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

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Long-lived halocarbon trends and budgets from atmospheric chemistry modelling constrained with measurements in polar firn

The budgets of seven halogenated gases (CFC-11, CFC-12, CFC-113, CFC-114, CFC-115, CCl4 and SF6) are studied by comparing measurements in polar firn air from two Arctic and three Antarctic sites, and simulation results of two numerical models: a 2-D atmospheric chemistry model and a 1-D firn diffusion model. The first one is used to calculate atmospheric concentrations from emission trends based on industrial inventories; the calculated concentration trends are used by the second one to produce depth concentration profiles in the firn. The 2-D atmospheric model is validated in the boundary layer by comparison with atmospheric station measurements, and vertically for CFC-12 by comparison with balloon and FTIR measurements. Firn air measurements provide constraints on historical atmospheric concentrations over the last century. Age distributions in the firn are discussed using a Green function approach. Finally, our results are used as input to a radiative model in order to evaluate the radiative forcing of our target gases. Multi-species and multi-site firn air studies allow to better constrain atmospheric trends. The low concentrations of all studied gases at the bottom of the firn, and their consistency with our model results confirm that their natural sources are small. Our results indicate that the emissions, sinks and trends of CFC-11, CFC-12, CFC-113, CFC-115 and SF6 are well constrained, whereas it is not the case for CFC-114 and CCl4. Significant emission-dependent changes in the lifetimes of halocarbons destroyed in the stratosphere were obtained. Those result from the time needed for their transport from the surface where they are emitted to the stratosphere where they are destroyed. Efforts should be made to update and reduce the large uncertainties on CFC lifetimes.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Green tea (Camellia sinensis) catechins and vascular function

The health benefits of green tea (Camellia sinensis) catechins are becoming increasingly recognised. Amongst the proposed benefits are the maintenance of endothelial function and vascular homeostasis and an associated reduction in atherogenesis and CVD risk. The mounting evidence for the influential effect of green tea catechins on vascular function from epidemiological, human intervention and animal studies is subject to review together with exploration of the potential mechanistic pathways involved. Epigallocatechin-3-gallate, one of the most abundant and widely studied catechin found in green tea, will be prominent in the present review. Since there is a substantial inconsistency in the published data with regards to the impact of green tea catechins on vascular function, evaluation and interpretation of the inter- and intra-study variability is included. In conclusion, a positive effect of green tea catechins on vascular function is becoming apparent. Further studies in animal and cell models using physiological concentrations of catechins and their metabolites are warranted in order to gain some insight into the physiology and molecular basis of the observed beneficial effects.

Daily consumption of an aqueous green tea extract supplement does not impair liver function or alter cardiovascular disease risk biomarkers in healthy men

Regular consumption of green tea polyphenols (GTP) is thought to reduce the risk of cardiovascular disease (CVD) but has also been associated with liver toxicity. The present trial aimed to assess the safety and potential CVD health beneficial effects of daily GTP consumption. We conducted a placebo-controlled parallel study to evaluate the chronic effects of GTP on liver function and CVD risk biomarkers in healthy men. Volunteers (treatment: n = 17, BMI 26.7 +/- 3.3 kg/m(2), age 41 +/- 9 y; placebo, n = 16, BMI 25.4 +/- 3.3 kg/m(2), age 40 +/- 10 y) consumed for 3 wk 6 capsules per day (2 before each principal meal) containing green tea extracts (equivalent to 714 mg/d GTP) or placebo. At the beginning and end of the intervention period, we collected blood samples from fasting subjects and measured vascular tone using Laser Doppler lontophoresis. Biomarkers of liver function and CVD risk (including blood pressure, plasma lipids, and asymmetric dimethylarginine) were unaffected by GTP consumption. After treatment, the ratio of total:HDL cholesterol was significantly reduced in participants taking GTP capsules compared with baseline. Endothelial-dependent and -independent vascular reactivity did not significantly differ between treatments. In conclusion, the present data suggests that the daily consumption of high doses of GTP by healthy men for 3 wk is safe but without effects on CVD risk biomarkers other than the total:HDL cholesterol ratio. J. Nutr. 139: 58-62, 2009.

The impact of the catechol-O-methyltransferase genotype on vascular function and blood pressure after acute green tea ingestion

SCOPE: Evidence for the benefits of green tea catechins on vascular function is inconsistent, with genotype potentially contributing to the heterogeneity in response. Here, the impact of the catechol-O-methyltransferase (COMT) genotype on vascular function and blood pressure (BP) after green tea extract ingestion are reported. METHODS AND RESULTS: Fifty subjects (n = 25 of the proposed low-activity [AA] and of the high-activity [GG] COMT rs4680 genotype), completed a randomized, double-blind, crossover study. Peripheral arterial tonometry, digital volume pulse (DVP), and BP were assessed at baseline and 90 min after 1.06 g of green tea extract or placebo. A 5.5 h and subsequent 18.5 h urine collection was performed to assess green tea catechin excretion. A genotype × treatment interaction was observed for DVP reflection index (p = 0.014), with green tea extract in the AA COMT group attenuating the increase observed with placebo. A tendency for a greater increase in diastolic BP was evident at 90 min after the green tea extract compared to placebo (p = 0.07). A genotypic effect was observed for urinary methylated epigallocatechin during the first 5.5 h, with the GG COMT group demonstrating a greater concentration (p = 0.049). CONCLUSION: Differences in small vessel tone according to COMT genotype were evident after acute green tea extract.

Enhancing and diminishing gene function in human embryonic stem cells

It is widely recognized that gain- and loss-of-function approaches are essential for understanding the functions of specific genes, and such approaches would be particularly valuable in studies involving human embryonic stem (hES) cells. We describe a simple and efficient approach using lipofection to transfect hES cells, which enabled us to generate hES cell lines expressing naturally fluorescent green or red proteins without affecting cell pluripotency. We used these cell lines to establish a means of diminishing gene function using small interfering (si)RNAs, which were effective at knocking down gene expression in hES cells. We then demonstrated that stable expression of siRNA could knock down the expression of endogenous genes. Application of these gain- and loss-of-function approaches should have widespread use, not only in revealing the developmental roles of specific human genes, but also for their utility in modulating differentiation.

The impact of catechol-O-methyltransferase genotype on the acute responsiveness of vascular reactivity to a green tea extract

The beneficial effects of green tea catechins, such as the proposed improvement in endothelial function, may be influenced by phase II metabolism during and after absorption. The methylation enzyme, catechol-O-methyltransferase (COMT), has a missense mutation rs4680 (G to A), proposed to result in a 40 % reduction in enzyme activity. In the present pilot study, twenty subjects (ten of each homozygous COMT genotype) were recruited. Green tea extract capsules (836 mg green tea catechins) were given in a fasted state, and a high-carbohydrate breakfast was given after 60 min. Blood samples and vascular function measurements were taken at regular intervals. The change in digital volume pulse stiffness index (SI) from baseline was shown to be different between genotype groups at 120 and 240 min, with a lower SI in the GG individuals (P ≤ 0·044). The change in blood pressure from baseline also differed between genotype groups, with a greater increase in systolic (P = 0·023) and diastolic (P = 0·034) blood pressure at 120 min in the GG group. The AA group was shown to have a greater increase in insulin concentrations at 120 min (P = 0·019) and 180 min (P = 0·008) compared with baseline, despite similar glucose profiles. No genotypic differences were found in vascular reactivity measured using laser Doppler iontophoresis, total nitrite, lipids, plasma total antioxidant capacity or inflammatory markers after ingestion of the green tea extract. In conclusion, SI and insulin response to the glucose load differed between the COMT genotype groups, and this may be suggestive of a green tea extract and genotype interaction.