A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch-angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler-mode waves generated by a temperature anisotropy can mediate this pitch-angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase-space diffusion, it is important to characterise the whistler-mode wave distributions that result from the instability. We use previously-published observations of number density, pitch-angle anisotropy and phase space density to model the plasma in the quiet pre-noon magnetosphere (defined as periods when AE<100nT). We investigate the global propagation and growth of whistler-mode waves by studying millions of growing ray paths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection, most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wavenormal angle is different. The wave distribution is asymmetric with respect to the wavenormal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L-shell.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Cocoa flavanol intake improves endothelial function and Framingham Risk Score in healthy men and women: a randomised, controlled, double-masked trial: the Flaviola Health Study

Cocoa flavanol (CF) intake improves endothelial function in patients with cardiovascular risk factors and disease. We investigated the effects of CF on surrogate markers of cardiovascular health in low risk, healthy, middle-aged individuals without history, signs or symptoms of CVD. In a 1-month, open-label, one-armed pilot study, bi-daily ingestion of 450 mg of CF led to a time-dependent increase in endothelial function (measured as flow-mediated vasodilation (FMD)) that plateaued after 2 weeks. Subsequently, in a randomised, controlled, double-masked, parallel-group dietary intervention trial (Clinicaltrials.gov: NCT01799005), 100 healthy, middle-aged (35–60 years) men and women consumed either the CF-containing drink (450 mg) or a nutrient-matched CF-free control bi-daily for 1 month. The primary end point was FMD. Secondary end points included plasma lipids and blood pressure, thus enabling the calculation of Framingham Risk Scores and pulse wave velocity. At 1 month, CF increased FMD over control by 1·2 % (95 % CI 1·0, 1·4 %). CF decreased systolic and diastolic blood pressure by 4·4 mmHg (95 % CI 7·9, 0·9 mmHg) and 3·9 mmHg (95 % CI 6·7, 0·9 mmHg), pulse wave velocity by 0·4 m/s (95 % CI 0·8, 0·04 m/s), total cholesterol by 0·20 mmol/l (95 % CI 0·39, 0·01 mmol/l) and LDL-cholesterol by 0·17 mmol/l (95 % CI 0·32, 0·02 mmol/l), whereas HDL-cholesterol increased by 0·10 mmol/l (95 % CI 0·04, 0·17 mmol/l). By applying the Framingham Risk Score, CF predicted a significant lowering of 10-year risk for CHD, myocardial infarction, CVD, death from CHD and CVD. In healthy individuals, regular CF intake improved accredited cardiovascular surrogates of cardiovascular risk, demonstrating that dietary flavanols have the potential to maintain cardiovascular health even in low-risk subjects.

Dietary nitrate improves vascular function in patients with hypercholesterolemia: a randomized, double-blind, placebo-controlled study

Background: The beneficial cardiovascular effects of vegetables may be underpinned by their high inorganic nitrate content. Objective: We sought to examine the effects of a 6-wk once-daily intake of dietary nitrate (nitrate-rich beetroot juice) compared with placebo intake (nitrate-depleted beetroot juice) on vascular and platelet function in untreated hypercholesterolemics. Design: A total of 69 subjects were recruited in this randomized, double-blind, placebo-controlled parallel study. The primary endpoint was the change in vascular function determined with the use of ultrasound flow-mediated dilatation (FMD). Results: Baseline characteristics were similar between the groups, with primary outcome data available for 67 patients. Dietary nitrate resulted in an absolute increase in the FMD response of 1.1% (an ∼24% improvement from baseline) with a worsening of 0.3% in the placebo group (P < 0.001). A small improvement in the aortic pulse wave velocity (i.e., a decrease of 0.22 m/s; 95% CI: −0.4, −0.3 m/s) was evident in the nitrate group, showing a trend (P = 0.06) to improvement in comparison with the placebo group. Dietary nitrate also caused a small but significant reduction (7.6%) in platelet-monocyte aggregates compared with an increase of 10.1% in the placebo group (P = 0.004), with statistically significant reductions in stimulated (ex vivo) P-selectin expression compared with the placebo group (P < 0.05) but no significant changes in unstimulated expression. No adverse effects of dietary nitrate were detected. The composition of the salivary microbiome was altered after the nitrate treatment but not after the placebo treatment (P < 0.01). The proportions of 78 bacterial taxa were different after the nitrate treatment; of those taxa present, 2 taxa were responsible for >1% of this change, with the proportions of Rothia mucilaginosa trending to increase and Neisseria flavescens (P < 0.01) increased after nitrate treatment relative to after placebo treatment. Conclusions: Sustained dietary nitrate ingestion improves vascular function in hypercholesterolemic patients. These changes are associated with alterations in the oral microbiome and, in particular, nitrate-reducing genera. Our findings provide additional support for the assessment of the potential of dietary nitrate as a preventative strategy against atherogenesis in larger cohorts. This trial was registered at clinicaltrials.gov as NCT01493752.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Renal ischemia in rats: Mitochondria function and laser autofluorescence

Ischemia-reperfusion injury is the major cause of organ dysfunction or even nonfunction following transplantation. It can attenuate the long-term survival of transplanted organs. To evaluate the severity of renal ischemia injury determined by histology, we applied laser(442 nm and 532 nm) induced fluorescence (LIF), mitochondria respiration, and membrane swelling to evaluate 28 Wistar rats that underwent left kidney warm ischemia for 20, 40, 60, or 80 minutes. LIF performed before ischemia (control) was repeated at 20, 40, 60, and 80 minutes thereafter. We harvested left kidney tissue samples immediately after LIF determination for histology and mitochondrial analyses: state 3 and 4 respiration, respiration control rate (RCR), and membrane swelling. The association of optic spectroscopy with histological damage showed: LIF, 442 nm (r(2) = 0.39, P < .001) and 532 nm, (r(2) = 0.18, P = .003); reflecting laser/fluorescence-induced, 442 nm (r(2) = 0.20, P = .002) and 532 nm (r(2) = 0.004, P = .67). The associations between mitochondria function and tissue damage were: state 3 respiration (r(2) = 0.43, P = .0004), state 4 respiration (r(2) = 0.03, P = 0.38), RCR (r(2) = 0.28, P = .007), and membrane swelling (r(2) = 0.02, P = .43). The intensity of fluorescence emitted by tissue excited by laser, especially at a wave length of 442 nm, was determined in real time. Mitochondrial state 3 respiration and respiratory control ratio also exhibited good correlations with the grade of ischemic tissue damage.

The effect of known cardiovascular risk factors on carotid-femoral pulse wave velocity in school-aged children: a population based twin study

Childhood cardiovascular risk factors affect vascular function long before overt cardiovascular disease. Twin studies provide a unique opportunity to examine the influence of shared genetic and environmental influences on childhood cardiovascular function. We examined the relationship between birth parameters, markers of adiposity, insulin resistance, lipid profile and blood pressure and carotid-femoral pulse wave velocity (PWV), a validated non-invasive measure of arterial stiffness in a healthy cohort of school-aged twin children. PWV was performed on a population-based birth cohort of 147 twin pairs aged 7-11 years. Fasting blood samples, blood pressure and adiposity measures were collected concurrently. Mixed linear regression models were used to account for twin clustering, within- and between-twin pair associations. There were positive associations between both markers of higher adiposity, insulin resistance, elevated triglycerides and PWV, which remained significant after accounting for twin birth-set clustering. There was a positive association between both diastolic and mean arterial blood pressure and PWV in within-pair analysis in dizygotic, but not monozygotic twins, indicating genetic differences evident in dizygotic not monozygotic twins may affect these associations. Increased blood pressure, triglycerides and other metabolic markers are associated with increased PWV in school-aged twins. These results support both the genetic and environmental contribution to higher PWV, as a marker of arterial stiffness, and reiterate the importance of preventing metabolic syndrome from childhood.

Blood pressure and cognitive function: the role of central aortic and brachial pressures

Central (aortic) blood pressures differ from brachial pressures and may be more relevant to the study of cognitive function, given that blood is delivered to the brain through the central large arteries. Pulse-pressure amplification reflects the augmentation of blood pressure between the central and peripheral arteries, which diminishes with aging. We aimed to determine the association between central blood pressure and cognitive function in independently living adults aged 20 to 82 years (N = 493). In adjusted regression models, higher central systolic pressure and higher central pulse pressure were each associated with poorer processing speed, Stroop processing, and recognition memory. Lower amplification was associated with poorer Stroop processing, working memory, and recognition memory. Higher brachial systolic pressure and brachial pulse pressure were both associated with poorer Stroop processing. In summary, central pressures and amplification were sensitive indicators of cognitive aging, predicting aspects of cognitive performance not predicted by brachial blood pressure.

Functional replacement across species pools of vertebrate scavengers separated at a continental scale maintains an ecosystem function

Summary: The composition of species pools can vary in space and time. While many studies are focused on understanding which factors influence the make-up of species pools, the question to which degree biogeographic variation in species composition propagates to biogeographic variation in ecological function is rarely examined. If different local species assemblages operate in ways that maintain specific ecological processes across continents, they can be regarded as functionally equivalent. Alternatively, variation in species assemblages might result in the loss of ecological function if different species fulfil different functions, and thereby fail to maintain the ecological process. Here, we test whether ecological function is affected by differences in the composition of species pools across a continental scale, comparing a tropical with a temperate pool. The model systems are assemblages of vertebrates foraging on ocean beaches, and the ecological function of interest is the consumption of wave-cast carrion, a pivotal process in sandy shore ecosystems. We placed fish carcasses (n = 179) at the beach-dune interface, monitored by motion-triggered cameras to record scavengers and quantify the detection and removal of carrion. Scavenging function was measured on sandy beaches in two distinct biogeographic regions of Australia: tropical north Queensland and temperate Victoria. The composition of scavenging assemblages on sandy beaches varied significantly across the study domain. Raptors dominated in the tropics, while invasive red foxes were prominent in temperate assemblages. Notwithstanding the significant biogeographic change in species composition, ecological function - as indexed by carcass detection and removal - was maintained, suggesting strong functional replacement at the continental scale. Species pools of vertebrate scavengers that are assembled from taxonomically distinct groups (birds vs. mammals) and located in distinct climatic regions (temperate vs. tropical) can maintain an ecological process via replacement of species with comparable functional traits.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.