A unified theory of available potential energy

Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together with energy conservation. This raises the questions of why such constructions are required in the first place, and whether there is some general method of deriving the available potential energy for an arbitrary fluid system. By appealing to the underlying Hamiltonian structure of geophysical fluid dynamics, it becomes clear why energy conservation is not enough, and why other conservation laws such as mass conservation need to be incorporated in order to construct an invariant, known as the pseudoenergy, that is a positive‐definite functional of disturbance quantities. The available potential energy is just the non‐kinetic part of the pseudoenergy, the construction of which follows a well defined algorithm. Two notable features of the available potential energy defined thereby are first, that it is a locally defined quantity, and second, that it is inherently definable at finite amplitude (though one may of course always take the small‐amplitude limit if this is appropriate). The general theory is made concrete by systematic derivations of available potential energy in a number of different contexts. All the well known expressions are recovered, and some new expressions are obtained. The possibility of generalizing the concept of available potential energy to dynamically stable basic flows (as opposed to statically stable basic states) is also discussed.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Impact of postprandial glycaemia on health and prevention of disease

Postprandial glucose, together with related hyperinsulinemia and lipidaemia, has been implicated in the development of chronic metabolic diseases like obesity, type 2 diabetes mellitus (T2DM) and cardiovascular disease (CVD). In this review, available evidence is discussed on postprandial glucose in relation to body weight control, the development of oxidative stress, T2DM, and CVD and in maintaining optimal exercise and cognitive performance. There is mechanistic evidence linking postprandial glycaemia or glycaemic variability to the development of these conditions or in the impairment in cognitive and exercise performance. Nevertheless, postprandial glycaemia is interrelated with many other (risk) factors as well as to fasting glucose. In many studies, meal-related glycaemic response is not sufficiently characterized, or the methodology with respect to the description of food or meal composition, or the duration of the measurement of postprandial glycaemia is limited. It is evident that more randomized controlled dietary intervention trials using effective low vs. high glucose response diets are necessary in order to draw more definite conclusions on the role of postprandial glycaemia in relation to health and disease. Also of importance is the evaluation of the potential role of the time course of postprandial glycaemia.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Transreal calculus

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Production and on-line comprehension of definiteness in English and Dutch by monolingual and sequential bilingual children

The present article examines production and on-line processing of definite articles in Turkish-speaking sequential bilingual children acquiring English and Dutch as second languages (L2) in the UK and in the Netherlands, respectively. Thirty-nine 6–8-year-old L2 children and 48 monolingual (L1) age-matched children participated in two separate studies examining the production of definite articles in English and Dutch in conditions manipulating semantic context, that is, the anaphoric and the bridging contexts. Sensitivity to article omission was examined in the same groups of children using an on-line processing task involving article use in the same semantic contexts as in the production task. The results indicate that both L2 children and L1 controls are less accurate when definiteness is established by keeping track of the discourse referents (anaphoric) than when it is established via world knowledge (bridging). Moreover, despite variable production, all groups of children were sensitive to the omission of definite articles in the on-line comprehension task. This suggests that the errors of omission are not due to the lack of abstract syntactic representations, but could result from processes implicated in the spell-out of definite articles. The findings are in line with the idea that variable production in child L2 learners does not necessarily indicate lack of abstract representations (Haznedar and Schwartz, 1997).

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Fish oil intakes providing dietary attainable levels of EPA and DHA reduces blood pressure in adults with systolic hypertension in a retrospective analysis

Background: Although a large number of randomized controlled trials (RCTs) have examined the impact of the n-3 (ω-3) fatty acids EPA (20:5n-3) and DHA (22:6n-3) on blood pressure and vascular function, the majority have used doses of EPA+DHA of > 3 g per d,which are unlikely to be achieved by diet manipulation. Objective: The objective was to examine, using a retrospective analysis from a multi-center RCT, the impact of recommended, dietary achievable EPA+DHA intakes on systolic and diastolic blood pressure and microvascular function in UK adults. Design: Healthy men and women (n = 312) completed a double-blind, placebo-controlled RCT consuming control oil, or fish oil providing 0.7 g or 1.8 g EPA+DHA per d in random order each for 8 wk. Fasting blood pressure and microvascular function (using Laser Doppler Iontophoresis) were assessed and plasma collected for the quantification of markers of vascular function. Participants were retrospectively genotyped for the eNOS rs1799983 variant. Results: No impact of n-3 fatty acid treatment or any treatment * eNOS genotype interactions were evident in the group as a whole for any of the clinical or biochemical outcomes. Assessment of response according to hypertension status at baseline indicated a significant (P=0.046) fish oil-induced reduction (mean 5 mmHg) in systolic blood pressure specifically in those with isolated systolic hypertension (n=31). No dose response was observed. Conclusions: These findings indicate that, in those with isolated systolic hypertension, daily doses of EPA+DHA as low as 0.7 g bring about clinically meaningful blood pressure reductions which, at a population level, would be associated with lower cardiovascular disease risk. Confirmation of findings in an RCT where participants are prospectively recruited on the basis of blood pressure status is required to draw definite conclusions. The Journal of Nutrition NUTRITION/2015/220475 Version 4

Effect of surface restoring on subsurface variability in a climate model during 1949-2005

Initializing the ocean for decadal predictability studies is a challenge, as it requires reconstructing the little observed subsurface trajectory of ocean variability. In this study we explore to what extent surface nudging using well-observed sea surface temperature (SST) can reconstruct the deeper ocean variations for the 1949–2005 period. An ensemble made with a nudged version of the IPSLCM5A model and compared to ocean reanalyses and reconstructed datasets. The SST is restored to observations using a physically-based relaxation coefficient, in contrast to earlier studies, which use a much larger value. The assessment is restricted to the regions where the ocean reanalyses agree, i.e. in the upper 500 m of the ocean, although this can be latitude and basin dependent. Significant reconstruction of the subsurface is achieved in specific regions, namely region of subduction in the subtropical Atlantic, below the thermocline in the equatorial Pacific and, in some cases, in the North Atlantic deep convection regions. Beyond the mean correlations, ocean integrals are used to explore the time evolution of the correlation over 20-year windows. Classical fixed depth heat content diagnostics do not exhibit any significant reconstruction between the different existing observation-based references and can therefore not be used to assess global average time-varying correlations in the nudged simulations. Using the physically based average temperature above an isotherm (14 °C) alleviates this issue in the tropics and subtropics and shows significant reconstruction of these quantities in the nudged simulations for several decades. This skill is attributed to the wind stress reconstruction in the tropics, as already demonstrated in a perfect model study using the same model. Thus, we also show here the robustness of this result in an historical and observational context.

El Niño 2015/2016 impact analysis, monthly outlook November 2015

During the summer and autumn 2015, El Niño conditions in the east and central Pacific have strengthened, disrupting weather patterns throughout the tropics and into the mid-latitudes. For example, rainfall during this summer’s Indian monsoon was approximately 15% below normal. The continued strong El Niño conditions have the potential to trigger damaging impacts (e.g., droughts, famines, floods), particularly in less-developed tropical countries, which would require a swift and effective humanitarian response to mitigate damage to life and property (e.g., health, migration, infrastructure). This analysis uses key climatic variables (temperature, soil moisture and precipitation) as measures to monitor the ongoing risk of these potentially damaging impacts. The previous 2015-2016 El Niño Impact Analysis was based on observations over the past 35 years and produced Impact Tables showing the likelihood and severity of the impacts on temperature and rainfall by season. The current report is an extension of this work providing information from seasonal forecast models to give a more detailed monthly outlook of the potential near-term impacts of the current El Niño conditions by region. This information has been added to the Impact Tables in the form of a monthly outlook column. This monthly outlook is an indication of the average likely conditions for that month and region and is not a definite prediction of weather impacts.

El Niño 2015/2016 impact analysis, monthly outlook December 2015

During the summer and autumn 2015, El Niño conditions in the east and central Pacific have strengthened, disrupting weather patterns throughout the tropics and into the mid-latitudes. For example, rainfall during this summer’s Indian monsoon was approximately 15% below normal. The continued strong El Niño conditions have the potential to trigger damaging impacts (e.g. droughts, famines, floods), particularly in less-developed tropical countries, which would require a swift and effective humanitarian response to mitigate damage to life and property (e.g. health, migration, infrastructure). This analysis uses key climatic variables (temperature, soil moisture and precipitation) as measures to monitor the ongoing risk of these potentially damaging impacts. The previous 2015-2016 El Niño Impact Analysis was based on observations over the past 35 years and produced Impact Tables showing the likelihood and severity of the impacts on temperature and rainfall by season. The current report is an extension of this work providing information from observations and seasonal forecast models to give a more detailed outlook of the potential near-term impacts of the current El Niño conditions by region. This information has been added to the Impact Tables in the form of an ‘Observations and Outlook’ row. This consists of observational information for the past seasons of JJA 2015 and SON 2015, a detailed monthly outlook from 5 modeling centres for Dec 2015 and then longer-term seasonal forecast information from 2 modeling centres for the future seasons of JF 2016 and MAM 2016. The seasonal outlook information is an indication of the average likely conditions for that coming month (or season) and region and is not a definite prediction of weather impacts.

El Niño 2015/2016 impact analysis, monthly outlook January 2016

During the summer and autumn of 2015, El Niño conditions in the east and central Pacific have strengthened, disrupting weather patterns throughout the tropics and into the mid-latitudes. For example, rainfall during this summer’s Indian monsoon was approximately 15% below normal. The continued strong El Niño conditions have the potential to trigger damaging impacts (e.g., droughts, famines, floods), particularly in less-developed tropical countries, which would require a swift and effective humanitarian response to mitigate damage to life and property (e.g., health, migration, infrastructure). This analysis uses key climatic variables (temperature, soil moisture and precipitation) as measures to monitor the ongoing risk of these potentially damaging impacts. The previous 2015-2016 El Niño Impact Analysis was based on observations over the past 35 years and produced Impact Tables showing the likelihood and severity of the impacts on temperature and rainfall by season. The current report is an extension of this work providing information from observations and seasonal forecast models to give a more detailed outlook of the potential near-term impacts of the current El Niño conditions by region. This information has been added to the Impact Tables in the form of an ‘Observations and Outlook’ row. This consists of observational information for the past seasons of JJA 2015, SON 2015 and Dec 2015, a detailed monthly outlook from 4 modeling centres for Jan 2016 and then longer-term seasonal forecast information from 2 modeling centres for the future seasons of Feb 2016, MAM 2016 and Jun 2016. The seasonal outlook information is an indication of the average likely conditions for that coming month (or season) and region and is not a definite prediction of weather impacts.