Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period, we constructed a system of linear equations by introducing time-dependent multipliers. The periodicity assumption helps simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.Peer ReviewedPostprint (author's final draft

Kinetic Intersections as a Source of Information on Rate Coefficients

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Periodic response of a nonlinear axially moving beam with a nonlinear energy sink and piezoelectric attachment

An efficient semi-numerical framework is used in this paper to analyze the dynamic model of an axially moving beam with a nonlinear attachment composed of a nonlinear energy sink and a piezoelectric device. The governing equations of motion of the system are derived by using the Hamilton’s principle with von Karman strain-displacement relation and Euler - Bernoulli beam theory. The nonlinear energy sink is modeled as a lumped - mass system composed of a point mass, a spring with nonlinear cubic stiffness and a linear viscous damping element. The piezoelectric device is placed in the ground configuration. Frequency response curves of the presented nonlinear system are determined by introducing the incremental harmonic balance and continuation method for different values of material parameters. Based on the Floquet theory, the stability of the periodic solution was determined. Moreover, the presented results are validated with the results obtained by a numerical method as well as the results from the literature. Numerical examples show a significant effect of the nonlinear attachment on frequency response diagrams and vibration amplitude reduction of the primary beam structure

Ultrashort filaments of light in weakly-ionized, optically-transparent media

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration, high energies beyond the Joule level and peak powers exceeding several terawatt (TW). When such pulses propagate through optically-transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium, and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid to the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. Differences between femtosecond pulses propagating in gaseous or condensed materials are underlined. Attention is also paid to the multifilamentation instability of broad, powerful beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy, and the possibility to guide electric discharges in air are finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure

Stability Chart of Generalized Bessel Equation

Stability analysis, due to its importance in dynamic analysis of appliedsystems, becomes very widely topic in real-world problems associated with significant effects in all applications of engineering and appliedsciences. Several contributions have been done by various authors onstability analysis of autonomous and non-autonomous systems to obtain interesting and attractive results. In these aforementioned works, and sofar, the Lyapunov methods (first and second) become the main nerve togive suitable criteria that guaranteed the stability of the dynamicalsystems,In this article, it is aimed to look for a semi-analytical relation between the eigenvalue and the order of generalized Bessel differential equation using the asymptotic iteration and perturbation methods for the periodic domain. Based on the analytical results, the stability chart between the eigenvalue and the order of theequation is constructed. Accordingly, through the path of verification and investigation by using the numerical results with Fourier spectral method, a strong fit with the analytical results is observed

Dam break problem for the focusing nonlinear Schr\"odinger equation and the generation of rogue waves

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schr\"odinger (NLS) equation with the initial condition in the form of a rectangular barrier (a "box"). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains --- the dispersive dam break flows --- generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.Comment: 29 pages, 15 figures, major revisio

Design of a low power switched-capacitor pipeline analog-to-digital converter

An Analog to Digital Converter (ADC) is a circuit which converts an analog signal into digital signal. Real world is analog, and the data processed by the computer or by other signal processing systems is digital. Therefore, the need for ADCs is obvious. In this thesis, several novel designs used to improve ADCs operation speed and reduce ADC power consumption are proposed. First, a high speed switched source follower (SSF) sample and hold amplifier without feedthrough penalty is implemented and simulated. The SSF sample and hold amplifier can achieve 6 Bit resolution with sampling rate at 10Gs/s. Second, a novel rail-to-rail time domain comparator used in successive approximation register ADC (SAR ADC) is implemented and simulated. The simulation results show that the proposed SAR ADC can only consume 1.3 muW with a 0.7 V power supply. Finally, a prototype pipeline ADC is implemented and fabricated in an IBM 90nm CMOS process. The proposed design is validated using measurement on a fabricated silicon IC, and the proposed 10-bit ADC achieves a peak signal-to-noise- and-distortion-ratio (SNDR) of 47 dB. This SNDR translates to a figure of merit (FOM) of 2.6N/conversion-step with a 1.2 V power supply

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p