328 research outputs found
Scaling laws associated with a symmetry-break in the energy distribution in a set of dynamical systems: application to discrete mappings
No full textNesta dissertação, investigamos propriedades estatísticas de alguns sistemas dinâmicos descritos por mapeamentos discretos nas proximidades de duas transições: (i) integrabilidade para não integrabilidade e; (ii) crescimento limitado de energia para crescimento ilimitado de energia (aceleração de Fermi). O foco principal está na descrição do comportamento da distribuição de probabilidade da velocidade/energia das partículas em dinâmica caótica. A quebra de simetria da distribuição de probabilidade leva a uma escala adicional àquelas já conhecidas na literatura e, com este estudo, acreditamos que a quebra de simetria também possa explicar um fenômeno que já vem sendo observado em mapeamentos discretos. Fenômeno este, até então descrito apenas fenomenologicamente, teve sua primeira observação na publicação seminal de investigação de leis de escala em mapeamentos discretos no periódico Phys. Rev. Let. 93, 014101 (2004), de Edson D. Leonel, Peter V. E. McClintock e Jafferson K. L. Silva. Nossa contribuição para o problema está no desenvolvimento de descrições analíticas e verificações numéricas, baseadas em um estudo sistemático do comportamento difusivo das trajetórias caóticas no espaço de fases dos sistemas dinâmicos de interesse.In this dissertation, we investigate statistical properties of some dynamical systems described by discrete mappings near two types of transitions: (i) integrability to non-integrability; (ii) limited to unlimited diffusion in energy (Fermi acceleration). The main goal is to describe the behaviour of the probability density of the velocity/energy for a set of particles moving in a chaotic dynamics. The break of symmetry in the probability distribution leads to an additional scaling to those are already known in the literature and, with this study, we believe that the symmetry break might also explain a well-known phenomenon observed for discrete mappings. This phenomenon, it has been reported so far phenomenologically. A first observation in an area-preserving mapping was in a letter published in Phys. Rev. Let. 93, 014101 (2004), authored by Edson D. Leonel, Peter V. E. McClintock and Jafferson K. L. Silva. Our contribution to the problem is on the development of an analytical approach and numerical verifications, based essentially on a systematic study of the diffusive behaviour of chaotic trajectories on the phase space of dynamical systems of interest.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP: 2014/27260-
Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
No full textA phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map. Copyright (C) 2009 Edson D. Leonel.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação para o Desenvolvimento da UNESP (FUNDUNESP)Univ Estadual Paulista, Dept Estatist Matemat Aplicada & Computacao, Inst Geociencias & Ciencias Exatas, BR-13506700 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Estatist Matemat Aplicada & Computacao, Inst Geociencias & Ciencias Exatas, BR-13506700 Rio Claro, SP, Brazi
O dano pessoal na sociedade de risco
No full textTese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Jurídicas.Estudo do dano pessoal e sua indenização, sob a ótica do dano corporal. Equaciona-se a matéria a partir do homem na pós-modernidade. Conclui-se que urge repensar as normas à luz de uma interpretação constitucional para atender à função mais importante da responsabilidade hoje reconhecida: indenizar a vítima. A indenização deverá ser reorientada para priorizar as necessidades da vítima em concreto. Estabelece-se como prioridade a reinserção social do lesado, com o auxílio nos amplos recursos tecnológicos, médicos, informáticos atualmente existentes. Propõe-se a criação de um fundo público apto a fornecer, subsidiariamente, os recursos necessários em prol desse objetivo
Preliminary fuselage structural configuration of a flying-wing type airline
No full textThe flying-wing is a type of configuration which is a tailless airplane accommodating all of its parts within the outline of a single airfoil. Theoretically, it has the most aerodynamic efficiency. The fuel consumption can be more efficient than the existed conventional airliner. It seems that this configuration can achieve the above mentioned requirements.
According to these outstanding advantages, many aircraft companies did a great deal of projects on the flying-wing concept. However, the application was only for sport and military use; for airliner, none of them entered production.
FW-11 is a flying-wing configuration airliner which is a design cooperation between Cranfield University and Aviation Industry Corporation of China (AVIC). Aiming the spatial economic and environmental needs, this 200-seat airliner would attract attention from airline companies for cost saving and environmental protection.
Before start, this program is designated for a new generation commercial aircraft to compete with the existing same capability airliner, such as Airbus A320 and Boeing 767. As the first team of this program, the aim is to finish the conceptual design and prepare the relevant document for next two teams that will perform preliminary and detail design.
As a member of FW-11 program and as part of the GDP, the author has been through the four conceptual design stages: engine manufacturers, aircraft family issues, structure design and the establishment of 3-D CAD model.
The aim of IRP study is to focus on the initial fuselage design
Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities
No full textSome dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.Institute for Multiscale Simulation Friedrich Alexander Universität Erlangen-Nürnberg, Naegelsbachstrasse 49b, D-91052-ErlangenCAMTP - Center for Applied Mathematics and Theoretical Physics University of Maribor, Krekova 2, SI-2000-MariborDepartamento de Física Universidade Estadual Paulista (UNESP), Av. 24A, 1515-13506-900-Rio Claro, SPDepartamento de Física Universidade Estadual Paulista (UNESP), Av. 24A, 1515-13506-900-Rio Claro, S
Defining universality classes for three different local bifurcations
No full textThe convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations
Corrugated waveguide under scaling investigation
No full textSome scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to nonintegrability, including that in classical billiard problems.Univ Estadual Paulista, Dept Estatist Matemat Aplicada & Comp, Inst Geociencias & Ciências Exatas, BR-13506700 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Estatist Matemat Aplicada & Comp, Inst Geociencias & Ciências Exatas, BR-13506700 Rio Claro, SP, Brazi
Breaking down the Fermi acceleration with inelastic collisions
No full textThe phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.Univ Estadual Paulista, IGCE, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, IGCE, Dept Estat Matemat Aplicada & Comp, BR-13506900 Rio Claro, SP, Brazi
Escape and transport for an open bouncer: Stretched exponential decays
No full textWe consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decays depending on the choice of the lead or hole, raising the question of whether this feature is due to special properties of the stadium. The system considered here is much more general, having a generic mixed phase space structure, time-dependence of the dynamics, and Fermi acceleration (trajectories with unbounded velocity). We propose an efficient numerical scheme for this model, observe escape and transport effects including similar asymmetry, and also clear stretched exponential decays. (C) 2011 Elsevier B.V. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação para o Desenvolvimento da UNESP (FUNDUNESP)Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, EnglandUniv Estadual Paulista, Dept Estat Matemat Aplicada & Comp, IGCE, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, Dept Estat Matemat Aplicada & Comp, IGCE, BR-13506900 Rio Claro, SP, Brazi
Fermi acceleration and its suppression in a time-dependent Lorentz gas
No full textSome dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. (C) 2010 Elsevier B.V. All rights reserved.Max Planck InstituteUniv Maribor, CAMTP Ctr Appl Math & Theoret Phys, SI-2000 Maribor, SloveniaMax Planck Inst Dynam & Self Org, D-37073 Gottingen, GermanyUniv Estadual Paulista, Inst Geociencias & Ciencias Exatas, Dept Estat Matemat Aplicada & Computacao, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, Inst Geociencias & Ciencias Exatas, Dept Estat Matemat Aplicada & Computacao, BR-13506900 Rio Claro, SP, Brazi
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