COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Robust tori-like Lagrangian coherent structures

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

Limit weierstrass points on nodal reducible curves

In the 1980s D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.

Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

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

Robust tori-like Lagrangian coherent structures

In general the term "Lagrangian coherent structure" (LCS) is used to make reference about structures whose properties are similar to a time-dependent analog of stable and unstable manifolds from a hyperbolic fixed point in Hamiltonian systems. Recently, the term LCS was used to describe a different type of structure, whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. A new kind of LCS was obtained. It consists of barriers, called robust tori that block the trajectories in certain regions of the phase space. We used the Double-Gyre Flow system as the model. In this system, the robust tori play the role of a skeleton for the dynamics and block, horizontally, vortices that come from different parts of the phase space. (C) 2012 Elsevier B.V. All rights reserved.

Bioelectrical impedance vector analysis (BIVA) in stable preterm newborns

Objective: To observe the behavior of the plotted vectors on the RXc (R - resistance - and Xc - reactance corrected for body height/length) graph through bioelectrical impedance analysis (BIVA) and phase angle (PA) values in stable premature infants, considering the hypothesis that preterm infants present vector behavior on BIVA suggestive of less total body water and soft tissues, compared to reference data for term infants. Methods: Cross-sectional study, including preterm neonates of both genders, in-patients admitted to an intermediate care unit at a tertiary care hospital. Data on delivery, diet and bioelectrical impedance (800 mA, 50 kHz) were collected. The graphs and vector analysis were performed with the BIVA software. Results: A total of 108 preterm infants were studied, separated according to age (< 7 days and >= 7 days). Most of the premature babies were without the normal range (above the 95% tolerance intervals) existing in literature for term newborn infants and there was a tendency to dispersion of the points in the upper right quadrant, RXc plan. The PA was 4.92 degrees (+/- 2.18) for newborns < 7 days and 4.34 degrees (+/- 2.37) for newborns >= 7 days. Conclusion: Premature infants behave similarly in terms of BIVA and most of them have less absolute body water, presenting less fat free mass and fat mass in absolute values, compared to term newborn infants.

Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.

Exploring physical processes related to past climate proxies: lake sediments and stable water isotopes

Proxy data are essential for the investigation of climate variability on time scales larger than the historical meteorological observation period. The potential value of a proxy depends on our ability to understand and quantify the physical processes that relate the corresponding climate parameter and the signal in the proxy archive. These processes can be explored under present-day conditions. In this thesis, both statistical and physical models are applied for their analysis, focusing on two specific types of proxies, lake sediment data and stable water isotopes.rnIn the first part of this work, the basis is established for statistically calibrating new proxies from lake sediments in western Germany. A comprehensive meteorological and hydrological data set is compiled and statistically analyzed. In this way, meteorological times series are identified that can be applied for the calibration of various climate proxies. A particular focus is laid on the investigation of extreme weather events, which have rarely been the objective of paleoclimate reconstructions so far. Subsequently, a concrete example of a proxy calibration is presented. Maxima in the quartz grain concentration from a lake sediment core are compared to recent windstorms. The latter are identified from the meteorological data with the help of a newly developed windstorm index, combining local measurements and reanalysis data. The statistical significance of the correlation between extreme windstorms and signals in the sediment is verified with the help of a Monte Carlo method. This correlation is fundamental for employing lake sediment data as a new proxy to reconstruct windstorm records of the geological past.rnThe second part of this thesis deals with the analysis and simulation of stable water isotopes in atmospheric vapor on daily time scales. In this way, a better understanding of the physical processes determining these isotope ratios can be obtained, which is an important prerequisite for the interpretation of isotope data from ice cores and the reconstruction of past temperature. In particular, the focus here is on the deuterium excess and its relation to the environmental conditions during evaporation of water from the ocean. As a basis for the diagnostic analysis and for evaluating the simulations, isotope measurements from Rehovot (Israel) are used, provided by the Weizmann Institute of Science. First, a Lagrangian moisture source diagnostic is employed in order to establish quantitative linkages between the measurements and the evaporation conditions of the vapor (and thus to calibrate the isotope signal). A strong negative correlation between relative humidity in the source regions and measured deuterium excess is found. On the contrary, sea surface temperature in the evaporation regions does not correlate well with deuterium excess. Although requiring confirmation by isotope data from different regions and longer time scales, this weak correlation might be of major importance for the reconstruction of moisture source temperatures from ice core data. Second, the Lagrangian source diagnostic is combined with a Craig-Gordon fractionation parameterization for the identified evaporation events in order to simulate the isotope ratios at Rehovot. In this way, the Craig-Gordon model can be directly evaluated with atmospheric isotope data, and better constraints for uncertain model parameters can be obtained. A comparison of the simulated deuterium excess with the measurements reveals that a much better agreement can be achieved using a wind speed independent formulation of the non-equilibrium fractionation factor instead of the classical parameterization introduced by Merlivat and Jouzel, which is widely applied in isotope GCMs. Finally, the first steps of the implementation of water isotope physics in the limited-area COSMO model are described, and an approach is outlined that allows to compare simulated isotope ratios to measurements in an event-based manner by using a water tagging technique. The good agreement between model results from several case studies and measurements at Rehovot demonstrates the applicability of the approach. Because the model can be run with high, potentially cloud-resolving spatial resolution, and because it contains sophisticated parameterizations of many atmospheric processes, a complete implementation of isotope physics will allow detailed, process-oriented studies of the complex variability of stable isotopes in atmospheric waters in future research.rn

A Stable Niche Assumption-Free Test of Ecological Divergence

Understanding the impact of geological events on diversification processes is central to evolutionary ecology. The recent amalgamation between ecological niche models (ENMs) and phylogenetic analyses has been used to estimate historical ranges of modern lineages by projecting current ecological niches of organisms onto paleoclimatic reconstructions. A critical assumption underlying this approach is that niches are stable over time. Using Notophthalmus viridescens (eastern newt), in which four ecologically diverged subspecies are recognized, we introduce an analytical framework free from the niche stability assumption to examine how refugial retreat and subsequent postglacial expansion have affected intraspecific ecological divergence. We found that the current subspecies designation was not congruent with the phylogenetic lineages. Thus, we examined ecological niche overlap between the refugial and modern populations, in both subspecies and lineage, by creating ENMs independently for modern and estimated last glacial maximum (LGM) newt populations, extracting bioclimate variables by randomly generated points, and conducting principal component analyses. Our analyses consistently showed that when tested as a hypothesis, rather than used as an assumption, the niches of N. viridescens lineages have been unstable since the LGM (both subspecies and lineages). There was greater ecological niche differentiation among the subspecies than the modern phylogenetic lineages, suggesting that the subspecies, rather than the phylogenetic lineages, is the unit of the current ecological divergence. The present study found little evidence that the LGM refugial retreat caused the currently observed ecological divergence and suggests that ecological divergence has occurred during postglacial expansion to the current distribution ranges.

Stable virulence levels in the HIV epidemic of Switzerland over two decades

OBJECTIVE: To determine whether the virulence of HIV-1 has been changing since its introduction into Switzerland. DESIGN: A prospective cohort study of HIV-1 infected individuals with well-characterized pre-therapy disease history. METHODS: To minimize the effect of recently imported viruses and ethnicity-associated host factors, the analysis was restricted to the white, north-west-European majority population of the cohort. Virulence was characterized by the decline slope of the CD4 cell count (n = 817 patients), the decline slope of the CD4:CD8 ratio (n = 815 patients) and the viral setpoint (n = 549 patients) in untreated patients with sufficient data points. Linear regression models were used to detect correlations between the date of diagnosis (ranging between 1984 and 2003) and the virulence markers, controlling for gender, exposure category, age and CD4 cell count at entry. RESULTS: We found no correlation between any of the virulence markers and the date of diagnosis. Inspection of short-term trends confirmed that virulence has fluctuated around a stable level over time. CONCLUSIONS: The lack of long-term time trends in the virulence markers indicates that HIV-1 is not evolving towards increasing or decreasing virulence at a perceptible rate. Both highly virulent and attenuated strains have apparently been unable to spread at the population level. This result suggests that either the evolution of virulence may be slow or inhibited due to evolutionary constraints, or HIV-1 may have already evolved to optimal virulence in the human host.

Social stratigraphy in Late Iron Age Switzerland: Stable carbon, nitrogen and sulphur isotope analysis of human remains from Münsingen

The Iron Age cemetery of Münsingen in Switzerland with 220 abundantly equipped burials marked a milestone for Iron Age research. The horizontal spread throughout the time of its occupancy laid the foundation for the chronology system of the Late Iron Age. Today, skulls of 77 individuals and some postcranial bones are still preserved. The aim of the study was to obtain information about diet, mobility and social stratification of the individuals. Stable isotope ratios of carbon, nitrogen and sulphur were analysed for 63 individuals. For all of them C3 plants were found to be the staple food. There are significant differences between males and females in δ13C and δ15N values. This points to a gender restriction in the access to animal protein with males probably having more access to meat and dairy products. Differences in δ15N values were also observed for different age classes. δ34S values indicate a terrestrial-based diet with no significant intake of marine or freshwater fish. Seven adults with enriched δ34S values might have immigrated to Münsingen, four of which were found in the oldest part of the cemetery. Furthermore, possible changes of the vegetation are indicated by the more positive stable carbon ratios in the later phases. The results lead to the suggestion that especially males buried with weapons might have played a special role in the Iron Age society.

Long-term summer temperature variations in the Pyrenees from detrended stable carbon isotopes

Substantial effort has recently been put into the development of climate reconstructions from tree-ring stable carbon isotopes, though the interpretation of long-term trends retained in such timeseries remains challenging. Here we use detrended δ13C measurements in Pinus uncinata tree-rings, from the Spanish Pyrenees, to reconstruct decadal variations in summer temperature back to the 13th century. The June-August temperature signal of this reconstruction is attributed using decadally as well as annually resolved, 20th century δ13C data. Results indicate that late 20th century warming has not been unique within the context of the past 750 years. Our reconstruction contains greater am-plitude than previous reconstructions derived from traditional tree-ring density data, and describes particularly cool conditions during the late 19th century. Some of these differences, including early warm periods in the 14th and 17th centuries, have been retained via δ13C timeseries detrending - a novel approach in tree-ring stable isotope chronology development. The overall reduced variance in earlier studies points to an underestimation of pre-instrumental summer temperature variability de-rived from traditional tree-ring parameters.