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Oscillator
Kinds of Oscillator Terms modified by Oscillator Selected AbstractsLaser Sources for Ultrashort Pulses , Oscillators and Amplifiers for Various ApplicationsLASER TECHNIK JOURNAL, Issue 1 2007Rüdiger Paschotta Dr. [source] Introductory quantum physics courses using a LabVIEW multimedia moduleCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2007Ismael Orquķn Abstract We present the development of a LabVIEW multimedia module for introductory Quantum Physics courses and our experience in the use of this application as an educational tool in learning methodologies. The program solves the time-dependent Schrödinger equation (TDSE) for arbitrary potentials. We describe the numerical method used for solving this equation, as well as some mathematical tools employed to reduce the calculation time and to obtain more accurate results. As an illustration, we present the evolution of a wave packet for three different potentials: the repulsive barrier potential, the repulsive step potential, and the harmonic oscillator. This application has been successfully integrated in the learning strategies of the course Quantum Physics for Engineering at the Polytechnic University of Valencia, Spain. © 2007 Wiley Periodicals, Inc. Comput Appl Eng Educ. 15: 124,133, 2007; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20100 [source] Design of an MR-compatible piezoelectric actuator for MR elastographyCONCEPTS IN MAGNETIC RESONANCE, Issue 4 2002Kai Uffmann Abstract Magnetic Resonance (MR) elastography is a method for measuring tissue elasticity via phase images acquired with an MR scanner. The propagation of periodic mechanical waves through the tissue can be captured by means of a modified phase contrast sequence. These waves are generated with a mechanical oscillator (actuator) and coupled into the tissue through the skin. The actuator must be capable of generating a sinusoidal excitation with excellent phase and amplitude stability, while not disturbing the MR imaging process. In this work, an actuator based on a piezoelectric principle was developed. Based on the imaging evaluation of several material samples, the housing for the piezoelectric ceramic was constructed of aluminum. Smaller parts of the housing were manufactured from brass and titanium to fulfill the mechanical constraints. A lever was used to transfer the oscillation generated by the piezoelectric ceramic to the point of excitation. The lever amplifies the piezoelectric motion, allowing for a more compact design. Three different lever designs were characterized by an acceleration sensor both outside and inside the magnet. It was shown that the rigidity of the lever, as determined by its material and form, was decisive in determining the resonant frequency of the system and therefore the maximum practical frequency of operation. It was also shown that the motion of the oscillator is unaffected by the electromagnetic fields of the MR imager. The final design can be placed directly in the magnet bore within a few centimeters of the tissue volume to be imaged without generating significant artifacts. An amplitude range of 0,1 mm in the frequency range from 0 to over 300 Hz was achieved, sufficient for performing most MR elastography applications. © 2002 Wiley Periodicals, Inc. Concepts in Magnetic Resonance (Magn Reson Engineering) 15: 239,254, 2002 [source] Estimation of strength reduction factors via normalized pseudo-acceleration response spectrumEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 6 2007Debasis Karmakar Abstract Estimation of design forces in ductility-based earthquake-resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo-spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto-plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period-dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd. [source] A preliminary prediction of seismic damage-based degradation in RC structuresEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2001Vinay K. Gupta Abstract Estimation of structural damage from a known increase in the fundamental period of a structure after an earthquake or prediction of degradation of stiffness and strength for a known damage requires reliable correlations between these response functionals. This study proposes a modified Clough,Johnston single-degree-of-freedom oscillator to establish these correlations in the case of a simple elasto-plastic oscillator. It is assumed that the proposed oscillator closely models the response of a given multi-degree-of-freedom system in its fundamental mode throughout the duration of the excitation. The proposed model considers the yield displacement level and ductility supply ratio-related parameter as two input parameters which must be estimated over a narrow range of ductility supply ratio from a frequency degradation curve. This curve is to be identified from a set of recorded excitation and response time-histories. Useful correlations of strength and stiffness degradation with damage have been obtained wherein a simple damage index based on maximum and yield displacements and ductility supply ratio has been considered. As an application, the proposed model has been used to demonstrate that ignoring the effects of aftershocks in the case of impulsive ground motions may lead to unsafe designs. Copyright © 2001 John Wiley & Sons, Ltd. [source] Pounding of structures modelled as non-linear impacts of two oscillatorsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 5 2001K. T. Chau Abstract A new formulation is proposed to model pounding between two adjacent structures, with natural periods T1 and T2 and damping ratios ,1 and ,2 under harmonic earthquake excitation, as non-linear Hertzian impact between two single-degree-of-freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis (,Pounding of buildings modelled by an impact oscillator' Earthquake Engineering and Structural Dynamics, 1992; 21:253,274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non-rigid impacts. When the difference in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the standoff distance. The maximum relative impact velocity of the coupled system can occur at an excitation period Tn* which is either between those of the two oscillators or less than both of them, depending on the ratios T1/T2 and ,1/,2. Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters. Copyright © 2001 John Wiley & Sons, Ltd. [source] Theoretical and conceptual issues in time,place discriminationEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 9 2009Jonathon D. Crystal Abstract The need to discover resources that are available under specific environmental constraints represents a fundamental environmental pressure on the evolution of behavior. Time,place discrimination refers to the ability to secure resources when they are available under specific temporal and spatial contingencies. This article reviews a number of examples of time,place discrimination. The review highlights theoretical and conceptual issues that are needed to behaviorally identify the mechanisms responsible for time,place performance. Next, limitations on time,place performance that may be imposed by a circadian system are described. Finally, a number of lines of research that broaden these limitations are discussed. These lines of research include studies that suggest that (i) a broad range of long intervals (outside the limited range of circadian entrainment) are timed, (ii) at least some long intervals (16,21 h) are timed with an endogenous self-sustaining oscillator, (iii) short intervals (in the range of 1,3 min) are timed with an endogenous self-sustaining oscillator, and (iv) memory for specific unique events (including when and where they occurred) is based on a circadian representation of time. It is concluded that a unified theory of timing that can retain the times of occurrence of individual events is needed. The time of occurrence of an event may be encoded not only with respect to a circadian oscillator but also with respect to other oscillators in the long-interval and short-interval ranges. [source] Spatial and temporal variation of passer Per2 gene expression in two distinct cell groups of the suprachiasmatic hypothalamus in the house sparrow (Passer domesticus)EUROPEAN JOURNAL OF NEUROSCIENCE, Issue 3 2002Ute Abraham Abstract In mammals, the major pacemaker controlling circadian rhythmicity is located in the hypothalamic suprachiasmatic nuclei. Although there is evidence for the presence of a hypothalamic circadian oscillator in birds from lesioning studies, neuroanatomical, neurochemical and functional investigations have failed to identify its exact location. Two cell groups in the avian hypothalamus have been shown to bear characteristics of the mammalian suprachiasmatic nucleus: the suprachiasmatic nucleus and the lateral hypothalamic retinorecipient nucleus. We cloned an avian period homologue (pPer2) and investigated the temporal and spatial expression pattern of this gene in the house sparrow hypothalamus using in situ hybridization. Applying quantitative morphometry, we found rhythmic expression of pPer2 during light,dark as well as in constant conditions in the suprachiasmatic nucleus and in the lateral hypothalamus. The temporal and spatial distribution of pPer2 expression in the suprachiasmatic nucleus suggest a longitudinal compartmentalization of the nucleus with period gene expression being initiated in the most rostral portion of the suprachiasmatic nucleus before lights on. In the lateral hypothalamus, phasing of pPer2 -rhythmicity appeared different from the suprachiasmatic nucleus. The major difference between light,dark and constant conditions was a decrease in the amplitude of pPer2 rhythmicity in the suprachiasmatic nucleus. Our data demonstrate that, unlike in mammals, Per gene expression in the suprachiasmatic hypothalamus of the house sparrow is not confined to a single cell group, indicating a more complex organization of the circadian oscillator in the hypothalamus of birds. [source] Phase-coupled oscillator models can predict hippocampal inhibitory synaptic connectionsEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 12 2001F. K. Skinner Abstract What factors are responsible for propagating electrical activity in the hippocampus? Using an intact, isolated hippocampus preparation, it is possible to observe spontaneous delta (, 4 Hz) waves of rhythmic field potentials. These rhythmic potentials are inhibitory in nature, mediated by GABAergic inhibitory potentials originating from a population of principal neurons. They start in the ventro-temporal region and move longitudinally towards the dorso-septal region with a phase lag of , 10% between the extracellular recordings. We use the mathematical framework of phase-coupled oscillators (PCO) to gain some insight into the underlying network system. A chain of 15 nearest-neighbour bidirectionally coupled PCOs is used where each oscillator refers to a segment of the CA1 region of the hippocampus that can generate these slow field potentials. We find that ventro-dorsal delta waves exist if there is a dominance in coupling strength in one direction. Without a one-way coupling dominance, ventro-dorsal waves can still exist, but then the coupling strengths need to be much larger. The relationship between entrained and intrinsic frequencies and the variation of propagation speeds along the longitudinal axis can be used to determine which case applies. Currently available experimental data supports one of the cases, predicting that there is a stronger ventral to dorsal inhibitory effect. [source] THE CONTRIBUTION OF AN HOURGLASS TIMER TO THE EVOLUTION OF PHOTOPERIODIC RESPONSE IN THE PITCHER-PLANT MOSQUITO, WYEOMYIA SMITHIIEVOLUTION, Issue 10 2003W. E. Bradshaw Abstract Photoperiodism, the ability to assess the length of day or night, enables a diverse array of plants, birds, mammals, and arthropods to organize their development and reproduction in concert with the changing seasons in temperate climatic zones. For more than 60 years, the mechanism controlling photoperiodic response has been debated. Photoperiodism may be a simple interval timer, that is, an hourglasslike mechanism that literally measures the length of day or night or, alternatively, may be an overt expression of an underlying circadian oscillator. Herein, we test experimentally whether the rhythmic response in Wyeomyia smithii indicates a causal, necessary relationship between circadian rhythmicity and the evolutionary modification of photoperiodic response over the climatic gradient of North America, or may be explained by a simple interval timer. We show that a day-interval timer is sufficient to predict the photoperiodic response of W. smithii over this broad geographic range and conclude that rhythmic responses observed in classical circadian-based experiments alone cannot be used to infer a causal role for circadian rhythmicity in the evolution of photoperiodic time measurement. More importantly, we argue that the pursuit of circadian rhyth-micity as the central mechanism that measures the duration of night or day has distracted researchers from consideration of the interval-timing processes that may actually be the target of natural selection linking internal photoperiodic time measurement to the external seasonal environment. [source] Dependence of s -waves on continuous dimension: The quantum oscillator and free systemsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006K.B. Wolf Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source] Quantum phenomena via complex measure: Holomorphic extensionFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006Article first published online: 11 MAY 200, S.K. Srinivasan The complex measure theoretic approach proposed earlier is reviewed and a general version of density matrix as well as conditional density matrix is introduced. The holomorphic extension of the complex measure density (CMD) is identified to be the Wigner distribution function of the conventional quantum mechanical theory. A variety of situations in quantum optical phenomena are discussed within such a holomorphic complex measure theoretic framework. A model of a quantum oscillator in interaction with a bath is analyzed and explicit solution for the CMD of the coordinate as well as the Wigner distribution function is obtained. A brief discussion on the assignment of probability to path history of the test oscillator is provided. [source] Dynamic changes in the direction of the theta rhythmic drive between supramammillary nucleus and the septohippocampal systemHIPPOCAMPUS, Issue 6 2006Bernat Kocsis Abstract Neurons in the supramammillary nucleus (SUM) of urethane-anesthetized rats fire rhythmically in synchrony with hippocampal theta rhythm. As these neurons project to the septum and hippocampus, it is generally assumed that their role is to mediate ascending activation, leading to the hippocampal theta rhythm. However, the connections between SUM and the septohippocampal system are reciprocal; there is strong evidence that theta remains in the hippocampus after SUM lesions and in the SUM after lesioning the medial septum. The present study examines the dynamics of coupling between rhythmic discharge in the SUM and hippocampal field potential oscillations, using the directionality information carried by the two signals. Using directed transfer function analysis, we demonstrate that during sensory-elicited theta rhythm and also during short episodes of theta acceleration of spontaneous oscillations, the spike train of a subpopulation of SUM neurons contains information predicting future variations in rhythmic field potentials in the hippocampus. In contrast, during slow spontaneous theta rhythm, it is the SUM spike signal that can be predicted from the preceding segment of the electrical signal recorded in the hippocampus. These findings indicate that, in the anesthetized rat, SUM neurons effectively drive theta oscillations in the hippocampus during epochs of sensory-elicited theta rhythm and short episodes of theta acceleration, whereas spontaneous slow theta in the SUM is controlled by descending input from the septohippocampal system. Thus, in certain states, rhythmically firing SUM neurons function to accelerate the septal theta oscillator, and in others, they are entrained by a superordinate oscillatory network. © 2006 Wiley-Liss Inc. [source] A 5-MHz AT-cut quartz crystal oscillating circuit functioning in 350 nAIEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 4 2007Tomio Sato Non-member Abstract An oscillating circuit functioning at ultra low power (350 nA) for a 5-MHz AT-cut quartz crystal oscillator was investigated. This circuit has a resistance between the power terminal of the CMOS-IC and the power supply, and another between the earth terminal of the CMOS-IC and the ground (GND). These resistances discourage an inrush of current, and set a gain (gm) necessary for oscillating the circuit at minimum. The developed circuit is quite simple, but enables driving at once-unthinkable, low power (below 1 µA). © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source] A numerical,analytical combined method for vibration of a beam excited by a moving flexible bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2007Huajiang Ouyang Abstract The vibration of a beam excited by a moving simple oscillator has been extensively studied. However, the vibration of a beam excited by an elastic body with conformal contact has attracted much less attention. This is the subject of the present paper. The established model is more complicated but has a much wider range of applications than the moving-oscillator model. Because the moving body is flexible, the moving loads at the contact interface are not known a priori and must be determined together with the dynamics of the whole system. In this paper, the equation of motion of the beam and the moving body are established separately using a numerical,analytical combined approach. It is found from the numerical results of the simulated example that the vibrations of the moving body and the beam excited by the moving body are significantly influenced by the travelling speed. At very low or very high speeds the dynamic effect is small and the beam deforms to take the shape of its static deflection. Vibrations tend to be greater in the intermediate speed range and the total moving force at the interface of the beam and the moving body can be compressive and tensile. Copyright © 2007 John Wiley & Sons, Ltd. [source] Variable structure robust state and parameter estimatorINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2001Alex S. Poznyak Abstract The problem of simultaneous robust state and parameters estimation for a class of SISO non-linear systems under mixed uncertainties (unmodelled dynamics as well as observation noises) is addressed. A non-linear variable structure robust ,observer,identifier' is introduced to obtain the corresponding estimates. Lie derivative technique is used to obtain the observability conditions for the equivalent extended non-linear system. It is shown that, in general, the extended system can lose the global observability property and a special procedure is needed to work well in this situation. The suggested adaptive observer has the non-linear high-gain observer structure with adjusted parameters that provides ,a good' upper bound for the identification error performance index. The van der Monde transformation is used to derive this bound which turns out to be tight. Three examples dealing with a simple pendulum, the Duffing equation and the van del Pol oscillator are considered to illustrate the effectiveness of the suggested approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Periodic noise analysis of electric circuits: Artifacts, singularities and a numerical methodINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 7 2010Angelo Brambilla Abstract In this paper it is shown that a numerical method largely adopted for the simulation of noise in autonomous circuits is affected by singularities that manifest when the frequency at which the noise analysis is carried out approaches a harmonic of the autonomous circuit. The resulting noise power spectral density (PSD) is thus characterized by spurious spikes. The presence of these singularities is for the first time justified from an analytical standpoint and their effects are shown by simulating some oscillators, employed as benchmarks. Furthermore, the presented approach justifies the 1/(fs,f)2 shape of the PSD of noise at the output when the fs frequency approaches the f fundamental of a stable oscillator and the 1/|fs,f|3 shape when the effects of flicker noise are manifest. Copyright © 2009 John Wiley & Sons, Ltd. [source] The effect of parameter mismatches on the output waveform of an LC -VCOINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2010Antonio Buonomo Abstract The effect of parameter mismatches on the output waveforms of a popular voltage-controlled oscillator is investigated, schematizing the circuit as a system of two mutually coupled oscillators, whose describing equations are derived in a perturbation form. The circuit is studied using the method of two time-scales showing the existence of synchronization phenomena leading in presence of mismatches to a locking frequency, which significantly differs from the natural frequencies of the tanks, and to an oscillation amplitude different from that of the symmetric case. We also show that in-phase and quadrature oscillations at the drain nodes can be generated with a proper parameter setting. Circuit simulations confirm the presence of a synchronized oscillation, which is consistent with the prediction of the presented analysis. Copyright © 2009 John Wiley & Sons, Ltd. [source] A 5,GHz quadrature relaxation oscillator with mixing for improved testability or compact front-end implementationINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2010Luis Bica Oliveira Abstract We demonstrate by measurements on a test circuit that a 5,GHz relaxation oscillator with accurate quadrature outputs and low phase-noise can be obtained, and that these favorable properties can be preserved while the mixing function is performed by this oscillator. This is useful either to measure the quadrature error at a low frequency, or to implement a low-intermediate frequency (IF) or zero-IF (homodyne) radio frequency front-end. Copyright © 2008 John Wiley & Sons, Ltd. [source] New structures of four-phase oscillators obtained by strongly interweaving mono-phase limit-cycle oscillatorsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2008D. Yardeny Abstract The present work is a part of our effort of developing multiphase oscillators. The particular system dealt with here is that of strongly nonlinearly coupled four oscillators that form a multiphase source. Such sources possess potential applications in power electronics, in phased-array antennas, and in modern methods of modulation and especially in demodulating multi-phased modulated signals. The present system can be interpreted as embracing four two-phase oscillators. Nevertheless, as a result of the strong coupling, the second state equation of each oscillator merges with the first equation of the following oscillator. The resulted four-phase source is, therefore, represented by merely four state equations. The applications related to communications (especially those related to receivers) may be susceptible to the noise performance of the source. We believe that the presently suggested system, which relies on strong coupling of oscillators, is advantageous in its noise performance in comparison to more straightforward recently described multiphase sources, which incorporate loosely coupled oscillators. Copyright © 2007 John Wiley & Sons, Ltd. [source] Harmonic Balance, Melnikov method and nonlinear oscillators under resonant perturbationINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2008Michele Bonnin Abstract The subharmonic Melnikov's method is a classical tool for the analysis of subharmonic orbits in weakly perturbed nonlinear oscillators, but its application requires the availability of an analytical expression for the periodic trajectories of the unperturbed system. On the other hand, spectral techniques, like the Harmonic Balance, have been widely applied to the analysis and design of nonlinear oscillators. In this manuscript, we show that bifurcations of subharmonic orbits in perturbed systems can be easily detected computing the Melnikov's integral over the Harmonic Balance approximation of the unperturbed orbits. The proposed method significantly extends the applicability of the Melnikov's method since the orbits of any nonlinear oscillator can be easily detected by the Harmonic Balance technique, and the integrability of the unperturbed equations is not required anymore. As examples, several case studies are presented, the results obtained are confirmed by extensive numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source] Bifurcation analysis of a piecewise smooth system with non-linear characteristicsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2005Takuji Kousaka Abstract In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non-linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non-linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincaré mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh-type oscillator containing a state- period-dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border-collision bifurcations. Some theoretical results are verified by laboratory experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Mixed-mode analysis of the sensitivity of a radiofrequency oscillator disturbed by parasitic signalsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1 2009Christian Gontrand Abstract The first step of this work is to study the susceptibility of a radiofrequency oscillator to deterministic disturbance sources. A Colpitts oscillator, working around a 4,GHz frequency, contains a heterojunction bipolar transistor with a silicon,germanium base as an active device. A mixed-mode analysis is involved, applying a microscopic drift diffusion model to the device, whereas the rest of the circuit used is governed by Kirchhoff's laws. We assume that this tool is very relevant to grasp the influence of intrinsic or extrinsic noisy sources of the oscillator. Our first simulation raw results motivate us to discuss, and perhaps extend, via some analytical models, the so-called impulse sensitivity function model. In this paper, we try to develop quantitative predictions about the phase noise of such oscillators, and to give some new tracks on this field. Copyright © 2008 John Wiley & Sons, Ltd. [source] Degeneracy in one-dimensional quantum mechanics: A case studyINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2010Adelio R. Matamala Abstract In this work we study the isotonic oscillator, V(x) = Ax2 + Bx,2, on the whole line ,, < x < + , as an example of a one-dimensional quantum system with energy level degeneracy. A symmetric double-well potential with a finite barrier is introduced to study the behavior of energy pattern between both limit: the harmonic oscillator (i.e., a system without degeneracy) and the isotonic oscillator (i.e., a system with degeneracy). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Systematic calculation of molecular vibrational spectra through a complete Morse expansionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2007Andrea Bordoni Abstract We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard-Jones oscillator, and to the ab initio potential of the H2 molecule. Global cm,1 accuracy is exhibited through the H2 spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi-dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Degeneracy of confined D -dimensional harmonic oscillatorINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2007H. E. Montgomery Jr. Abstract Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D -dimensional (D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius Rc. Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Common generating function for two-dimensional hydrogen atom complete wave functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2007L. Chaos-Cador Abstract The Schrödinger equation for the two-dimensional hydrogen atom is known to be separable and integrable in circular, parabolic, and elliptical coordinates. This makes it possible to construct a common generating function for the complete wave functions of the atom in the respective coordinates. The connections with the corresponding generating function and wave functions for the harmonic oscillator are recognized and applied in this work. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Computation of the eigenvalues of the one-dimensional Schrödinger equation by symplectic methodsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2006Z. Kalogiratou Abstract The computation of high-state eigenvalues of the one-dimensional time-independent Schrödinger equation is considered by symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Yoshida-type symplectic integrators are used as well as symplectic integrators based on the Magnus expansion. Numerical results are obtained for a wide range of eigenstates of the one-dimensional harmonic oscillator, the doubly anharmonic oscillator, and the Morse potential. The eigenvalues found by the symplectic methods are compared with the eigenvalues produced by Numerov-type methods. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Wigner function of the rotating Morse oscillatorINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005Jerzy Stanek Abstract We present an analytical expression of the Wigner distribution function (WDF) for the bound eigenstates of the rotating Morse oscillator (RMO). The effect of rotational excitation on the WDF on the quantum phase space has been demonstrated. This effect has been visualized by a series of contour diagrams for given rovibrational quantum states. Rotations of the molecule have been proved to qualitatively and quantitatively change the Wigner function. As a result, the most probable distance between atoms in a rotating molecule changes, and depends on the parity of the vibrational quantum number. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Logarithmic perturbation theory for a spiked oscillator and sum rulesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005S. K. Bandyopadhyay Abstract We show that logarithmic perturbation theory nicely yields the wavefunction correction terms in closed forms for the spiked perturbation ,/x2 on the first excited state of the harmonic oscillator, where the conventional Rayleigh-Schrödinger scheme is known to encounter serious problems. The study also provides a direct route to obtain several sum rules, some of which appear to be new. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] | |||||||||||||||||||||||||||||||||||||||||||