Recent advances in experimental condensed matter physics suggest a powerful new paradigm for the realization of exotic phases of quantum matter in the laboratory. Rather than conducting an exhaustive search for materials that realize these phases at low temperatures, it may be possible to design quantum systems that exhibit the desired properties. With the numerous advances made recently in the fields of cold atomic gases, superconducting qubits, trapped ions, and nitrogen-vacancy centers in diamond, it appears that we will soon have a host of platforms that can be used to put exotic theoretical predictions to the test. In this dissertation, I will highlight two ways in which theorists can interact productively with this fast-emerging field. First, there is a growing interest in driving quantum systems out of equilibrium in order to induce novel topological phases where they would otherwise never appear. In particular, systems driven by time-periodic perturbations—known as “Floquet systems”—offer fertile ground for theoretical investigation. This approach to designer quantum matter brings its own unique set of challenges. In particular, Floquet systems explicitly violate conservation of energy, providing no notion of a ground state. In the first part of my dissertation, I will present research that addresses this problem in two ways. First, I will present studies of open Floquet systems, where coupling to an external reservoir drives the system into a steady state at long times. Second, I will discuss examples of isolated quantum systems that exhibit signatures of topological properties in their finite-time dynamics. The second part of this dissertation presents another way in which theorists can benefit from the designer approach to quantum matter; in particular, one can design analytically tractable theories of exotic phases. I will present an exemplar of this philosophy in the form of coupled-wire constructions. In this approach, one builds a topological state of matter from the ground up by coupling together an array of one-dimensional quantum wires with local interactions. I will demonstrate the power of this technique by showing how to build both Abelian and non-Abelian topological phases in three dimensions by coupling together an array of quantum wires.

La miniaturisation est l’objectif actuel de tous les fabricants de composants radio-fréquence depuis plusieursdécennies. Si les composants actifs pour la microélectronique sont fondés sur la structuration de plaquesde silicium, les composants passifs reposent sur l’utilisation de cristaux tels que le quartz ou le niobate delithium. Ce dernier est particulièrement utilisé quand il s’agit de générer et exploiter des ondes élastiques, ainsique pour le guidage de faisceaux lumineux afin de réaliser des filtres ou des capteurs sensibles à différentsparamètres environnementaux. L’amélioration du guidage de ces ondes permet un gain en consommation et encompacité des dispositifs mais nécessite une structuration de la matière souvent tridimensionnelle. Cette étapetechnologique clé est industriellement mature pour la mise en forme du silicium, mais s’avère di_cilementtransposable à des matériaux tels que le quartz ou le niobate de lithium. Les travaux présentés dans cemanuscrit visent à réaliser des structures tridimensionnelles à hauts facteurs de forme dans des matériauxmonocristallins à l’aide d’une scie circulaire de précision. Des structures utilisant l’inversion périodique dedomaine ferroélectrique seront réalisées afin de les utiliser pour y guider des ondes élastiques possédant descouplages électromécaniques particulièrement élevées. Le guidage d’ondes optiques par le biais de ces mêmesstructures permet une amélioration du confinement par rapport aux systèmes de guidage massifs classiquescouramment utilisés pour la réalisation de filtre ou de modulateur électro-optiques. En utilisant conjointementle guidage d’ondes optiques et les domaines ferroélectriques alternés, les structures ainsi découpées permettentl’apparition de phénomènes optiques non-linéaires exaltés par l’amélioration du confinement. Ces structuresont ainsi montré leur intérêt dans plusieurs domaines de la physique avec un champ applicatif particulièrementvaste / Over the past decades, minutiarization and compacity have become a focus subject for companies specialisedin the manufacturing of radio-frequency components. Active components are typically manuafctured onsilicon wafers with well-known structuring methods. Passive ones are often manufactured on single cristalsuch as Quartz or Lithium Niobate, especially for acoustic wave generation or lightwave guiding. Theguiding of optical or acoustical waves leads to the manufacturing of sensors or filters which can be usedfor telecommunications or for the industry. Improvement in waveguiding allows for less power-consuming andmore compact devices but a 3D-structuring is usually required. This technology readness is high leveled forsilicon structuring but not for single crystals such as Lithium Niobate. This work presents the development andthe manufacturing of high aspect ratio three-dimensionnal structures in single-crystals using precise sawing.These structures show an optical waveguiding capability which allow the improvements of electro-opticmodulators or filters. Combined with a periodic reversing of Lithium Niobate polarization, these structuresallows for bulk acoustic wave generation leading to high electromechanical coupling and equivalent phasevelocity resonant modes. In non-linear optic field, this kind of structures lead to the improvement of secondharmonic generation e_ciency by reducing the cross section of waveguide. The manufactured devices in theframework of this project can actuelly be used in several domains of physic.

In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.

In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.

¡@¡@We integrated the laser-heated pedestal growth (LHPG) system with accurately controlled electrodes to build up our in situ poling system. The ZnO and MgO doped periodically poled lithium niobate crystal fiber were fabricated with the poling system. This poling system has the advantage of convenience and fast growth, but the ¡§screen effect¡¨ caused by free charges which exist near the molten zone must be eliminated. The micro swing resulted from the electric force is a feasible solution, because it can disarrange the free charges and reduce the ¡§screen effect¡¨. However, without excellently controlled micro swing, the uniformity of the poled domain pitch will loose and the conversion efficiency can not be improved. After analysis of the measured current data, the approximate system current model was presented and the proportional dependence between system current and micro swing was verified. Thus the system current was applied as the micro swing feedback signal, with that the variation of the micro swing was reduced from 25% to 15%. The stability of CO2 laser power is also a dominant factor to determine the quality of poled crystal fiber. The variation of the CO2 laser power was controlled within 1%. All the complicated works and precise control during the crystal fiber growth were accomplished with the LabVIEW program. ¡@¡@A novel and simple self-cascaded SHG + SFG scheme is presented for the generation of tunable blue/green light using ZnO doped periodically poled lithium niobate crystal fiber (PPLNCF) with a single designed pitch. A PPLNCF with a uniform period of 15.45£gm, the maximum conversion efficiency for the second harmonic generation and the cascaded SHG + SFG blue light can reach up to -9.2 dB and -31.9 dB, respectively. The 3 dB bandwidth of the tunable blue light is 3 nm (475-478 nm). In order to expand the tuning bandwidth range, a QPM gradient periodical structure was designed and can provide a 3 dB bandwidth of 65 nm for the tunable blue/green light output by simulation. We have successfully grown a crystal fiber with the domain pitch of 18.9 £gm for the C-band wavelength converter. The crystal length is 1.8 mm, the effective nonlinear coefficient of the lithium niobate crystal fiber is 18.2 pm/V that equals 0.53¡Ñdideal (34.4 pm/V). The conversion efficiency for converting the CW laser in C-band is about -59.3 dB.

In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.

In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.

The heat transfer and friction augmentation in the fully developed portion of a 2:1 aspect ratio rectangular channel with orthogonal ribs at channel Reynolds numbers of 20,000, 30,000, and 40,000 is studied both experimentally and computationally. Ribs are applied to the two opposite wide walls. The rib aspect ratio is varied systematically at 1, 3, and 5, with a constant rib height and constant rib pitch (rib-pitch-to-rib-height ratio of 10). The purpose of the study is to extend the knowledge of the performance of rectangular channels with ribs to include high aspect ratio ribs. The experimental investigation is performed using transient Thermochromic Liquid Crystals technique to measure the distribution of the local Nusselt numbers on the ribbed walls. Overall channel pressure drop and friction factor augmentation is also obtained with the experimental setup. A numerical simulation is also performed by solving the 3-D Reynolds-averaged Navier-Stokes equations using the realizable-k-Greek lowercase letter episilon] turbulence model for closure. Flow visualization is obtained from the computational results as well as numerical predictions of local distributions of Nusselt numbers and overal channel pressure drop. Results indicate that with increasing rib width, the heat transfer augmentation of the ribbed walls decreases with a corresponding reduction in channel pressure drop.

In 1980’s a new class of material named as dendrimer became popular both in the field of polymer science and engineering. Dendrimer is an example of symmetric, highly branched three dimensional globular nano-object. It possess several interesting physical and chemical properties like low solution and melt-viscosity, lower intermolecular chain entanglement, large number of end groups placed at the molecular periphery, relatively high solubility with respect to their linear counterpart. In order to get this perfectly branched structure, one has to go through the tedious multistep synthetic approach, repetitive chromatographic purification and protection-deprotection strategies in every step; all of which limits the large scale production and thus commercialization. On the other hand, hyperbranched polymer, a highly branched analogue of dendritic polymer with few defects in their branching architecture, which can be prepared in a single step, show similar physical and chemical properties as that of dendrimer. Polymerization of AB2 monomer is one of the well established method to generate hyperbranched polymer which upon polymerization, generates plenty of ‘B ’groups at the periphery along with a single ‘A’ group as a focal point in the resulting hyperbranched polymer as shown in Figure 1. From the structural point of view, hyperbranched polymers consist of three distinctly different compartments such as periphery, interior and a (single) focal point. During the past decade our lab have developed a novel melt trans-etherification process to generate polyethers and have utilized to access to a wide variety of hyperbranched structures. One of the challenges we addressed is to selectively functionalize the periphery of the hyperbranched polymer during the polymerization process. Polycondensation of ‘AB2’ monomer is not sufficient enough to generate a wide variety of hyperbranched polymer as the periphery of hyperbranched polymer is limited to the ‘B’ functional group unless it could be modified via ‘post-polymerization modifications’. Copolymerization of ‘AB2’ monomer with stoichiometric amount of ‘A-R’ monomer should result in hyperbranched polymer decorated with ‘R’ groups in the periphery that can be prepared in a single step. One of the prerequisite in the ‘AB2+A-R’ approach is that the comonomer ‘A-R’ should have silent ‘R’ group which does not interfere during the polymerization. During the copolymerization process with stoichiometric amount of ‘A-R’ monomer, ‘AB2’ monomer having one equivalent excess of ‘B’ can react with the ‘A’ group from ‘A-R’ monomer eventually generating the hyperbranched structure with peripheral ‘R’ groups. By appropriately choosing the ‘R’ group, one can access a wide class of hyperbranched polymer with the required functionality. Further by having a reactive ‘R’ group that is not participating in polymerization can act as a handle for post-polymerization modifications. For instance, copolymerization of 1-(6-Hydroxyhexyloxy)-3,5-bis(methoxymethyl)-2,4,6-trimethylbenzene (Hydroxy as ‘A’ and methoxy as ‘B’) and 6-bromo-1-hexanol where ‘OH’ and ‘-(CH2)6Br’ is ‘A’ and ‘R’ functional groups respectively, generates hyperbranched polymer with peripheral alkyl bromide functional groups as shown in Figure 2. The peripheral alkylbromides has been quantitatively transformed to quaternary ammonium or pyridinium salts using trimethyl amine or pyridine respectively. Thus by the post polymerization modification, we have transformed a hydrophobic hyperbranched polymer to a water soluble cationic hyperbranched polymer by simple and efficient post-polymerization modification. In a slightly different objective we Another problem that I have addressed is the difficulty associated with the aforementioned copolymerization approach. In spite of the fact that stoichiometric amounts of ‘A-R’ type monomer was taken in ‘AB2 + A-R’ approach, the extent of peripheral functionalization i.e. the incorporation of ‘R’ group is relatively lower. Further the molecular weight of the hyperbranched polymer obtained is also not high. One of the reasons we adopted ‘AB2 + A-R’ approach is to provide a functional handle for the subsequent post-polymerization modification. We modified the ‘AB2’ type monomer with a functionalizable handle to circumvent the lower amount of incorporation of the ‘A-R’ type monomer in ‘AB2 + A-R’ approach. Of all the readily functionalizable handles, click chemistry found to be a very useful tool for the post-polymerization modifications as the reactions conditions are mild, no side product, high selectivity, easy purification, etc. Another advantage of this reaction is that, we can incorporate any type of functional group starting from a single clickable parent hyperbranched polymer. In this particular project, I have Earlier design of the ‘AB2’ type monomer in our group, to prepare hyperbranched polymer via melt transetherification process, involved benzylic methoxy groups as ‘B’ in ‘AB2’ monomer leading to a hyperbranched polymer with peripheral methoxy groups. Transetherification under melt-conditions is an equilibrium reaction which was driven towards the hyperbranched polymer by continuous removal of methanol from the system as a volatile alcohol. In the new design of ‘AB2’ monomer; we have used benzylic allyloxy groups as ‘B’ in ‘AB2’ monomer, where in polymerization is driven by the continuous removal of allyl alcohol (instead of methanol as in the previous case), generates hyperbranched polymer with peripheral allyloxy group containing hyperbranched polymer. The allyloxy groups can be subsequently functionalized with a variety of thiol, we prepared a hydrocarbon-soluble octadecyl-derivative, amphiphilic systems using 2-mercaptoethanol and chiral amino acid (N-benzoyl cystine) hyperbranched structures by using thiol-ene click reactions (Figure 3). Polymers prepared from the parent hyperbranched polymer have significantly different physical properties like glass transition temperature (Tg), melting point (Tm) etc; thus considering the versatility of functionalization, parent polymer could be envisioned as a clickable hyperscaffold. More interestingly by functionalizing cystine derivative, we have demonstrated the possibility of biconjugation of the hyperbranched polymer. In summary, the limitations of ‘AB2+A-R’ copolymerization approach (low molecular weight Molecular weight and molecular weight distribution are very important parameters that influence the physical property and thus the application of the polymeric materials. As predicted by Flory, hyperbranched polymers are inherently polydisperse in nature and it tends to infinity when the percent of conversion is very high. Experimentally observed value of polydispersity is also significantly higher compared to their linear analogues. Control of the molecular weight and polydispersity of hyperbranched polymer by using a suitable amount of reactive multifunctional core has been demonstrated in this project. We have substantiated by using very little amount of ‘B3’ core along with ‘AB2’ monomer; wherein ‘B’ in ‘B3’ are more reactive than ‘B’ in ‘AB2’ monomer, regulate the molecular weight and polydispersity of the resulting hyperbranched polymer. As the ratio of core to monomer increases the molecular weight and polydispersity reduces in nearly linear fashion. In a slightly different objective, the core and periphery are functionalized with two different fluorophore by using orthogonal click reactions and demonstrated the possibility of energy transfer from periphery to the core of the hyperbranched polymer. In this section of my thesis, the self-assembly behavior of a periodically grafted amphiphilic copolymer has been studied. Polymer was synthesized via melt transesterification approach where hexaethylene glycol monomethyl ether (HEG) containing diester monomers are reacted with alkylyne diol monomers with varying carbon spacer (C12 and Another interesting problem, I approached is to functionalize the interior part of the hyperbranched polymer. In the case of dendrimer, as it is a step-wise synthesis, internal functionalization could be accomplished with the order of monomer addition i.e. by putting the internal functional group containing monomer first followed by other monomer not having those functional groups, whereas it is a bit challenging task for hyperbranched polymers especially when dealing with polycondensation of AB2 monomers, as it is a single step polymerization process. For a hyperbranched polymer in the polycondensation of ‘AB2’ monomer, the internal functional group should reside in between of the ‘A’ and ‘B’ functional group wherein the internal functional groups are silent during the process of polymerization. In order to do so, we have designed and synthesized a new AB2 monomer (a in Figure: 4). Here decanol is the volatile condensate that was removed during the transetherification reactions leading to a hyperbranched polymer having allyl group as the internal functional group and decyloxy as the peripheral functional group (b in Figure: 4). As a post-polymerization modification, the interior allyl groups were modified by thiol-ene click reaction with variety of thiol derivatives. In one example, the inherent hydrophobic nature of the parent hyperbranched polymer which is enhanced by the decyl chain at the molecular periphery, is converted to a alkaline water soluble hyperbranched polymer by the click reaction with mercapto succinic acid (d in Figure: 4) or mercapto propionic acid (c in Figure: 4) to the internal allyl groups, generating a novel amphiphilic hypersystem. This kind of amphiphilic systems are very interesting to study for their self-assembly behavior, in this particular case, the modified hyperbranched polymer adopts as a large spherical aggregates in alkaline water evidenced by FESEM (Figure: 4) and AFM images. Further investigation is being carried out to understand the exact nature of these aggregates. As the hyperbranched polymer contained ‘-S-‘ group in the interior, we utilized this as the scaffold for scavenging heavy metal ions like Hg2+ from aqueous solutions to the chloroform solution containing polymer. This hyperbranched polymer could trap Hg2+ ions even when present in ppm level of contamination.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / This paper presents a numerical investigation of the propagation and cover (100fs) short pulse switching in a nonlinear coupler dual-core photonic crystal fiber with periodically modulated constructed fiber nonlinearity ( PMN - PFC ). Our main objective was to study the effect of amplitude modulations (AM) and frequency modulation (Wm) in the refractive index of nonlinearity (gamma) at a spread of Photonic Crystal Fiber with initially fixed range with frequency and amplitude periodically varying modulation. The implementation of modulation was inserted into dual-fiber couplers, which has been studied for its use as a whole using ultra switching optical switch and as an optical processor. Our simulations are taking into account the amplitude and frequency modulations of different PMN - PFC. Coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics of the compression factor , the crosstalk ( Xtalk ) and extinction rate ( Xratio ) levels were studied in the first descending order solitons of high energy pump for considering 2LC. An analysis of the reference (channel 2) channel was observed that the low frequency modulation is an increase in the switching power by increasing the transmission efficiency. For high modulation frequencies transmitted energy efficiency loses. The switching pulses are stronger in the low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1) revealed that this increase in unwanted high-frequency energy, to reduce the extent of amplitude modulation. In summary, we have demonstrated that the introduction of a non- linear profile leads to a frequency modulated PMN - PFC high variations in transmission efficiency , Xtalk , Xratio function of frequency and modulation amplitude and the input power. / Este trabalho apresenta uma investigaÃÃo numÃrica da propagaÃÃo e a comutaÃÃo de pulsos curtos capa ( 100fs ) em um acoplador nÃo-linear de dois nÃcleos de fibras de cristal fotÃnico construÃdos com periodicamente modulada a fibra nÃo-linearidade (PMN - PFC). Nosso principal objetivo foi estudar o efeito das modulaÃÃes de amplitude (Am) e modulaÃÃo da frequÃncia (Wm) no Ãndice de refraÃÃo da nÃo-linearidade (gama) em uma propagaÃÃo de Fibra de Cristais FotÃnicos, com o gama inicialmente fixo com frequÃncia e amplitude de modulaÃÃo variando periodicamente. A execuÃÃo da modulaÃÃo foi inserida em uma fibra com acopladores duplo, que tem sido estudados quanto à sua utilizaÃÃo como um todo utilizando ultracomutaÃÃo Ãptica e processador como interruptor Ãptico. Nossas simulaÃÃes estÃo levando em conta da amplitude e frequÃncia diferentes modulaÃÃes do PMN - PFC. Foram estudados acoplador para acoplamento cujo comprimento à Lc = 1,8 centÃmetros, as caracterÃsticas de transmissÃo, o fator de compressÃo, o crosstalk (Xtalk) e taxa de extinÃÃo ( Xratio ) nos nÃveis dos primeiros sÃlitons de ordem decrescente para altas energias bomba considerando 2LC. Uma anÃlise do canal de referÃncia ( canal 2 ) , observou-se que a baixas frequÃncias de modulaÃÃo ocorre um aumento na potÃncia de comutaÃÃo aumentando a eficiÃncia da transmissÃo. Para alta modulaÃÃo freqÃÃncias a eficiÃncia energÃtica transmitida perde. Os pulsos de comutaÃÃo sÃo mais fortes para a baixa frequÃncia e alta amplitude de modulaÃÃo. O Xtalk à uma funÃÃo da mediÃÃo feita no canal secundÃrio ( canal 1 ) , observou-se que este aumento de energia indesejados de alta frequÃncia, para reduzir a medida da modulaÃÃo de amplitude. Em resumo, temos demonstrado que a introduÃÃo de um perfil nÃo-linearidade leva a uma periodicidade modulada PMN - PFC a fortes variaÃÃes na eficiÃncia de transmissÃo, Xtalk , Xratio funÃÃo da freqÃÃncia e modulaÃÃo de amplitude e a potÃncia de entrada.