Dissertations / Theses on the topic 'Harmonic oscillators'
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Bartlett, Stephen D., Hubert de Guise, Barry C. Sanders, and Andreas Cap@esi ac at. "Quantum Computation with Harmonic Oscillators." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi962.ps.
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Peidaee, Pantea, and pantea peidaee@rmit edu au. "Strongly Perturbed Harmonic Oscillator." RMIT University. SECE, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080804.094824.
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The limits of current micro-scale technology is approaching rapidly. As the technology is going toward nano-scale devices, physical phenomena involved are fundamentally different from micro-scale ones [1], [2]. Principles in classical physics are no longer powerful enough to explicate the phenomena involved in nano-scale devices. At this stage, quantum mechanic sheds some light on those topics which cannot be described by classical physics. The primary focus of this research work is the development of an analysis technique for understanding the behavior of strongly perturbed harmonic oscillators. Developing ``auxiliary'' boundary value problems we solve monomially perturbed harmonic oscillators. Thereby, we assume monomial terms of arbitrary degree and any finite coefficient desired. The corresponding eigenvalues and eigenvectors can be utilized to solve more complex anharmonic oscillators with non polynomial anharmonicity or numerically defined anharmonicity. A large number of numerical calculations demonstrate the robustness and feasibility of our technique. Particular attention has been paid to the details as have implemented the underlying formula. We have developed iterative expressions for the involved integrals and the introduced ``Universal Functions.'' The latter are applications and adaptations of a concept which was developed in 1990's to accelerate computations in the Boundary Element Method.
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Penbegul, Ali Yetkin. "Synchronization Of Linearly And Nonlinearly Coupled Harmonic Oscillators." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613258/index.pdf.
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In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results.
The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic oscillators are presented. The theoretical results say that linearly coupled identical harmonic oscillators synchronize for any frequency of oscillation. For nonlinearly coupled identical harmonic oscillators, synchronization is shown to occur at large enough frequency values.
In the second part, the simulator and simulation results are presented. A GUI is designed in MATLAB to run the simulations. In the simulations, synchronization of coupled harmonic oscillators are studied according to different coupling strength values, different frequency values, different coupling graph types (e.g. all-to-all, ring, tree) and different coupling function types (e.g. linear, saturation, cubic). The simulation results do not only support the theoretical part of the thesis but also give some idea about the part of the synchronization of coupled harmonic oscillators uncovered by theory.
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Marquart, Chad A. "Sliding-mode amplitude control techniques for harmonic oscillators." Texas A&M University, 2003. http://hdl.handle.net/1969.1/5767.
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This thesis investigates both theoretical and implementation-level aspects of switching-
feedback control strategies for the development of voltage-controlled oscillators. We
use a modified sliding-mode compensation scheme based on various norms of the
system state to achieve amplitude control for wide-tuning range oscillators. The
proposed controller provides amplitude control at minimal cost in area and power
consumption. Verification of our theory is achieved with the physical realization of
an amplitude controlled negative-Gm LC oscillator. A wide-tuning range RF ring
oscillator is developed and simulated, showing the effectiveness of our methods for
high speed oscillators. The resulting ring oscillator produces an amplitude controlled
sinusoidal signal operating at frequencies ranging from 170 MHz to 2.1 GHz. Total
harmonic distortion is maintained below 0:8% for an oscillation amplitude of 2 Vpp
over the entire tuning range. Phase noise is measured as -105.6 dBc/Hz at 1.135 GHz
with a 1 MHz offset.
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Sousa, Antonio C. Torrezan de (Antonio Carlos Torrezan de). "Frequency-tunable second-harmonic submillimeter-wave gyrotron oscillators." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/62463.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 175-185).
This thesis reports the design and experimental demonstration of frequency-tunable submillimeter-wave gyrotrons operating in continuous wave (CW) at the second harmonic of the electron cyclotron frequency. An unprecedented continuous frequency tuning range of more than 1 GHz has been achieved in both a 330- and a 460-GHz gyrotron via magnetic field tuning or voltage tuning. The 330-GHz gyrotron has generated 19 W of power in a cylindrical TE4,3,q mode from a 13-kV 190-mA electron beam. The minimum start current was measured to be 21 mA, where good agreement was verified between the measured start current values and the calculation from linear theory for the first six axial modes, q = 1 through 6. A continuous tuning range of 1.2 GHz with a minimum output power of 1 W has been achieved experimentally via magnetic or beam voltage tuning. The output stability of the gyrotron running under a computerized control system was assessed to be ±0.4% in power and ±3 ppm in frequency during a 110-hour uninterrupted CW test. Evaluation of the gyrotron microwave output beam using a pyroelectric camera indicated a Gaussian-like mode content of 91%. Measurements were also carried out in microsecond pulse operation at a higher beam current (610 mA), yielding a minimum output power of 20 W over a tuning range of 1.2 GHz obtained by means of cyclotron frequency tuning and thermal tuning. The 330-GHz gyrotron will be used as a source for 500 MHz nuclear magnetic resonance (NMR) experiments with sensitivity enhanced by dynamic nuclear polarization (DNP). In addition to the 330-GHz gyrotron, the design and CW operation of a tunable second-harmonic 460-GHz gyrotron are described. The 460-GHz gyrotron operates in the whispering gallery mode TE1 1 ,2 and has generated 16 W of output power with a 13-kV 100-mA electron beam. The start oscillation current measured over a range of magnetic field values is in good agreement with theoretical start currents obtained from linear theory for successive high order axial modes TE1,2,q. The minimum start current is 27 mA. Power and frequency tuning measurements as a function of the electron cyclotron frequency have also been carried out. A smooth frequency tuning range of 1 GHz with a minimum output power of 2 W has been obtained for the operating second-harmonic mode either by magnetic field tuning or beam voltage tuning. Long-term CW operation was evaluated during an uninterrupted period of 48 hours, where the gyrotron output power and frequency were kept stable to within ±0.7% and ±6 ppm, respectively, by a computerized control system. Proper operation of an internal quasi-optical mode converter implemented to transform the operating whispering gallery mode to a Gaussian-like beam was also verified. Based on images of the gyrotron output beam taken with a pyroelectric camera, the Gaussian-like mode content of the output beam was computed to be 92% with an ellipticity of 12%. The 460-GHz gyrotron is intended to be used as a submillimeter-wave source in a 700-MHz DNP/NMR spectrometer.
by Antonio C. Torrezan de Sousa.
Ph.D.
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Venkataraman, Vignesh. "Understanding open quantum systems with coupled harmonic oscillators." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/30715.
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When a quantum system interacts with many other quantum mechanical objects, the behaviour of the system is strongly affected; this is referred to as an open quantum system (OQS). Since the inception of quantum theory the development of OQSs has been synonymous with realistic descriptions of quantum mechanical models. With recent activity in the advancement of quantum technologies, there has been vested interest in manipulating OQSs. Therefore understanding and controlling environmental effects, by structuring environments, has become an important field. The method of choice for tackling OQSs is the master equation approach, which requires approximations and doesn't allow direct assessment of the environment. This thesis tackles the issues of OQSs with an unorthodox method; we employ a series of coupled quantum harmonic oscillators to simulate an OQS. This permits the use of the covariance matrix technique which allows us to avoid approximations and analyse the environment modes. We investigate the Markov approximation and Rotating-Wave approximation (RWA), which are commonly used in the field. By considering four OQS models, we study an entanglement-based non-Markovian behaviour (NMB) quantifier (ENMBQ). The relevance of detuning, coupling strength and bath structures in determining the amount of NMB is noted. A brief study of the factors that affect a fidelity-based NMB quantifier is also conducted. We also analyse the effect on the ENMBQ if the terms excluded by the RWA are included in the models. Finally, an examination of the applicability of the RWA in the presence of strong coupling is undertaken in a three oscillator model. The fidelity-based analysis utilised could allow one to ascertain when and if the RWA can be applied to a model of interest, including OQSs. The knowledge within, and the methodology used throughout this thesis, could arm researchers with insights to control the flow of quantum information in their systems.
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Cheng, Ching-Chuan. "Prediction of snap-through instability under harmonic excitation." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/42077.
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Shiri-Garakani, Mohsen. "Finite Quantum Theory of the Harmonic Oscillator." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5078.
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We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a
finite quantum theory with three quantum constants instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a
dipole rotator with N=l(l+1) states where l is very large for physically interesting case. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N there are three broad classes of FLHO: soft, medium, and hard corresponding respectively to cases where ratio of the of potential energy to kinetic energy in the Hamiltonian is very small, almost equal to one, or very large
The field oscillators responsible for infra-red and
ultraviolet divergences are soft and hard respectively. Medium oscillators approximate the QLHO. Their
low-lying states have nearly the same zero-point
energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z-axis.
The soft and hard FLHO's have infinitesimal
0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators polaroizd along x-axis or y-axis respectively. Soft oscillators have
frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
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Wang, Le. "The design of a low noise VCO with innovative harmonic filtering resistor." Embargo, 2006. http://www.dissertations.wsu.edu/Thesis/Summer2006/l%5Fwang%5F080906.pdf.
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Contreras, Carmen Rosa. "On some physical aspects of the group properties of point transformations of harmonic oscillators." Scholarly Commons, 1991. https://scholarlycommons.pacific.edu/uop_etds/2220.
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The purpose of our work is to study the physical aspects of the application of the Lie group analysis to simple harmonic oscillators and related systems which can or cannot be canonical ones. The mathematical part of the problem has been studied by many authors. Quite recently L. Hubbard, C.Wulfman and H. Rabitz and C. Wulfman and H.Rabitz have developed a method for a group theoretical analysis applicable to a more general class of linear systems of Ordinary Differential Equations (ODE).
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Kopalle, Deepika Niu Guofu. "RF linearity analysis in nano scale CMOS using harmonic balance device simulations." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Thesis/KOPALLE_DEEPIKA_43.pdf.
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Cleante, Vinícius Germanos [UNESP]. "Effects of railway track vibration induced by passing trains on an energy harvesting device." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/128026.
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000849610.pdf: 1060639 bytes, checksum: f7f529a2c97b379eced359bb7ae14e34 (MD5)Com avanços em tecnologia, e com a necessidade em buscar soluções para reduzir efeitos do aquecimento global, tornou captação de energia uma área de pesquisa popular. O particular interesse deste projeto é a extração de energia a partir de vibrações em ambientes no qual possui aplicação em ambientes hostis ou em áreas remotas. Este tipo de dispositivo possui a capacidade de alimentar sistemas microeletrônicos que utilizam pouca energia, por exemplo sensores de monitoramento da saúde estrutural, sensores sem fio, radio comunicação, etc. Neste trabalho, uma investigação é conduzida para determinar a quantidade de energia que pode ser extraída a partir de vibrações devido a passagem do trem. Um estudo é conduzido para investigar o design dos parâmetros ótimos para um extrator de energia submetido a vibrações induzidas por trens passando com diferentes velocidades. Dados de vibração de dois locais no Reino Unido é utilizado para este propósito. Uma expressão analítica aproximada para energia extraída por um extrator linear submetido a excitação periódica de tempo limitado é avaliado utilizando os componentes harmônicos das vibrações em um dormente. Os resultados são comparados com os obtidos através da análise numérica. Também, o comportamento de um extrator de energia linear submetido a vibrações induzidas por diversos trens passantes, é avaliado para trens com uma faixa de velocidade observado nos dados mensurados em Steventon
With advances in technology, and with the need to seek for solutions to reduce the effects of global warming, makes energy harvesting a popular research topic. The particular interest in this project is the harvesting of energy from ambient vibrations, which has applications in hostile environments or in remote areas. This type of device has the capacity feed microelectromechanical systems that use a low power, for example sensors for structural health monitoring, wireless sensors, radio communications, etc. In this work, an investigation is conducted to determine how much energy can be scavenged from vibrations due the passage of a train. A study is conducted to investigate the optimum parameters design of an energy harvester subject to vibrations induced by trains passing at different speeds. Vibration Data from two sites in the United Kingdom is used for this purpose. An approximate analytical expression for energy harvested from a linear harvester subject to a time-limited periodic excitation is evaluated using the harmonic components of the sleeper vibrations. The results are compared with those obtained through numerical analysis. Also, the behaviour of the linear energy harvester subject to vibrations induced by several passing trains is evaluated for ranges of speeds observed in measurement data sets at Steventon site
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Cleante, Vinícius Germanos. "Effects of railway track vibration induced by passing trains on an energy harvesting device /." Ilha Solteira, 2015. http://hdl.handle.net/11449/128026.
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Orientador: Michael John BrennanBanca: Fabricio César Lobato de Almeida
Banca: Gianluca Gatti
Título em portugues: Efeitos da vibração em linha férrea induzida pela passagem de trens em dispositivo de captação de energia
Resumo: Com avanços em tecnologia, e com a necessidade em buscar soluções para reduzir efeitos do aquecimento global, tornou captação de energia uma área de pesquisa popular. O particular interesse deste projeto é a extração de energia a partir de vibrações em ambientes no qual possui aplicação em ambientes hostis ou em áreas remotas. Este tipo de dispositivo possui a capacidade de alimentar sistemas microeletrônicos que utilizam pouca energia, por exemplo sensores de monitoramento da saúde estrutural, sensores sem fio, radio comunicação, etc. Neste trabalho, uma investigação é conduzida para determinar a quantidade de energia que pode ser extraída a partir de vibrações devido a passagem do trem. Um estudo é conduzido para investigar o design dos parâmetros ótimos para um extrator de energia submetido a vibrações induzidas por trens passando com diferentes velocidades. Dados de vibração de dois locais no Reino Unido é utilizado para este propósito. Uma expressão analítica aproximada para energia extraída por um extrator linear submetido a excitação periódica de tempo limitado é avaliado utilizando os componentes harmônicos das vibrações em um dormente. Os resultados são comparados com os obtidos através da análise numérica. Também, o comportamento de um extrator de energia linear submetido a vibrações induzidas por diversos trens passantes, é avaliado para trens com uma faixa de velocidade observado nos dados mensurados em Steventon
Abstract: With advances in technology, and with the need to seek for solutions to reduce the effects of global warming, makes energy harvesting a popular research topic. The particular interest in this project is the harvesting of energy from ambient vibrations, which has applications in hostile environments or in remote areas. This type of device has the capacity feed microelectromechanical systems that use a low power, for example sensors for structural health monitoring, wireless sensors, radio communications, etc. In this work, an investigation is conducted to determine how much energy can be scavenged from vibrations due the passage of a train. A study is conducted to investigate the optimum parameters design of an energy harvester subject to vibrations induced by trains passing at different speeds. Vibration Data from two sites in the United Kingdom is used for this purpose. An approximate analytical expression for energy harvested from a linear harvester subject to a time-limited periodic excitation is evaluated using the harmonic components of the sleeper vibrations. The results are compared with those obtained through numerical analysis. Also, the behaviour of the linear energy harvester subject to vibrations induced by several passing trains is evaluated for ranges of speeds observed in measurement data sets at Steventon site
Mestre
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Baker, Charles Edmond. "On the Determination of Spectral Properties of Certain Families of Operators." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449153836.
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Summers, Jonathan lewis. "Applications of the method of two time scale harmonic balance to problems of autonomous and periodically forced mechanical oscillators." Thesis, University of Leeds, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303381.
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Hellström, Jonas. "Nanosecond optical parametric oscillators and amplifiers based on periodically poled KTiOPO4." Doctoral thesis, KTH, Physics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3269.
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Optical parametric oscillators (OPOs) and optical parametricamplifiers (OPAs) constitute a class of optical frequencyconverting devices that have many possible applications, e.g.in range finding, molecular spectroscopy and medicine. They canconvert the frequency of the incident pump field with highefficiency, and generate two waves at new frequencies that willbe continuously tuneable over a wide spectral range. Virtuallyany wavelengths within the transparency region of the nonlinearmaterial can be generated if the material can bequasi-phasematched (QPM). In addition, QPM gives thepossibility to utilise the largest nonlinear tensor element ofthe material and allows walk-off free interaction between thewaves.
The aims of this thesis have been to investigate thepossibility to use QPM KTiOPO4crystals as nonlinear material in nanosecond OPOsand OPAs operating at room-temperature, and to explore theadvantages and shortcomings of these devices. The technique ofelectric field poling has been employed to implement the QPMstructure in flux grown KTiOPO4(KTP).
The main conclusion is that periodically poled KTP (PPKTP)is a suitable material to use in nanosecond OPOs and OPAs. Thematerial properties that foremost make KTP into an attractivenonlinear material are: The large value of the nonlinearcoefficient d33, the high resistance to optically inducedbreakdown, the low susceptibility to grey-track formation, theinsensitivity to the photorefractive effect, the widetransparency and the low coercive field.
The thesis shows that it is possible to pole large volumesof KTP with a high quality of the QPM structure. Highlyefficient nanosecond OPOs have been constructed during thisproject. Maximum conversion efficiencies have reached 45 % inthe case of a singly resonant OPO (SRO) built around a 3 mmthick PPKTP crystal. Total pulse energies for both the signal(1.72 µm) and the idler (2.8 µm) of up to 18 mJ wasreached and an average output power of 2 W was obtained forthis sample. However, up to 24 W was produced in a doublyresonant OPO operating close to degeneracy. The efficiencyreached 48 % for that case. Truly continuous and very widespectral tuning has also been demonstrated, as well as a narrowbandwidth OPO operating on one single longitudinal mode.
Keywords:optical parametric oscillators, opticalparametric amplifiers, quasi-phasematching, KTiOPO4, nonlinear optics, frequency conversion, periodicelectric field poling, ferroelectrics, high-order secondharmonic generation, electro-optic effect.
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Chaitanya, Kumar Suddapalli. "High-power, fiber-laser-pumped optical parametric oscillators from the visible to mid-infrared." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/83528.
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High-power, continuous-wave (cw), mid-infrared (mid-IR) laser sources are of interest
for variety of applications such as trace gas detection and remote sensing, which
require broad spectral coverage to address the most prominent absorption features
of a wide range of molecular species particularly in the mid-IR fingerprint region. On
the other hand, surgical applications require high energy sources with unique pulse
structure at specific wavelength in the mid-IR ranging from 6-6.5 m.
Optical parametric oscillators (OPOs) offer potential sources for all the above
applications. The output wavelengths of a singly-resonant oscillator (SRO) can be
coarsely tuned over wide ranges through the adjustment of the nonlinear crystal
temperature, phase-matching angle or, in the case of quasi-phase-matched (QPM) the first time. The high-energy CSP OPO marked the first demonstration of a
compact, high-repetition-rate OPO synchronously pumped by a master oscillator
power amplifier system at 1064 nm, generating an milli-joule pulses in the 6-6.5 m
spectral range, which is technologically important for surgical applications.
Additionally, we also demonstrated a fiber-based-green source at 532 nm, based
on single-pass second harmonic generation (SHG) in MgO:sPPLT, as an alternative
pump source for Ti:sapphire laser, pointing towards the future, compact fiber-laser
pumped Ti:sapphire lasers. Further efforts to improve the SHG efficiency led to
the development of a novel multi-crystal scheme, enabling single-pass SHG efficiency
as high as 56%. This generic technique is simple and can be implemented at any
wavelength.
materials, the QPM grating period. The combination of SRO with a tunable pump
laser allows the development of uniquely flexible and rapidly tunable class of mid-IR
sources.
In this thesis we have demonstrated several mid-IR OPOs in the cw as well as
ultrafast picosecond regime pumped by fiber-lasers making them compact and robust.
In the cw regime, we developed a high-power, Yb-fiber-laser pumped mid-IR OPO
based on MgO:PPLN spanning 1506-1945 nm in the near-IR and 2304-3615 nm
wavelength range in the mid-IR, efficiently addressing the thermal effects by implementing
the optimum signal output coupling. Novel materials such a MgO:sPPLT,
with better optical and thermal properties for cw mid-IR generation are explored.
High-power broadband, cw mid-IR generation is also demonstrated by using the
extended phase-matching properties of MgO:PPLN.
Further, we also demonstrated a simple, inexpensive and novel interferometric
technique for absolute optimization of output power from a ring optical oscillator.
We deployed a picosecond Yb-fiber-laser pumped mid-IR OPO based on MgO:PPLN
in ring cavity configuration to demonstrate this proof-of-principle experiment forFuentes coherentes de luz continua y de alta potencia en el infrarrojo-medio (mid-IR) son de gran interés por su aplicación en la detección de gases, detección remota y la observación de imágenes. Estas aplicaciones requieren un ancho de banda amplio para evidenciar las características que ofrece la absorción de una gran variedad de especies moleculares, particularmente en la región “finger print” del mid-IR. Por otra parte, fuentes altamente energéticas con pulsos que posean estructuras peculiares en rangos específicos de longitud de onda en el mid-IR, entre 6-6.5 m. , prometen características únicas para nuevas aplicaciones en cirugía. Osciladores ópticos paramétricos (OPOs) constituyen fuentes de luz versátiles y apropiadas para todas las aplicaciones mencionadas anteriormente. La longitud de En el régimen ultrarápido, hemos demostrado una nueva técnica de interferometría para la optimización absoluta de la potencia de salida de un oscilador óptico con una cavidad de anillo. Como demostración de principio, implementamos, por primera vez, un OPO de picosegundos en el mid-IR basado en MgO:PPLN con una cavidad de anillo bombeado por un láser de fibra de Yb. Además, hemos desarrollado un nuevo OPO de alta energía en el mid-IR basado en el material nolineal CSP. Esto representa la primera demostración de un OPO compacto de alta repetición sincrónicamente bombeado por un láser de estado sólido a 1064 nm generando pulsos de milijulios en el rango espectral 6-6.5 m. Esta radiación es importante para aplicaciones en cirugía. Adicionalmente, hemos demostrado una fuente verde, 532 nm, basada en láseres de fibra. Esta radiación se obtiene por medio de la generación de segundo harmónico (SHG) en un paso individual en MgO:sPPLT. Esto representa una nueva alternativa de bombeo para los láseres de Ti:sapphire que los harán compactos en el futuro. Los esfuerzos para mejorar la eficiencia de segundo harmónico resultaron en el desarrollo de un novedoso esquema que utiliza múltiples cristales y permite eficiencias de SHG de paso individual del 56%. Este esquema es general y simple y puede ser implementado para cualquier longitud de onda. onda de un OPO puede ser sintonizada en regiones amplias del espectro cambiando la temperatura del cristal no-lineal, el ángulo de ajuste de fase o, al considerar materiales cuasi ajuste de fase (QPM), cambiando el periodo de red. En esta tesis, hemos demostrado una gran variedad de OPOs en el mid-IR en régimen continuo y de pulsos de picosegundo. Estos OPOs han sido bombeados por láseres de fibra permitiendo un diseño compacto y resistente. En el régimen de emisión continua, hemos implementado un OPO de alta potencia basado en MgO:PPLN bombeado por un láser de fibra. Este OPO es sintonízable en el rango 1506-1945 nm correspondiente al infrarrojo-cercano y en el rango 2304-3615 nm correspondiente al mid-IR. Esta capacidad de sintonización se logra al sobrepasar eficientemente los efectos térmicos optimizando el acoplamiento de salida. Materiales nuevos como el MgO:sPPLT, con propiedades ópticas y térmicas mejoradas para la generación de radiación continua en el mid-IR han sido estudiados. Utilizando las propiedades ajuste de la fase extendió del MgO:sPPLT, fuentes continuas de alta potencia con un gran ancho de banda en el infrarrojo-medio también han sido implementadas.
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Zhou, Dawei. "Development of active integrated antennas and optimization for harmonic suppression antennas : simulation and measurement of active antennas for amplifiers and oscillators and numerical solution on design and optimization of active patch antennas for harmonic suppression with adaptive meshing using genetic algorithms." Thesis, University of Bradford, 2007. http://hdl.handle.net/10454/4763.
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The objectives of this research work are to investigate, design and implement active integrated antennas comprising active devices connected directly to the patch radiators, for various applications in high efficiency RF front-ends, integrated oscillator antennas, design and optimization of harmonic suppression antennas using a genetic algorithm (GA). A computer-aided design approach to obtain a class F operation to optimizing the optimal fundamental load impedance and designing the input matching circuits for an active integrated antenna of the transmitting type is proposed and a case study of a design for 1.6 GHz is used to confirm the design principle. A study of active integrated oscillator antennas with a series feed back using a pseudomorphic high electronmobility transistor (PHEMT) confirms the design procedure in simulation and measurement for the oscillator circuit connected directly to the active antenna. Subsequently, another design of active oscillator antenna using bipolar junction transistor (BJT) improves the phase noise of the oscillation and in addition to achieve amplitude shift keying (ASK) and amplitude modulation (AM) modulation using the proposed design circuit. Moreover, the possibility of using a sensor patch technique to find the power accepted by the antenna at harmonic frequencies is studied. A novel numerical solution, for designing and optimizing active patch antennas for harmonic suppression using GA in collaboration with numerical electromagnetic computation (NEC), is presented. A new FORTRAN program is developed and used for adaptively meshing any planar antenna structure in terms of wire grid surface structures. The program is subsequently implemented in harmonic suppression antenna design and optimization using GA. The simulation and measurement results for several surface structures show a good agreement.
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Khanolkar, Ankita Nayankumar. "Effect of Spectral Filtering on Pulse Dynamics of Ultrafast Fiber Oscillators at Normal Dispersion." University of Dayton / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1628171764933755.
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Bessa, Vagner Henrique Loiola. "Osciladores log-periódicos e tipo Caldirola-Kanai." reponame:Repositório Institucional da UFC, 2012. http://www.repositorio.ufc.br/handle/riufc/13625.
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BESSA, Vagner Henrique Loiola. Osciladores log-periódicos e tipo Caldirola-Kanai. 2012. 66 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012.Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-19T18:23:14Z No. of bitstreams: 1 2012_dis_vhlbessa.pdf: 26350485 bytes, checksum: 4eb844c05187fb66d3b274a9f8d1b0ed (MD5)
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In this work we present the classical and quantum solutions of two classes of time-dependent harmonic oscillators, namely: (a) the log-periodic and (b) the Caldirola-Kanai-type oscillators. For class (a) we study the following oscillators: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ and (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. In all three cases $omega(t)=omega_0frac{t_0}{t}$. For class (b) we study the Caldirola-Kanai oscillator (IV)where $omega(t)=omega_0$ and $m(t)=m_0 ext{exp}ajust{gamma t}$ and the oscillator with $omega(t)=omega_0$ and $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, for $alpha=2$ (V) and $alpha=4$ (VI). To obtain the classical solution for each oscillator we solve the respective equation of motion and analyze the behavior of $q(t)$, $p(t)$ as well as the phase diagram $q(t)$ vs $p(t)$. To obtain the quantum solutions we use a unitary transformation and the Lewis and Riesenfeld quantum invariant method. The wave functions obtained are written in terms of a function ($ ho$) which is solution of the Milne-Pinney equation. Futhermore, for each system we solve the respective Milne-Pinney equation and discuss how the uncertainty product evolves with time.
Nesse trabalho apresentamos as soluções clássicas e quânticas de duas classes de osciladores harmônicos dependentes de tempo, a saber: (a) o oscilador log-periódico e (b) o oscilador tipo Caldirola-Kanai. Para a classe (a) estudamos os seguintes osciladores: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ e (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. Nesses três casos $omega(t)=omega_0frac{t_0}{t}$. Para a classe (b) estudamos o oscilador (IV) de Caldirola-Kanai onde $omega(t)=omega_0$ e $m(t)=m_0 ext{Exp}ajust{gamma t}$ e osciladores com $omega(t)=omega_0$ e $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, para (V) $alpha=2$ e (VI) $alpha=4$. Para obter as soluções clássicas de cada oscilador resolvemos suas respectivas equações de movimento e analisamos o comportamento de $q(t)$, $p(t)$ assim como do diagrama de fase $q(t)$ vs $p(t)$. Para obter as soluções quânticas usamos uma transformação unitária e o método dos invariantes quânticos de Lewis e Riesenfeld. A função de onda obtida é escrita em termos de uma função $ ho$, que é solução da equação de Milne-Pinney. Ainda, para cada sistema resolvemos a respectiva equação de Milne-Pinney e discutimos como o produto da incerteza evolui no tempo.
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Gryga, Michal. "Silná vazba v plazmonických strukturách." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382251.
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This diploma thesis deals with numerical simulations of the optical response of plasmonic infrared antennas placed on silicon substrates with thin film of silicon dioxide and subsequently with fitting of scattering spectra by model of coupled harmonic oscillators. In this work, we study an influence of length of antennas on the strength of coupling of localized surface plasmons in the antennas with phonons in silicon dioxide film. Also, the influence of silicon dioxide film thickness on this coupling is investigated.
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Deymier, P. A., K. Runge, and J. O. Vasseur. "Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice." AMER INST PHYSICS, 2016. http://hdl.handle.net/10150/622819.
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We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Rosendo, Danilo Castro. "Sobre a função de Mittag-Leffler." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307007.
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Orientador: Edmundo Capelas de OliveiraDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho abordamos um estudo da equação diferencial ordinária, linear, homogênea de segunda ordem com três singularidades regulares, incluindo uma no infinito de onde obtivemos a equação hipergeométrica e, através do método de Frobenius, introduzimos a função hipergeométrica com singularidade na origem. Por um conveniente processo de limite na equação hipergeométrica obtivemos a equação hipergeométrica confluente, bem como a função hipergeométrica confluente. Apresentamos a função de Mittag-Le²er como uma generalização da função exponencial e suas relações com outras funções, em especial com a função hipergeométrica confluente. Abordamos o conceito de integral e derivada de ordens fracionárias de algumas funções conhecidas. Através da metodologia da transformada de Laplace discutimos uma equação diferencial fracionária com coeficientes constantes de onde emergem as funções de Mittag-Leffler. Por fim, definimos as equações diferenciais fracionárias e, como aplicação, efetuamos um estudo sistemático do oscilador harmônico fracionário.
Abstract: This work presents an introductory study of a second order, linear and homogeneous, ordinary differential equation with three singular regular points, including a singularity at the infinity. We obtain the hypergeometric equation and, by means of the Frobenius method, we introduce the hypergeometric function which is regular at the origin. By a convenient limit process we obtain the confluent hypergeometric equation which has the confluent hypergeometric function as a regular solution at the origin. We introduce the Mittag-Leffler function as a generalization of the exponential function and present a relation with the confluent hypergeometric function. Finally, we present the so-called fractional ordinary differential equation and as an application we discuss the fractional harmonic oscillator
Mestrado
Mestre em Matemática
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Tazón, Puente Antonio. "Estudio del comportamiento no lineal de dispositivos activos de microondas." Doctoral thesis, Universidad de Cantabria, 1987. http://hdl.handle.net/10803/22712.
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Dentro de los sistemas de comunicación han adquirido gran importancia las aplicaciones en alta frecuencia, lo que conlleva un gran desarrollo en este tipo de tecnologías; aplicaciones bajo ruido, potencia monolítico, etc. Este tipo de tecnologías precisan un conocimiento no lineal de los circuitos. Por ello el presente trabajo se ha orientado hacia la resolución de tres problemas no lineales fundamentales que son: modelización física, análisis no lineal de sistemas activos autónomos trabajando en microondas y el desarrollo de una formulación matemática compacta dirigida hacia la optimización gran señal de sistemas activos a transistor Mesfet. El trabajo se completa con una verificación experimental de los comportamientos simulados teóricamente lo que confiere a los métodos matemáticos un amplio rango de validez
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Mohsen, Ali. "Harmonic feedback multi-oscillator for 5G application." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0335/document.
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Le projet de thèse porte sur l'oscillateur harmonique; l'oscillateur dépend du signal de fréquence fondamentale à 25 GHz, qui est amplifié à l'aide d'un LNA et d'un amplificateur de puissance afin de générer un troisième signal harmonique à 75 GHz en sortie et de faire une contre-réaction du signal fondamental afin d'assurer la continuité de l'oscillation. Un diplexeur est utilisé pour séparer les deux fréquences à l’étage de sortie, en tenant compte de l’amélioration de la puissance de sortie, du bruit de phase et de l’efficacité de puissance ajoutée PAE à la fréquence candidate de l’application 5G. La technologie de transistor choisie est le FDSOI 28 nm de STMicroelectronicsThe PhD project is about harmonic oscillator; the oscillator depends on the fundamental frequency signal at 25 GHz which is amplified using an LNA and power amplifier in order to generate third harmonic signal at 75 GHz at the output, and feedback the fundamental signal to ensure the continuity of the oscillation. A diplexer is used to separate between both frequencies at the output stage, taking in consideration the improvement of the output power, phase noise, and the power added efficiency PAE at the candidate frequency of 5G application. The transistor technology chosen is the 28nm FDSOI from the STMicroelectronics
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Boldt, Frank [Verfasser], Karl Heinz [Akademischer Betreuer] Hoffmann, Karl Heinz [Gutachter] Hoffmann, and Peter [Gutachter] Salamon. "A Framework for Modeling Irreversible Processes Based on the Casimir Companion : Time-Optimal Equilibration of a Collection of Harmonic Oscillators: A Geometrical Approach Illustrating the Framework / Frank Boldt ; Gutachter: Karl Heinz Hoffmann, Peter Salamon ; Betreuer: Karl Heinz Hoffmann." Chemnitz : Universitätsbibliothek Chemnitz, 2014. http://d-nb.info/1214302254/34.
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Murugan, Deepak. "Design of a Voltage Controlled Oscillator for Galileo/GPS Receiver." Thesis, Linköpings universitet, Institutionen för systemteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-76279.
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The main aim of this thesis is to implement a voltage-controlled oscillator for a Galileo/GPS receiver with a center frequency of 1.5 GHz in 150 nm CMOS process. As the designed VCO has to be integrated in a phase locked loop, VCO gain is selected high enough for the PLL to lock even with process variations. A new state of art architecture called double harmonic tuned VCO is selected and designed for this GPS application. It uses a complex combination of inductors and capacitors to reduce phase-noise of the VCO by suppressing second harmonic oscillations in the tail node of VCO. The designed VCO shows significant improvement in phase-noise performance compared to a normal LC tank VCO by reducing phase-noise around 4 dBc/Hz. The VCO has a phase-noise of -128 dBc/Hz at 1 MHz offset from center frequency with a power consumption of 5 mW and a tuning range of about 257 MHz for a 1 V tuning voltage range.
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Bessa, Vagner Henrique Loiola. "Osciladores log-periÃdicos e tipo Caldirola-Kanai." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8210.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorNesse trabalho apresentamos as soluÃÃes clÃssicas e quÃnticas de duas classes de osciladores harmÃnicos dependentes de tempo, a saber: (a) o oscilador log-periÃdico e (b) o oscilador tipo Caldirola-Kanai. Para a classe (a) estudamos os seguintes osciladores: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ e (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. Nesses trÃs casos $omega(t)=omega_0frac{t_0}{t}$. Para a classe (b) estudamos o oscilador (IV) de Caldirola-Kanai onde $omega(t)=omega_0$ e $m(t)=m_0 ext{Exp}ajust{gamma t}$ e osciladores com $omega(t)=omega_0$ e $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, para (V) $alpha=2$ e (VI) $alpha=4$. Para obter as soluÃÃes clÃssicas de cada oscilador resolvemos suas respectivas equaÃÃes de movimento e analisamos o comportamento de $q(t)$, $p(t)$ assim como do diagrama de fase $q(t)$ vs $p(t)$. Para obter as soluÃÃes quÃnticas usamos uma transformaÃÃo unitÃria e o mÃtodo dos invariantes quÃnticos de Lewis e Riesenfeld. A funÃÃo de onda obtida à escrita em termos de uma funÃÃo $ ho$, que à soluÃÃo da equaÃÃo de Milne-Pinney. Ainda, para cada sistema resolvemos a respectiva equaÃÃo de Milne-Pinney e discutimos como o produto da incerteza evolui no tempo.
In this work we present the classical and quantum solutions of two classes of time-dependent harmonic oscillators, namely: (a) the log-periodic and (b) the Caldirola-Kanai-type oscillators. For class (a) we study the following oscillators: (I) $m(t)=m_0frac{t}{t_0}$, (II) $m(t)=m_0$ and (III) $m(t)=m_0ajust{frac{t}{t_0}}^2$. In all three cases $omega(t)=omega_0frac{t_0}{t}$. For class (b) we study the Caldirola-Kanai oscillator (IV)where $omega(t)=omega_0$ and $m(t)=m_0 ext{exp}ajust{gamma t}$ and the oscillator with $omega(t)=omega_0$ and $m(t)=m_0ajust{1+frac{t}{t_0}}^alpha$, for $alpha=2$ (V) and $alpha=4$ (VI). To obtain the classical solution for each oscillator we solve the respective equation of motion and analyze the behavior of $q(t)$, $p(t)$ as well as the phase diagram $q(t)$ vs $p(t)$. To obtain the quantum solutions we use a unitary transformation and the Lewis and Riesenfeld quantum invariant method. The wave functions obtained are written in terms of a function ($ ho$) which is solution of the Milne-Pinney equation. Futhermore, for each system we solve the respective Milne-Pinney equation and discuss how the uncertainty product evolves with time.
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Hall, Richard L., Wolfgang Lucha, Franz F. Schoeberl, and lucha@oeaw ac at. "Energy Bounds for the Spinless Salpeter Equation: Harmonic Oscillator." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi984.ps.
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Wiser, Justin Allen. "Harmonic Resonance Dynamics of the Periodically Forced Hopf Oscillator." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1373380266.
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SANTOS, Desiane Maiara Gomes dos. "Amplificação de pequenos sinais em osciladores parametricamente forçados." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1578.
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Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento.
In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.
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Hornstein, Melissa K. (Melissa Kristen) 1977. "A continuous-wave second harmonic gyrotron oscillator at 460 GHz." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33939.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 255-266).
We report the short pulse and CW operation of a 460 GHz gyrotron oscillator both at the fundamental (near 230 GHz) and second harmonic (near 460 GHz) of electron cyclotron resonance. During operation in a complete CW regime with 12.4 kV beam voltage and 135 mA beam current, the gyrotron generates a record 8 W of power in the second harmonic TE0,6,1 mode at 458.6 GHz. Design at high frequency, second harmonic, and low beam power is challenging because the latter two involve lower gain than at fundamental modes and all three necessitate higher Q cavities. Under complete computer control, the gyrotron has stably operated continuously for over an hour near 460 GHz. Diagnostic radiation pattern measurements of the beam using an array of pyroelectric sensors show a bi-Gaussian beam with 4% ellipticity. Operation in the fundamental modes, including the TE₀ ₃ ₁ mode at 237.91 GHz and the TE₂ ₃ ₁ at 233.15 GHz, is observed at peak output powers up to 70 W. CW studies of the fundamental TE₂ ₃ mode at low voltage reveal that the mode can be excited with less than 7 W of beam power at less than 3.5 kV. Further, we demonstrate broadband continuous frequency tuning of the fundamental modes of the oscillator over a range of more than 2 GHz through variation of the magnetic field alone.
(cont.) We interpret these results in terms of smooth transitions between higher order axial modes of the resonator. In a related experiment, second harmonic (in addition to fundamental) operation of a nominally 250 GHz gyrotron oscillator was characterized to verify the possibility of second harmonic excitation at 460 GHz. The characterization experiments yielded results of extremely low second harmonic start oscillation currents, as low as 12 mA, and have been interpreted as an unintentionally high Q cavity. A computer-controlled stable CW source, the 250 GHz gyrotron was the first gyro-device specifically designed with the purpose of seamless integration into an NMR spectrometer. Under complete computer control, the gyrotron's operation for over 10 days has been observed, yielding a power stability of better than 1% and frequency stability of better than 400 Hz. Overmoded corrugated waveguide was designed and implemented to enable low loss quasi-Gaussian transmission. In conjunction with the corrugated waveguide, a quasi-optical directional coupler was designed and implemented to enable feedback on the forward (and reflected) power to further stabilize the signal. Radiation intensity patterns were compared using four techniques: thermal paper, liquid crystal paper, an array of pyroelectric sensors, and a mechanized scanner.
(cont.) The liquid crystalline technique was adapted from a technique employed in temperature measurements in electronic devices. Originally employed for use in diagnosing laser beams, we demonstrate the first use of a pyroelectric camera at millimeter frequencies. A study of the overmoded microwave transmission and mode conversion system of a 140 GHz gyrotron oscillator, the first in a series of DNP gyrotrons, is also presented. The losses were characterized under a succession of iterative configurations for optimization of power transmission, including the design and implementation of a new TE₀ ₁ to TE₁ ₁ waveguide mode converter. The result of this study was a reduction of the total loss of the transmission system from nearly 9 dB to 4.5 dB. In addition to becoming a milestone in high frequency second harmonic design, the successful completion of the 460 GHz gyrotron experiment will allow the highest field DNP experiments to date. The success of experiments on three gyrotron oscillators, at 460, 250, and 140 GHz makes an important contribution to the body of knowledge on the development of high frequency, CW, second harmonic, and low power gyrotrons.
by Melissa Kristen Hornstein.
Ph.D.
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Sorrell, Ian. "High energy asymptotics and trace formulas for the perturbed harmonic oscillator." Thesis, Loughborough University, 2005. https://dspace.lboro.ac.uk/2134/12982.
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Votýpka, František. "Aplikace moderních funkčních bloků v harmonických oscilátorech." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-218398.
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This work deals with using modern active functional blocks in electronic circuits. These blocks have better features than classical operational amplifiers and are characterized especially by working in current mode. Therefore these blocks can be used in higher frequencies. Using those blocks it is possible to design e.g. electronically variable-frequency filters of types low-pass filter, high-pass filter, band-pass filter, etc. Then it is also possible to easily realize electronically variable-frequency oscillators. This work is focused on some of these blocks, their basic characteristics and principles. Also three oscillators with current conveyors of second generation are designed. Its made simulation, sensitivity and tolerance analysis and magnitude stabilization. Everything is performed in OrCAD PSpice program. These made oscillators are electronic tunable in the band frequency ones of MHz.
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Platz, Daniel. "Reconstructing force from harmonic motion." Doctoral thesis, KTH, Nanostrukturfysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-122583.
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High-quality factor oscillators are often used in measurements of verysmall force since they exhibit an enhanced sensitivity in the narrow frequencyband around resonance. Forces containing frequencies outside this frequencyband are often not detectable and the total force acting on the oscillatorremains unknown. In this thesis we present methods to eciently use theavailable bandwidth around resonance to reconstruct the force from partialspectral information.We apply the methods to dynamic atomic force microscopy (AFM) wherea tip at the end of a small micro-cantilever oscillates close to a sample surface.By reconstructing the force between the tip and the surface we can deducedierent properties of the surface. In contrast, in conventional AFM only oneof the many frequency components of the time-dependent tip-surface forceallowing for only qualitative conclusions about the tip-surface force.To increase the number of measurable frequency components we developed Intermodulation AFM (ImAFM). ImAFM utilizes frequency mixing ofa multifrequency drive scheme which generates many frequencies in the response to the nonlinear character of the tip-surface interaction. ImAFM,amplitude-modulated AFM and frequency-modulated AFM can be considered as special cases of narrow-band AFM, where the tip motion can bedescribed by a rapidly oscillating part and a slowly-varying envelope function. Using the concept of force quadratures, each rapid oscillation cycle canbe analyzed individually and ImAFM measurements can be interpreted as arapid measurement of the dependence of the force quadratures on the oscillation amplitude or frequency. To explore the limits of the force quadraturesdescription we introduce the force disk which is a complete description of thetip-surface force in narrow-band AFM at xed static probe height.We present a polynomial force reconstruction method for multifrequencyAFM data. The polynomial force reconstruction is a linear approximativeforce reconstruction method which is based on nding the parameters of amodel force which best approximates the tip-surface force. Another classof reconstruction methods are integral techniques which aim to invert theintegral relation between the tip-surface force and the measured spectraldata. We present an integral method, amplitude-dependence force spectroscopy (ADFS), which reconstructs the conservative tip-surface force fromthe amplitude-dependence of the force quadratures. Together with ImAFMwe use ADFS to combine high-resolution AFM imaging at high speeds withhighly accurate force measurements in each point of an image. For the measurement of dissipative forces we discuss how methods from tomography canbe used to reconstruct forces that are a function of both tip position andvelocity.The methods developed in this thesis are not limited to dynamic AFM andwe describe them in the general context of a harmonic oscillator subject to anexternal force. We hope that theses methods contribute to the transformationof AFM from a qualitative imaging modality into quantitative microscopy andwe hope that they nd application in other measurements which exploit theenhanced sensitivity of a high-quality factor oscillator.QC 20130527
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Cabral, Luís Antônio. "Transparência eletromagneticamente induzida em diferentes sistemas físicos e seu análogo em osciladores acoplados." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5057.
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The simultaneously incidence of two light beams on one or more atoms causes destructive interference of these beams in atomic states causing cancellation of the absorption of one of the incident beams and this phenomenon is called Electromagnetically Induced Transparency (EIT). The main objective of this work is to show that the Electromagnetically Induced Transparency, which is usually studied in the quantum context, can be modeled classically as a function of coupled harmonic oscillators subject to an external force and dissipation. To will establish the classical equivalence, it will be presented the theory of the EIT in diferent quantum systems and also the theory of classic harmonic oscillators. Analogies will be performed comparing the classical and quantum equations of motion obtained for each scheme. For this, we perform the equivalence of EIT in quantum systems as atoms in three levels in Λ configuration, two-level atoms plus a cavity mode and the cavity optomechanics with the classical system of two coupled harmonics oscillator forced and damped. We also analyze the equivalence of two diferent quantum systems: three level atoms plus one cavity mode and four levels atoms in free space with a classical system composed by three coupled harmonic oscilators, forced and damped, in diferent configurations.
A incidência simultânea de dois feixes luminosos em um ou mais átomos provoca a interferência destrutiva desses feixes em um dos estados atômicos causando o cancelamento da absorção de um dos feixes incidentes e esse fenômeno é denominado Transparência Eletromagneticamente Induzida (\Electromagnetically Induced Transparency", EIT). O objetivo principal deste trabalho é mostrar que a Transparência Eletromagneticamente Induzida, que é normalmente estudada no contexto quântico, pode ser modelada classicamente em função de osciladores harmônicos amortecidos forçados e acoplados. Para que a equivalência clássica seja bem fundamentada, será apresentada a teoria da EIT em diversos sistemas quânticos e também a teoria dos osciladores harmônicos clássicos. As equivalências serão realizadas comparando as equações de movimento clássicas e quânticas obtidas para cada regime. Para isso, vamos realizar a equivalência da EIT em sistemas quânticos de átomos de três níveis em configuração Λ, dois níveis atômicos mais um modo da cavidade e a optomecânica de cavidades com o sistema clássico de dois osciladores harmônicos amortecidos forçados e acoplados. Logo após, será analisada a equivalência de dois sistemas quânticos compostos por átomos de três níveis mais um modo da cavidade e átomos de quatro níveis com os sistemas clássicos de três osciladores harmônicos amortecidos forçados e acoplados em diferentes configurações.
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Aksentijevic, Aleksandar. "Psychophysical effects of auditory gamma-band entrainment : evidence for oscillatory harmonic binding." Thesis, Birkbeck (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406289.
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Owen, Edmund Thomas. "Entanglement and quantum gate processes in the one-dimensional quantum harmonic oscillator." Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/244947.
Full textAbstract:
Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies. The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function. In Ch. 3, a new method for generating maximally entangled two-qubit states using a pair of interacting particles in a one-dimensional harmonic oscillator is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two qubits are initially in the same state, no entanglement is generated as there is no direct qubit-qubit interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor systems are suggested. One of the most commonly used qubits is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this qubit to the electron's momentum. In order to incorporate this e ffect into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields. In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.
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Alberts, Antonie Craig. "Phase noise reduction in a multiphase oscillator." Diss., University of Pretoria, 2017. http://hdl.handle.net/2263/66581.
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Oscillators are ubiquitous to radio frequency circuits, where frequency translations and channel selection play a central role in the analogue communications channel. Oscillators also form part of digital systems as a time reference. Typical heterodyne receivers require an intermediate frequency channel. The associated oscillators and variable filters can only be centred perfectly at a single frequency, and degrade performance at the boundaries of the channel. These circuits also require image-rejecting filters and phase-locked loops in order to enable down-conversion. The penalties for these components are increased circuit area and power consumption. A direct down-conversion circuit will reduce the number of components in the system. A requirement added by the structural change is a passive sub-harmonic mixer. Quadrature oscillators may be achieved by cross-coupling two nominally identical LC differential voltage-controlled oscillators. Because of the widespread use of voltage-controlled oscillators in wireless communication systems, the development of comprehensive nonlinear analysis is pertinent in theory and applications. A key characteristic that defines the performance of an oscillator is the phase noise measurement. The voltage-controlled oscillator is also a key component in phase-locked loops, as it contributes to most of the out-of-band phase noise, as well as a significant portion of in-band noise. Current state-of-the-art modulation techniques, implemented at 60 GHz, such as quadrature amplitude modulation, and orthogonal frequency domain multiplexing, require phase noise specifications superior to 90 dBc/Hz at a 1 MHz offset. It has been shown that owing to the timing of the current injection, the Colpitts oscillator tends to outperform other oscillator structures in terms of phase noise performance. The Colpitts oscillator has a major flaw in that the start-up gain must be relatively high in comparison to the cross-coupled oscillator. The oscillation amplitude cannot be extended as in the cross-coupled case. The oscillator’s bias current generally limits the oscillation amplitude. The phase noise is defined by a stochastic differential equation, which can be used to predict the system’s phase noise performance. The characteristics of the oscillator can then be defined using the trajectory. The model projects the noise components of the oscillator onto the trajectory, and then translates the noise into the resulting phase and amplitude shift. The phase noise performance of an oscillator may be improved by altering the shape of the trajectory. The trajectory of the oscillator is separated into slow and fast transients. Improving the shape of the oscillator’s slow manifold may improve its phase noise performance, and improving the loaded quality factor of the tank circuit may be shown to directly improve upon close-in phase noise.
The approach followed describes oscillator behaviour from a circuit-level analysis. The derived equations do not have a closed form solution, but are reformulated using harmonic balance techniques to yield approximate solutions. The results from this closed form approximation are very close to both the numerical solutions of the differential equations, as well as the Simulation Program with Integrated Circuit Emphasis solutions for the same circuits. The derived equations are able to predict the amplitude and frequency in the single-phase example accurately, and are extended to provide a numerical platform for defining the amplitude and frequency of a multiphase oscillator. The analysis identifies various circuit components that influence the oscillator’s phase noise performance. A circuit-level modification is then identified, enabling the decoupling of some of the factors and their interactions. This study demonstrates that the phase noise performance of a Colpitts oscillator may be significantly improved by making the proposed changes to the oscillator. The oscillator’s figure of merit is improved even further. When a given oscillator is set at its optimum phase noise level, the collector current will account for approximately 85% of the phase noise; with the approach in this work, the average collector current is reduced and phase noise performance is improved. The key focus of the work was to identify circuit level changes to an oscillator’s structure that could be improved or changed to achieve better phase noise performance. The objective was not to improve passive components, but rather to identify how the noise-to-phase noise transfer function could be improved. The work successfully determines what can be altered in an oscillator that will yield improved phase noise performance by altering the phase noise transfer function.The concept is introduced on a differential oscillator and then extended to the multiphase oscillator. The impulse sensitivity function of the modified multiphase oscillator is improved by altering the typical feedback structure of the oscillator. The multiphase oscillator in this work is improved from -106 dBc/Hz to -113 dBc/Hz when considering the phase noise contribution from the tank circuits’ bias current alone. This is achieved by uniquely altering the feedback method of the oscillator. This change alters the noise-to-phase noise properties of the oscillator, reducing phase noise. The improvement in the phase noise does not account for further improvements the modification would incorporate in the oscillator’s limit cycle. For a given tank circuit, supply current and voltage, compared to an optimised Colpitts oscillator, the modifications to the feedback structure proposed in this work would further improve the figure of merit by 9 dB. This is not considering the change in the power consumption, which would yield a further improvement in the figure of merit by 7 dB. This is achieved by relaxing the required start-up current of the oscillator and effecting an improvement in the impulse sensitivity function. Future research could include further modelling of the phase shift in the feedback network, including the transmission lines in the feedback networks using the harmonic balance technique in a numerical form. The feedback technique can also be modified to be applicable to single and differential oscillators.
Dissertation (MEng)--University of Pretoria, 2017.
National Research Foundation
The Department of Science and Technology, South Africa
GEW Technologies (Pty) Ltd
Electrical, Electronic and Computer Engineering
MEng
Unrestricted
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Moore, Michael Wayne. "Measuring the second harmonic amplitude of an oscillating torsion pendulum to detect small forces /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/9666.
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Hornstein, Melissa K. (Melissa Kristen) 1977. "Design of a 460 GHz second harmonic gyrotron oscillator for use in dynamic nuclear polarization." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/86777.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 91-96).
by Melissa K. Hornstein.
S.M.
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Yagi, Masakazu. "Analysis of Nonlinear Oscillations Using Computer Algebra." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/61310.
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Kyoto University (京都大学)0048
新制・課程博士
博士(工学)
甲第14049号
工博第2961号
新制||工||1439(附属図書館)
26328
UT51-2008-F441
京都大学大学院工学研究科電気工学専攻
(主査)教授 和田 修己, 教授 引原 隆士, 准教授 久門 尚史, 教授 萩原 朋道
学位規則第4条第1項該当
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Bergeron, Mario. "Coherent state path integral for the harmonic oscillator and a spin particle in a constant magnetic field." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/27391.
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The definition and formulas for the harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism is also reviewed with its relation and the partition function of a sytem is also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level, and its relation with various regularizations is established. The use of harmonic oscillator coherent states and spin coherent states for the computation of the path integral for a particle of spin s put in a magnetic field is caried out in several ways, and a careful analysis of infinitesimal terms (in 1/N where TV is the number of time slices) is done explicitly. The theory of the magnetic monopole and its relation with the spin system are explained, and the equivalence of these two system is established up to infinitesimal order by the introduction of an exterior interaction to the monopole. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral. The coefficient of the topological term in the spin system appears explicitly without ambiguity, as being 2s.Science, Faculty of
Physics and Astronomy, Department of
Graduate
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Voon, Lok Chong Lew Yan. "An investigation of coherent state path integrals as applied to a harmonic oscillator and a single spin." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/27581.
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In this project two steps involved in the handling of path integrals are reexamined in detail for coherent state path integals. They concern the continuum limit approximation and the regularization of the formal path integrals. Restricting oneself to the harmonic oscillator, the technique of time splitting is used to set up the coherent state path integrals and the proper way to pass to the continuum limit is demonstrated. The manipulation of these path integrals calls for regularization procedures and the validity of discrete, Riemann zeta function and 'derivative' regularization methods is observed. A modification to a fermionic theory is briefly mentioned and, finally, the above results are implemented in writing down a path integral for a single spin.Science, Faculty of
Physics and Astronomy, Department of
Graduate
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Mercadé, Morales Laura. "Phonons Manipulation in Silicon Chips Using Cavity Optomechanics." Doctoral thesis, Universitat Politècnica de València, 2021. http://hdl.handle.net/10251/171461.
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[ES] La optomecánica de cavidades se ocupa de la interacción entre la luz y la materia a través del efecto de presión de radiación cuando las ondas ópticas y mecánicas implicadas están confinadas en una cavidad. En estos sistemas optomecánicos, la interacción entre fotones y fonones da lugar a multitud de fenómenos en función de las condiciones en las que se excita el sistema. En particular, se pueden obtener dos regímenes distintos en los que se puede, o bien absorber fonones (denominado como enfriamiento de la cavidad), o bien éstos se pueden amplificar (régimen conocido como calentamiento de la cavidad). El primer régimen puede usarse, por ejemplo, para reducir la ocupación térmica del sistema y se usa comúnmente para aplicaciones relativas al procesado de información cuántica. Sin embargo, la amplificación de fonones, que puede ser desarrollada a temperatura ambiente, ha permitido conseguir alcanzar incluso las condiciones necesarias para obtener láseres de fonones, lo cual permite poder usar esta característica como elemento de referencia en aplicaciones relativas al procesado de señales de radiofrecuencia (RF).
En esta tesis se aborda el confinamiento simultáneo y la interacción de fotones y fonones en estructuras periódicas y en guías no suspendidas desarrolladas en sistemas CMOS compatibles basados en tecnología de silicio. A través del estudio experimental de estas estructuras periódicas, hemos demostrado que las cavidades optomecánicas pueden actuar como elementos clave en el dominio de la fotónica de microondas, donde todo el procesado de la información puede ser realizado en el dominio óptico a través de la manipulación de fonones en este sistema. En particular, mostramos que un solo oscilador optomecánico puede actuar tanto como un oscilador local y un mezclador de RF, y éste puede operar como un conversor de frecuencias de señales de cadenas de datos reales. Para mejorar esta funcionalidad, también se demuestra que es posible obtener tanto peines de frecuencias ópticos así como múltiples modos mecánicos confinados, aumentando así su rendimiento. Por otro lado, con el objetivo de poder solventar las posibles limitaciones de estos sistemas, en esta tesis también se exploran diferentes configuraciones que permiten la interacción acusto-óptica simultánea en la misma estructura. Específicamente, se analiza la interacción optomecánica en discos de alto índice que soportan estados cuasi-ligados en el continuo así como una propuesta de guías no suspendidas que soportan altas ganancias de Brillouin. Este último estudio debería permitir el desarrollo de sistemas optomecánicos no suspendidos donde el problema de la pérdida de fonones hacia el sustrato se resuelva, hecho que permitiría enormemente simplificar la fabricación de estos sistemas optomecánicos en chips de silicio así como su uso en múltiples aplicaciones.[CA] L'optomecànica de cavitats s'ocupa de la interacció entre la llum i la matèria a través de l'efecte de pressió de radiació quan les ones òptiques i mecàniques implicades estan confinades en una cavitat. En aquests sistemes optomecànics, la interacció entre fotons i fonons dona lloc a multitud de fenòmens en funció de les condicions de les condicions en les quals s'excita el sistema. En particular, es poden obtindre dos règims diferents en els quals es pot, o bé, absorbir fonons (denominat com a refredament de la cavitat), o bé, es poden amplificar (règim conegut com a calfament de la cavitat). El primer règim pot usar-se, per exemple, per a reduir l'ocupació tèrmica del sistema i s'usa comunament per a aplicacions relatives al processament d'informació quàntica. No obstant això, l'amplificació de fonons, que pot ser desenvolupada a temperatura ambient, ha permés aconseguir fins i tot les condicions necessàries per a obtindre làsers de fonons, la qual cosa permet poder usar aquesta característica com a element de referència en aplicacions relatives al processament de senyals de radiofreqüència (RF). En aquesta tesi s'aborda el confinament simultani i la interacció de fotons i fonons en estructures periòdiques i en guies no suspeses en sistemes CMOS compatibles basats en tecnologia de silici. A través de l'estudi experimental d'aquestes estructures periòdiques, hem demostrat que les cavitats optomecàniques poden actuar com a elements clau en el domini de la fotònica de microones, on tot el processament de la informació pot ser realitzat en el domini òptic a través de la manipulació de fonons en aquest sistema. En particular, vam mostrar que només un oscil·lador optomecànic pot actuar tant com un oscil·lador local i un mesclador de RF, i aquest pot operar com un convertidor de freqüències de senyals de cadenes de dades reals. Per a millorar aquesta funcionalitat, també es demostra que és possible obtindre tant tren de freqüències òptics així com múltiples modes mecànics confinats, augmentant així el seu rendiment. D'altra banda, amb l'objectiu de poder solucionar les possibles limitacions d'aquests sistemes, en aquesta tesi també s'exploren diferents configuracions que permeten la interacció acusto-òptica simultània en la mateixa estructura. Específicament, s'analitza la interacció optomecànica en discos d'alt índex que suporten estats quasi-lligats en el continu així com una proposta de guies no suspeses que suporten altes ganancies de Brillouin. Aquest últim estudi hauria de permetre el desenvolupament de sistemes optomecànics no suspesos on el problema de la pèrdua de fonons cap al substrat es resolga, fet que permetria enormement simplificar la fabricació d'aquests sistema optomecànics en xips de silici així com el seu ús en diverses aplicacions.
[EN] Cavity optomechanics deals with the interaction of light and matter through the radiation pressure effect, when the involved optical and mechanical waves are confined in a cavity. In optomechanical systems, photon and phonon interaction give rise to a plethora of phenomena as a function of the driving conditions of the system. Relative to that, two distinctive regimes can be obtained which enable either the absorption of phonons (cavity cooling) or their amplification (cavity heating). The first regime can be used to reduce the thermal occupancy of the system and it is commonly used for quantum processing information applications. However, the amplification of phonons, which can be performed at room temperature, has enabled to even reach phonon lasing conditions, a feature that could be used as a reference element for RF processing applications. In this thesis, we address the simultaneous confinement and interaction of photons and phonons in periodic structures and unreleased waveguides on CMOS-compatible silicon-based technology. Throughout the experimental study of those periodic structures, we demonstrate that optomechanical cavities can perform as key blocks in the microwave photonics domain where all the information processing can be performed in the optical domain through phonon manipulation. In particular, we show that a single optomechanical oscillator can perform as both a local oscillator and an RF mixer, and it can operate as a frequency-converted of real data stream signals. To improve its performance, it is also demonstrated that optical frequency combs can be obtained by means of this system and multiple mechanical mode confinement can also be achieved, thus improving the functionality of the system. On the other hand, in order to fulfill the possible limitations of those systems, we explore different configurations enabling the simultaneous acousto-optic interaction together into the same structure. Especially, optomechanical interaction in high-index disks supporting quasi-bound states in the continuum is addressed, as well as a proposal of unreleased waveguides supporting strong Brillouin gains is also reported. The last one should lead to unreleased optomechanical interacting systems where the issue of phonon leakage into the substrate is solved, which could enormously simplify the fabrication of optomechanical systems in silicon chips as well as their practical use in multiple applications.
This work has been carried out under the framework of the H2020 FET-Open EU project PHENOMEN. This Thesis was also supported by the Programa de Ayudas de Investigación y Desarrollo (PAID-01-16) de la Universitat Politècnica de València
Mercadé Morales, L. (2021). Phonons Manipulation in Silicon Chips Using Cavity Optomechanics [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/171461
TESIS
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Frost, david L. Mr, and Frank Hagelberg. "Isotropic Oscillator Under a Magnetic and Spatially Varying Electric Field." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/honors/415.
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We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.
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Stellato, M. "FROM OSCILLATIONS TO NORMAL MODES: AN EDUCATIONAL PATH FOR THE UPPER SECONDARY SCHOOL." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/258261.
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The present thesis work starts from the assumption that harmonic oscillations and
normal modes are key physical concepts. They are fundamental in quantum physics,
in electromagnetism (especially in treating coupled oscillating circuits and electromagnetic
waves), in acoustics and in mechanical systems. The conceptual and practical
importance of normal modes emerges also clearly from the fact that every small
and sufficiently smooth oscillation of a complex system is given by a linear superposition
of its normal modes. The notion of normal modes is thus a powerful conceptual
organizer. Nevertheless, in teaching practice (at least in Italy), only short time is
devoted to harmonic motion, rarely coupled oscillators are treated and, in secondary
school text-books, normal modes are usually not even present. The purpose of this
thesis work is to develop an effective path on scillations for the upper secondary
school that leads to the normal modes of oscillations. To do this, an educational reconstruction
of the concept of harmonic motion has been necessary as the harmonic
motion is a fundamental prerequisite for the understanding of normal modes. The
introduction of normal modes is, for upper secondary school students, complicated
by the complexity of the mathematics involved. In our path we propose to overcome
the mathematical difficulties through an experimental approach and the use of different
tools such as video and picture analysis, also in slow motion, data logging and
data analysis techniques and applet simulations, with the goal of being as simple
as possible from the mathematical point of view but without losing the advantages
that mathematics (even at simple level) can provide. In this perspective, a multiple
representation approach has been used. The path on oscillations that we present
here is the result of a Design Based Research on normal modes with Italian upper
secondary school students. The complete path has been proposed to three classes of
11th grade students during curricular lessons. A version of the sequence has been
proposed also to other three classes (one of grade 11th and two of grade 12th) during
afternoon extra-curricular lessons, and a version with university-level formalism has
also been proposed to a group of undergraduate students in mathematics during
the third year course “Preparation of Didactical Experiments”. A reduced version
of the path has also been proposed to a number of classes of 12th grade students
within the one-shot lessons on oscillations (afternoon extra-curricular activities) in
the framework of PLS (Piano Lauree Scientifiche) activities. The one-shot lessons
have been attended, over time, by about six hundred students.
The all path is based on a number of activities in which we start from a real experiment
or a video or else an applet simulation to introduce and discuss a limited
topic. The general purpose is to identify, among the oscillations, those that give rise
to a peculiar kind of motion, the harmonic motion, and determine the conditions
under which such motion can be obtained. A number of significant situations of
harmonic and anharmonic motions are investigated and criteria to establishing the
harmonicity/anharmonicity of the oscillation are discussed. An important tool for
the analysis of the data is then introduced: the Fast Fourier Transform. The FFT is
introduced as a tool and not discussed through mathematics. Then the concept on
resonance is introduced in a phenomenological way through experiments and exploring
related videos in the Internet videos database. The next step is the introduction
of the coupling between two oscillators and the discovery of particular motion configurations:
the Normal Modes of Oscillation. We then extend the experiments to
three, four, five....many coupled oscillators until we arrive to the continuous case;
first in one dimension with the string and then in two dimensions with the Cladni
plates and we study the normal modes of such complex systems.
The structure of the thesis is as follows: an introduction to the motivations, a description
of the state of the art and the formulation of the research questions. Then
a brief description of the methodological framework mainly based on the Design
Based Research approach and the Model of the Educational Reconstruction. The
reconstruction of the Harmonic motion at university level follows; the translation
of such a reconstruction into upper secondary school level is developed in chapter
five. In chapter four normal modes for a system of two, three, N coupled oscillators
are treated with the proper formalism; also in this case the translation into upper
secondary school level is developed in chapter five. Then the very core of the thesis
follows , namely the developing of the path, as briefly described above. The next
chapter reports a path developed with undergraduate students as an implementation
of the study of oscillations. It is the study of the modes of oscillation in the interesting
case of a parametric oscillator were there is a non-linear coupling between modes
of oscillation. In the last section, the main results of the experimentation of the path
with threes classes of 11th grade students are briefly presented. These results are
based on questionnaires (pre-test and post-test), discussions and interviews.
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Bakka, Haakon Christopher. "Applications of p-adic Numbers to well understood Quantum Mechanics : With a focus on Weyl Systems and the Harmonic Oscillator." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19366.
Full textAbstract:
In this thesis we look at how it is possible to construct models in quantum mechanics by using p-adic numbers. First we look closely at different quantum mechanical models using the real numbers, as it is necessary to understand them well before moving on to p-adic numbers. The most promising model, where Weyl systems are used, is studied in detail. Here time translation is not generated by the Hamiltonian, but constructed directly as an operator possessing some fundamental structure in relation to the classical dynamics. Then we develop the relevant theory of the field of p-adic numbers Qp , with a focus on the properties of Qp as a locally compact abelian group. Here we present alternative proofs to those found in the literature. In particular, we give an independent proof of the selfduality of Qp. In the last chapters we look at some models using Qp . We generalize the idea of Weyl systems from real to p-adic numbers, and we discuss the physical implications. When using Weyl systems, time is p-adic. We also produce MatLab algorithms for numerical computations in connection with approximations of p-adic models by finite models.
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Veselý, Jiří. "Elektronicky přeladitelný harmonický oscilátor." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-218599.
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This masters project describes properties and primary parameters of active function blocks (OPA, VCA, OTA, CFA, CC) usable in construction of harmonic oscillators. Basic principles of harmonic generators, especially feedback oscillators, are introduced. In next section are presented five particular schematics of harmonic tuned oscillators. For this oscillators are indicated basic formulas, essential qualities performed by simulations and results of sensitivity and tolerance analysis. In the last part of diploma thesis there are selected three circuits which are made and their features are measured.
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Grobler, Trienko Lups. "Sequential and non-sequential hypertemporal classification and change detection of Modis time-series." Thesis, University of Pretoria, 2012. http://hdl.handle.net/2263/25427.
Full textAbstract:
Satellites provide humanity with data to infer properties of the earth that were impossible a century ago. Humanity can now easily monitor the amount of ice found on the polar caps, the size of forests and deserts, the earth’s atmosphere, the seasonal variation on land and in the oceans and the surface temperature of the earth. In this thesis, new hypertemporal techniques are proposed for the settlement detection problem in South Africa. The hypertemporal techniques are applied to study areas in the Gauteng and Limpopo provinces of South Africa. To be more specific, new sequential (windowless) and non-sequential hypertemporal techniques are implemented. The time-series employed by the new hypertemporal techniques are obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor, which is on board the earth observations satellites Aqua and Terra. One MODIS dataset is constructed for each province. A Support Vector Machine (SVM) [1] that uses a novel noise-harmonic feature set is implemented to detect existing human settlements. The noise-harmonic feature set is a non-sequential hypertemporal feature set and is constructed by using the Coloured Simple Harmonic Oscillator (CSHO) [2]. The CSHO consists of a Simple Harmonic Oscillator (SHO) [3], which is superimposed on the Ornstein-Uhlenbeck process [4]. The noise-harmonic feature set is an extension of the classic harmonic feature set [5]. The classic harmonic feature set consists of a mean and a seasonal component. For the case studies in this thesis, it is observed that the noise-harmonic feature set not only extends the harmonic feature set, but also improves on its classification capability. The Cumulative Sum (CUSUM) algorithm was developed by Page in 1954 [6]. In its original form it is a sequential (windowless) hypertemporal change detection technique. Windowed versions of the algorithm have been applied in a remote sensing context. In this thesis CUSUM is used in its original form to detect settlement expansion in South Africa and is benchmarked against the classic band differencing change detection approach of Lunetta et al., which was developed in 2006 [7]. In the case of the Gauteng study area, the CUSUM algorithm outperformed the band differencing technique. The exact opposite behaviour was seen in the case of the Limpopo dataset. Sequential hypertemporal techniques are data-intensive and an inductive MODIS simulator was therefore also developed (to augment datasets). The proposed simulator is also based on the CSHO. Two case studies showed that the proposed inductive simulator accurately replicates the temporal dynamics and spectral dependencies found in MODIS data.Thesis (PhD(Eng))--University of Pretoria, 2012.
Electrical, Electronic and Computer Engineering
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