Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

An evaluation of the correlation between open solar flux and total solar irradiance

The correlation between the coronal source flux F_{S} and the total solar irradiance I_{TS} is re-evaluated in the light of an additional 5 years' data from the rising phase of solar cycle 23 and also by using cosmic ray fluxes detected at Earth. Tests on monthly averages show that the correlation with F_{S} deduced from the interplanetary magnetic field (correlation coefficient, r = 0.62) is highly significant (99.999%), but that there is insufficient data for the higher correlation with annual means (r = 0.80) to be considered significant. Anti-correlations between I_{TS} and cosmic ray fluxes are found in monthly data for all stations and geomagnetic rigidity cut-offs (r ranging from −0.63 to −0.74) and these have significance levels between 85% and 98%. In all cases, the t is poorest for the earliest data (i.e., prior to 1982). Excluding these data improves the anticorrelation with cosmic rays to r = −0:93 for one-year running means. Both the interplanetary magnetic field data and the cosmic ray fluxes indicate that the total solar irradiance lags behind the open solar flux with a delay that is estimated to have an optimum value of 2.8 months (and is within the uncertainty range 0.8-8.0 months at the 90% level).

Long-term drift of the coronal source magnetic flux and the total solar irradiance

We test the method of Lockwood et al. [1999] for deriving the coronal source flux from the geomagnetic aa index and show it to be accurate to within 12% for annual means and 4.5% for averages over a sunspot cycle. Using data from four solar constant monitors during 1981-1995, we find a linear relationship between this magnetic flux and the total solar irradiance. From this correlation, we show that the 131% rise in the mean coronal source field over the interval 1901-1995 corresponds to a rise in the average total solar irradiance of {\Delta}I = 1.65 +/- 0.23 Wm^{-2}.

Investigation of the accuracy of historical irradiance products and interannual variability of solar irradiance using Met Office ground data

Met Office station data from 1980 to 2012 has been used to characterise the interannual variability of incident solar irradiance across the UK. The same data are used to evaluate four popular historical irradiance products to determine which are most suitable for use by the UK PV industry for site selection and system design. The study confirmed previous findings that interannual variability is typically 3–6% and weighted average probability of a particular percentage deviation from the mean at an average site in the UK was calculated. This weighted average showed that fewer than 2% of site-years could be expected to fall below 90% of the long-term site mean. The historical irradiance products were compared against Met Office station data from the input years of each product. This investigation has found that all products perform well. No products have a strong spatial trend. Meteonorm 7 is most conservative (MBE = −2.5%), CMSAF is most optimistic (MBE = +3.4%) and an average of all four products performs better than any one individual product (MBE = 0.3%)

The only way is up: retail format saturation and the demise of the American five and dime store, 1914-1941

We examine a classic ‘wheel of retailing’ episode – the abandonment of the five and dime pricing formula by American variety chains. These switched from a conventional product lifecycle, focusing on cost reduction through standardisation, to a reverse path up the ‘service cost - unit value’ continuum. We show that, rather than reflecting deteriorating managerial acumen, this was a response to the continued imperative for growth following retail format saturation. Firm-specific (rather than format-specific) competitive advantages were too weak for any chain to be confident it could win a within-format price war, making inter-format competition through raising price points more attractive.

Downwelling solar irradiance in the biomass burning region of the southern Amazon: Dependence on aerosol intensive optical properties and role of water vapor

The sensitivity of solar irradiance at the surface to the variability of aerosol intensive optical properties is investigated for a site (Alta Floresta) in the southern portion of the Amazon basin using detailed comparisons between measured and modeled irradiances. Apart from aerosol intensive optical properties, specifically single scattering albedo (omega(o lambda)) and asymmetry parameter (g(lambda)), which were assumed constant, all other relevant input to the model were prescribed based on observation. For clean conditions, the differences between observed and modeled irradiances were consistent with instrumental uncertainty. For polluted conditions, the agreement was significantly worse, with a root mean square difference three times larger (23.5 Wm(-2)). Analysis revealed a noteworthy correlation between the irradiance differences (observed minus modeled) and the column water vapor (CWV) for polluted conditions. Positive differences occurred mostly in wet conditions, while the differences became more negative as the atmosphere dried. To explore the hypothesis that the irradiance differences might be linked to the modulation of omega(o lambda) and g(lambda) by humidity, AERONET retrievals of aerosol properties and CWV over the same site were analyzed. The results highlight the potential role of humidity in modifying omega(o lambda) and g(lambda) and suggest that to explain the relationship seen between irradiances differences via aerosols properties the focus has to be on humidity-dependent processes that affect particles chemical composition. Undoubtedly, there is a need to better understand the role of humidity in modifying the properties of smoke aerosols in the southern portion of the Amazon basin.

Life-history, thallus ontogeny, and the effects of temperature, irradiance and salinity on growth of the edible green seaweed Gayralia spp. (Chlorophyta) from Southern Brazil

Gayralia K.L. Vinogr. is a monostromatic green alga of commercial importance in the southern Brazil, and its cultivation is being considered. This paper reports some basic aspects of the biology of this poorly known genus. Two populations of Gayralia spp., from outer and inner sectors of Paranagua Bay, showed an asexual life history with a distinct pattern of thallus ontogeny. In one population (Gayralia sp. 1), zooids developed an expanded monostromatic blade directly, while in the other (Gayralia sp. 2) zooids produced an intermediate saccate stage, before giving rise to a monostromatic blade. Thalli of the two species differ in size and in cell diameter. The effects of temperature (16-30 degrees C), irradiance (50-100 mu mol photons m(-2) s(-1)), and salinity (5-40 psu) on the growth of both populations were assessed. Plantlets of Gayralia sp. 1 from in vitro cultures showed a broader tolerance to all salinity and irradiance levels tested, with the highest growth rate (GR; mean 17% day-1) at 21.5 degrees C and 100 mu mol photons m(-2) s(-1). Plantlets of Gayralia sp. 1 collected during the winter in the field showed higher GR, ranging from 5% day(-1) to 7.5% day(-1) in salinities from 20 to 40 psu, and 2.0% day(-1) and 4.3% day(-1) for plantlets collected during the summer. Gayralia sp. 2 from the field showed highest GR at salinity of 15 psu. These results suggest distinct physiological responses of the two species, in accordance with their distribution: Gayralia sp. 2 is limited to the inner areas of the estuary, while Gayralia sp. 1 grows in outer areas, where salinity values are higher than 20 psu. These data indicate that Gayralia sp. 1 has a higher potential for aquaculture than Gayralia sp. 2 due to its larger thalli, higher GR, and wider tolerance to environmental variations.

GLUON SATURATION AND THE TOTAL PROTON-AIR CROSS SECTION

In this work we propose a simple model for the total proton-air cross section, which is an improvement of the minijet model with the inclusion of a window in the p(T)-spectrum associated to the saturation physics. Our approach introduces a natural cutoff for the perturbative calculations which modifies the energy behavior of this component. The saturated component is calculated with a dipole model. The results are compared with experimental cross sections measured in cosmic ray experiments.

GLUON SATURATION AND THE FROISSART BOUND: A SIMPLE APPROACH

At very high energies we expect that the hadronic cross sections satisfy the Froissart bound, which is a well-established property of the strong interactions. In this energy regime we also expect the formation of the Color Glass Condensate, characterized by gluon saturation and a typical momentum scale: the saturation scale Q(s). In this paper we show that if a saturation window exists between the nonperturbative and perturbative regimes of Quantum Chromodynamics (QCD), the total cross sections satisfy the Froissart bound. Furthermore, we show that our approach allows us to described the high energy experimental data on pp/p (p) over bar total cross sections.

Could saturation effects be visible in a future electron-ion collider?

We expect to observe parton saturation in a future electron-ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron-ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total. longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A and small Q(2), allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton Saturation. (C) 2008 Elsevier B.V. All rights reserved.

Spatial variations at different observational scales and the seasonal distributions of stream macroalgae in a Brazilian subtropical region

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variação sazonal da abundância de Ecballocystis pulvinata Bohlin em um riacho da região centro-sul do estado do Paraná

Seasonal variation of abundance of Ecballocystis pulvinata Bohlin in a stream of central-southern region of Parana State. The temporal dynamics of E. pulvinata and its relation to abiotic variables were evaluated monthly during January to December 2007 in a stream located in the central-southern part of Parana State (25 degrees 11'16 '' S - 51 degrees 021'25 '' W). The abundance of the population in terms of percentage cover was obtained by means of the quadrat technique and the following stream water variables were measured: current velocity, irradiance, depth, substrate type, temperature, oxygen saturation, conductivity, pH and turbidity. The abundance of E. pulvinata was considered high (X = 26.7%), with more development (22-46%) during autumn/winter. The low values (0-0.08) of niche width and the few associations with environmental variables shows that the population evaluated is a generalist with regards to the environment in which it occurs. Factors most strictly related were the water flow and the particle size of the substrate, which positively correlated to the seasonal pattern of the population investigated.

Effects of irradiance and spectral composition on the establishment of macroalgae in streams in southern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)