Effects of allometry, productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade's evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.

Operating models for a multi-polar world: balancing global integration and local responsiveness

Purpose – Multinationals have always needed an operating model that works – an effective plan for executing their most important activities at the right levels of their organization, whether globally, regionally or locally. The choices involved in these decisions have never been obvious, since international firms have consistently faced trade‐offs between tailoring approaches for diverse local markets and leveraging their global scale. This paper seeks a more in‐depth understanding of how successful firms manage the global‐local trade‐off in a multipolar world. Design methodology/approach – This paper utilizes a case study approach based on in‐depth senior executive interviews at several telecommunications companies including Tata Communications. The interviews probed the operating models of the companies we studied, focusing on their approaches to organization structure, management processes, management technologies (including information technology (IT)) and people/talent. Findings – Successful companies balance global‐local trade‐offs by taking a flexible and tailored approach toward their operating‐model decisions. The paper finds that successful companies, including Tata Communications, which is profiled in‐depth, are breaking up the global‐local conundrum into a set of more manageable strategic problems – what the authors call “pressure points” – which they identify by assessing their most important activities and capabilities and determining the global and local challenges associated with them. They then design a different operating model solution for each pressure point, and repeat this process as new strategic developments emerge. By doing so they not only enhance their agility, but they also continually calibrate that crucial balance between global efficiency and local responsiveness. Originality/value – This paper takes a unique approach to operating model design, finding that an operating model is better viewed as several distinct solutions to specific “pressure points” rather than a single and inflexible model that addresses all challenges equally. Now more than ever, developing the right operating model is at the top of multinational executives' priorities, and an area of increasing concern; the international business arena has changed drastically, requiring thoughtfulness and flexibility instead of standard formulas for operating internationally. Old adages like “think global and act local” no longer provide the universal guidance they once seemed to.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Mathematical relationships between scoring parameters in capped tendering

Mathematical relationships between Scoring Parameters can be used in Economic Scoring Formulas (ESF) in tendering to distribute the score among bidders in the economic part of a proposal. Each contracting authority must set an ESF when publishing tender specifications and the strategy of each bidder will differ depending on the ESF selected and the weight of the overall proposal scoring. This paper introduces the various mathematical relationships and density distributions that describe and inter-relate not only the main Scoring Parameters but the main Forecasting Parameters in any capped tender (those whose price is upper-limited). Forecasting Parameters, as variables that can be known in advance before the deadline of a tender is reached, together with Scoring Parameters constitute the basis of a future Bid Tender Forecasting Model.

On competitive bidding: scoring and position probability graphs

Iso-score curves graph (iSCG) and mathematical relationships between Scoring Parameters (SP) and Forecasting Parameters (FP) can be used in Economic Scoring Formulas (ESF) used in tendering to distribute the score among bidders in the economic part of a proposal. Each contracting authority must set an ESF when publishing tender specifications and the strategy of each bidder will differ depending on the ESF selected and the weight of the overall proposal scoring. The various mathematical relationships and density distributions that describe the main SPs and FPs, and the representation of tendering data by means of iSCGs, enable the generation of two new types of graphs that can be very useful for bidders who want to be more competitive: the scoring and position probability graphs.

On the parameterization of turbulent surface fluxes over heterogeneous sea ice surfaces

Turbulent surface fluxes of momentum and sensible and latent heat as well as surface temperature, air temperature, air humidity, and wind speed were measured by the German Falcon research aircraft over the marginal ice zone (MIZ) of the northern Baltic Sea and the Fram Strait. Applying the bulk formulas and the stability functions to the measurements, the roughness lengths for momentum z0, sensible heat zT, and latent heat zq were calculated. As mean values over a wide range of sea ice conditions, we obtain z0 = 5 � 10�4 m, zT = 1 � 10�8 m, and zq = 1 � 10�7 m. These correspond to the following mean values (± standard deviations) of neutral transfer coefficients reduced to 10 m height, CDN10 = (1.9 ± 0.8) � 10�3, CHN10 = (0.9 ± 0.3) � 10�3, and CEN10 = (1.0 ± 0.2) � 10�3. An average ratio of z0/zT � 104 was observed over the range of 10�6 m < z0 < 10�2 m and differs from previously published results over compact sea ice (10�1 < z0/zT < 103). Other observational results over heterogeneous sea ice do not exist. However, our z0/zT ratio approximately agrees with observations over heterogeneous land surfaces. Flux parameterizations based on commonly used roughness lengths ratios (z0 = zT = zq) overestimate the surface heat fluxes compared to our measurements by more than 100%.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

Comparison of properties of native and extruded amaranth (Amaranthus cruentus L. - BRS Alegria) flour

The aim of this study was to compare some of the properties of native and extruded amaranth flour obtained under mild and severe extrusion conditions. The chemical composition of the flours was similar. Flours obtained by both extrusion processes presented high solubility in water, low values of L* (luminosity) and an absence of endothermic peak on the DSC method. Water absorption, retrogradation tendency, final viscosity and the viscous behavior by rheology analysis were also studied. The results indicate that extruded flours have a good potential as an ingredient for food exposed to heat treatment at a high temperature and mechanical shear, for use in instant meal products. On the other hand, original flour properties are comparable to those of amaranth starch, which exhibits similarly high quality paste stability, low solubility in water, and elastic behavior, and could be used as a substitute for raw flour in a range of food formulas. (C) 2011 Elsevier Ltd. All rights reserved.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

Can retired galaxies mimic active galaxies? Clues from the Sloan Digital Sky Survey

The classification of galaxies as star forming or active is generally done in the ([O III]/H beta, [N II]/H alpha) plane. The Sloan Digital Sky Survey (SDSS) has revealed that, in this plane, the distribution of galaxies looks like the two wings of a seagull. Galaxies in the right wing are referred to as Seyfert/LINERs, leading to the idea that non-stellar activity in galaxies is a very common phenomenon. Here, we argue that a large fraction of the systems in the right wing could actually be galaxies which stopped forming stars. The ionization in these `retired` galaxies would be produced by hot post-asymptotic giant branch stars and white dwarfs. Our argumentation is based on a stellar population analysis of the galaxies via our STARLIGHT code and on photoionization models using the Lyman continuum radiation predicted for this population. The proportion of LINER galaxies that can be explained in such a way is, however, uncertain. We further show how observational selection effects account for the shape of the right wing. Our study suggests that nuclear activity may not be as common as thought. If retired galaxies do explain a large part of the seagull`s right wing, some of the work concerning nuclear activity in galaxies, as inferred from SDSS data, will have to be revised.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Discovery of two distinct red clumps in NGC 419: a rare snapshot of a cluster at the onset of degeneracy

Colour-magnitude diagrams (CMDs) of the Small Magellanic Cloud (SMC) star cluster NGC 419, derived from Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS) data, reveal a well-delineated secondary clump located below the classical compact red clump typical of intermediate-age populations. We demonstrate that this feature belongs to the cluster itself, rather than to the underlying SMC field. Then, we use synthetic CMDs to show that it corresponds very well to the secondary clump predicted to appear as a result of He-ignition in stars just massive enough to avoid e(-)-degeneracy settling in their H-exhausted cores. The main red clump instead is made of the slightly less massive stars which passed through e(-) degeneracy and ignited He at the tip of the red giant branch. In other words, NGC 419 is the rare snapshot of a cluster while undergoing the fast transition from classical to degenerate H-exhausted cores. At this particular moment of a cluster`s life, the colour distance between the main-sequence turn-off and the red clump(s) depends sensitively on the amount of convective core overshooting, Lambda(c). By coupling measurements of this colour separation with fits to the red clump morphology, we are able to estimate simultaneously the cluster mean age (1.35(-0.04)(+0.11) Gyr) and overshooting efficiency (Lambda(c) = 0.47(-0.04)(+0.14)). Therefore, clusters like NGC 419 may constitute important marks in the age scale of intermediate-age populations. After eye inspection of other CMDs derived from HST/ACS data, we suggest that the same secondary clump may also be present in the Large Magellanic Cloud clusters NGC 1751, 1783, 1806, 1846, 1852 and 1917.

A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS

In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form u(tt) + beta(t)u(t) - Delta u + f(u) (1) in a bounded smooth domain Omega subset of R(n) with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping beta : R -> (0, infinity) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of nonautonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.