Energy fluctuations in a biharmonically driven nonlinear system

We study the fluctuations of work done and dissipated heat of a Brownian particle in a symmetric double well system. The system is driven by two periodic input signals that rock the potential simultaneously. Confinement in one preferred well can be achieved by modulating the relative phase between the drives. We show that in the presence of pumping the stochastic resonance signal is enhanced when analysed in terms of the average work done on the system per cycle. This is in contrast with the case when pumping is achieved by applying an external static bias, which degrades resonance. We analyse the nature of work and heat fluctuations and show that the steady state fluctuation theorem holds in this system.     

Energy harvesting under excitations of time-varying frequency

The design and optimization of energy harvesters capable of scavenging energy efficiently from realistic environments require a deep understanding of their transduction under non-stationary and random excitations. Otherwise, their small energy outputs can be further decreased lowering their efficiency and rendering many critical and possibly life saving technologies inefficient. As a first step towards this critical understanding, this effort investigates the response of energy harvesters to harmonic excitations of time-varying frequency. Such excitations can be used to represent the behavior of realistic vibratory environments whose frequency varies or drifts with time. Specifically, we consider a piezoelectric stack-type harvester subjected to a harmonic excitation of constant amplitude and a sinusoidally varying frequency. We analyze the response of the harvester in the fixed-frequency scenario then use the Jacobi-Anger's expansion to analyze the response in the time-varying case. We obtain analytical expressions for the harvester's response, output voltage, and power. In-depth analysis of the attained results reveals that the solution to the more complex time-varying frequency can be understood through a process which “samples” the fixed-frequency response curve at a discrete and fixed frequency interval then multiplies the response by proper weights. Extensive discussions addressing the effect of the excitation parameters on the output power is presented leading to some initial suggestions pertinent to the harvester's design and optimization in the sinusoidally varying frequency case.     

Sustained high-frequency energy harvesting through a strongly nonlinear electromechanical system under single and repeated impulsive excitations

This work investigates a vibration-based energy harvesting system composed of two oscillators coupled with essential (nonlinearizable) stiffness nonlinearity and subject to impulsive loading of the mechanical component. The oscillators in the system consist of one grounded, weakly damped linear oscillator mass (primary system), which is coupled to a second light-weight, weakly damped oscillating mass attachment (the harvesting element) through a piezoelastic cable. Due to geometric/kinematic mechanical effects the piezoelastic cable generates a nonlinearizable cubic stiffness nonlinearity, whereas electromechanical coupling simply sees a resistive load. Under single and repeated impulsive inputs the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing high-frequency ‘bursts’ or instabilities in the response of the harvesting element. In turn, these high-frequency dynamic instabilities result in strong and sustained energy transfers from the directly excited primary system to the lightweight harvester, which, through the piezoelastic element, are harvested by the electrical component of the system or, in the present case, dissipated across a resistive element in the circuit. The primary goal of this work is to demonstrate the efficacy of employing this type of high-frequency dynamic instability to achieve enhanced nonlinear vibration energy harvesting under impulsive excitations.     

Energy harvesting from the nonlinear oscillations of magnetic levitation

This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to investigate the energy harvesting potential of this prototypical nonlinear system. Theoretical investigations are followed by a series of experimental tests that validate the response predictions. The motivating hypothesis for the current work was that nonlinear phenomenon could be exploited to improve the effectiveness of energy harvesting devices.     

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance(SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory(LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density(PSD) and signal-to-noise ratio(SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.     

Activation by nonlinear oscillations and solitonic excitations

Local excitations in molecular systems are studied taking into account the influence of soft impurities. The dynamics of activation processes (high-energy events) due to nonlinear mechanisms is studied. The following examples of classical macroscopic systems with strong nonlinear interaction are investigated: 1D Toda chains, 1D Morse rings, and 3D systems of hard spheres including impurities. It is shown that solitonlike excitations may lead to the concentration of energy at definite sites (weak springs or soft spheres). The accumulation of energy is mainly due to soliton-fusion effects. In thermal equilibrium an optimum temperature exists, where the thermally averaged potential energy is preferably partitioned to the soft springs embedded into a hard-spring solvent. Further, we show that the effect of thermal energy localization and the temperature dependence also persists for solutions of soft spheres in hard-sphere solvents.     

窄带随机激励双稳压电悬臂梁响应机制与能量采集研究

具有中心频率的窄带随机振动是一种典型的环境振动,其振动特征与环境的变化密切相关.本文以双稳压电悬臂梁能量采集系统为研究对象,分析系统在不同磁铁间距下的等效线性固有频率特性,以带通滤波器输出一定带宽的窄带随机激励模拟环境振动,研究系统的响应和能量采集特征.研究表明,对于一定带宽的窄带随机激励,一方面系统始终存在一个固定的磁铁间距使其输出达到峰值,另一方面当激励中心频率在一定范围内变化时,系统还分别存在另外两个或一个不同磁铁间距也能使系统输出达到峰值,而且该峰值特性是系统在其等效线性固有频率处诱导双稳或单稳“共振”形成的.研究结果可为具有窄带随机激励特征的振动能量采集提供一定的理论和技术支持.     

Electrostatic instability driven by nonlinear forces

Summary The physical mechanism for the generation of an ELF electrostatic wave in the presence of a coherent electromagnetic ion cyclotron wave is presented. A high-frequency nonlinear force which arises as a result of the resonant interaction between electrons and modulated fields is found to drive the instability. The growth rate of this electrostatic instability is obtained and the results are applied to observations in the magnetospheric plasma.

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Riassunto Si presenta il meccanismo fisico per la produzione di un'onda elettrostatica ELF in presenza di un'onda ciclotronica elettromagnetica di ioni. Si trova che una forza non lineare ad alta frequenza che si ottiene come risultato dell'interazione risonante tra elettroni e campi modulati dirige l'instabilità. Si ottiene la velocità di crescita di questa instabilità elettrostatica e si applicano i risultati alle osservazioni nel plasma magneto-sferico.

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Резюме Описьівается физический механизм для генерации электростатической волньі в присутствии когерентной электромагнитной ионной циклотронной волньі. Обнаружено, что вьісокочастотная нелинейная сила, которая возникает в результате резонансного взаимодействия между электронами и модулированньіми полями, воэбуждает неустойчивость. Определяется скорость роста этой электростатической неустойчивости. Полученньіе результатьі применяются для анализа наблюдений магнитосферной плазмьі.

     

Scaling for the ensemble statistics prediction of a random system subjected to harmonic excitations

This paper is concerned with the ensemble statistics of the dynamic responses of a random system subjected to harmonic excitations. Random point process theory is employed to derive general scaling laws with the Gaussian orthogonal ensemble assumption about the system natural frequencies. A scaled model is built to simulate the high-frequency vibrations of the original system. Specific forms of the scaling laws are presented for a mass-loaded plate regarding the scaling factors for the structural parameters. The ensemble statistics predicted from the scaled model are compared favorably with those obtained from the original system.     

采用双脉冲驱动产生高次谐波阿秒脉冲

提出了采用双脉冲机理来产生阿秒脉冲的方法.研究发现采用双脉冲不仅可以产生单个的阿秒脉冲，从而突破目前产生阿秒脉冲的驱动源（几个飞秒的超短激光脉冲）的能量限制，而且在相同的峰值强度下，双脉冲能够产生强度更高的阿秒脉冲. 关键词： 阿秒脉冲 双脉冲机理 高次谐波     

A method of investigation of the evolution of a nonlinear system driven by pulsed noise

A numerical method is proposed for determining the evolution of nonlinear systems subjected to noise. The method is based on a recurrence equation for the probability density which has been obtained analytically due to the choice of noise in the form of discrete series of random pulses. The method is applied to a dynamical system which describes the motion of a particle in a plane-wave field. The evolution of the probability density in phase and energy space is obtained. It is shown that because of noise effects, the region in phase space where particles can be found rapidly reaches the separatrix and then spreads over the phase space, mainly along the separatrix. In the energy spectrum a new peak appears at the separatrix's energy. This peak grows in time, while the main peak corresponding to the initial energy drops in time and shifts to lower energy. The moments of motion were analyzed. The character of their evolution indicates a high rate of chaotization. The growth of the fraction of energetic particles is very rapid (exponential at the beginning), whereas the mean energy grows linearly.     

Phase jump in resonance harmonic emission driven by strong laser fields

We present a theoretical investigation of the multiphoton resonance dynamics in the high-order-harmonic generation(HHG) process driven by a strong driving continuous wave(CW) field along with a weak control harmonic field.The Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the combined laser field.Multiple multiphoton-transition paths for the harmonic emission are coherently summed.The phase information about paths can be extracted via the Fourier transform analysis of the harmonic signals which oscillate as a function of the relative phase between driving and control fields.Phase jumps are observed when sweeping across the resonance by varying the frequency or intensity of the driving field.The phase variation as a function of driving frequency at a fixed intensity and as a function of the intensity at a fixed driving frequency allows us to determine the intensity dependence of the transition energy of quantum systems.     

Inversion in harmonic noise driven bistable oscillators

We consider the dynamics in a asymmetrical bistable oscillator driven externally by a noisy harmonic oscillator. The basic for our approach is the energy dynamics in each well of the oscillator in the low friction limit. We discuss the possibility of energy inversion states generated by harmonic noise and show this effect by simulations.     

飞秒强激光在充气毛细管中产生三次谐波的效率

利用描写飞秒强激光在充气毛细管中产生三次谐波的一个理论模型讨论了三次谐波产生的信号-压强曲线.结果发现：在毛细管参量和激光参量确定的条件下，三次谐波效率受管内气压，三次谐波模式，走离效应（walk-off）和相调制效应的影响.同时，发现，得到的三次谐波效率接近实验值. 关键词： 效率 三次谐波 飞秒激光 充气毛细管     

Multi-level effects in the high-order harmonic generation driven by intense frequency-comb laser fields

High harmonic generation(HHG) driven by intense frequency-comb laser fields can be dramatically enhanced via multiphoton resonance by tuning the carrier-envelope phase(CEP) shift, without increasing the driving intensity. However,the multiphoton-resonant enhancement(MRE) factor in the realistic atomic hydrogen is much smaller than that in a twolevel system. To study the deviation, we present a theoretical investigation of the multiphoton resonance dynamics of three-level systems driven by intense frequency-comb laser fields. The many-mode Floquet theorem(MMFT) is employed to provide a nonperturbative and exact treatment of the interaction between the quantum system and the laser fields. The investigations show that the dipole interaction of a two-level system with the third level affects the multiphoton resonance dynamics and enhances the HHG spectra. It is the dipole interaction of the excited level of the two-level system with other levels that results in the smaller MRE factor in the realistic atomic system.