Symmetry of chaotic attractors and kink-antikink structures in CMLs

In this paper the symmetries of coupled map lattices (CMLs) and their attractors are investigated by group and dynamical system theory, as well as numerical simulation, by means of which the kink-antikink patterns of CMLs in space-amplitude plots are discussed.

A quantitative witness for Greenberger-Horne-Zeilinger entanglement

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger-type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Effects produced in GaAs by MeV ion bombardment

Presented in the first part of this thesis is work performed on the ionizing energy beam induced adhesion enhancement of thin (~ 500 Angstrom) Au films on GaAs substrates. The ionizing beam, employed in the present thesis, is the MeV ions (i.e., ¹⁶O, ¹⁹F, and ³⁵Cl), with energies between 1 and 20 MeV. Using the "Scratch" test for adhesion measurement, and ESCA for chemical analysis of the film-substrate interface, the native oxide layer at the interface is shown to play an important role in the adhesion enhancement by the ionizing radiation. A model is discussed which explains the experimental data on the the dependence of adhesion enhancement on the energy which was deposited into electronic processes at the interface. The ESCA data indicate that the chemical bonds (or compounds), which are responsible for the increase in the thin film adherence, are hydroxides rather than oxides.

In the second part of the thesis we present a research performed on the radiation damage in GaAs crystals produced by MeV ions. Lattice parameter dilatation in the surface layers of the GaAs crystals becomes saturated after a high dose bombardment at room temperature. The strain produced by nuclear collisions is shown to relax partially due to electronic excitation (with a functional dependence on the nuclear and electronic stopping power of bombarding ions). Data on the GaAs and GaP crystals suggest that low temperature recovery stage defects produce major crystal distortion. The x-ray rocking curve technique with a dynamical diffraction theory analysis provides the depth distribution of the strain and damage in the MeV ion bombarded crystals.

Sistemas complexos, séries temporais e previsibilidade

Para qualquer sistema observado, físico ou qualquer outro, geralmente se deseja fazer predições para sua evolução futura. Algumas vezes, muito pouco é conhecido sobre o sistema. Se uma série temporal é a única fonte de informação no sistema, predições de valores futuros da série requer uma modelagem da lei da dinâmica do sistema, talvez não linear. Um interesse em particular são as capacidades de previsão do modelo global para análises de séries temporais. Isso pode ser um procedimento muito complexo e computacionalmente muito alto. Nesta dissertação, nos concetraremos em um determinado caso: Em algumas situações, a única informação que se tem sobre o sistema é uma série sequencial de dados (ou série temporal). Supondo que, por detrás de tais dados, exista uma dinâmica de baixa dimensionalidade, existem técnicas para a reconstrução desta dinâmica.O que se busca é desenvolver novas técnicas para poder melhorar o poder de previsão das técnicas já existentes, através da programação computacional em Maple e C/C++.

Sistema Único de Saúde: de que sistema se trata?

Constata-se que a reforma sanitária brasileira representa um avanço na direção de uma concepção avançada de sistema de saúde. Entretanto o SUS, com toda a materialidade das reformas ao nível macro induzidas a partir dos avanços na legislação, a implantação da regionalização e hierarquização da assistência, e dos instrumentos de gestão, assim como todas as grandes organizações modernas, padece de problemas de coordenação na operação de suas ações. Este trabalho pretende discutir as possibilidades e limites das mudanças organizacionais induzidas pela implementação do SUS na configuração dos sistemas locoregionais de saúde, à luz das experiências internacionais e das contribuições mais recentes das teorias organizacionais, no contexto da transição do fordismo à acumulação flexível. A partir do referencial da teoria dos sistemas, considera-se a contribuição das teorias organizacionais fordistas, pós-fordistas e pós-modernistas na especificidade do campo da saúde coletiva, para discutir a efetividade dos seus subsistemas cibernéticos do SUS: controle, avaliação, regulação, auditoria e vigilância em saúde, no complexo contexto da configuração do poder deste setor. Verifica-se que o SUS, constituído a partir de culturas organizacionais fordistas, do antigo INAMPS e da Saúde Pública tradicional, não tem obtido êxito em configurar estruturas organizacionais competentes, na medida em que reproduz os modelos tradicionais nos seus sistemas de controle. Esta dificuldade em parte deve-se ao momento histórico, que fez coincidir o momento dos avanços na legislação, em direção à ampliação do direito à saúde, com o momento das reestruturações dos aparelhos estatais decorrente da crise global do modo de produção fordista, e com as profundas transformações demográficas, epidemiológicas e da tecnologia da assistência médica. Por outro lado, a disponibilidade de soluções pósfordistas propicia um padrão para a conformação de novas regras e novos modos de regulação do sistema de saúde, que induzam a comportamentos auto-reguladores por parte dos prestadores de serviços de saúde, considerando as metas de equidade e de melhoria da saúde da população. Conclui-se que a necessária reforma do setor saúde demanda o fortalecimento de uma tecno-burocracia protegida contra injunções político-partidárias, que possibilite a incubação uma cultura organizacional profissional em todas as esferas de governo e níveis de gestão, que incentive um trabalho em saúde competente e moralmente comprometido com as finalidades do SUS nesse país.

O jogo e os jogos: o jogo da leitura, o jogo de xadrez e a sanidade mental em A defesa Lujin, de Vladimir Nabokov

No romance A defesa Lujin, de Vladimir Nabokov, publicado em russo em 1930, o texto procura levar o leitor a adotar processos mentais similares ao de um jogador de xadrez e de um esquizofrênico, características do personagem-título do romance. Delineiam-se as expectativas e circunstâncias de um ser de papel que se vê jogando um xadrez em que também é peça e traçam-se paralelos com as expectativas e circunstâncias do leitor perante esse texto literário. O prefácio de Nabokov à edição em inglês de 1964 é tomado como indício de um leitor e um autor implícitos que ele procura moldar. Para análise dos elementos textuais e níveis de abstração mental envolvidos, recorre-se à estética da recepção de Wolfgang Iser e a diversas ideias do psiquiatra e etnólogo Gregory Bateson, entre elas o conceito de duplo vínculo, com atenção às distinções entre mapa/território e play/game. Um duplo duplo vínculo é perpetrado na interação leitor-texto: 1) o leitor é convidado a sentir empatia pela situação do personagem Lujin e a considerá-lo lúcido e louco ao mesmo tempo; e 2) o leitor é colocado como uma instância pseudo-transcendental incapaz de comunicação com a instância inferior (Lujin), gerando uma angústia diretamente relacionável ao seu envolvimento com a ficção, replicando de certa forma a loucura de Lujin. A sinestesia do personagem Lujin é identificada como um dos elementos do texto capaz de recriar a experiência de jogar xadrez até para quem não aprecia o jogo. Analisa-se a conexão entre a esquizofrenia ficcional do personagem Lujin e a visão batesoniana do alcoolismo

Releitura sistêmico-teórica das relações entre direito, política e economia: a crise de 2008 como ponto de inflexão para a emergência do constitucionalismo societal

O trabalho busca na teoria dos sistemas de Niklas Luhmann, tal como desenvolvida por Gunther Teubner, Marcelo Neves e outros doutrinadores, elementos para explicar as relações entre os subsistemas jurídico, político e econômico na sociedade contemporânea. Com base nas ferramentas teóricas obtidas, revisa o conceito de constituição econômica como a relação de acoplamento estrutural entre o direito e a economia, e a Constituição do Estado como a relação de acoplamento estrutural entre o direito e a política. As crises econômicas são então explicadas pelas tendências inflacionárias na produção de símbolos e pelos choques entre racionalidades sistêmicas parciais. A crise de 2008 consolida a constatação de que a globalização restringe a capacidade de influência da política e do direito sobre o sistema econômico desterritorializado. Em vista disso, propõe-se a adoção da teoria do constitucionalismo societal de Teubner como proposta para a democracia no século XXI; através dela, é possível reconhecer a constitucionalização no interior de cada subsistema social e o desenvolvimento de foros de razão pública internos, nos quais a política pode ser desenvolvida de forma autônoma em relação à política institucionalizada do Estado. Finalmente, vê-se como o combate à crise econômica invariavelmente redesenha os papéis dos Poderes de Estado, reconhecendo certa liberdade ao Executivo, embora isso não signifique ausência de quaisquer freios e contrapesos.

Shock transmission and eigenvalue veering within a coupled system.

The operation of dynamical systems in harsh environments requires continuous monitoring. Internal sensors may be used to monitor the conditions in real time. A typical example is the sensor and electronic components used in space structures which, especially during launch, are subject to huge g force. The paper will present an experimental and theoretical study on a simplified model used to analyze the possible cause of high acceleration on the enclosed sensors and equipments due to impulsive loading. The model system consists of two beams coupled using compliant connections. An impulse hammer excites one beam, and vibrations are transmitted to the indirectly driven beam. A theoretical model is developed using a Rayleigh-Ritz approach and validated using experimental results in both the frequency and time domains. Monto Carlo simulation was done with random masses positioned on the indirectly driven beam to determine the worst-case conditions for maximum peak acceleration. Highest acceleration levels were found when mode matching in the two beams led to veering behavior in the coupled modes. The results suggest guidelines for the detailed design of internal components of a structure exposed to shock loading from its environment. [The authors thank Schlumberger Cambridge Research for financial support.].

The post-processed Galerkin method applied to non-linear shell vibrations

We present the results of a computational study of the post-processed Galerkin methods put forward by Garcia-Archilla et al. applied to the non-linear von Karman equations governing the dynamic response of a thin cylindrical panel periodically forced by a transverse point load. We spatially discretize the shell using finite differences to produce a large system of ordinary differential equations (ODEs). By analogy with spectral non-linear Galerkin methods we split this large system into a 'slowly' contracting subsystem and a 'quickly' contracting subsystem. We then compare the accuracy and efficiency of (i) ignoring the dynamics of the 'quick' system (analogous to a traditional spectral Galerkin truncation and sometimes referred to as 'subspace dynamics' in the finite element community when applied to numerical eigenvectors), (ii) slaving the dynamics of the quick system to the slow system during numerical integration (analogous to a non-linear Galerkin method), and (iii) ignoring the influence of the dynamics of the quick system on the evolution of the slow system until we require some output, when we 'lift' the variables from the slow system to the quick using the same slaving rule as in (ii). This corresponds to the post-processing of Garcia-Archilla et al. We find that method (iii) produces essentially the same accuracy as method (ii) but requires only the computational power of method (i) and is thus more efficient than either. In contrast with spectral methods, this type of finite-difference technique can be applied to irregularly shaped domains. We feel that post-processing of this form is a valuable method that can be implemented in computational schemes for a wide variety of partial differential equations (PDEs) of practical importance.

An organizing center in a planar model of neuronal excitability

This paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the classical FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. © 2012 Society for Industrial and Applied Mathematics.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.