Choreographic Three Bodies on the Lemniscate

We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic functions sn and cn with modulus k^2 = (2+sqrt{3})/4, conserve the center of mass and the angular momentum, where x-hat and y-hat are the orthogonal unit vectors defining the plane of the motion. They also conserve the moment of inertia, the kinetic energy, the sum of square of the curvature, the product of distance and the sum of square of distance between bodies. We find that they satisfy the equation of motion under the potential energy sum_{i<j}(1/2 ln r_{ij} -sqrt{3}/24 r_{ij}^2) or sum_{i<j}1/2 ln r_{ij} -sum_{i}sqrt{3}/8 r_{i}^2, where r_{ij} the distance between the body i and j, and r_{i} the distance from the origin. The first term of the potential energies is the Newton's gravity in two dimensions but the second term is the mutual repulsive force or a repulsive force from the origin, respectively. Then, geometric construction methods for the positions of the choreographic three bodies are given

Generic Twistless Bifurcations

We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this bifurcation, the twist, which is the derivative of the rotation number with respect to the action, vanishes. The twistless torus moves outward after it is created, and eventually collides with the saddle-center bifurcation that creates the period three orbits. The existence of the twistless bifurcation is responsible for the breakdown of the nondegeneracy condition required in the proof of the KAM theorem for flows or the Moser twist theorem for maps. When the twistless torus has a rational rotation number, there are typically reconnection bifurcations of periodic orbits with that rotation number.Comment: 29 pages, 9 figure

Light-driven cycling of dimethylsulfide (DMS) in the Sargasso Sea : closing the loop

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 31 (2004): L09308, doi:10.1029/2004GL019581.The factors driving dimethylsulfide (DMS) cycling in oligotrophic environments are isolated using a time-series of DMS sampled in the Sargasso Sea. The observed distribution of DMS is inconsistent with bottom-up processes related to phytoplankton production, biomass, or community structure changes. DMS concentrations and estimates of net biological community production are most highly correlated with physical and optical properties, with the dose of ultraviolet radiation (UVR) accounting for 77% of the variability in mixed layer DMS concentrations. Physiological stresses associated with shallow mixed layers and high UVR are the first order determinant of biological production of DMS, indicating that DMS cycling in open-ocean regions is fundamentally different than in eutrophic regions where phytoplankton blooms provide the conditions for elevated DMS concentrations. The stress regime presented here effectively closes the DMS-climate feedback loop for open-ocean environments. This response may also provide a climatic role for phytoplanktonic processes in response to anthropogenic forcing.This work was supported by a NASA Earth System Science Fellowship

L'Ecostratigrafia i la seva problemàtica

This is a brief analysis about ecostratigraphy, based on bibliographical as well as personal inquiries on the subject

Measuring the mixing efficiency in a simple model of stirring:some analytical results and a quantitative study via Frequency Map Analysis

We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing.Comment: 10 figure

Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio

We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt{2}-1$. We show that the Poincar\'e-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisfies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon$, generalizing the results previously known for the golden number.Comment: 17 pages, 2 figure

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows

Dieta de la viuda negra, <i>Latrodectus mirabilis</i> (Theridiidae) en dos cultivos de cereales del centro de Argentina

The spider Latrodectus mirabilis (Holmberg, 1876) is commonly found in cereals crops of central Argentina. We studied its diet composition at the field and capture rate on leaf-cutting ants based on laboratory experiments. This study comprises the first approach that documents the diet of L. mirabilis in wheat and oat fields of central Argentina. We identified 1,004 prey items collected from its webs during the last phenological stages of both cereal crops. The prey composition was variable but the spiders prey mainly on ants (Formicidae, Hymenoptera), who represented more than 86% of the total. Meanwhile, in the capture rate experiences we registered a high proportion of ants captured by spiders at the beginning of experiences, capturing the half of the ants from total in the first four hours. Summarizing, we reported a polyphagous diet of this spider species in wheat and oat fields. Ants were the most important prey item of this spider, as found in other Latrodectus spiders around the world.La araña Latrodectus mirabilis (Holmberg, 1876) se encuentra comúnmente en cultivos de cereales del centro de Argentina. Se estudió la composición de la dieta a campo y la tasa de captura sobre hormigas cortadoras negras a laboratorio. Este estudio documenta el primer registro de la dieta de L. mirabilis en cultivos de trigo y avena del centro de Argentina. Se identificaron 1004 ítem presa colectados de las telas de L. mirabilis en las últimas etapas fenológicas de ambos cultivos. La composición de presas fue variable, pero las arañas se alimentaron principalmente de hormigas (Formicidae, Hymenoptera), las cuales representaban más del 86% del total de las presas capturadas. A su vez, en las experiencias de tasa de captura, registramos una alta tasa de captura de hormigas al inicio de las mismas, capturando la mitad de las hormigas en las primeras cuatro horas. En resumen, reportamos una dieta polífaga en esta especie de araña en los cultivos de trigo y avena. El ítem presa más importante fueron las hormigas, resultados similares a los encontrados en otras especies del género Latrodectus.Centro de Estudios Parasitológicos y de Vectore

Dieta de la viuda negra, <i>Latrodectus mirabilis</i> (Theridiidae) en dos cultivos de cereales del centro de Argentina

The spider Latrodectus mirabilis (Holmberg, 1876) is commonly found in cereals crops of central Argentina. We studied its diet composition at the field and capture rate on leaf-cutting ants based on laboratory experiments. This study comprises the first approach that documents the diet of L. mirabilis in wheat and oat fields of central Argentina. We identified 1,004 prey items collected from its webs during the last phenological stages of both cereal crops. The prey composition was variable but the spiders prey mainly on ants (Formicidae, Hymenoptera), who represented more than 86% of the total. Meanwhile, in the capture rate experiences we registered a high proportion of ants captured by spiders at the beginning of experiences, capturing the half of the ants from total in the first four hours. Summarizing, we reported a polyphagous diet of this spider species in wheat and oat fields. Ants were the most important prey item of this spider, as found in other Latrodectus spiders around the world.La araña Latrodectus mirabilis (Holmberg, 1876) se encuentra comúnmente en cultivos de cereales del centro de Argentina. Se estudió la composición de la dieta a campo y la tasa de captura sobre hormigas cortadoras negras a laboratorio. Este estudio documenta el primer registro de la dieta de L. mirabilis en cultivos de trigo y avena del centro de Argentina. Se identificaron 1004 ítem presa colectados de las telas de L. mirabilis en las últimas etapas fenológicas de ambos cultivos. La composición de presas fue variable, pero las arañas se alimentaron principalmente de hormigas (Formicidae, Hymenoptera), las cuales representaban más del 86% del total de las presas capturadas. A su vez, en las experiencias de tasa de captura, registramos una alta tasa de captura de hormigas al inicio de las mismas, capturando la mitad de las hormigas en las primeras cuatro horas. En resumen, reportamos una dieta polífaga en esta especie de araña en los cultivos de trigo y avena. El ítem presa más importante fueron las hormigas, resultados similares a los encontrados en otras especies del género Latrodectus.Centro de Estudios Parasitológicos y de Vectore