Periodic orbits in tall laterally heated rectangular cavities

This study elucidates the origin of the multiplicity of stable oscillatory flows detected by time integration in tall rectangular cavities heated from the side. By using continuation techniques for periodic orbits, it is shown that initially unstable branches, arising at Hopf bifurcations of the basic steady flow, become stable after crossing Neimark-Sacker points. There are no saddle-node or pitchfork bifurcations of periodic orbits, which could have been alternative mechanisms of stabilization. According to the symmetries of the system, the orbits are either fixed cycles, which retain at any time the center symmetry of the steady flow, or symmetric cycles involving a time shift in the global invariance of the orbit. The bifurcation points along the branches of periodic flows are determined. By using time integrations, with unstable periodic solutions as initial conditions, we determine which of the bifurcations at the limits of the intervals of stable periodic orbits are sub- or supercritical.Postprint (author's final draft

A case of modular phenotypic plasticity in the depth gradient for the gorgonian coral Antillogorgia bipinnata (Cnidaria: Octocorallia)

Background: Phenotypic plasticity, as a phenotypic response induced by the environment, has been proposed as a key factor in the evolutionary history of corals. A significant number of octocoral species show high phenotypic variation, exhibiting a strong overlap in intra- and inter-specific morphologic variation. This is the case of the gorgonian octocoral Antillogorgia bipinnata (Verrill 1864), which shows three polyphyletic morphotypes along a bathymetric gradient. This research tested the phenotypic plasticity of modular traits in A. bipinnata with a reciprocal transplant experiment involving 256 explants from two morphotypes in two locations and at two depths. Vertical and horizontal length and number of new branches were compared 13 weeks following transplant. The data were analysed with a linear mixed-effects model and a graphic approach by reaction norms. Results: At the end of the experiment, 91.8% of explants survived. Lower vertical and horizontal growth rates and lower branch promotion were found for deep environments compared to shallow environments. The overall variation behaved similarly to the performance of native transplants. In particular, promotion of new branches showed variance mainly due to a phenotypic plastic effect. Conclusions: Globally, environmental and genotypic effects explain the variation of the assessed traits. Survival rates besides plastic responses suggest an intermediate scenario between adaptive plasticity and local adaptation that may drive a potential process of adaptive divergence along depth cline in A. bipinnata

The Intensifiers this/that in Some Varieties of English

The intensifiers this/that acquired their adverbial status as a result of a grammaticalization process by means of which the deictic demonstratives became degree adverbs with the meaning of ‘to this/that extent, so much, so’ (OED s.v. this/that adv). The intensifier use of that has been traced back to the second half of the 14th century, originally associated with expressions of quantity like as much as that, as far as that, as long as that and eventually developing into proper degree words like that much, that far and that long, respectively. The use of this, on the other hand, developed in the second half of the 15th century. The phenomenon disseminated in the early 19th century as a typical resource of spoken English and since then, these intensifiers have found their room in the written domain imposing a scalar construal on adjectives for which scale is not the default construal. These intensifiers have been hitherto ignored in the literature, perhaps as a result of an erroneous accusation of informality, and consequently so has been traditionally recommended in these contexts. Despite the intensifiers this/that are observed in practically all the varieties of English worldwide, it has a variable distribution. The present study, therefore, contributes to the study of the development of these intensifiers in some varieties of English worldwide with the following objectives: a) to analyse their use and compare their distribution in different varieties of English; and b) to cast light on the lexico-semantic structure of the right-hand collocates. The evidence comes from the New Zealand, Indian, Singaporean and Philippines components of the Corpus of Global Web- based English. This corpus contains 1.9 billion words from 340,000 websites in 20 different English-speaking countries using a random selection of web pages and blogs, thus becoming the appropriate input for the study of the phenomenon in the varieties of English worldwide.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.Comment: 4 pages, 2 figures; you can also visit http://add.unizar.es/public/100_16613/index.htm

Are There Arbitrage Opportunities in Credit Derivatives Markets? A New Test and an Application to the Case of CDS and ASPs

This paper analyzes possible arbitrage opportunities in credit derivatives markets using selffinancing strategies combining Credit Default Swaps and Asset Swaps Packages. We present a new statistical arbitrage test based on the subsampling methodology which has lower Type I error than existing alternatives. Using four different databases covering the period from 2005 to 2009, long-run (cointegration) and statistical arbitrage analysis are performed. Before the subprime crisis, we find long-run arbitrage opportunities in 26% of the cases and statistical arbitrage opportunities in 24% of the cases. During the crisis, arbitrage opportunities decrease to 8% and 19%, respectively. Arbitrage opportunities are more frequent in the case of relatively low rated bonds and bonds with a high coupon rate

Torsional solutions of convection in rotating fluid spheres

A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small Pr. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time- and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for E=10-4 at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with Ra. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.Postprint (published version