Showing papers on "Superposition principle published in 1998"
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01 Dec 1998
TL;DR: In this paper, the authors present a method for dynamic analysis of a single-degree-of-freedom (SDOF) system, based on the principle of virtual displacements, which is used to distinguish features of a dynamic problem.
Abstract: 1. Basic Concepts. Introduction to Structural Dynamics. Types of Dynamic Loads. Sources of Dynamic Loads. Distinguishing Features of a Dynamic Problem. Methodology for Dynamic Analysis. Types of Structural Vibration. Organization of the Text. Systems of Units. References. I. SINGLE-DEGREE-OF-FREEDOM (SDOF) SYSTEMS. 2. Equation of Motion and Natural Frequency. Fundamental Components of a Vibrating System. D'Alembert's Principle of Dynamic Equilibrium. The Energy Method. The Principle of Virtual Displacements. References. Notation. Problems. 3. Undamped Free Vibration. Simple Harmonic Motion. Interpretation of the Solution. Equivalent Stiffness. Rayleigh Method. References. Notation. Problems. 4. Damped Free Vibration. Free Vibration with Viscous Damping. Logarithmic Decrement. Hysteresis Damping. Coulomb Damping. References. Notation. Problems. 5. Response to Harmonic Excitation. Forced Harmonic Response of Undamped Systems. Beating and Resonance. Forced Harmonic Vibrations with Viscous Damping. Effect of Damping Factor on Steady-State Response and Phase Angle. Harmonic Excitation Caused by Rotating Unbalance. Base Excitation. Vibration Isolation and Transmissibility. References. Notation. Problems. 6. Response to Periodic and Arbitrary Dynamic Excitation. Response to Periodic Excitation. Response to Unit Impulse. Duhamel Integral. Response to Arbitrary Dynamic Excitation. Response Spectrum. References. Notation. Problems. 7. Numerical Evaluation of Dynamic Response. Interpolation of the Excitation. Direct Integration of the Equation of Motion. Central Difference Method. Runge-Kutta Methods. Average Acceleration Method. Linear Acceleration Method. Response to Base Excitation. Response Spectra by Numerical Integration. References. Notation. Problems. 8. Frequency Domain Analysis. Alternative Forms of the Fourier Series. Discrete Fourier Transform. Fast Fourier Transform. Discrete Fourier Transform Implementation Considerations. Fourier Integral. References. Notation. Problems. II. MULTI-DEGREE-OF-FREEDOM (MDOF) SYSTEMS. 9. General Property Matrices for Vibrating Systems. Flexibility Matrix. Stiffness Matrix. Inertia Properties: Mass Matrix. The Eigenproblem in Vibration Analysis. Static Condensation of the Stiffness Matrix. References. Notation. Problems. 10. Equations of Motion and Undamped Free Vibration. Hamilton's Principle and the Lagrange Equations. Natural Vibration Frequencies. Natural Vibration Modes. Orthogonality of Natural Modes. Systems Admitting Rigid-Body Modes. Generalized Mass and Stiffness Matrices. Free Vibration Response to Initial Conditions. Approximate Methods for Estimating the Fundamental Frequency. References. Notation. Problems. 11. Numerical Solution Methods for Natural Frequencies and Mode Shapes. General Solution Methods for Eigenproblems. Inverse Vector Iteration. Forward Vector Iteration. Generalized Jacobi Method. Solution Methods for Large Eigenproblems References. Notation. Problems. 12. Analysis of Dynamic Response by Mode Superposition. Mode Displacement Method for Undamped Systems. Modal Participation Factor. Mode Superposition Solution for Systems with Classical Damping. Numerical Evaluation of Modal Response. Normal Mode Response to Support Motions. Response Spectrum Analysis. Mode Acceleration Method. References. Notation. Problems. 13. Analysis of Dynamic Response by Direct Integration. Basic Concepts of Direct Integration Methods. The Central Difference Method. The Wilson-u Method. The Newmark Method. Practical Considerations for Damping. Stability and Accuracy of Direct Integration Methods. Direct Integration versus Mode Superposition. References. Notation. Problems. III. CONTINUOUS SYSTEMS. 14. Vibrations of Continuous Systems. Longitudinal Vibration of a Uniform Rod. Transverse Vibration of a Pretensioned Cable. Free Transverse Vibration of Uniform Beams. Orthogonality of Normal Modes. Undamped Forced Vibration of Beams by Mode Superposition. Approximate Methods. References. Notation. Problems. IV. NONLINEAR DYNAMIC RESPONSE. 15. Analysis of Nonlinear Response. Classification of Nonlinear Analyses. Systems with Nonlinear Characteristics. Formulation of Incremental Equations of Equilibrium. Numerical Solution of Nonlinear Equilibrium Equations. Response of Elastoplastic SDOF Systems. Response of Elastoplastic MDOF Systems. References. Notation. Problems. V. PRACTICAL APPLICATIONS. 16. Elastic Wave Propagation in Solids. Stress and Strain at a Point. Constitutive Relations. Equations of Motion. Stress Wave Propagation. Applications. References. Notation. Problems. 17. Earthquakes and Earthquake Ground Motion. Causes of Earthquakes. Faults. Seismic Waves. Earthquake Intensity. Earthquake Magnitude. Seismicity. Earthquake Ground Motion. Earthquake Damage Mechanisms. References. Notation. 18. Earthquake Response of Structures. Time-History Analysis: Basic Concepts. Earthquake Response Spectra. Earthquake Design Spectra. Response of MDOF Systems. Generalized SDOF Systems. In-Building Response Spectrum. Inelastic Response. Seismic Design Codes. References. Notation. Problems. 19. Blast Loads on Structures. Sources of Blast Loads. Shock Waves. Determination of Blast Loads. Strain-Rate Effects. Approximate Solution Technique for SDOF Systems. References. Problems. Notations. 20. Basic Concepts of Wind Waves. Linear Wave Theory. Nonlinear Waves. Wave Transformations. Wave Statistics. Wave Information Damping. References. Notation. Problems. 21. Response of Structures to Waves. Morison Equation. Force Coefficients. Linearized Morison Equation. Inclined Cylinders. Transverse Lift Forces. Froude-Krylov Theory. Diffraction Theory: The Scattering Problem. Diffraction Theory: The Radiation Problem. References. Notation. Problems. Appendix A. Appendix B. Index.
263 citations
TL;DR: In this article, a general linear theory describes the extension of the convolutional method to nonstationary processes, which can apply any linear, non-stationary filter with arbitrary time and frequency variation, in the time, Fourier, or mixed domains.
Abstract: A general linear theory describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier transforms or generalized convolutional integrals. Nonstationary transforms such as the wavelet transform are not required. There are many possible applications of this theory including: the one-way propagation of waves through complex media, time migration, normal moveout removal, time-variant filtering, and forward and inverse Q filtering. Two complementary nonstationary filters are developed by generalizing the stationary convolution integral. The first, called nonstationary convolution, corresponds to the linear superposition of scaled impulse responses of a nonstationary filter. The second, called nonstationary combination, does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum. Both extensions have stationary convolution as a limiting form and, in the discrete case, can be formulated as matrix operations. Fourier transformation shows that both filter types are nonstationary filter integrals in the Fourier domain as well. This result is a generalization of the convolution theorem for stationary signals because, as the filter becomes stationary in one domain, the integral in the other domain collapses to a scalar multiplication. For discrete signals, stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix, while nonstationary filters require off-diagonal terms. For quasi-stationary filters, a computational advantage is obtained by computing only the significant terms near the diagonal. Unlike stationary theory, a mixed domain of time and frequency is also possible. In this context, the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse. Nonstationary convolution becomes a generalized forward Fourier integral and nonstationary combination is a generalized inverse Fourier integral.
235 citations
TL;DR: In this article, the authors describe a method for creating an arbitrary coherent superposition of two atomic states in a controlled and robust way by using a sequence of three pulses in a four-state system.
170 citations
TL;DR: In this article, an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure is presented, and a validation of its usefulness is provided. But the scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions.
Abstract: This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.
124 citations
TL;DR: A method is proposed to simulate the propagation of a broadband ultrasound pulse in a lossy medium whose attenuation exhibits a power law frequency dependence using a bank of Gaussian filters and a time causal model.
Abstract: A method is proposed to simulate the propagation of a broadband ultrasound pulse in a lossy medium whose attenuation exhibits a power law frequency dependence. Using a bank of Gaussian filters, the broadband pulse is first decomposed into narrowband components. The effects of the attenuation and dispersion are then applied to each component based on the superposition principle. When the bandwidth of each component is narrow enough, these effects can be evaluated at the center frequency of the component, resulting in a magnitude reduction, a constant phase angle lag, and a relative time delay. The accuracy of the proposed method is tested by comparing the model-produced pulses with the experimentally measured pulses using two different phantoms. The first phantom has an attenuation function which exhibits a nearly linear frequency dependence. The second phantom has an attenuation function which exhibits a nearly quadratic frequency dependence. In deriving the dispersion from the measured attenuation, a nearly local model and a time causal model are used. For linear attenuation, the two models converge and both predict accurately the waveform of the transmitted pulse. For nonlinear attenuation, the time causal model is found more accurate than the nearly local model in predicting the waveform of the transmitted pulse.
110 citations
TL;DR: In this article, two identical femtosecond pulses are used to create a coherent superposition of two vibrational wave packets in a bound electronic state of cesium dimers.
Abstract: Two identical femtosecond pulses are used to create a coherent superposition of two vibrational wave packets in a bound electronic state of cesium dimers. The oscillations of these two wave packets are further detected after photoionization of the system. Quantum interferences between the two wave packets result in a temporal coherent control of the ionization probability. The interferogram exhibits the following features as a function of the time delay between the two laser pulses: high-frequency oscillation corresponding to Ramsey fringes (at the Bohr frequency of the transition) modulated by a slow envelope corresponding to the oscillations of vibrational wave packets (vibrational recurrences). Here the control parameter is the time delay between the two laser pulses which can be used to control the preparation of a wave packet in a quantum system and monitor its evolution. The detailed theory of this experiment is presented and compared with the pump-probe experiment. The temporal coherent control exp...
99 citations
TL;DR: In this article, a pulse in the strongly dispersion managed fiber is represented as a linear superposition of Hermite-Gaussian harmonics, with the zeroth harmonic being a chirped Gaussian with periodically varying width.
Abstract: We represent a pulse in the strongly dispersion managed fiber as a linear superposition of Hermite-Gaussian harmonics, with the zeroth harmonic being a chirped Gaussian with periodically varying width. We obtain the same conditions for the stationary pulse propagation as were obtained earlier by the variational method. Moreover, we find a simple approximate formula for the pulse shape, which accounts for the numerically observed transition of that shape from a hyperbolic secant to the Gaussian. Finally, using the same approach, we systematically derive the equations for the evolution of a pulse under a general perturbation. This systematic derivation justifies the validity of similar equations obtained earlier from the conservation laws.
93 citations
TL;DR: In this paper, a perturbation analysis of non-linear flow behavior of viscoelastic fluids can be studied in detail by means of an analysis of the spectral content of the material under the nonlinear steady flow, where small amplitude oscillations can be superimposed on the steady state shear flow.
Abstract: The non-linear flow behaviour of viscoelastic fluids can be studied in detail by means of a perturbation analysis. For that purpose small amplitude oscillations can be superimposed on the steady-state shear flow. In this manner, detailed information about the spectral content of the material under the non-linear steady flow is obtained. The oscillatory flow can be either parallel or perpendicular to the main shear flow. Devices for both types are becoming readily available and apparently are being used without realizing the intricate nature of these flows. An analysis shows that linear superposition moduli do not obey the basic rules of linear viscoelasticity. This includes deviations from the Kramers–Kronig relation and from the usual relation between steady-state and dynamic viscosities. This is demonstrated on the basis of a Wagner I model for which analytical solutions of the superposition moduli can be derived. Other models give different results, consequently superposition flows could be used for the critical evaluation of rheological models. Preliminary data for both parallel and orthogonal superposition flows on a polyisobutene solution illustrate the potential of this technique. The relation between parallel and orthogonal superposition moduli derived by Bernstein for the K-BKZ model seems to be in agreement with the data. The results offer a potential for further theoretical work. The data also suggest that a physical interpretation of superposition moduli is not straightforward.
84 citations
TL;DR: In this paper, the authors demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements, and show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadratures phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors.
Abstract: We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.
84 citations
TL;DR: In this article, a wavelet correlation analysis is proposed to decompose the correlation of arbitrary signals over a two-dimensional time delay-period plane, by analyzing two superposition functions implicating several pure frequencies.
Abstract: In order to identify coherent structure of turbulent shear flow, a new combination of familiar techniques of signal processing, called wavelet correlation analysis, is developed based on the wavelet transform. The wavelet correlation analysis provides the unique capability for decomposing the correlation of arbitrary signals over a two-dimensional time delay-period plane. By analyzing two superposition functions implicating several pure frequencies, the correlation of periodic oscillations at several frequencies can well be separated and observed clearly. Coherent structures in the intermediate region of a plane turbulent jet are investigated using the wavelet correlation method
82 citations
TL;DR: It is proved that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way and that the proposed method resists noise well.
Abstract: Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite–Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.
TL;DR: In this article, a quantitative analysis of core level electron energy loss spectra for uniaxial anisotropic materials is presented, taking into account the presence of a convergent electron probe as is the case in a scanning transmission electron microscope (STEM) or transmission electron microscopy (TEM) in convergent probe mode.
TL;DR: In this article, a numerical model is presented that predicts the evolution of a directional spectral sea state over a varying bathymetry using superposition of results of a parabolic monochromatic wave model run for each initial frequency-direction component.
Abstract: A numerical model is presented that predicts the evolution of a directional spectral sea state over a varying bathymetry using superposition of results of a parabolic monochromatic wave model run for each initial frequency-direction component. The model predicts dissipation due to wave breaking using a statistical breaking model and has been tested with existing data for unidirectional random waves breaking over a plane beach. Experiments were also conducted for a series of random directional waves breaking over a circular shoal to test the model in a two-dimensional wave field. The model performs well in both cases, although directional effects are not included in the breaking dissipation formulation.
TL;DR: In this paper, group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle, and the Wei-Norman method is applied to obtain the associated differential equation in the group SL(2, ℝ).
Abstract: Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei–Norman method is applied to obtain the associated differential equation in the group SL(2, ℝ). The superposition principle for first order differential equation systems and Lie–Scheffers theorem are also analyzed from this group theoretical perspective. Finally, the theory is applied in the solution of second order differential equations like time independent Schrodinger equation.
TL;DR: In this article, an integral representation for a possibly high-aperture, finite-Fresnel-number lens and a homogeneous medium of propagation is obtained for vectorial diffraction of electromagnetic waves.
Abstract: The problem of vectorial diffraction of electromagnetic waves is addressed. An integral representation is obtained for a possibly high-aperture, finite-Fresnel-number lens and a homogeneous medium of propagation. The solution is given in terms of coherent superposition of plane electromagnetic waves with position coordinates scaled with the well-known Li–Wolf scaling factor [J. Opt. Soc. Am. A1, 801 (1984)]. This integral representation is then used to obtain formulas for the case in which light is focused through a plane dielectric interface. The solution is given by the linear combination of three functions, each of which consists of only a single integral. The aberration function, representing spherical aberration, is shown to be analytical. Numerical examples are given to demonstrate the effectiveness of the solution.
TL;DR: For collisionless plasmas with initial conditions (ICs) near linearly stable equilibria, there exist critical initial states that mark the transition between the ICs from which the electric field evolves to a nonzero timeasymptotic state and those from which it Landau damps to zero as mentioned in this paper.
Abstract: We show that for collisionless plasmas with initial conditions (ICs) near ``single-humped'' linearly stable equilibria, there exist critical initial states that mark the transition between the ICs from which the electric field evolves to a nonzero time-asymptotic state $A(x,t)$, and those from which it Landau damps to zero We develop an equation for $A(x,t)$ and study it as a bifurcation problem, and we obtain the asymptotic field, at leading order, as a finite superposition of waves whose frequencies obey a Vlasov dispersion relation and whose amplitudes satisfy a set of nonlinear algebraic equations
TL;DR: In this article, the authors address the long history of the classical two-dimensional biharmonic problem for a rectangular domain and provide a considerable simplification of the numerical algorithm for solving it.
Abstract: This paper addresses the fascinating long history of the classical two-dimensional biharmonic problem for a rectangular domain. Among various mathematical and engineering approaches, the method of superposition is effective for solving mechanical problems concerning creeping flow of viscous fluid set up in a rectangular cavity by tangential velocities applied along its walls, an equilibrium of an elastic rectangle, and bending of a clamped thin rectangular elastic plate by a normal load. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm. The method is illustrated by several examples of steady Stokes flow in a square cavity.
TL;DR: The activity of ODC in embryos exposed to the superposition of the incoherent and 60 Hz fields was indistinguishable from the control activity during both gastrulation and neurulation, adding to the body of experimental evidence which demonstrates that thesuperposition of an incoherent field inhibits the response of biological systems to a coherent MF.
Abstract: Previously, we have shown that the application of a weak (4 mT) 60 Hz magnetic field (MF) can alter the magnitudes of the ornithine decarboxylase (ODC) activity peaks which occur during gastrulation and neurulation of chick embryos. We report here the ODC activity of chick embryos which were exposed to the superposition of a weak noise MF over a 60 Hz MF of equal (rms strength). In contrast to the results we obtain with a 60 Hz field alone, the activity of ODC in embryos exposed to the superposition of the incoherent and 60 Hz fields was indistinguishable from the control activity during both gastrulation and neurulation. This result adds to the body of experimental evidence which demonstrates that the superposition of an incoherent field inhibits the response of biological systems to a coherent MF. The observation that a noise field inhibits ODC activity changes is consistent with our speculation that MF-induced ODC activity changes during early development may be related to MF-induced neural tube defects at slightly later stages (which are also inhibited by the superposition of a noise field). Bioelectromagnetics 19:53‐56, 1998. ! 1998 Wiley-Liss, Inc.
TL;DR: Solutions to the Einstein equations that represent the superposition of static isolated bodies with axial symmetry are presented in this paper, where the equations' nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies.
Abstract: Solutions to the Einstein equations that represent the superposition of static isolated bodies with axial symmetry are presented. The equations' nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut-like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detail.
TL;DR: In this article, an analytical free energy for polymeric liquids is developed in the framework of the perturbation theory to provide a better understanding of the T−P superposition principle.
Abstract: Recently, it was found that polymers follow the principle of temperature−pressure (T−P) superposition. This principle states the temperature insensitiveness of the shape of the configurational free energy. An analytical free energy for polymeric liquids is developed in the framework of the perturbation theory to provide a better understanding of the T−P superposition principle. The intermer potential is separated into the repulsive reference and the attractive perturbed parts. The hard sphere potential is taken as the repulsive reference. The attractive part of the Mie (p,6) potential is taken as the perturbation. The free energy for the reference system of hard chains is obtained from the integration of the hard chain equation of state from the Baxter−Chiew theory. The limiting case of the reference free energy at infinite dilution is derived from the direct evaluation of the configurational partition function. The average packing energy is added as a perturbation energy. The local packing in the nearest...
TL;DR: In this article, the authors model the arm of a star polymer as an anchored random walk in an array of fixed obstacles with the added assumption of an energetic cost associated with the walk retracing its previous step.
Abstract: We model the arm of a star polymer as an anchored random walk in an array of fixed obstacles with the added assumption of an energetic cost associated with the walk retracing its previous step. By including this energetic penalty for such "hairpin" turns on the chain, we are able to account for the thermorheological complexity of long-branched hydrogenated polybutadiene yet not introduce deviations from time-temperature superposition in a melt of the linear chains. We also show that the same assumption leads to a prediction for the thermal expansion coefficient of the linear chains that is in reasonable agreement with the latest data.
TL;DR: In this paper, the Fourier approach is applied to the analysis of the superposition of two geometrically transformed periodic layers, where the geometric transformation is a weighted sum of the geometric transformations of the individual layers.
Abstract: The best method for investigating moire phenomena in the superposition of periodic layers is based on the Fourier approach. However, superposition moire effects are not limited to periodic layers, and they also occur between repetitive structures that are obtained by geometric transformations of periodic layers. We present in this paper the basic rules based on the Fourier approach that govern the moire effects between such repetitive structures. We show how these rules can be used in the analysis of the obtained moires as well as in the synthesis of moires with any required intensity profile and geometric layout. In particular, we obtain the interesting result that the geometric layout and the periodic profile of the moire are completely independent of each other; the geometric layout of the moire is determined by the geometric layouts of the superposed layers, and the periodic profile of the moire is determined by the periodic profiles of the superposed layers. The moire in the superposition of two geometrically transformed periodic layers is a geometric transformation of the moire formed between the original layers, the geometric transformation being a weighted sum of the geometric transformations of the individual layers. We illustrate our results with several examples, and in particular we show how one may obtain a fully periodic moire even when the original layers are not necessarily periodic.
TL;DR: In this paper, weakly nonlinear analysis of weak electrolyte model is presented, which provides the coefficients of the complex Ginzburg-Landau equation in the oblique-roll range.
Abstract: The recently introduced weak electrolyte model (WEM) has successfully explained many linear properties of electroconvection in planarly aligned nematic liquid crystals such as the crossover from a stationary to a Hopf bifurcation in the parameter range observed experimentally. Here we present the first weakly nonlinear analysis of the WEM providing the coefficients of the complex Ginzburg-Landau equation. Whereas the Hopf bifurcation is always supercritical, the stationary bifurcation is for typical materials subcritical, which appears to be in agreement with experiments. In the oblique-roll range the (complex) cross coupling coefficient between the two degenerate roll systems (``zig'' and ``zag'') are also calculated leading to the superposition of traveling rectangles as observed in recent experiments on the material I52.
TL;DR: In this article, the mean field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed, where the reflection symmetry is broken to facilitate oscillator synchronization to rotating wave phases.
Abstract: The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical simulations support the results based on bifurcation theory and high-frequency calculations. In the latter case, the order parameter is a linear superposition of parameters corresponding to rotating and counterrotating phases.
TL;DR: A general strategy of quantum state engineering is presented and an arbitarily prescribed superposition of internal Zeeman levels of an atom can be prepared by Raman pulses.
Abstract: We present a general strategy of quantum state engineering. We describe how an arbitarily prescribed superposition of internal Zeeman levels of an atom can be prepared by Raman pulses.
TL;DR: In this article, the authors used the vibrational conductivity approach to evaluate the spatial partition of the energy density of dynamical structural/acoustic systems in the high frequency range, which is a significant improvement on the Statistical Energy Analysis which provides only a single energy value per sub-system.
TL;DR: In this article, the effects of damping and nonlinear material behaviour were introduced in the modelling of an ultrasonic oscillator and the results of the analytical calculation allow an accurate definition of the geometry of the oscillator, so that the two vibration modes have the same resonance frequency.
TL;DR: In this article, the authors study the stochastic stability of a system described by two coupled ordinary differential equations parameterically driven by dichotomous noise with finite correlation time, and compare the corresponding threshold with a threshold from a simple mean-field decoupling and with the threshold describing stability of moments.
Abstract: We study the stochastic stability of a system described by two coupled ordinary differential equations parameterically driven by dichotomous noise with finite correlation time. For a given realization of the driving noise ~a sample!, the long time behavior is described by an infinite product of random matrices. The transfer matrix formalism leads to a Frobenius-Perron equation, which seems not solvable. We use an alternative method to calculate the largest Lyapunov exponent in terms of generalized hypergeometric functions. At the threshold, where the largest Lyapunov exponent is zero, we have an exact analytical expression also for the second Lyapunov exponent. The characteristic times of the system correspond to the inverse of the Lyapunov exponents. At the threshold the first characteristic time diverges and is thus well separated from the correlation time of the noise. The second time, however, depending on control parameters, may reach the order of the correlation time. We compare the corresponding threshold with a threshold from a simple mean-field decoupling and with the threshold describing stability of moments. The different stability criteria give similar results if the characteristic times of the system and the noise are well separated, the results may differ drastically if these times become of similar order. Digital simulation strongly confirms the criterion of sample stability. The stochastic differential equations describe in the frame of a simple one-dimensional model and a more realistic two-dimensional model the appearance of normal rolls in nematic liquid crystals. The superposition of a deterministic field with a ‘‘fast’’ stochastic field may lead to stable region that extends beyond the threshold values for deterministic or stochastic excitation alone, forming thus a stable tongue in the space of control parameters. For a certain measuring procedure the threshold curve may appear discontinuous as observed previously in experiment. For a different set of material parameters the stable tongue is absent. @S1063-651X~98!14508-7#
TL;DR: In this article, generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem and also present definition of moving dynamic coefficient which reflects moving effect.
Abstract: Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reverses moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.
TL;DR: In this article, the authors proposed a simple modification to the superposition result, based on the incorporation of image effects, that can dramatically improve its regime of validity, and assessed the validity and accuracy of the resulting superposition formulae by comparison with results of a rigorous boundary element calculation of the electrostatic interaction.