Stochastic resonance in underdamped,bistable systems

We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the nonperturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behaviour and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime.     

Stochastic resonance, reverse-resonance and stochastic multi-resonance in an underdamped quartic double-well potential with noise and delay

The stochastic resonance in an underdamped quartic double-well potential with time delayed feedback is studied numerically. The signal power amplification is employed to characterize the stochastic resonance of the system. Simulation results indicate that: (i) for moderate frequency of the periodic driving, the stochastic resonance is decreased monotonically by increasing the delay time, but at high frequency, the reverse-resonance is induced to transform into a stochastic resonance by time delay; (ii) the damping coefficient has a critical value for which the stochastic resonance is optimum; (iii) a stochastic multi-resonance emerges when the signal power amplification is a function of the driving frequency.     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

Weak signal detection based on underdamped stochastic resonance with an exponential bistable potential

Stochastic resonance (SR) is a vital approach to detect weak signals submerged in strong background noise, which is useful for mechanical fault diagnosis. The underdamped bistable SR (UBSR) is a kind of the most used SR, however, their potential structures are deficient to match with the complicated and diverse mechanical vibration signals and their parameters are selected subjectively which probably resulting in poor performance of UBSR. To overcome these shortcomings, this paper proposes an underdamped SR with exponential potential (UESR) which is generalized by using a harmonic model and a Gaussian potential (GP) model. The dynamics in UESR system is evaluated by the signal-to-noise ratio (SNR) which represents the effectiveness of noise utilization. Then, the effects of system parameters on system performance are investigated by output SNR versus noise intensity D for different parameters. Finally, the proposed method is used to process bearing experimental data and further perform bearing fault diagnosis. The experimental results demonstrate that a larger output SNR and higher spectrum peaks at fault characteristic frequencies can be obtained by the proposed method compared with the UBSR method, which confirm the effectiveness of the proposed method.     

Vibrational resonance in Duffing systems with fractional-order damping

The phenomenon of vibrational resonance (VR) is investigated in over- and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single- or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies α?>?1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is α?>?1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is α?相似文献   

Novel vibrational resonance in multistable systems

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.     

Critical exponent of the fractional Langevin equation

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.     

相位匹配下锥形光纤激发出的回廊模谐振

分别计算不同直径下锥形光纤基模和玻璃微球谐振腔内最低阶径向回廊模的传播常量,利用相位匹配条件,作出了锥形光纤与石英玻璃微球腔的直径对应关系曲线.在此基础上,选择锥腰直径2.8 μm左右的低损耗锥形光纤与直径143.1 μm球形度很好的玻璃微球腔进行近场耦合以激发球内的最低阶径向回廊模谐振,在锥形光纤的两端进行通光测试,在输出端获得了等间距分布的窄线宽滤波谱线,其吸收峰位置与利用Mie理论计算的球内最低阶径向回廊模谐振峰位置相一致.     

Non-markovian resonance fluorescence

The power spectrum of a strong field resonance fluorescence is derived from non-markovian Bloch equations. It is shown that the Mollow spectrum is modified by non-markovian corrections. The main feature of the non-markovian behavior is a nonsymmetric power spectrum even at exact resonance. The magnitude of the non-markovian asymmetry depends on the power of the driving light.     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Characteristic time scales of tick quotes on foreign currency markets: an empirical study and agent-based model

Power spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) for periods from January 1999 to December 2000 are analyzed. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and confirm that stochastic resonance occurs for the market activity of this model. We propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to stochastic resonance.     

Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

We study an underdamped oscillator with random frequency jumps. We describe the oscillator spectrum in terms of coupled susceptibilities for different-frequency states. Depending on the parameters, the spectrum has a fine structure or displays a single asymmetric peak. For nanomechanical resonators with a fluctuating number of attached molecules, it is found in a simple analytical form. The results bear on dephasing in various types of systems with jumping frequency.     

Stochastic resonance in multidimensional periodic potential

We study the mobility and diffusion of an underdamped Brownian particle moving in a two-dimensional (2D) periodic potential which subjects to a thermal white noise and a weak external driving force. Both the signal power amplification and the diffusion rate are calculated via Langevin simulations. It is shown that the stochastic resonance (SR) can be observed in the two dimension, namely, the output quantities as functions of the temperature show a nonmonotonic behavior, however, the SR cannot be obtained in the one dimension (1D). In the 2D potential, the height of dynamical barrier is decreased effectively along the direction of transport if the curvature of the potential at the barrier is less than that at the local minima. This leads to the SR condition being obeyed, i.e., the Kramers frequency over the barrier roughly matches the frequency of external signal.     

Bragg-resonance-induced Rabi oscillations in photonic lattices

We show that propagation of optical beams in periodic lattices induces power oscillations between the Fourier spectrum peaks, with the indices related by the Bragg resonance condition. In the spatial coordinates, this is reflected in the beam position oscillations. A simple resonant theory explains the phenomenon. The effect can be used for controlled generation of the Floquet-Bloch modes in photonic lattices.     

Eigenvalues and eigenfunctions of the Fokker-Planck equation for the extremely underdamped Brownian motion in a double-well potential

The eigenvalues and eigenfunctions of the Fokker-Planck equation describing the extremely underdamped Brownian motion in a symmetric double-well potential are investigated. By transforming the Fokker-Planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate, a differential equation depending only on energy is derived. For finite temperatures this equation is solved by numerical integration, whereas in the weak-noise limit an analytic result for the lowest nonzero eigenvalue is obtained. Furthermore, by using a boundary-layer theory near the critical trajectory, the correction term to the zero-friction-limit result is found.     

Resonances in chaotic dynamics

We present a discussion and some numerical results on the actual possibility of making accessible, by numerical techniques, the complex singularities of the power spectrum (resonances) for a chaotic signal. Hénon's transformation is investigated in detail, showing that the position of the leading resonance in the complex frequency plane determines the kind of mixing rate in the time evolution.     

Empirical refinements applicable to the recording of fish sounds in small tanks

Many underwater bioacoustical recording experiments (e.g., fish sound production during courtship or agonistic encounters) are usually conducted in a controlled laboratory environment of small-sized tanks. The effects of reverberation, resonance, and tank size on the characteristics of sound recorded inside small tanks have never been fully addressed, although these factors are known to influence the recordings. In this work, 5-cycle tone bursts of 1-kHz sound were used as a test signal to investigate the sound recorded in a 170-l rectangular glass tank at various depths and distances from a transducer. The dominant frequency, sound-pressure level, and power spectrum recorded in small tanks were significantly distorted compared to the original tone bursts. Due to resonance, the dominant frequency varied with water depth, and power spectrum level of the projected frequency decreased exponentially with increased distance between the hydrophone and the sound source; however, the resonant component was nearly uniform throughout the tank. Based on the empirical findings and theoretical calculation, a working protocol is presented that minimizes distortion in fish sound recordings in small tanks. To validate this approach, sounds produced by the croaking gourami (Trichopsis vittata) during staged agonistic encounters were recorded according to the proposed protocol in an 1800-l circular tank and in a 37-l rectangular tank to compare differences in acoustic characteristics associated with tank size and recording position. The findings underscore pitfalls associated with recording fish sounds in small tanks. Herein, an empirical solution to correct these distortions is provided.     

Crossover between the extremely low damping and moderate underdamped regime in the thermal activation theory: Preliminary experimental results

Summary The problem of the decay of metastable state due to thermal activation is studied. Experimental data referring to the supercurrent decay of an underdamped Josephson junction are compared with Kramers theory and its recent improvements. Significative aspects of the crossover region between the extremely underdamped regime and the moderate underdamped one are discussed.     

Direct observation of terahertz surface modes in nanometer-sized liquid water pools

The far-infrared absorption spectrum of nanometer-sized water pools at the core of AOT micelles exhibits a pronounced resonance which is absent in bulk water. The amplitude and spectral position of this resonance are sensitive to the size of the confined water core. This resonance results from size-dependent modifications in the vibrational density of states, and thus has far-reaching implications for chemical processes which involve water sequestered within small cavities. These data represent the first study of the terahertz dielectric properties of confined liquids.     

基于辐射度的光谱校正与自适应拟合相结合的SPR共振波长确定方法

表面等离子体共振(SPR)传感技术因其灵敏度高、无需标记、可原位实时监测的特点,被广泛应用在生物医学、化学检测、食品安全、环境监测等领域。对于波长调制型SPR传感器,由于光谱测量系统各部件对不同波长响应度不同,从而对光谱共振波长的实际位置产生干扰,影响到实验检测结果。为消除这种影响,提出了一种基于辐射度空间的SPR相对反射率校正方法,并使用阶数自适应拟合算法对共振波长进行精确测定。通过标定光谱测量系统的仪器响应曲线,将光谱仪得到的原始光谱转换成辐射光谱,进而计算出不依赖于光谱仪系统中任何部件的SPR相对反射率。相比于传统的反射率校正方式(以共振光谱除以非共振光谱的结果作为反射率光谱),此方法校正后的光谱在光谱形状上具备半峰宽更窄和共振峰更对称的优势,从而为精确确定共振波长提供了可靠的保障。随后基于拟合误差最小化的目标,对共振区域采用阶数自适应多项式拟合算法确定共振波长。实验测量了不同入射角度下的SPR共振光谱,使用此方法校正得到反射率光谱的半峰全宽保持在(100±10) nm,表明此方法的光谱峰形优势具备普适性;连续采集了4 000组光谱并计算共振波长,其相对标准偏差为0.007 8%,处理速度为每个光谱12 ms,表明此方法具备良好的抗噪声波动鲁棒性和光谱数据处理的实时性;测量了不同浓度下NaCl溶液的SPR共振光谱,其共振波长与溶液折射率线性相关系数为0.998 5,品质因数为传统校正方式的3倍,表明此方法具备良好的可靠性,并且从光谱的处理算法层面提高了传感性能,相比于从工艺制备上提高品质因数的传统方式,处理简便,效果更突出。结果表明,基于辐射度空间的相对反射率矫正与阶数自适应拟合相结合的SPR共振波长检测方法具备可靠性好、运算速度快、分辨率高、抗噪声、品质因数高等特点,能够有效提高SPR传感器的数据处理与传感性能。