A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Strong Optomechanical Squeezing of Light

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.Comment: 12 pages, 8 figure

Control of Material Damping in High-Q Membrane Microresonators

We study the mechanical quality factors of bilayer aluminum/silicon-nitride membranes. By coating ultrahigh-Q Si3N4 membranes with a more lossy metal, we can precisely measure the effect of material loss on Q's of tensioned resonator modes over a large range of frequencies. We develop a theoretical model that interprets our results and predicts the damping can be reduced significantly by patterning the metal film. Using such patterning, we fabricate Al-Si3N4 membranes with ultrahigh Q at room temperature. Our work elucidates the role of material loss in the Q of membrane resonators and informs the design of hybrid mechanical oscillators for optical-electrical-mechanical quantum interfaces

Improved hydrogen gas production in microbial electrolysis cells using inexpensive recycled carbon fibre fabrics

Growing energy demands of wastewater treatment have made it vital for water companies to develop less energy intensive processes for treating wastewater if net zero emissions are to be achieved by 2050. Microbial electrolysis cells (MECs) have the potential to do this by treating water and producing renewable hydrogen gas as a product, but capital and operational costs have slowed their deployment. By using recycled carbon fibre mats, commercially viable MECs can brought closer to reality, where recycled carbon fibre anode MECs treating real wastewater (normalised ~3100 L d−1) were producing 66.77 L H2 d−1 while graphite felt anode MECs produced 3.65 L H2 d−1 per 1 m3 reactor, anodes costing £5.53 m−2 and £88.36 m−2 respectively, resulting in a total anode cost saving of 93%. This could incentivise the development of larger pilot systems, opening the door for generating greater value and a more sustainable wastewater treatment industry

Cavity optomechanics with Si3N4 membranes at cryogenic temperatures

We describe a cryogenic cavity-optomechanical system that combines Si3N4 membranes with a mechanically-rigid Fabry-Perot cavity. The extremely high quality-factor frequency products of the membranes allow us to cool a MHz mechanical mode to a phonon occupation of less than 10, starting at a bath temperature of 5 kelvin. We show that even at cold temperatures thermally-occupied mechanical modes of the cavity elements can be a limitation, and we discuss methods to reduce these effects sufficiently to achieve ground state cooling. This promising new platform should have versatile uses for hybrid devices and searches for radiation pressure shot noise.Comment: 19 pages, 5 figures, submitted to New Journal of Physic

Metabolic flexibility as a major predictor of spatial distribution in microbial communities

A better understand the ecology of microbes and their role in the global ecosystem could be achieved if traditional ecological theories can be applied to microbes. In ecology organisms are defined as specialists or generalists according to the breadth of their niche. Spatial distribution is often used as a proxy measure of niche breadth; generalists have broad niches and a wide spatial distribution and specialists a narrow niche and spatial distribution. Previous studies suggest that microbial distribution patterns are contrary to this idea; a microbial generalist genus (Desulfobulbus) has a limited spatial distribution while a specialist genus (Methanosaeta) has a cosmopolitan distribution. Therefore, we hypothesise that this counter-intuitive distribution within generalist and specialist microbial genera is a common microbial characteristic. Using molecular fingerprinting the distribution of four microbial genera, two generalists, Desulfobulbus and the methanogenic archaea Methanosarcina, and two specialists, Methanosaeta and the sulfate-reducing bacteria Desulfobacter were analysed in sediment samples from along a UK estuary. Detected genotypes of both generalist genera showed a distinct spatial distribution, significantly correlated with geographic distance between sites. Genotypes of both specialist genera showed no significant differential spatial distribution. These data support the hypothesis that the spatial distribution of specialist and generalist microbes does not match that seen with specialist and generalist large organisms. It may be that generalist microbes, while having a wider potential niche, are constrained, possibly by intrageneric competition, to exploit only a small part of that potential niche while specialists, with far fewer constraints to their niche, are more capable of filling their potential niche more effectively, perhaps by avoiding intrageneric competition. We suggest that these counter-intuitive distribution patterns may be a common feature of microbes in general and represent a distinct microbial principle in ecology, which is a real challenge if we are to develop a truly inclusive ecology