940 resultados para Nonlinear Dynamical Systems


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Future broadband wireless systems are expected to cope with severely time dispersive channels, due to multi-path signal propagation between the transmitter and the receiver while having high power and spectral efficiency. Thus, advanced Frequency Domain Equalization techniques are required. The implementation complexity in mobile terminals should be as low as possible to achieve highest possible efficiency. Therefore, most of the signal processing requirements will be shifted to the base station and we will employ signals compatible with an efficient, grossly nonlinear power amplification. For this reason, we will consider offset modulation signals with quasi-constant envelope and develop receivers that will obtain good BER performance. However, these signals require a bandwidth significantly above the Nyquist rate, which can be reduced by an overlap of different frequency channels.

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The work described in this thesis was performed at the Laboratory for Intense Lasers (L2I) of Instituto Superior Técnico, University of Lisbon (IST-UL). Its main contribution consists in the feasibility study of the broadband dispersive stages for an optical parametric chirped pulse amplifier based on the nonlinear crystal yttrium calcium oxi-borate (YCOB). In particular, the main goal of this work consisted in the characterization and implementation of the several optical devices involved in pulse expansion and compression of the amplified pulses to durations of the order of a few optical cycles (20 fs). This type of laser systems find application in fields such as medicine, telecommunications and machining, which require high energy, ultrashort (sub-100 fs) pulses. The main challenges consisted in the preliminary study of the performance of the broadband amplifier, which is essential for successfully handling pulses with bandwidths exceeding 100 nm when amplified from the μJ to 20 mJ per pulse. In general, the control, manipulation and characterization of optical phenomena on the scale of a few tens of fs and powers that can reach the PW level are extremely difficult and challenging due to the complexity of the phenomena of radiation-matter interaction and their nonlinearities, observed at this time scale and power level. For this purpose the main dispersive components were characterized in detail, specifically addressing the demonstration of pulse expansion and compression. The tested bandwidths are narrower than the final ones, in order to confirm the parameters of these elements and predict the performance for the broadband pulses. The work performed led to additional tasks such as a detailed characterization of laser oscillator seeding the laser chain and the detection and cancelling of additional sources of dispersion.

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The development of organic materials displaying high two-photon absorption (TPA) has attracted much attention in recent years due to a variety of potential applications in photonics and optoelectronics, such as three-dimensional optical data storage, fluorescence imaging, two-photon microscopy, optical limiting, microfabrication, photodynamic therapy, upconverted lasing, etc. The most frequently employed structural motifs for TPA materials are donor–pi bridge–acceptor (D–pi–A) dipoles, donor–pi bridge–donor (D–pi–D) and acceptor–pi bridge-acceptor (A–pi–A) quadrupoles, octupoles, etc. In this work we present the synthesis and photophysical characterization of quadrupolar heterocyclic systems with potential applications in materials and biological sciences as TPA chromophores. Indole is a versatile building block for the synthesis of heterocyclic systems for several optoelectronic applications (chemosensors, nonlinear optical, OLEDs) due to its photophysical properties and donor electron ability and 4H-pyran-4-ylidene fragment is frequently used for the synthesis of red light-emitting materials. On the other hand, 2-(2,6-dimethyl-4H-pyran-4-ylidene)malononitrile (1) and 1,3-diethyl-dihydro-5-(2,6-dimethyl-4H-pyran-4-ylidene)-2-thiobarbituric (2) units are usually used as strong acceptor moieties for the preparation of π-conjugated systems of the push-pull type. These building blocks were prepared by Knoevenagel condensation of the corresponding ketone precursor with malononitrile or 1,3-diethyl-dihydro-2-thiobarbituric acid. The new quadrupolar 4H-pyran-4-ylidene fluorophores (3) derived from indole were prepared through condensation of 5-methyl-1H-indole-3-carbaldehyde with the acceptor precursors 1 and 2, in the presence of a catalytical amount of piperidine. The new compounds were characterized by the usual spectroscopic techniques (UV-vis., FT-IR and multinuclear NMR - 1H, 13C).

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It is a difficult task to avoid the “smart systems” topic when discussing smart prevention and, similarly, it is a difficult task to address smart systems without focusing their ability to learn. Following the same line of thought, in the current reality, it seems a Herculean task (or an irreparable omission) to approach the topic of certified occupational health and safety management systems (OHSMS) without discussing the integrated management systems (IMSs). The available data suggest that seldom are the OHSMS operating as the single management system (MS) in a company so, any statement concerning OHSMS should mainly be interpreted from an integrated perspective. A major distinction between generic systems can be drawn between those that learn, i.e., those systems that have “memory” and those that have not. These former systems are often depicted as adaptive since they take into account past events to deal with novel, similar and future events modifying their structure to enable success in its environment. Often, these systems, present a nonlinear behavior and a huge uncertainty related to the forecasting of some events. This paper seeks to portray, for the first time as we were able to find out, the IMSs as complex adaptive systems (CASs) by listing their properties and dissecting the features that enable them to evolve and self-organize in order to, holistically, fulfil the requirements from different stakeholders and thus thrive by assuring the successful sustainability of a company. Based on the revision of literature carried out, this is the first time that IMSs are pointed out as CASs which may develop fruitful synergies both for the MSs and for CASs communities. By performing a thorough revision of literature and based on some concepts embedded in the “DNA” of the subsystems implementation standards it is intended, specifically, to identify, determine and discuss the properties of a generic IMS that should be considered to classify it as a CAS.

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A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.

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Tese de Doutoramento em Biologia Ambiental e Molecular

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"Available online 22 March 2016"

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

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Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

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Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

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A fundamental question in developmental biology is how tissues are patterned to give rise to differentiated body structures with distinct morphologies. The Drosophila wing disc offers an accessible model to understand epithelial spatial patterning. It has been studied extensively using genetic and molecular approaches. Bristle patterns on the thorax, which arise from the medial part of the wing disc, are a classical model of pattern formation, dependent on a pre-pattern of trans-activators and –repressors. Despite of decades of molecular studies, we still only know a subset of the factors that determine the pre-pattern. We are applying a novel and interdisciplinary approach to predict regulatory interactions in this system. It is based on the description of expression patterns by simple logical relations (addition, subtraction, intersection and union) between simple shapes (graphical primitives). Similarities and relations between primitives have been shown to be predictive of regulatory relationships between the corresponding regulatory factors in other Systems, such as the Drosophila egg. Furthermore, they provide the basis for dynamical models of the bristle-patterning network, which enable us to make even more detailed predictions on gene regulation and expression dynamics. We have obtained a data-set of wing disc expression patterns which we are now processing to obtain average expression patterns for each gene. Through triangulation of the images we can transform the expression patterns into vectors which can easily be analysed by Standard clustering methods. These analyses will allow us to identify primitives and regulatory interactions. We expect to identify new regulatory interactions and to understand the basic Dynamics of the regulatory network responsible for thorax patterning. These results will provide us with a better understanding of the rules governing gene regulatory networks in general, and provide the basis for future studies of the evolution of the thorax-patterning network in particular.

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Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

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Secondary accident statistics can be useful for studying the impact of traffic incident management strategies. An easy-to-implement methodology is presented for classifying secondary accidents using data fusion of a police accident database with intranet incident reports. A current method for classifying secondary accidents uses a static threshold that represents the spatial and temporal region of influence of the primary accident, such as two miles and one hour. An accident is considered secondary if it occurs upstream from the primary accident and is within the duration and queue of the primary accident. However, using the static threshold may result in both false positives and negatives because accident queues are constantly varying. The methodology presented in this report seeks to improve upon this existing method by making the threshold dynamic. An incident progression curve is used to mark the end of the queue throughout the entire incident. Four steps in the development of incident progression curves are described. Step one is the processing of intranet incident reports. Step two is the filling in of incomplete incident reports. Step three is the nonlinear regression of incident progression curves. Step four is the merging of individual incident progression curves into one master curve. To illustrate this methodology, 5,514 accidents from Missouri freeways were analyzed. The results show that secondary accidents identified by dynamic versus static thresholds can differ by more than 30%.

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We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties.

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For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces. 2000 American Institute of Physics.