal restrictions limiting human interaction remained consistent, minimising the impact of changes in human interaction. We introduce a lag from weather conditions to daily cases to accommodate an incubation period and delays in obtaining test results. By modelling spatio-temporal random effects we account for the nature of a human transmissible virus, allowing the model to isolate meteorological effects. RESULTS: Our analysis considers cases across England's 312 local authorities for a 55-day period. We find relative humidity is negatively associated with COVID-19 cases, with a 1% increase in relative humidity corresponding to a reduction in relative risk of 0.2% [95% highest posterior density (HPD): 0.1-0.3%]. However, we find no evidence for temperature, wind speed, precipitation or solar radiation being associated with COVID-19 spread. The inclusion of weekdays highlights systematic under reporting of cases on weekends with between 27.2-43.7% fewer cases reported on Saturdays and 26.3-44.8% fewer cases on Sundays respectively (based on 95% HPDs). CONCLUSION: By applying a Bayesian conditional auto-regressive model to COVID-19 case data we capture the underlying spatio-temporal trends present in the data. This enables us to isolate the main meteorological effects and make robust claims about the association of weather variables to COVID-19 incidence. Overall, we find no strong association between meteorological factors and COVID-19 transmission