877 resultados para Fractional-order systems


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The dispersion compensation characteristics of the chirped fiber grating (CFG) for different dispersion compensation positions are analyzed in externally modulated cable television (CATV) lightwave system and the analytic expression of the composite second order (CSO) distortion is derived. The analyses give a reasonable explanation for the position-dependent effect of CFG dispersion compensator, which was found in practical systems. Moreover, the theoretical result is also verified by an experiment. It is believed that the theory will be helpful in designing optical CATV fiber links with nodes at proper positions both for intensity amplification and dispersion compensation.

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This thesis presents investigations in four areas of theoretical astrophysics: the production of sterile neutrino dark matter in the early Universe, the evolution of small-scale baryon perturbations during the epoch of cosmological recombination, the effect of primordial magnetic fields on the redshifted 21-cm emission from the pre-reionization era, and the nonlinear stability of tidally deformed neutron stars.

In the first part of the thesis, we study the asymmetry-driven resonant production of 7 keV-scale sterile neutrino dark matter in the primordial Universe at temperatures T >~ 100 MeV. We report final DM phase space densities that are robust to uncertainties in the nature of the quark-hadron transition. We give transfer functions for cosmological density fluctuations that are useful for N-body simulations. We also provide a public code for the production calculation.

In the second part of the thesis, we study the instability of small-scale baryon pressure sound waves during cosmological recombination. We show that for relevant wavenumbers, inhomogenous recombination is driven by the transport of ionizing continuum and Lyman-alpha photons. We find a maximum growth factor less than ≈ 1.2 in 107 random realizations of initial conditions. The low growth factors are due to the relatively short duration of the recombination epoch.

In the third part of the thesis, we propose a method of measuring weak magnetic fields, of order 10-19 G (or 10-21 G if scaled to the present day), with large coherence lengths in the inter galactic medium prior to and during the epoch of cosmic reionization. The method utilizes the Larmor precession of spin-polarized neutral hydrogen in the triplet state of the hyperfine transition. We perform detailed calculations of the microphysics behind this effect, and take into account all the processes that affect the hyperfine transition, including radiative decays, collisions, and optical pumping by Lyman-alpha photons.

In the final part of the thesis, we study the non-linear effects of tidal deformations of neutron stars (NS) in a compact binary. We compute the largest three- and four-mode couplings among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We demonstrate the near-exact cancellation of their effects, and resolve the question of the stability of the tidally deformed NS to leading order. This result is significant for the extraction of binary parameters from gravitational wave observations.

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The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time.

The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.

Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.

The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.

It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance.

One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon.

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We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function (PSF) of an incoherant defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invarient to the defocous-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.

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The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

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The feedback coding problem for Gaussian systems in which the noise is neither white nor statistically independent between channels is formulated in terms of arbitrary linear codes at the transmitter and at the receiver. This new formulation is used to determine a number of feedback communication systems. In particular, the optimum linear code that satisfies an average power constraint on the transmitted signals is derived for a system with noiseless feedback and forward noise of arbitrary covariance. The noisy feedback problem is considered and signal sets for the forward and feedback channels are obtained with an average power constraint on each. The general formulation and results are valid for non-Gaussian systems in which the second order statistics are known, the results being applicable to the determination of error bounds via the Chebychev inequality.

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The subject of this thesis is the measurement and interpretation of thermopower in high-mobility two-dimensional electron systems (2DESs). These 2DESs are realized within state-of-the-art GaAs/AlGaAs heterostructures that are cooled to temperatures as low as T = 20 mK. Much of this work takes place within strong magnetic fields where the single-particle density of states quantizes into discrete Landau levels (LLs), a regime best known for the quantum Hall effect (QHE). In addition, we review a novel hot-electron technique for measuring thermopower of 2DESs that dramatically reduces the influence of phonon drag.

Early chapters concentrate on experimental materials and methods. A brief overview of GaAs/AlGaAs heterostructures and device fabrication is followed by details of our cryogenic setup. Next, we provide a primer on thermopower that focuses on 2DESs at low temperatures. We then review our experimental devices, temperature calibration methods, as well as measurement circuits and protocols.

Latter chapters focus on the physics and thermopower results in the QHE regime. After reviewing the basic phenomena associated with the QHE, we discuss thermopower in this regime. Emphasis is given to the relationship between diffusion thermopower and entropy. Experimental results demonstrate this relationship persists well into the fractional quantum Hall (FQH) regime.

Several experimental results are reviewed. Unprecedented observations of the diffusion thermopower of a high-mobility 2DES at temperatures as high as T = 2 K are achieved using our hot-electron technique. The composite fermion (CF) effective mass is extracted from measurements of thermopower at LL filling factor ν = 3/2. The thermopower versus magnetic field in the FQH regime is shown to be qualitatively consistent with a simple entropic model of CFs. The thermopower at ν = 5/2 is shown to be quantitatively consistent with the presence of non-Abelian anyons. An abrupt collapse of thermopower is observed at the onset of the reentrant integer quantum Hall effect (RIQHE). And the thermopower at temperatures just above the RIQHE transition suggests the existence of an unconventional conducting phase.

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The dispersion compensation effect of the chirped fiber grating (CFG) is analyzed theoretically, and analytic expressions are derived for composite second-order (CSO) distortion in analog modulated sub-carrier multiplexed (AM-SCM) cable television (CATV) systems with externally and directly modulated transmitters. Simulations are given for the two kinds of modulations and for standard single mode fiber and non-zero dispersion shift fiber (NZDSF) systems. The results show that CFG could be used as a dispersion compensator in directly modulated systems, but its dispersion coefficient should be adjusted much more precisely than the externally modulated system. The requirements for the NZDSF system could be loosened much. It is proposed that directly modulated source may be used as a transmitter in CATV systems combined with tunable CFG dispersion compensator being adjusted precisely, which may be more cost-effective than externally modulation technology. (c) 2006 Elsevier GmbH. All rights reserved.

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We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

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The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

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This thesis examines two problems concerned with surface effects in simple molecular systems. The first is the problem associated with the interaction of a fluid with a solid boundary, and the second originates from the interaction of a liquid with its own vapor.

For a fluid in contact with a solid wall, two sets of integro-differential equations, involving the molecular distribution functions of the system, are derived. One of these is a particular form of the well-known Bogolyubov-Born-Green-Kirkwood-Yvon equations. For the second set, the derivation, in contrast with the formulation of the B.B.G.K.Y. hierarchy, is independent of the pair-potential assumption. The density of the fluid, expressed as a power series in the uniform fluid density, is obtained by solving these equations under the requirement that the wall be ideal.

The liquid-vapor interface is analyzed with the aid of equations that describe the density and pair-correlation function. These equations are simplified and then solved by employing the superposition and the low vapor density approximations. The solutions are substituted into formulas for the surface energy and surface tension, and numerical results are obtained for selected systems. Finally, the liquid-vapor system near the critical point is examined by means of the lowest order B.B.G.K.Y. equation.

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[EN] This PhD work started in March 2010 with the support of the University of the Basque Country (UPV/EHU) under the program named “Formación de Personal Investigador” at the Chemical and Environmental Engineering Department in the Faculty of Engineering of Bilbao. The major part of the Thesis work was carried out in the mentioned department, as a member of the Sustainable Process Engineering (SuPrEn) research group. In addition, this PhD Thesis includes the research work developed during a period of 6 months at the Institut für Mikrotechnik Mainz GmbH, IMM, in Germany. During the four years of the Thesis, conventional and microreactor systems were tested for several feedstocks renewable and non-renewable, gases and liquids through several reforming processes in order to produce hydrogen. For this purpose, new catalytic formulations which showed high activity, selectivity and stability were design. As a consequence, the PhD work performed allowed the publication of seven scientific articles in peer-reviewed journals. This PhD Thesis is divided into the following six chapters described below. The opportunity of this work is established on the basis of the transition period needed for moving from a petroleum based energy system to a renewable based new one. Consequently, the present global energy scenario was detailed in Chapter 1, and the role of hydrogen as a real alternative in the future energy system was justified based on several outlooks. Therefore, renewable and non-renewable hydrogen production routes were presented, explaining the corresponding benefits and drawbacks. Then, the raw materials used in this Thesis work were described and the most important issues regarding the processes and the characteristics of the catalytic formulations were explained. The introduction chapter finishes by introducing the concepts of decentralized production and process intensification with the use of microreactors. In addition, a small description of these innovative reaction systems and the benefits that entailed their use were also mentioned. In Chapter 2 the main objectives of this Thesis work are summarized. The development of advanced reaction systems for hydrogen rich mixtures production is the main objective. In addition, the use and comparison between two different reaction systems, (fixed bed reactor (FBR) and microreactor), the processing of renewable raw materials, the development of new, active, selective and stable catalytic formulations, and the optimization of the operating conditions were also established as additional partial objectives. Methane and natural gas (NG) steam reforming experimental results obtained when operated with microreactor and FBR systems are presented in Chapter 3. For these experiments nickel-based (Ni/Al2O3 and Ni/MgO) and noble metal-based (Pd/Al2O3 and Pt/Al2O3) catalysts were prepared by wet impregnation and their catalytic activity was measured at several temperatures, from 973 to 1073 K, different S/C ratios, from 1.0 to 2.0, and atmospheric pressure. The Weight Hourly Space Velocity (WHSV) was maintained constant in order to compare the catalytic activity in both reaction systems. The results obtained showed a better performance of the catalysts operating in microreactors. The Ni/MgO catalyst reached the highest hydrogen production yield at 1073 K and steam-to-carbon ratio (S/C) of 1.5 under Steam methane Reforming (SMR) conditions. In addition, this catalyst also showed good activity and stability under NG reforming at S/C=1.0 and 2.0. The Ni/Al2O3 catalyst also showed high activity and good stability and it was the catalyst reaching the highest methane conversion (72.9 %) and H2out/CH4in ratio (2.4) under SMR conditions at 1073 K and S/C=1.0. However, this catalyst suffered from deactivation when it was tested under NG reforming conditions. Regarding the activity measurements carried out with the noble metal-based catalysts in the microreactor systems, they suffered a very quick deactivation, probably because of the effects attributed to carbon deposition, which was detected by Scanning Electron Microscope (SEM). When the FBR was used no catalytic activity was measured with the catalysts under investigation, probably because they were operated at the same WHSV than the microreactors and these WHSVs were too high for FBR system. In Chapter 4 biogas reforming processes were studied. This chapter starts with an introduction explaining the properties of the biogas and the main production routes. Then, the experimental procedure carried out is detailed giving concrete information about the experimental set-up, defining the parameters measured, specifying the characteristics of the reactors used and describing the characterization techniques utilized. Each following section describes the results obtained from activity testing with the different catalysts prepared, which is subsequently summarized: Section 4.3: Biogas reforming processes using γ-Al2O3 based catalysts The activity results obtained by several Ni-based catalysts and a bimetallic Rh-Ni catalyst supported on magnesia or alumina modified with oxides like CeO2 and ZrO2 are presented in this section. In addition, an alumina-based commercial catalyst was tested in order to compare the activity results measured. Four different biogas reforming processes were studied using a FBR: dry reforming (DR), biogas steam reforming (BSR), biogas oxidative reforming (BOR) and tri-reforming (TR). For the BSR process different steam to carbon ratios (S/C) from 1.0 to 3.0, were tested. In the case of BOR process the oxygen-to-methane (O2/CH4) ratio was varied from 0.125 to 0.50. Finally, for TR processes different S/C ratios from 1.0 to 3.0, and O2/CH4 ratios of 0.25 and 0.50 were studied. Then, the catalysts which achieved high activity and stability were impregnated in a microreactor to explore the viability of process intensification. The operation with microreactors was carried out under the best experimental conditions measured in the FBR. In addition, the physicochemical characterization of the fresh and spent catalysts was carried out by Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES), N2 physisorption, H2 chemisorption, Temperature Programmed Reduction (TPR), SEM, X-ray Photoelectron Spectroscopy (XPS) and X-ray powder Diffraction (XRD). Operating with the FBR, conversions close to the ones predicted by thermodynamic calculations were obtained by most of the catalysts tested. The Rh-Ni/Ce-Al2O3 catalyst obtained the highest hydrogen production yield in DR. In BSR process, the Ni/Ce-Al2O3 catalyst achieved the best activity results operating at S/C=1.0. In the case of BOR process, the Ni/Ce-Zr-Al2O3 catalyst showed the highest reactants conversion values operating at O2/CH4=0.25. Finally, in the TR process the Rh-Ni/Ce-Al2O3 catalyst obtained the best results operating at S/C=1.0 and O2/CH4=0.25. Therefore, these three catalysts were selected to be coated onto microchannels in order to test its performance under BOR and TR processes conditions. Although the operation using microreactors was carried out under considerably higher WHSV, similar conversions and yields as the ones measured in FBR were measured. Furthermore, attending to other measurements like Turnover Frequency (TOF) and Hydrogen Productivity (PROD), the values calculated for the catalysts tested in microreactors were one order of magnitude higher. Thus, due to the low dispersion degree measured by H2-chemisorption, the Ni/Ce-Al2O3 catalyst reached the highest TOF and PROD values. Section 4.4: Biogas reforming processes using Zeolites L based catalysts In this section three type of L zeolites, with different morphology and size, were synthesized and used as catalyst support. Then, for each type of L zeolite three nickel monometallic and their homologous Rh-Ni bimetallic catalysts were prepared by the wetness impregnation method. These catalysts were tested using the FBR under DR process and different conditions of BSR (S/C ratio of 1.0 and 2.0), BOR (O2/CH4 ratio of 0.25 and 0.50) and TR processes (at S/C=1.0 and O2/CH4=0.25). The characterization of these catalysts was also carried out by using the same techniques mentioned in the previous section. Very high methane and carbon dioxide conversion values were measured for almost all the catalysts under investigation. The experimental results evidenced the better catalytic behavior of the bimetallic catalysts as compared to the monometallic ones. Comparing the catalysts behavior with regards to their morphology, for the BSR process the Disc catalysts were the most active ones at the lowest S/C ratio tested. On the contrary, the Cylindrical (30–60 nm) catalysts were more active under BOR conditions at O2/CH4=0.25 and TR processes. By the contrary, the Cylindrical (1–3 µm) catalysts showed the worst activity results for both processes. Section 4.5: Biogas reforming processes using Na+ and Cs+ doped Zeolites LTL based catalysts A method for the synthesis of Linde Type L (LTL) zeolite under microwave-assisted hydrothermal conditions and its behavior as a support for heterogeneously catalyzed hydrogen production is described in this section. Then, rhodium and nickel-based bimetallic catalysts were prepared in order to be tested by DR process and BOR process at O2/CH4=0.25. Moreover, the characterization of the catalysts under investigation was also carried out. Higher activities were achieved by the catalysts prepared from the non-doped zeolites, Rh-Ni/D and Rh-Ni/N, as compared to the ones supported on Na+ and Cs+ exchanged supports. However, the differences between them were not very significant. In addition, the Na+ and Cs+ incorporation affected mainly to the Disc catalysts. Comparing the results obtained by these catalysts with the ones studied in the section 4.4, in general worst results were achieved under DR conditions and almost the same results when operated under BOR conditions. In Chapter 5 the ethylene glycol (EG) as feed for syngas production by steam reforming (SR) and oxidative steam reforming (OSR) was studied by using microchannel reactors. The product composition was determined at a S/C of 4.0, reaction temperatures between 625°C and 725°C, atmospheric pressure and Volume Hourly Space Velocities (VHSV) between 100 and 300 NL/(gcath). This work was divided in two sections. The first one corresponds to the introduction of the main and most promising EG production routes. Then, the new experimental procedure is detailed and the information about the experimental set-up and the measured parameters is described. The characterization was carried out using the same techniques as for the previous chapter. Then, the next sections correspond to the catalytic activity and catalysts characterization results. Section 5.3: xRh-cm and xRh-np catalysts for ethylene glycol reforming Initially, catalysts with different rhodium loading, from 1.0 to 5.0 wt. %, and supported on α-Al2O3 were prepared by two different preparation methods (conventional impregnation and separate nanoparticle synthesis). Then, the catalysts were compared regarding their measured activity and selectivity, as well as the characterization results obtained before and after the activity tests carried out. The samples prepared by a conventional impregnation method showed generally higher activity compared to catalysts prepared from Rh nanoparticles. By-product formation of species such as acetaldehyde, ethane and ethylene was detected, regardless if oxygen was added to the feed or not. Among the catalysts tested, the 2.5Rh-cm catalyst was considered the best one. Section 5.4: 2.5Rh-cm catalyst support modification with CeO2 and La2O3 In this part of the Chapter 5, the catalyst showing the best performance in the previous section, the 2.5Rh-Al2O3 catalyst, was selected in order to be improved. Therefore, new Rh based catalysts were designed using α-Al2O3 and being modified this support with different contents of CeO2 or La2O3 oxides. All the catalysts containing additives showed complete conversion and selectivities close to the equilibrium in both SR and OSR processes. In addition, for these catalysts the concentrations measured for the C2H4, CH4, CH3CHO and C2H6 by-products were very low. Finally, the 2.5Rh-20Ce catalyst was selected according to its catalytic activity and characterization results in order to run a stability test, which lasted more than 115 hours under stable operation. The last chapter, Chapter 6, summarizes the main conclusions achieved throughout this Thesis work. Although very high reactant conversions and rich hydrogen mixtures were obtained using a fixed bed reaction system, the use of microreactors improves the key issues, heat and mass transfer limitations, through which the reforming reactions are intensified. Therefore, they seem to be a very interesting and promising alternative for process intensification and decentralized production for remote application.

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The focusing characteristics of long-distance flying optics were studied systemically for TEMmn Gaussian beams. The results show that the ABCD law of parameter q can be extended to Gaussian modes of any order when waist radius w in the imaginary part of parameter q is replaced by Rayleigh range Z(R) of a certain resonator in the equation. The difference between the real focal length and the geometric focal length, defined as Delta f, was calculated for laser applications. A novel self-adaptive optical system was demonstrated for precisely controlling the focusing characteristics of long-distance flying optics, Theoretical analyses and experimental results were consistent. (c) 2006 Optical Society of America.

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This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.