Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

Control sideband generation for dual-recycled laser interferometric gravitational wave detectors

We present a discussion of the problems associated with generation of multiple control sidebands for length sensing and control of dual-recycled, cavity-enhanced Michelson interferometers and the motivation behind more complicated sideband generation methods. We focus on the Mach–Zehnder interferometer as a topological solution to the problem and present results from tests carried out at the Caltech 40 m prototype gravitational wave detector. The consequences for sensing and control for advanced interferometry are discussed, as are the implications for future interferometers such as Advanced LIGO

Hybrid integration of diamond membranes with GaN waveguides

The nitrogen vacancy (NV) is a photostable emitter in diamond which is optically accessible at room temperature and a potential candidate for quantum information processing as a spin register. The challenge facing research today is the efficient collection and manipulation of the NV’s emissions, such as by enhancing the zero phonon line transitions for a coherent spin-photon interface.Integrating diamond with other photonic materials would allow for resonant coupling of the defect centre to optical devices on large area photonic integrated circuits (PICs). Emitted photons collected by bus waveguides could then be guided elsewhere on chip for entanglement or measurements.This work focuses on integrating ultra-thin diamond membranes with GaN waveguide and resonator devices. Mode simulations (see Fig. 1(a)) show that light can be coupled significantly into and out of the membranes by this method. Membranes of < 200 nm have been fabricated using Ar-Cl2 etch recipes that cumulatively smooth the diamond over time; an r.m.s roughness value of 0.19 nm has been achieved.1 The smooth surface and ultra-low thickness allow a good conformation and strong bonding of the membrane to other materials. This should allow for the integration of diamond membranes with photonic integrated circuits as shown schematically in Fig. (b).Free standing ultra-thin diamond membranes can also be used in tuneable open access cavities – where a low mode volume and high Q factor are desired; 2 or as templates for fabricating diamond optical devices on non-native substrates.

Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II

Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in $\R^3$ with non-trivial swirl. Let $z$ denote the axis of symmetry and $r$ measure the distance to the z-axis. Suppose the solution satisfies either $|v (x,t)| \le C_*{|t|^{-1/2}}$ or, for some \e > 0, $|v (x,t)| \le C_* r^{-1+\epsilon} |t|^{-\epsilon /2}$ for $-T_0\le t < 0$ and $0<C_*<\infty$ allowed to be large. We prove that $v$ is regular at time zero.Comment: More explanations and a new appendi

Riboflavin status, MTHFR genotype and blood pressure: current evidence and implications for personalised nutrition

Clinical deficiency of the B-vitamin riboflavin (vitamin B2) is largely confined to developing countries; however accumulating evidence indicates that suboptimal riboflavin status is a widespread problem across the developed world. Few international data are available on riboflavin status as measured by the functional biomarker, erythrocyte glutathione reductase activation coefficient, considered to be the gold standard index. One important role of riboflavin in the form of flavin dinucleotide is as a co-factor for the folate-metabolising enzyme methylenetetrahydrofolate reductase (MTHFR). Homozygosity for the common C677T polymorphism in MTHFR, affecting over 10 % of the UK and Irish populations and up to 32 % of other populations worldwide, has been associated with an increased risk of CVD, and more recently with hypertension. This review will explore available studies reporting riboflavin status worldwide, the interaction of riboflavin with theMTHFRC677T polymorphism and the potential role of riboflavin in personalised nutrition. Evidence is accumulating for a novel role of riboflavin as an important modulator of blood pressure (BP) specifically in individuals with theMTHFR677TT genotype, with results from a number of recent randomised controlled trials demonstrating that riboflavin supplementation can significantly reduce systolic BP by 5–13 mmHg in these genetically at risk adults. Studies are however required to investigate the BP-lowering effect of riboflavin in different populations and in response to doses higher than 1·6 mg/d. Furthermore, work focusing on the translation of this research to health professionals and patients is also required.</jats:p

Проблеми управління фінансовою безпекою підприємства

Expanding urbanization in estuaries and the increase in pollutants from anthropogenic point sources can affect nearby benthic assemblages. Using a paired impact-control design, we assessed the effects of pollution from anthropogenic point sources (marinas, storm-water drains, sewage outfalls and fish farms) on algal and sessile invertebrate recruits to pavers placed in an industrialized Tasmanian estuary. Species number and cover of native recruits were lower after 12 months at sites outside marinas relative to paired control sites, whereas non-native and cryptogenic recruits were significantly higher outside marinas and near sewage outfalls. The cover of fast-growing, opportunistic species was significantly higher at sites near fish farms and sewage outfalls, and the cover of native species was also greater at sites near sewage outfalls relative to the paired control sites. Our results suggest an increased management focus on controlling pollution from marinas and sewage outfalls is warranted to limit the spread of non-native and cryptogenic species

Deep three-dimensional solid-state qubit arrays with long-lived spin coherence

Nitrogen-vacancy centers (NVCs) in diamond show promise for quantum computing, communication, and sensing. However, the best current method for entangling two NVCs requires that each one is in a separate cryostat, which is not scalable. We show that single NVCs can be laser written 6–15-µm deep inside of a diamond with spin coherence times that are an order of magnitude longer than previous laser-written NVCs and at least as long as naturally occurring NVCs. This depth is suitable for integration with solid immersion lenses or optical cavities and we present depth-dependent T2 measurements. 200 000 of these NVCs would fit into one diamond

The color of a Dalmatian's spots: Linkage evidence to support the TYRP1 gene

BACKGROUND: The distinctive coat pattern of a Dalmatian is the result of the interaction of several loci. While the encoded function of these genes is not fully understood, it is known the Piebald, Ticking, and Flecking loci interact to produce the Dalmatian's classic pigmented spots on a white background. The color of the pigmented spots in purebred Dalmatians can either be black or liver, but the locus responsible for color determination is unknown. Studies have been conducted to determine the underlying genes involved in coat color determination in the dog, e.g., in the Labrador Retriever, but none to date have addressed black versus liver in the Dalmatian. RESULTS: A genome scan was conducted in a multi-generational kindred of Dalmatians segregating black and liver spot color. Linkage analysis was performed using a total of 113 polymorphic microsatellite markers from the kindred. Linkage was found between spot color and a single microsatellite marker, FH2319 (LOD = 12.5) on chromosome 11. CONCLUSION: The TYRP1 (Brown) locus is located at position 50.1 Mb on chromosome 11, which is approximately 0.4 Mb from marker FH2319. Given the recent characterization of TYRP1 genetic variations in the dog and the linkage evidence reported here, TYRP1 is likely responsible for the spot color variation of black versus liver seen in the Dalmatian

Huddle test measurement of a near Johnson noise limited geophone

In this paper, the sensor noise of two geophone configurations (L-22D and L-4C geophones from Sercel with custom built amplifiers) was measured by performing two huddle tests. It is shown that the accuracy of the results can be significantly improved by performing the huddle test in a seismically quiet environment and by using a large number of reference sensors to remove the seismic foreground signal from the data. Using these two techniques, the measured sensor noise of the two geophone configurations matched the calculated predictions remarkably well in the bandwidth of interest (0.01 Hz–100 Hz). Low noise operational amplifiers OPA188 were utilized to amplify the L-4C geophone to give a sensor that was characterized to be near Johnson noise limited in the bandwidth of interest with a noise value of 10−11 m/Hz⎯⎯⎯⎯⎯√10−11 m/Hz at 1 Hz