Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Limit Cycles for a class of three dimensional polynomial differential systems

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Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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Evolution of holometabola insect digestive systems: physiological and biochemical aspects

This review takes into account primarily the work done in our laboratory with insects from the major Holometabola orders. Only the most significant data for each insect will be presented and a proposal on the evolution of Holometabola insect digstive systems will be advanced.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

The evolution of inbred social systems in spiders and other organisms: from short-term gains to long-term evolutionary dead-ends?

The question of why some social systems have evolved close inbreeding is particularly intriguing given expected short- and long-term negative effects of this breeding system. Using social spiders as a case study, we quantitatively show that the potential costs of avoiding inbreeding through dispersal and solitary living could have outweighed the costs of inbreeding depression in the origin of inbred spider sociality. We further review the evidence that despite being favored in the short term, inbred spider sociality may constitute in the long run an evolutionary dead end. We also review other cases, such as the naked mole rats and some bark and ambrosia beetles, mites, psocids, thrips, parasitic ants, and termites, in which inbreeding and sociality are associated and the evidence for and against this breeding system being, in general, an evolutionary dead end.

Colloidal systems for the delivery of cyclosporin A to the anterior segment of the eye.

Due to the eye's specific anatomical and physiological conformation, the treatment of eye diseases is a real challenge for pharmaceutical therapy. The presence of efficient protective barriers (i.e., the conjunctival and corneal membranes) and protective mechanisms (i.e., blinking and nasolachrymal drainage) makes this organ particularly impervious to local drug therapy. To overcome these issues, numerous strategies have been envisioned using pharmaceutical technology. Many formulations currently on the market or still under development are emulsions or colloidal systems intended to enhance precorneal residence time and corneal penetration, causing a consequent increase in drug bioavailability after instillation. After a review of some recent developments in the field of cyclosporin A formulations for the eye, a novel micellar formulation of cyclosporine A based on a diblock methoxy-poly(ethylene glycol)-hexysubstituted poly(lactides) (MPEG-hexPLA) is described.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.