Moller operators and Lippmann-Schwinger equations for step-like potentials

The Moller operators and the asociated Lippman-Schwinger equations obtained from different partitionings of the Hamiltonian for a step-like potential barrier are worked out, compared and related.Comment: 15 pages, 1 inlined figure, iopart.cl

Incorporating the geometry of dispersal and migration to understand spatial patterns of species distributions

Dispersal and migration can be important drivers of species distributions. Because the paths followed by individuals of many species are curvilinear, spatial statistical models based on rectilinear coordinates systems would fail to predict population connectivity or the ecological consequences of migration or species invasions. I propose that we view migration/dispersal as if organisms were moving along curvilinear geometrical objects called smooth manifolds. In that view, the curvilinear pathways become the ‘shortest realised paths’ arising from the necessity to minimise mortality risks and energy costs. One can then define curvilinear coordinate systems on such manifolds. I describe a procedure to incorporate manifolds and define appropriate coordinate systems, with focus on trajectories (1D manifolds), as parts of mechanistic ecological models. I show how a statistical method, known as ‘manifold learning’, enables one to define the manifold and the appropriate coordinate systems needed to calculate population connectivity or study the effects of migrations (e.g. in aquatic invertebrates, fish, insects and birds). This approach may help in the design of networks of protected areas, in studying the consequences of invasion, range expansions, or transfer of parasites/diseases. Overall, a geometrical view to animal movement gives a novel perspective to the understanding of the ecological role of dispersal and migration

Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence

This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEstOE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Phytoplankton dynamics in relation to seasonal variability and upwelling and relaxation patterns at the mouth of Ria de Aveiro (West Iberian Margin) over a four-year period

From June 2004 to December 2007, samples were weekly collected at a fixed station located at the mouth of Ria de Aveiro (West Iberian Margin). We examined the seasonal and inter-annual fluctuations in composition and community structure of the phytoplankton in relation to the main environmental drivers and assessed the influence of the oceano-graphic regime, namely changes in frequency and intensity of upwelling events, over the dynamics of the phytoplankton assemblage. The samples were consistently handled and a final subset of 136 OTUs (taxa with relative abundance > 0.01%) was subsequently submitted to various multivariate analyses. The phytoplankton assemblage showed significant changes at all temporal scales but with an overriding importance of seasonality over longer-(inter-annual) or shorter-term fluctuations (upwelling-related). Sea-surface temperature, salinity and maximum upwelling index were retrieved as the main driver of seasonal change. Seasonal signal was most evident in the fluctuations of chlorophyll a concentration and in the high turnover from the winter to spring phytoplankton assemblage. The seasonal cycle of production and succession was disturbed by upwelling events known to disrupt thermal stratification and induce changes in the phytoplankton assemblage. Our results indicate that both the frequency and intensity of physical forcing were important drivers of such variability, but the outcome in terms of species composition was highly dependent on the available local pool of species and the timing of those events in relation to the seasonal cycle. We conclude that duration, frequency and intensity of upwelling events, which vary seasonally and inter-annually, are paramount for maintaining long-term phytoplankton diversity likely by allowing unstable coexistence and incorporating species turnover at different scales. Our results contribute to the understanding of the complex mechanisms of coastal phytoplankton dynamics in relation to changing physical forcing which is fundamental to improve predictability of future prospects under climate change.Portuguese Foundation for Science and Technology (FCT, Portugal) [SFRH/BPD/ 94562/2013]; FEDER funds; national funds; CESAM [UID/AMB/50017]; FCT/MEC through national funds; FEDERinfo:eu-repo/semantics/publishedVersio

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

Vortices enable the complex aerobatics of peregrine falcons

The peregrine falcon (Falco peregrinus) is known for its extremely high speeds during hunting dives or stoop. Here we demonstrate that the superior manoeuvrability of peregrine falcons during stoop is attributed to vortex-dominated flow promoted by their morphology, in the M-shape configuration adopted towards the end of dive. Both experiments and simulations on life-size models, derived from field observations, revealed the presence of vortices emanating from the frontal and dorsal region due to a strong spanwise flow promoted by the forward sweep of the radiale. These vortices enhance mixing for flow reattachment towards the tail. The stronger wing and tail vortices provide extra aerodynamic forces through vortex-induced lift for pitch and roll control. A vortex pair with a sense of rotation opposite to that from conventional planar wings interacts with the main wings vortex to reduce induced drag, which would otherwise decelerate the bird significantly during pull-out. These findings could help in improving aircraft performance and wing suits for human flights

Measurement of the Branching Fraction for B- --> D0 K*-

We present a measurement of the branching fraction for the decay B- --> D0 K*- using a sample of approximately 86 million BBbar pairs collected by the BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the K*- through its decay to K0S pi-. We measure the branching fraction to be B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}.Comment: 7 pages, 1 postscript figure, submitted to Phys. Rev. D (Rapid Communications

Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions

The weak nucleon axial-vector form factor for quasi-elastic interactions is determined using neutrino interaction data from the K2K Scintillating Fiber detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of which half are charged-current quasi-elastic interactions nu-mu n to mu- p occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for oxygen and assume the form factor is approximately a dipole with one parameter, the axial vector mass M_A, and fit to the shape of the distribution of the square of the momentum transfer from the nucleon to the nucleus. Our best fit result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated vector form factors from recent electron scattering experiments and a discussion of the effects of the nucleon momentum on the shape of the fitted distributions.Comment: 14 pages, 10 figures, 6 table