Mean Curvature Flow of Spacelike Graphs

We prove the mean curvature flow of a spacelike graph in $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\Sigma_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\leq K_1$, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption $K_2\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\leq -c$, $c>0$ constant, any map $f:\Sigma_1\to \Sigma_2$ is trivially homotopic provided $f^*g_2<\rho g_1$ where $\rho=\min_{\Sigma_1}K_1/\sup_{\Sigma_2}K_2^+\geq 0$, in case $K_1>0$, and $\rho=+\infty$ in case $K_2\leq 0$. This largely extends some known results for $K_i$ constant and $\Sigma_2$ compact, obtained using the Riemannian structure of $\Sigma_1\times \Sigma_2$, and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo-Riemannian setting then in the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one. We add an applicatio

Dynamics of the giant planets of the solar system in the gaseous proto-planetary disk and relationship to the current orbital architecture

We study the orbital evolution of the 4 giant planets of our solar system in a gas disk. Our investigation extends the previous works by Masset and Snellgrove (2001) and Morbidelli and Crida (2007, MC07), which focussed on the dynamics of the Jupiter-Saturn system. The only systems that we found to reach a steady state are those in which the planets are locked in a quadruple mean motion resonance (i.e. each planet is in resonance with its neighbor). In total we found 6 such configurations. For the gas disk parameters found in MC07, these configurations are characterized by a negligible migration rate. After the disappearance of the gas, and in absence of planetesimals, only two of these six configurations (the least compact ones) are stable for a time of hundreds of millions of years or more. The others become unstable on a timescale of a few My. Our preliminary simulations show that, when a planetesimal disk is added beyond the orbit of the outermost planet, the planets can evolve from the most stable of these configurations to their current orbits in a fashion qualitatively similar to that described in Tsiganis et al. (2005).Comment: The Astronomical Journal (17/07/2007) in pres

Functional kernel estimators of conditional extreme quantiles

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed kernel estimators. A Weissman-type estimator and kernel estimators of the conditional tail-index are derived, permitting to estimate extreme conditional quantiles of arbitrary order.Comment: arXiv admin note: text overlap with arXiv:1107.226

Effective models of quantum gravity induced by Planck scale modifications in the covariant quantum algebra

In this paper we introduce a modified covariant quantum algebra based in the so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive at a class of higher derivative models of gravity. The study of the particle spectra of these models reveals an equivalence with the physical content of the well-known renormalizable and super-renormalizable higher derivative gravities. The particle spectrum exhibits the presence of spurious complex ghosts and, in light of this problem, we suggest an interesting interpretation in the context of minimal length theories. Also, a discussion regarding the non-relativistic potential energy is proposed.Comment: Small corrections were made; improved figures; results unchanged; published versio

Reaction of potato cultivars to Meloidogyne Hapla and M. Morocciensis.

Edição dos Proceedings do 6th International Congress of Nematology, Cape Town, South Africa, May 2014

Structural properties of crumpled cream layers

The cream layer is a complex heterogeneous material of biological origin which forms spontaneously at the air-milk interface. Here, it is studied the crumpling of a single cream layer packing under its own weight at room temperature in three-dimensional space. The structure obtained in these circumstances has low volume fraction and anomalous fractal dimensions. Direct means and noninvasive NMR imaging technique are used to investigate the internal and external structure of these systems.Comment: 9 pages, 4 figures, accepted in J. Phys. D: Appl. Phy

Planning a sustainable reverse logistics system: balancing costs with environmental and social concerns

The present work aims to support tactical and operational planning decisions of reverse logistics systems while considering economical, environmental and social objectives. In the literature, when addressing such systems economical aspects have been often used, while environmental concerns have been only recently emerging. The social component is the one less studied, and rarely the combination of the three concerns has been analyzed. This work address the three objectives and was motivated by the challenge of supporting decisions makers when managing a real case study of a recyclable waste collection system, where strategic decisions on the number and location of depots, vehicles and containers were taken beforehand. Tactical and operational decisions are studied involving the establishment of service areas for each depot and the definition and scheduling of collection routes for each vehicle. Such decisions should represent a compromise solution between the three objectives considered and support a sustainable reverse logistics plan. A multi-objective solution approach based on mixed-integer linear programming models is developed. Trade-offs between the objectives are discussed. Moreover the solutions obtained when each objective is tackled individually are compared between themselves and with the balanced solution.info:eu-repo/semantics/publishedVersio

Economic and environmental concerns in planning recyclable waste collection systems

This paper addresses the planning of recyclable waste collection systems while accounting for economic and environmental concerns. Service areas and vehicle routes are defined for multiple-depot logistics networks where different products have to be collected. The problem is modeled as a multi-product, multi-depot vehicle routing problem with two objective functions: distance and CO2 emissions minimization. A decomposition solution method is developed and applied to a real case-study. Six scenarios are studied regarding different service areas configuration and different objective functions. Savings up to 22% in distance and 27% in CO2 emissions are achieved, excelling economical and environmental goals.info:eu-repo/semantics/publishedVersio

T-Duality in 2-D Integrable Models

The non-conformal analog of abelian T-duality transformations relating pairs of axial and vector integrable models from the non abelian affine Toda family is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear in J. Phys.