Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

The effect of copper(II), iron(II) sulphate and vitamin C combinations on the weak antimicrobial activity of (+)-catechin against Staphylococcus aureus and other microbes

Few attempts have been made to improve the activity of plant compounds with low antimicrobial efficacy. (+)-Catechin, a weak antimicrobial tea flavanol, was combined with putative adjuncts and tested against different species of bacteria. Copper(II) sulphate enhanced (+)-catechin activity against Pseudomonas aeruginosa but not Staphylococcus aureus, Proteus mirabilis or Escherichia coli. Attempts to raise the activity of (+)-catechin against two unresponsive species, S. aureus and E. coli, with iron(II) sulphate, iron(III) chloride, and vitamin C, showed that iron(II) enhanced (+)-catechin against S. aureus, but not E. coli; neither iron(III) nor combined iron(II) and copper(II), enhanced (+)-catechin activity against either species. Vitamin C enhanced copper(II) containing combinations against both species in the absence of iron(II). Catalase or EDTA added to active samples removed viability effects suggesting that active mixtures had produced H2O2via the action of added metal(II) ions. H2O2 generation by (+)-catechin plus copper(II) mixtures and copper(II) alone could account for the principal effect of bacterial growth inhibition following 30 minute exposures as well as the antimicrobial effect of (+)-catechin–iron(II) against S. aureus. These novel findings about a weak antimicrobial flavanol contrast with previous knowledge of more active flavanols with transition metal combinations. Weak antimicrobial compounds like (+)-catechin within enhancement mixtures may therefore be used as efficacious agents. (+)-Catechin may provide a means of lowering copper(II) or iron(II) contents in certain crop protection and other products.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Promotion carryover as a missing data problem

An important feature of agribusiness promotion programs is their lagged impact on consumption. Efficient investment in advertising requires reliable estimates of these lagged responses and it is desirable from both applied and theoretical standpoints to have a flexible method for estimating them. This note derives an alternative Bayesian methodology for estimating lagged responses when investments occur intermittently within a time series. The method exploits a latent-variable extension of the natural-conjugate, normal-linear model, Gibbs sampling and data augmentation. It is applied to a monthly time series on Turkish pasta consumption (1993:5-1998:3) and three, nonconsecutive promotion campaigns (1996:3, 1997:3, 1997:10). The results suggest that responses were greatest to the second campaign, which allocated its entire budget to television media; that its impact peaked in the sixth month following expenditure; and that the rate of return (measured in metric tons additional consumption per thousand dollars expended) was around a factor of 20.

Environmental oestrogens and breast cancer: long-term low-dose effects of mixtures of various chemical combinations

The incidence of breast cancer has risen worldwide to unprecedented levels in recent decades, making it now the major cancer of women in many parts of the world.1 Although diet, alcohol, radiation and inherited loss of BRCA1/2 genes have all been associated with increased incidence, the main identified risk factors are life exposure to hormones including physiological variations associated with puberty/pregnancy/menopause,1 personal choice of use of hormonal contraceptives2 and/or hormone replacement therapy.3–6 On this basis, exposure of the human breast to the many environmental pollutant chemicals capable of mimicking or interfering with oestrogen action7 should also be of concern.8 Hundreds of such environmental chemicals have now been measured in human breast tissue from a range of dietary and domestic exposure sources7 ,9 including persistent organochlorine pollutants (POPs),10 polybrominated diphenylethers and polybromobiphenyls,11 polychlorinated biphenyls,12 dioxins,13 alkyl phenols,14 bisphenol-A and chlorinated derivatives,15 as well as other less lipophilic compounds such as parabens (alkyl esters of p-hydroxybenzoic acid),16 but studies investigating any association between raised levels of such compounds and the development of breast cancer remain inconclusive.7–16 However, the functionality of these chemicals has continued to be assessed on the basis of individual chemicals rather than the environmental reality of long-term low-dose exposure to complex mixtures. This misses the potential for individuals to have high concentrations of different compounds but with a common mechanism of action. It also misses the complex interactions between chemicals and physiological hormones which together may act to alter the internal homeostasis of the oestrogenic environment of mammary tissue.

Combinations of parabens at concentrations measured in human breast tissue can increase proliferation of MCF-7 human breast cancer cells

The alkyl esters of p-hydroxybenzoic acid (parabens), which are used as preservatives in consumer products, possess oestrogenic activity and have been measured in human breast tissue. This has raised concerns for a potential involvement in the development of human breast cancer. In this paper, we have investigated the extent to which proliferation of MCF-7 human breast cancer cells can be increased by exposure to the five parabens either alone or in combination at concentrations as recently measured in 160 human breast tissue samples. Determination of no-observed-effect concentrations (NOEC), lowest-observed-effect concentrations (LOEC), EC50 and EC100 values for stimulation of proliferation of MCF-7 cells by five parabens revealed that 43/160 (27%) of the human breast tissue samples contained at least one paraben at a concentration ≥ LOEC and 64/160 (40%) > NOEC. Proliferation of MCF-7 cells could be increased by combining all five parabens at concentrations down to the 50th percentile (median) values measured in the tissues. For the 22 tissue samples taken at the site of ER + PR + primary cancers, 12 contained a sufficient concentration of one or more paraben to stimulate proliferation of MCF-7 cells. This demonstrates that parabens, either alone or in combination, are present in human breast tissue at concentrations sufficient to stimulate the proliferation of MCF-7 cells in vitro, and that functional consequences of the presence of paraben in human breast tissue should be assessed on the basis of all five parabens and not single parabens individually.

The use of land-sea warming contrast under climate change to improve impact metrics

A favoured method of assimilating information from state-of-the-art climate models into integrated assessment models of climate impacts is to use the transient climate response (TCR) of the climate models as an input, sometimes accompanied by a pattern matching approach to provide spatial information. More recent approaches to the problem use TCR with another independent piece of climate model output: the land-sea surface warming ratio (φ). In this paper we show why the use of φ in addition to TCR has such utility. Multiple linear regressions of surface temperature change onto TCR and φ in 22 climate models from the CMIP3 multi-model database show that the inclusion of φ explains a much greater fraction of the inter-model variance than using TCR alone. The improvement is particularly pronounced in North America and Eurasia in the boreal summer season, and in the Amazon all year round. The use of φ as the second metric is beneficial for three reasons: firstly it is uncorrelated with TCR in state-of-the-art climate models and can therefore be considered as an independent metric; secondly, because of its projected time-invariance, the magnitude of φ is better constrained than TCR in the immediate future; thirdly, the use of two variables is much simpler than approaches such as pattern scaling from climate models. Finally we show how using the latest estimates of φ from climate models with a mean value of 1.6—as opposed to previously reported values of 1.4—can significantly increase the mean time-integrated discounted damage projections in a state-of-the-art integrated assessment model by about 15 %. When compared to damages calculated without the inclusion of the land-sea warming ratio, this figure rises to 65 %, equivalent to almost 200 trillion dollars over 200 years.

Radar bright band correction using the linear depolarisation ratio

The enhanced radar return associated with melting snow, ‘the bright band’, can lead to large overestimates of rain rates. Most correction schemes rely on fitting the radar observations to a vertical profile of reflectivity (VPR) which includes the bright band enhancement. Observations show that the VPR is very variable in space and time; large enhancements occur for melting snow, but none for the melting graupel in embedded convection. Applying a bright band VPR correction to a region of embedded convection will lead to a severe underestimate of rainfall. We revive an earlier suggestion that high values of the linear depolarisation ratio (LDR) are an excellent means of detecting when bright band contamination is occurring and that the value of LDR may be used to correct the value of Z in the bright band.

Quantifying the contributions to stratospheric ozone changes from ozone depleting substances and greenhouse gases

A state-of-the-art chemistry climate model coupled to a three-dimensional ocean model is used to produce three experiments, all seamlessly covering the period 1950–2100, forced by different combinations of long-lived Greenhouse Gases (GHGs) and Ozone Depleting Substances (ODSs). The experiments are designed to quantify the separate effects of GHGs and ODSs on the evolution of ozone, as well as the extent to which these effects are independent of each other, by alternately holding one set of these two forcings constant in combination with a third experiment where both ODSs and GHGs vary. We estimate that up to the year 2000 the net decrease in the column amount of ozone above 20 hPa is approximately 75% of the decrease that can be attributed to ODSs due to the offsetting effects of cooling by increased CO2. Over the 21st century, as ODSs decrease, continued cooling from CO2 is projected to account for more than 50% of the projected increase in ozone above 20 hPa. Changes in ozone below 20 hPa show a redistribution of ozone from tropical to extra-tropical latitudes with an increase in the Brewer-Dobson circulation. In addition to a latitudinal redistribution of ozone, we find that the globally averaged column amount of ozone below 20 hPa decreases over the 21st century, which significantly mitigates the effect of upper stratospheric cooling on total column ozone. Analysis by linear regression shows that the recovery of ozone from the effects of ODSs generally follows the decline in reactive chlorine and bromine levels, with the exception of the lower polar stratosphere where recovery of ozone in the second half of the 21st century is slower than would be indicated by the decline in reactive chlorine and bromine concentrations. These results also reveal the degree to which GHGrelated effects mute the chemical effects of N2O on ozone in the standard future scenario used for the WMO Ozone Assessment. Increases in the residual circulation of the atmosphere and chemical effects from CO2 cooling more than halve the increase in reactive nitrogen in the mid to upper stratosphere that results from the specified increase in N2O between 1950 and 2100.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Cyclic prefixed OQAM-OFDM and its application to single-carrier FDMA

Single-carrier frequency division multiple access (SC-FDMA) has appeared to be a promising technique for high data rate uplink communications. Aimed at SC-FDMA applications, a cyclic prefixed version of the offset quadrature amplitude modulation based OFDM (OQAM-OFDM) is first proposed in this paper. We show that cyclic prefixed OQAMOFDM CP-OQAM-OFDM) can be realized within the framework of the standard OFDM system, and perfect recovery condition in the ideal channel is derived. We then apply CP-OQAMOFDM to SC-FDMA transmission in frequency selective fading channels. Signal model and joint widely linear minimum mean square error (WLMMSE) equalization using a prior information with low complexity are developed. Compared with the existing DFTS-OFDM based SC-FDMA, the proposed SC-FDMA can significantly reduce envelope fluctuation (EF) of the transmitted signal while maintaining the bandwidth efficiency. The inherent structure of CP-OQAM-OFDM enables low-complexity joint equalization in the frequency domain to combat both the multiple access interference and the intersymbol interference. The joint WLMMSE equalization using a prior information guarantees optimal MMSE performance and supports Turbo receiver for improved bit error rate (BER) performance. Simulation resultsconfirm the effectiveness of the proposed SC-FDMA in termsof EF (including peak-to-average power ratio, instantaneous-toaverage power ratio and cubic metric) and BER performances.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.