Relevant bibliographies by topics / Model of coupled harmonic oscillators

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Model of coupled harmonic oscillators'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Model of coupled harmonic oscillators"

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Wang, Shijiao, Xiao San Ma, and Mu-Tian Cheng. "Multipartite Entanglement Generation in a Structured Environment." Entropy 22, no. 2 (February 7, 2020): 191. http://dx.doi.org/10.3390/e22020191.

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In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.
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Laszuk, Dawid, Jose O. Cadenas, and Slawomir J. Nasuto. "KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem." Advances in Data Science and Adaptive Analysis 10, no. 02 (April 2018): 1840002. http://dx.doi.org/10.1142/s2424922x18400028.

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Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals.
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Velichko, Andrey, Maksim Belyaev, Vadim Putrolaynen, Alexander Pergament, and Valentin Perminov. "Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks." International Journal of Modern Physics B 31, no. 02 (January 18, 2017): 1650261. http://dx.doi.org/10.1142/s0217979216502611.

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In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.
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HAUPTMANN, C., F. KAISER, and C. EICHWALD. "SIGNAL TRANSFER AND STOCHASTIC RESONANCE IN COUPLED NONLINEAR SYSTEMS." International Journal of Bifurcation and Chaos 09, no. 06 (June 1999): 1159–67. http://dx.doi.org/10.1142/s0218127499000808.

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A model of coupled nonlinear oscillators is discussed, wherein Langevin-type bistable systems are combined with self-sustained oscillators. An external harmonic signal is coupled in a subthreshold manner into the bistable systems at the initial stage of the signal chain. Signal transfer through the oscillators is studied under the influence of noise. Different noise contributions, including spatially-incoherent and spatially-coherent noise sources are considered. Results reveal a stochastic resonance kind of behavior at different stages of the signal transfer, specifically the harmonic signal is transduced through the whole system of coupled oscillators. The combined action of spatially-incoherent and spatially-coherent noise exhibits constructive as well as destructive influences on signal amplification.
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Li, Wei, and Gen-Xiang Chen. "Classical coupled oscillators model of the rational harmonic mode locked laser." Journal of Applied Physics 100, no. 4 (August 15, 2006): 043115. http://dx.doi.org/10.1063/1.2335598.

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Gallo, James Mendoza, and Bienvenido Masirin Butanas Jr. "Quantum Propagator Derivation for the Ring of Four Harmonically Coupled Oscillators." Jurnal Penelitian Fisika dan Aplikasinya (JPFA) 9, no. 2 (December 31, 2019): 92. http://dx.doi.org/10.26740/jpfa.v9n2.p92-104.

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The ring model of the coupled oscillator has enormously studied from the perspective of quantum mechanics. The research efforts on this system contribute to fully grasp the concepts of energy transport, dissipation, among others, in mesoscopic and condensed matter systems. In this research, the dynamics of the quantum propagator for the ring of oscillators was analyzed anew. White noise analysis was applied to derive the quantum mechanical propagator for a ring of four harmonically coupled oscillators. The process was done after performing four successive coordinate transformations obtaining four separated Lagrangian of a one-dimensional harmonic oscillator. Then, the individual propagator was evaluated via white noise path integration where the full propagator is expressed as the product of the individual propagators. In particular, the frequencies of the first two propagators correspond to degenerate normal mode frequencies, while the other two correspond to non-degenerate normal mode frequencies. The full propagator was expressed in its symmetric form to extract the energy spectrum and the wave function.
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Komarov, M., and A. Pikovsky. "The Kuramoto model of coupled oscillators with a bi-harmonic coupling function." Physica D: Nonlinear Phenomena 289 (December 2014): 18–31. http://dx.doi.org/10.1016/j.physd.2014.09.002.

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Golovinski, P. A., A. V. Yakovets, and E. S. Khramov. "Application of the coupled classical oscillators model to the Fano resonance build-up in a plasmonic nanosystem." Computer Optics 43, no. 5 (October 2019): 747–55. http://dx.doi.org/10.18287/2412-6179-2019-43-5-747-755.

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We study the excitation dynamics of Fano resonance within the classical model framework of two linear coupled oscillators. An exact solution for the model with a damped harmonic force is obtained. Details of the growth of a Fano profile under the harmonic excitation are shown. For an incident ultra-wideband pulse, the reaction of the system becomes universal and coincides with the time-dependent response function. The results of numerical calculations clarify two alternative ways for the experimental measurement of complete characteristics of the system: via direct observation of the system response to a monochromatic force by frequency scanning or recording the time-dependent response to a d-pulse. As a specific example, the time-dependent excitation in a system consisting of a quantum dot and a metal nanoparticle is calculated. Then, we show the use of an extended model of damped oscillators with radiative correction to describe the plasmon Fano resonance build-up when a femtosecond laser pulse is scattered by a nanoantenna.
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ROMEO, FRANCESCO, and GIUSEPPE REGA. "PROPAGATION PROPERTIES OF BI-COUPLED NONLINEAR OSCILLATORY CHAINS: ANALYTICAL PREDICTION AND NUMERICAL VALIDATION." International Journal of Bifurcation and Chaos 18, no. 07 (July 2008): 1983–98. http://dx.doi.org/10.1142/s021812740802149x.

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Harmonic wave propagation in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. The study extends previous results obtained for the mono-coupled oscillators to bi-coupled ones. The considered bi-coupled model refers to a chain of linearly coupled mechanical oscillators characterized by on-site cubic nonlinearities in both the longitudinal and rotational degrees of freedom. Pass, stop and complex regions are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized map arising from the relevant linear stability analysis. By varying the parameters governing both the coupling between the two d.o.f. and the nonlinearity, a variable scenario of propagation regions can be obtained, which includes the limit case of mono-coupled behavior. Theoretical predictions are validated through numerical results in terms of orbits, bifurcation diagrams and basins of attraction, obtained via nonlinear map iteration. They highlight a rich variety of regular and nonregular bounded solutions.
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Giraldi, F., and F. Petruccione. "Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion II." Open Systems & Information Dynamics 20, no. 04 (November 25, 2013): 1350015. http://dx.doi.org/10.1142/s1230161213500157.

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The analysis of a strongly coupled harmonic quantum Brownian motion has been performed in [1] for a special class of spectral densities obtained as a generalization of the Drude model. In the present scenario, we extend the study of the strongly coupled harmonic quantum Brownian motion to regular spectral densities that are structured as sub-Ohmic at low frequencies and arbitrarily shaped at high frequencies. The bosonic environment is initially in the vacuum state unentangled from the coherent state of the main oscillator. As a generalization of the previous results, we obtain that the long time dynamics is determined uniquely by the initial condition and the low frequency structure of the spectral density. Also in the present framework, inverse power law regressions to the asymptotics appear. The position and the momentum tend to undamped oscillations. The number of excitations relaxes to its initial value with damped oscillations enveloped in inverse power law relaxations. For the momentum and the number of excitations the inverse power law decays become arbitrarily slow in critical configurations by approaching the upper bound of the sub-Ohmic regime. The critical frequencies of the main oscillator are determined by the first negative moment of the spectral densities. Differences with respect to the weak coupling regime arise.
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Dissertations / Theses on the topic "Model of coupled harmonic oscillators"

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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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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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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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Chen, Bolun. "Dimensional Reduction for Identical Kuramoto Oscillators: A Geometric Perspective." Thesis, Boston College, 2017. http://hdl.handle.net/2345/bc-ir:107589.

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Thesis advisor: Jan R. Engelbrecht
Thesis advisor: Renato E. Mirollo
Many phenomena in nature that involve ordering in time can be understood as collective behavior of coupled oscillators. One paradigm for studying a population of self-sustained oscillators is the Kuramoto model, where each oscillator is described by a phase variable, and interacts with other oscillators through trigonometric functions of phase differences. This dissertation studies $N$ identical Kuramoto oscillators in a general form \[ \dot{\theta}_{j}=A+B\cos\theta_{j}+C\sin\theta_{j}\qquad j=1,\dots,N, \] where coefficients $A$, $B$, and $C$ are symmetric functions of all oscillators $(\theta_{1},\dots,\theta_{N})$. Dynamics of this model live in group orbits of M\"obius transformations, which are low-dimensional manifolds in the full state space. When the system is a phase model (invariant under a global phase shift), trajectories in a group orbit can be identified as flows in the unit disk with an intrinsic hyperbolic metric. A simple criterion for such system to be a gradient flow is found, which leads to new classes of models that can be described by potential or Hamiltonian functions while exhibiting a large number of constants of motions. A generalization to extended phase models with non-identical couplings gives rise to richer structures of fixed points and bifurcations. When the coupling weights sum to zero, the system is simultaneously gradient and Hamiltonian. The flows mimic field lines of a two-dimensional electrostatic system consisting of equal amounts of positive and negative charges. Bifurcations on a partially synchronized subspace are discussed as well
Thesis (PhD) — Boston College, 2017
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics
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Devalle, Federico. "Collective phenomena in networks of spiking neurons with synaptic delays." Doctoral thesis, Universitat Pompeu Fabra, 2019. http://hdl.handle.net/10803/666912.

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A prominent feature of the dynamics of large neuronal networks are the synchrony-driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity.
Una característica fonamental de la dinàmica d'una xarxa neuronal és l'emergència d'oscil·lacions degudes a sincronització. L'origen d'aquestes oscil·lacions és molt sovint degut les interaccions sinàptiques i als seus retards temporals inherents. Aquesta tesi analitza la emergència d'oscil·lacions produïdes per retards sinàptics en xarxes neuronals heterogènies. A partir de troballes recents en teories de camp mig per xarxes neuronals, aquest treball explora la dinàmica i les bifurcacions d'un model de {\it rate} amb diferents tipus de retards sinàptics. En paral·lel els resultats obtinguts mitjançant el nou model de rate són comparats amb simulacions numèriques de grans xarxes neuronals. Aquestes simulacions confirmen l'existència de nombrosos estats oscil·latoris produïts per sincronització. Alguns d'aquests estats són nous I mostren formes complexes de sincronització parcial i de caos col·lectiu. Gran part d'aquestes oscil·lacions han estat àmpliament ignorades a la literatura, degut a la limitació dels models tradicionals de rate per descriure estats amb un alt nivell de sincronització. Així doncs aquesta tesi ofereix una exploració única dels possibles escenaris oscil·latoris en xarxes neuronals amb retards sinàptics, i amplia significativament les eines matemàtiques disponibles per a la modelització de la gran diversitat d'oscil·lacions neuronals presents en les mesures elèctriques de l'activitat cerebral.
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Oukil, Walid. "Systèmes couplés et morphogénèse auto-organisation de systèmes biologiques." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0459/document.

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On s’intéresse dans cette thèse à des systèmes couplés de type champ moyen en étudiant l’existence de l’état de synchronisation qui se caractérise par une distance uniformément bornée dans le temps entre chaque paire de composantes d’une solution. L’étude se base sur une méthode perturbative. Néanmoins les résultats obtenus ne sont pas évidents dans le cas non-perturbé. En outre dans le cas où le système couplé est périodique et grâce au Théorème du point fixe on montre l’existence d’une solution périodique sur le tore. L’étude de stabilité et de stabilité exponentielle est établie dans le cas linéaire et appliquée à ce type de systèmes couplés
We study in this thesis a class of a perturbed interconnected mean-field system, also known as a coupled systems. Under some assumptions we prove the existence of an invariant open set by the flow of the perturbed system ; in other word, we prove that the distance between the components of an orbit is uniformly bounded, this property is also called synchronization. We use the perturbation method to obtain the result. However the result is not trivial for the not perturbed system. We use the fixed point theorem to prove the existence of a periodic orbit in the torus. We study in addition the stability and the exponential stability of such systems by studying the stability of a linear systems
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Figueiredo, Almeida Sofia José. "Synchronisation d'oscillateurs biologiques : modélisation, analyse et couplage du cycle cellulaire et de l’horloge circadienne." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4239/document.

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Le cycle de division cellulaire et l'horloge circadienne sont deux processus fondamentaux de la régulation cellulaire qui génèrent une expression rythmique des gènes et des protéines. Dans les cellules mammifères, les mécanismes qui sous-tendent les interactions entre le cycle cellulaire et l'horloge restent très mal connus. Dans cette thèse, nous étudions ces deux oscillateurs biologiques, à la fois individuellement et en tant que système couplé, pour comprendre et reproduire leurs principales propriétés dynamiques, détecter les composants essentiels du cycle cellulaire et de l'horloge, et identifier les mécanismes de couplage. Chaque oscillateur biologique est modélisé par un système d'équations différentielles ordinaires non linéaires et ses paramètres sont calibrés par rapport à des données expérimentales: le modèle du cycle cellulaire se base sur les modifications post-traductionnelles du complexe Cdk1-CycB et mène à un oscillateur de relaxation dont la dynamique et la période sont contrôlés par les facteurs de croissance; le modèle de l'horloge circadienne reproduit l'oscillation antiphasique BMAL1/PER:CRY et l'adaptation de la durée des états d'activation et répression par rapport à deux signaux d’entrée hormonaux déphasés. Pour analyser les interactions entre les deux oscillateurs nous étudions la synchronisation des deux rythmes pour des régimes de couplage uni- ou bi-directionnels. Les simulations numériques reproduisent les ratios entre les périodes de l'horloge et du cycle cellulaire, tels que 1:1, 3:2 et 5:4. Notre étude suggère des mécanismes pour le ralentissement du cycle cellulaire avec des implications pour la conception de nouvelles chronothérapies
The cell division cycle and the circadian clock are two fundamental processes of cellular control that generate cyclic patterns of gene activation and protein expression, which tend to be synchronous in healthy cells. In mammalian cells, the mechanisms that govern the interactions between cell cycle and clock are still not well identified. In this thesis we analyze these two biological oscillators, both separately and as a coupled system, to understand and reproduce their main dynamical properties, uncover essential cell cycle and clock components, and identify coupling mechanisms. Each biological oscillator is first modeled by a system of non-linear ordinary differential equations and its parameters calibrated against experimental data: the cell cycle model is based on post-translational modifications of the mitosis promoting factor and results in a relaxation oscillator whose dynamics and period are controlled by growth factor; the circadian clock model is transcription-based, recovers antiphasic BMAL1/PER:CRY oscillation and relates clock phases to metabolic states. This model shows how the relative duration of activating and repressing molecular clock states is adjusted in response to two out-of-phase hormonal inputs. Finally, we explore the interactions between the two oscillators by investigating the control of synchronization under uni- or bi-directional coupling schemes. Simulations of experimental protocols replicate the oscillators’ period-lock response and recover observed clock to cell cycle period ratios such as 1:1, 3:2 and 5:4. Our analysis suggests mechanisms for slowing down the cell cycle with implications for the design of new chronotherapies
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Jhih-YuanGao and 高至遠. "A Study of Coupled Harmonic Oscillator Models toward Quantum Entanglement Dynamics in Macroscopic Quantum Phenomena." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/96826573450199014221.

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碩士
國立成功大學
物理學系
102
Peres-Horodecki-Simon criterion and logarithmic negativity are very powerful tools to determine the separability and to measure the entanglement of Gaussian states. In this thesis, we set up several models, all of which comprise a number of coupled oscillators, and by facilitating the separability criterion and measure we're able to calculate the entanglement between each pair of oscillators at any time analytically, which reveals several interesting phenomena, including entanglement sudden death and revival of entanglement. Also, we compare the entanglement between center of mass coordinates and that of their member oscillators, and thereby understand the role of it in a composite system. Lastly, we'll make an attempt at appreciating the effects of particle numbers on entanglement. We hope these analytically solvable models can help us understand more about the entanglement of interacting systems and of large systems.
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Abdul-Latif, Mohammed. "Frequency Synthesizers and Oscillator Architectures Based on Multi-Order Harmonic Generation." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10281.

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Frequency synthesizers are essential components for modern wireless and wireline communication systems as they provide the local oscillator signal required to transmit and receive data at very high rates. They are also vital for computing devices and microcontrollers as they generate the clocks required to run all the digital circuitry responsible for the high speed computations. Data rates and clocking speeds are continuously increasing to accommodate for the ever growing demand on data and computational power. This places stringent requirements on the performance metrics of frequency synthesizers. They are required to run at higher speeds, cover a wide range of frequencies, provide a low jitter/phase noise output and consume minimum power and area. In this work, we present new techniques and architectures for implementing high speed frequency synthesizers which fulfill the aforementioned requirements. We propose a new architecture and design approach for the realization of wideband millimeter-wave frequency synthesizers. This architecture uses two-step multi-order harmonic generation of a low frequency phase-locked signal to generate wideband mm-wave frequencies. A prototype of the proposed system is designed and fabricated in 90nm Complementary Metal Oxide Semiconductor (CMOS) technology. Measurement results demonstrated that a very wide tuning range of 5 to 32 GHz can be achieved, which is costly to implement using conventional techniques. Moreover the power consumption per octave resembles that of state-of-the art reports. Next, we propose the N-Push cyclic coupled ring oscillator (CCRO) architecture to implement two high performance oscillators: (1) a wideband N-Push/M-Push CCRO operating from 3.16-12.8GHz implemented by two harmonic generation operations using the availability of different phases from the CCRO, and (2) a 13-25GHz millimeter-wave N-Push CCRO with a low phase noise performance of -118dBc/Hz at 10MHz. The proposed oscillators achieve low phase noise with higher FOM than state of the art work. Finally, we present some improvement techniques applied to the performance of phase locked loops (PLLs). We present an adaptive low pass filtering technique which can reduce the reference spur of integer-N charge-pump based PLLs by around 20dB while maintaining the settling time of the original PLL. Another PLL is presented, which features very low power consumption targeting the Medical Implantable Communication Standard. It operates at 402-405 MHz while consuming 600microW from a 1V supply.
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Chen, Fu-Chi, and 陳福基. "Synchronization of A New Model of Pulse-Coupled Integrate-and-Fire Oscillators." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/16360205157163125029.

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碩士
國立成功大學
物理學系碩博士班
96
Synchronization is a natural phenomenon which is an active research topic. Many models were published to approximate these phenomena. In one of these models, all basic entities are considered as identical oscillators with pulse-coupled interaction among them. We use a model to approximate these synchronous phenomena. And we discuss the conditions of two, three and N oscillators. Finally, we find some compatible domains of parameters to make all oscillators be synchronous for all initial conditions.
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Book chapters on the topic "Model of coupled harmonic oscillators"

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Garrett, Steven L. "The Simple Harmonic Oscillator." In Understanding Acoustics, 59–131. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_2.

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Abstract This chapter will introduce a system that is fundamental to our understanding of more physical phenomena than any other. Although the “simple” harmonic oscillator seems to be only the combination of the most mundane components, the formalism developed to explain the behavior of a mass, spring, and damper is used to describe systems that range in size from atoms to oceans. Our investigation goes beyond the “traditional” treatments found in the elementary physics textbooks. For example, the introduction of damping will open a two-way street: a damping element (i.e., a mechanical resistance, Rm) will dissipate the oscillator’s energy, reducing the amplitudes of successive oscillations, but it will also connect the oscillator to the surrounding environment that will return thermal energy to the oscillator. The excitation of a harmonic oscillator by an externally applied force, displacement, or combination of the two will result in a response that is critically dependent upon the relationship between the frequency of excitation and the natural frequency of the oscillator and will introduce the critical concepts of mechanical impedance, resonance, and quality factor. Finally, the harmonic oscillator model will be extended to coupled oscillators that are represented by combinations of several masses and several springs.
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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 129–41. New York, NY: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4684-0233-9_7.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 142–56. New York, NY: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4684-0233-9_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 145–57. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0167-7_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 158–72. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0167-7_9.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Distinguishable Particles." In The Picture Book of Quantum Mechanics, 157–69. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3951-6_8.

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Brandt, Siegmund, and Hans Dieter Dahmen. "Coupled Harmonic Oscillators: Indistinguishable Particles." In The Picture Book of Quantum Mechanics, 170–84. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3951-6_9.

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Brandt, Siegmund, Hans Dieter Dahmen, and Tilo Stroh. "A Two-Particle System: Coupled Harmonic Oscillators." In Interactive Quantum Mechanics, 122–37. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7424-2_5.

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Brandt, Siegmund, Hans Dieter Dahmen, and Tilo Stroh. "A Two-Particle System: Coupled Harmonic Oscillators." In Interactive Quantum Mechanics, 91–106. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21653-9_5.

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Brandt, Siegmund, and Hans Dieter Dahmen. "A Two-Particle System: Coupled Harmonic Oscillators." In Quantum Mechanics on the Personal Computer, 82–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97199-0_5.

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Conference papers on the topic "Model of coupled harmonic oscillators"

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Go, Clark Kendrick C., Joel T. Maquiling, Boonchoat Paosawatyanyong, and Pornrat Wattanakasiwich. "Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules." In INTERNATIONAL CONFERENCE ON PHYSICS EDUCATION: ICPE-2009. AIP, 2010. http://dx.doi.org/10.1063/1.3479873.

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Haaker, T. I. "Analysis of a Class of Coupled Nonlinear Oscillators With an Application to Flow Induced Vibrations." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21416.

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Abstract We consider in this paper the following system of coupled nonlinear oscillatorsx..+x-k(y-x)=εf(x,x.),y..+(1+δ)y-k(x-y)=εf(y,y.). In this system we assume ε to be a small parameter, i.e. 0 < ε ≪ 1. A coupling between the two oscillators is established through the terms involving the positive parameter k. The coupling may be interpreted as a mutual force depending on the relative positions of the two oscillators. For both ε and k equal to zero the two oscillators are decoupled and behave as harmonic oscillators with frequencies 1 and 1+δ, respectively. The parameter δ may therefore be viewed as a detuning parameter. Finally, the term ε f represents a small force acting upon each oscillator. Note that this force depends only on the position and velocity of the oscillator upon which the force is acting. To analyse the system’s dynamic behaviour we use the method of averaging. When k and δ are choosen such that no internal resonance occurs, one typically observes the following behaviour. If the trivial solution is unstable, solutions asymptotically tend to one of the two normal modes or to a mixed mode solution. For the special case with δ = 0 a system of two identical oscillators is found. If in addition k is O(ε) we obtain a 1 : 1 internal resonant system. The averaged equations may then be reduced to a system of three coupled equations — two for the amplitudes and one for the phase difference. Due to the fact that we consider identical oscillators there is a symmetry in the averaged equations. The normal mode solutions, as found for the non-resonant case, are still present. New mixed mode solutions appear. Moreover, Hopf bifurcations in the averaged system lead to limit cycles that correspond to oscillations in the original system with periodically modulated amplitudes and phases. We also consider the case with δ = O(ε), i.e. the case with nearly identical oscillators. If k = O(ε) again a 1 : 1 internal resonant system is found. Contrary to the previous cases the normal mode solutions no longer exist. Moreover, different bifurcations are observed due to the disappearance of the symmetry present in the system for s = 0. We apply some of the results obtained to a model describing aeroelastic oscillations of a structure with two-degrees-of-freedom.
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Achar, B. N. Narahari, Tanya Prozny, and John W. Hanneken. "Linear Chain of Coupled Fractional Oscillators: Response Dynamics and Its Continuum Limit." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35403.

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The standard model of a chain of simple harmonic oscillators of Condensed Matter Physics is generalized to a model of linear chain of coupled fractional oscillators in fractional dynamics. The set of integral equations of motion pertaining to the chain of harmonic oscillators is generalized by taking the integrals to be of arbitrary order according to the methods of fractional calculus to yield the equations of motion of a chain of coupled fractional oscillators. The solution is obtained by using Laplace transforms. The continuum limit of the equations is shown to yield the fractional diffusion-wave equation in one dimension. The solution and numerical application of the set of equations and the continuum limit there of are discussed.
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Harata, Yuji, and Takashi Ikeda. "Modal Analysis to Interpret Localization Phenomena of Harmonic Oscillations in Nonlinear Oscillator Arrays." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97780.

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Abstract This paper investigates localization phenomena in a nonlinear array with N Duffing oscillators connected by weak, linear springs when the array is subjected to harmonic excitation. In the theoretical analysis, the equations of motion are derived for: (1) the physical coordinate system, and (2) modal coordinate system. The modal equations of motion form an autoparametric system, i.e., the excitation acts directly on the first mode of vibration, and the other modes are indirectly excited because they are nonlinearly coupled with the first mode. Van der Pol’s method is employed to obtain the solutions of the harmonic oscillations, and then the expressions of the frequency response curves are given. In the numerical calculations, the frequency response curves of the amplitudes and phase angles in the cases of N = 2 and 3 are presented. The frequency response curves, obtained in the modal coordinate system, demonstrate that localization phenomena occur in the physical coordinate system when multiple vibrational modes simultaneously appear. When imperfections exist in the N Duffing oscillators, the modal equations of motion do not form an autoparametric system because the external excitation directly acts on all modes. Instead, internal resonances may occur in such systems.
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Gourc, Etienne, Guilhem Michon, Se´bastien Seguy, and Alain Berlioz. "Experimental Investigation and Theoretical Analysis of a Nonlinear Energy Sink Under Harmonic Forcing." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48090.

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In the present works, we examine experimentally and theoretically the dynamic behavior of linear oscillator strongly coupled to a nonlinear energy sink under external periodic forcing. The nonlinear oscillator has a nonlinear restoring force realized geometrically with two linear springs that extend axially and are free to rotate. Hence, the force-displacement relationship is cubic. The linear oscillator is directly excited via an electrodynamic shaker. Experiments realized on the test bench consist of measuring the displacement of the oscillators while increasing and decreasing frequencies around the fundamental resonance of the linear oscillator. Many nonlinear dynamical phenomena are observed on the experimental setup such as jumps, bifurcation, and quasiperiodic regimes. The retained nonlinear model is a two degree of freedom system. The behavior of the system is then explained analytically and numerically. The complexification averaging technique is used to derive a set of modulation equation governing the evolution of the complex amplitude at the frequency of excitation, and a stability analysis is performed.
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Xiros, Nikolaos I., and Ioannis T. Georgiou. "Analysis of Coupled Electromechanical Oscillators by a Band-Pass, Reduced Complexity, Volterra Method." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81487.

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Nonlinear analysis of a typical electromechanical coupled oscillator is approached by using Volterra polynomial series representation for nonlinear systems. The problem is formulated in a band-pass framework, allowing the study of transmission of power and information over the same line from the excitation voltage source to the final electromagnetic transducer stage. An input-output, black-box, monochromatic identification technique is applied, in order to obtain a simple, yet nonlinear, small-signal model for the low-pass modulating envelope of the excitation. The small-signal model consists of a low-order static polynomial nonlinearity intermitted between two linear MA filters. The procedure is carried completely in the frequency domain. The most important of the advantages, offered by the proposed methodology, is that identification is performed by employing only the fundamental harmonic component of the response to single sinusoidal inputs of various frequencies and amplitudes that sweep the band and range of interest.
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Muraki, Yasushi. "Application of a Coupled Harmonic Oscillator Model to Solar Activity and El Niño Phenomena." In 35th International Cosmic Ray Conference. Trieste, Italy: Sissa Medialab, 2017. http://dx.doi.org/10.22323/1.301.0084.

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Lee, Young S., and Heng Chen. "Bifurcation of Nonlinear Normal Modes by Means of Synge’s Stability." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48690.

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We study bifurcation of fundamental nonlinear normal modes (FNNMs) in 2-degree-of-freedom coupled oscillators by utilizing geometric mechanics approach based on Synges concept, which dictates orbital stability rather than Lyapunovs classical asymptotic stability. Use of harmonic balance method provides reasonably accurate approximation for NNMs over wide range of energy; and Floquet theory incorporated into Synges stability analysis predicts the respective bifurcation points as well as their types. Constructing NNMs in the frequency-energy domain, we seek applications to study of efficient targeted energy transfers.
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Romeo, Francesco, and Ioannis T. Georgiou. "Multiphysics Chaotic Interaction in a Coupled Electro-Magneto-Mechanical System." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38714.

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The dynamic response of an electro-magneto-mechanical coupled system excited by a harmonic voltage is addressed. The system mathematical model involves coupling quadratic nonlinearities due to the dependence of the inductance on the displacement of the metallic oscillator mass; as a result, a strongly nonlinear behavior characterizes the system’s dynamic response. The numerical analysis is carried out through Poincaré mappings and dynamic continuation. The initial periodic attractor is shown to evolve into higher order and quasi-periodic attractors as the forcing amplitude increases. The peculiar irregular dynamics involving a number of bifurcations characterized by dramatic qualitative changes of both the mechanical and electrical responses for high excitation amplitude is discussed.
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Nico, Valeria, Declan O’Donoghue, Ronan Frizzell, Gerard Kelly, and Jeff Punch. "A Multiple Degree-of-Freedom Velocity-Amplified Vibrational Energy Harvester: Part B — Modelling." In ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/smasis2014-7511.

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Vibrational energy harvesting has become relevant as a power source for the reduced power requirement of electronics used in wireless sensor networks (WSNs). Vibrational energy harvesters (VEHs) are devices that can convert ambient kinetic energy into electrical energy using three principal transduction mechanisms: piezoelectric, electromagnetic and electrostatic. In this paper, a macroscopic two degree-of-freedom (2Dof) nonlinear energy harvester, which employs velocity amplification to enhance the power scavenged from ambient vibrations, is presented. Velocity amplification is achieved through sequential collisions between free-moving masses, and the final velocity is proportional to the mass ratio and the number of masses. Electromagnetic induction is chosen as the transduction mechanism because it can be readily implemented in a device which uses velocity amplification. The experimental results are presented in Part A of this paper, while in Part B three theoretical models are presented: (1) a coupled model where the two masses of the non-linear oscillator are considered as a coupled harmonic oscillators system; (2) an uncoupled model where the two masses are not linked and collisions between masses can occur; (3) a model that considers both the previous cases. The first two models act as necessary building blocks for the accurate development of the third model. This final model is essential for a better understanding of the dynamics of the 2-Dof device because it can represent the real behaviour of the system and captures the velocity amplification effect which is a key requirement of modelling device of interest in this work. Moreover, this model is essential for a future optimization of geometric and magnetic parameters in order to develop a MEMS scale multi-degree-of-freedom device.
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Reports on the topic "Model of coupled harmonic oscillators"

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Yeon, Kyu-Hwang, Chung-In Um, Woo-Hyung Kahng, and Thomas F. George. Propagators for Driven Coupled Harmonic Oscillators. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada199418.

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Maidanik, G. Loss Factors of a Complex Composed of a Number of Coupled Harmonic Oscillators. Fort Belvoir, VA: Defense Technical Information Center, February 1997. http://dx.doi.org/10.21236/ada325092.

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