Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of Alloying Elements on Thermal Diffusivity of Gray Cast Iron Used in Automotive Brake Disks

The purpose of this work was to experimentally investigate the thermal diffusivity of four different gray cast iron alloys, regularly used to produce brake disks for automotive vehicles. Thermal diffusivity measurements were performed at temperatures ranging from room temperature to 600 A degrees C. The influence of the thermal conductivity on the thermomechanical fatigue life is also briefly presented. The measurements were sensitive to the influence of the carbon equivalent and alloying elements, such as molybdenum, copper and chromium. Molybdenum, unlike copper, lowered the thermal diffusivity of the gray cast iron, and alloy E (without molybdenum), besides presenting a relatively low carbon equivalent content and an increase in the values of the thermal diffusivity, presented the best performance during the thermomechanical fatigue. The molybdenum present in alloys B and C did not fulfill the expectations of providing the best thermomechanical fatigue behavior. Consequently, its elimination in the gray cast iron alloy for this application will result in a significant economy.

The Cramer-Rao bound for initial conditions estimation of chaotic orbits

We derive the Cramer-Rao Lower Bound (CRLB) for the estimation of initial conditions of noise-embedded orbits produced by general one-dimensional maps. We relate this bound`s asymptotic behavior to the attractor`s Lyapunov number and show numerical examples. These results pave the way for more suitable choices for the chaotic signal generator in some chaotic digital communication systems. (c) 2006 Published by Elsevier Ltd.

Executive "brake failure" following deactivation of human frontal lobe

In the course of daily living, humans frequently encounter situations in which a motor activity, once initiated, becomes unnecessary or inappropriate. Under such circumstances, the ability to inhibit motor responses can be of vital importance. Although the nature of response inhibition has been studied in psychology for several decades, its neural basis remains unclear. Using transcranial magnetic stimulation, we found that temporary deactivation of the pars opercularis in the right inferior frontal gyrus selectively impairs the ability to stop an initiated action. Critically, deactivation of the same region did not affect the ability to execute responses, nor did it influence physiological arousal. These findings confirm and extend recent reports that the inferior frontal gyrus is vital for mediating response inhibition.

Homoclinic orbits and chaos in a multimode laser

We show experimentally that under certain conditions the chaotic intensity dynamics of an optically pumped NH3 bidirectional ring laser could be well described in terms of Shil'nikov homoclinic orbits and chaos. We found that the mechanism that resulted in this kind of dynamics of the laser is the competition between effects caused by the mode interaction between the forward and the backward modes of the laser and by the intrinsic single-mode dynamics of the interacting modes. (C) 1997 Optical Society of America.

Optimal brake specific fuel consumption trajectory for stand-alone variable speed Diesel Gen-Set

Energy efficiency plays an important role to the CO2 emissions reduction, combating climate change and improving the competitiveness of the economy. The problem presented here is related to the use of stand-alone diesel gen-sets and its high specific fuel consumptions when operates at low loads. The variable speed gen-set concept is explained as an energy-saving solution to improve this system efficiency. This paper details how an optimum fuel consumption trajectory based on experimentally Diesel engine power map is obtained.

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Periodic orbits in complex Abel equation

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

"Vegeu el resum a l'inici del document del fitxer adjunt."

A system to test the toxicity of brake wear particles

Fine particulate matter from traffic increases mortality and morbidity. An important source of traffic particles is brake wear. American studies reported cars to emit break wear particles at a rate of about 11mg/km to 20mg/km of driven distance. A German study estimated that break wear contributes about 12.5% to 21% of the total traffic particle emissions. The goal of this study was to build a system that allows the study of brake wear particle emissions during different braking behaviours of different car and brake types. The particles should be characterize in terms of size, number, metal, and elemental and organic carbon composition. In addition, the influence of different deceleration schemes on the particle composition and size distribution should be studied. Finally, this system should allow exposing human cell cultures to these particles. An exposure-box (0.25 cubic-m volume) was built that can be mounted around a car's braking system. This allows exposing cells to fresh brake wear particles. Concentrations of particle numbers, mass and surface, metals, and carbon compounds were quantified. Tests were conducted with A549 lung epithelial cells. Five different cars and two typical braking behaviours (full stop and normal deceleration) were tested. Particle number and size distribution was analysed for the first six minutes. In this time, two braking events occurred. Full stop produced significantly higher particle concentrations than normal deceleration (average of 23'000 vs. 10'400 #/cm3, p= 0.016). The particle number distribution was bi-modal with one peak at 60 to 100 nm (depending on the tested car and braking behaviour) and a second peak at 200 to 400 nm. Metal concentrations varied depending on the tested car type. Iron (range of 163 to 15'600 μg/m3) and Manganese (range of 0.9 to 135 μg/m3) were present in all samples, while Copper was absent in some samples (<6 to 1220 μg/m3). The overall "fleet" metal ratio was Fe:Cu:Mn = 128:14:1. Temperature and humidity varied little. A549-cells were successfully exposed in the various experimental settings and retained their viability. Culture supernatant was stored and cell culture samples were fixated to test for inflammatory response. Analysis of these samples is ongoing. The established system allowed testing brake wear particle emissions from real-world cars. The large variability of chemical composition and emitted amounts of brake wear particles between car models seems to be related to differences between brake pad compositions of different producers. Initial results suggest that the conditions inside the exposure box allow exposing human lung epithelial cells to freshly produced brake wear particles.