In situ estimation of crack concentration in hard rock

Results of a 2004 field experiment aimed at determining the quadratic nonlinearity parameter in granite that forms the shore of the Ladoga lake are presented. The measurements were based on the observation of the nonlinear interaction between monochromatic waves excited by two hydroacoustic radiators of 1 kW each positioned near the shore. The initial level of nonlinear distortions was much lower than the level of the received difference-frequency signal. The quadratic nonlinearity parameter proved to be higher than that reported in the majority of publications. An assumption was put forward that the high nonlinearity of granite is caused by the high concentration of cracks in it. Pieces of rock were taken from the measurement site, and rectangular samples were prepared from them. The samples were studied by the acoustic spectroscopy method in laboratory conditions. As a result, estimates of crack concentration were obtained, which proved to be consistent with the field measurements of the quadratic nonlinearity parameter. Thus, the possibility of estimating the crack concentration in situ from the measurements of the quadratic nonlinearity parameter was demonstrated.     

强耦合激子-声子系统中的三阶非线性光学系数的理论计算

应用Dyson-Maleev变换,对强耦合激子—声子系统中非线性光学性质进行了理论研究.结果表明,当信号光场频率与激子频率的失谐量等于光学声子的频率时,系统的非线性光学吸收和克尔（Kerr）系数显著增大,从而证明了激子-声子的强相互作用对介质的非线性光学性质的影响相当大,并且当考虑激子偏离玻色子模型时,这种影响将进一步增大.     

不同方式地下爆炸地震耦合效应的数值模拟

通过一种Euler与Lagrange相结合的有限差分法,开展地下爆炸地震耦合效应的数值模拟.比较花岗岩介质中填实和空腔两种爆炸方式在地震耦合效应方面的差异,进一步分析初始空腔大小在填实以及空腔爆炸地震效应中的作用以及空腔爆炸解耦因子随频率的变化特性.计算结果表明,花岗岩介质中完全空腔解耦因子能达到50~60倍.     

Estimating the nonlinear resonant frequency of a single pile in nonlinear soil

Analytical expressions are determined for the nonlinear resonant frequency (or natural frequency) of the fundamental lateral mode of a pile. A pile with a floating toe, with and without pile cap is considered in this paper. The influence of a nonlinear soil spring model that varies with depth and a nonlinear damping model that is strain amplitude dependent is considered. A non-dimensional equation of motion for the system dynamics is derived from an energy based formulation. This equation is a Duffing's type nonlinear differential system that has nonlinear damping. Harmonic balance with numerical continuation is employed to determine the nonlinear resonance curves of the system. Comparison with some experimental results is made.     

平均电流控制型Boost功率因数校正变换器中的中频振荡现象分析

基于输入电压可用其有效值代替以及电感电流与输出电压的波动频率远低于变换器开关频率的假设,建立了用于描述平均电流控制型Boost PFC变换器动力学行为的小信号模型,研究了该变换器中的中频振荡现象问题,揭示了系统发生中频振荡现象的内在物理机理,并给出了系统发生中频振荡现象的参数边界.研究结果表明,该非线性现象不同于已发现的快尺度不稳定性现象和慢尺度不稳定性现象,其主要特征是其振荡频率介于交流输入电压线频率和开关频率之间.最后,电路实验结果证实了理论分析的正确性. 关键词： 中频振荡 平均电流控制 Boost功率因数校正变换器 小信号模型     

Nonlinear effects in the dynamics of clouds of bubbles

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.     

Frequency dependence of phase-synchronization time in nonlinear dynamical systems

It has been found recently that the averaged phase-synchronization time between the input and the output signals of a nonlinear dynamical system can exhibit an extremely high sensitivity to variations in the noise level. In real-world signal-processing applications, sensitivity to frequency variations may be of considerable interest. Here we investigate the dependence of the averaged phase-synchronization time on frequency of the input signal. Our finding is that, for typical nonlinear oscillator systems, there can be a frequency regime where the time exhibits significant sensitivity to frequency variations. We obtain an analytic formula to quantify the frequency dependence, provide numerical support, and present experimental evidence from a simple nonlinear circuit system.     

Adiabatic processes in frequency conversion

Adiabatic evolution, an important dynamical process in a variety of classical and quantum systems providing a robust way of steering a system into a desired state 1 - 5 , was introduced only recently to frequency conversion 6 - 9 . Adiabatic frequency conversion allowed the achievement of efficient scalable broadband frequency conversion 8 , 9 and was applied successfully to the conversion of ultrashort pulses, demonstrating near‐100% efficiency for ultrabroadband spectrum 10 - 16 . The underlying analogy between undepleted pump nonlinear processes and coherently excited quantum systems was extended in the past few years to multi‐level quantum systems, demonstrating new concepts in frequency conversion, such as complete frequency conversion through an absorption band 17 - 20 . Additionally, the undepleted pump restriction was removed, enabling the exploration of adiabatic processes in the fully nonlinear dynamics regime of nonlinear optics 21 - 26 . In this article, the basic concept of adiabatic frequency conversion is introduced, and recent advances in ultrashort physics, multi‐process systems, and the fully nonlinear dynamics regime are reviewed.     

Nonlinear Effects in Quantum Dynamics of Atom Laser: Mean-Field Approach

Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.     

非线性频率转换新原理新平台与新应用研究

作为最早发现的非线性光学现象之一,非线性频率转换经过几十年的发展,从原理到应用均已不断成熟。非线性频率转换过程中新的相位匹配原理被不断提出和实现。除此之外,随着集成光学、结构光子学及量子光学等领域的不断发展,非线性频率转换在各领域的研究和应用又重新焕发活力,并发挥着不可替代的作用。本篇综述围绕非线性频率转换主题,突出非线性频率转换的新原理、新平台与新应用研究,并以本团队研究成果为基础,介绍相关领域的研究进展,主要分为以下几个方面:非线性界面相位匹配新原理;结构光场非线性谐波调控;铌酸锂薄膜集成非线性光学新平台;单光子频率转换、光量子接口等新应用。     

Use of the application of heterodyne laser interferometer in power ultrasonics

We are particularly interested in the measurement of nonlinear acoustic waves in air, within the range of the Raman-Nath diffraction regime. We used a heterodyne laser interferometric system with a Bragg cell frequency of 80 MHz. A harmonic power acoustic wave with a frequency in the range of 20 kHz was generated, but higher harmonics appear when nonlinear propagation occurs in restricted volumes or waveguides. This topic raises a number of interesting questions. The most complex problem arises when processing an extremely wide-band output signal from a photo-detector, where the signal contains a huge number of high amplitude harmonics in a measured acoustic signal. The wide-band output signal from nonlinear wave measurement was simulated by means of similar wide-band output signals obtained by measuring known dynamic mechanical displacements. Because the frequency band of common analog circuits used for signal processing is too narrow, the output signal from the interferometer was digitalized and processed. This paper discusses the results of these tests and provides estimates of the frequency restrictions of signal processing.     

Dynamical behaviour of transverse plasmons in pair plasmas

This paper analytically investigates the nonlinear behaviour of transverse plasmons in pair plasmas on the basis of the nonlinear governing equations obtained from Vlasov--Maxwell equations. It shows that high frequency transverse plasmons are modulationally unstable with respect to the uniform state of the pair plasma. Such an instability would cause wave field collapse into a localized region. During the collapse process, ponderomotive expulsion is greatly enhanced for the increase of wave field strength, leading to the formation of localized density cavitons which are significant for the future experimental research in the interaction between high frequency electromagnetic waves and pair plasmas.     

Nonlinear Effects in Quantum Dynamics of Atom Laser: Mean-Field Approach

Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated in the framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable. It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matter wave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.     

Modulated transfer process forced at phonon frequencies in optical heterodyne spectroscopy

A simple spectroscopic technique is used to detect low-frequency acoustical phonons. Resonantly enhanced modulated transfer processes in optical heterodyne spectroscopy are accomplished from a frequency shifted modulated beam to an unmodulated beam in a nonlinear medium having low-frequency induced phonons. The resonance condition is achieved when the phonon frequency is set equal to the beat frequency of the two beams.     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

Dimensional resonances and second-harmonic generation in a semibounded nonlinear layered periodic medium

A theory for the nonlinear interaction of electromagnetic waves in a semibounded periodic dielectric structure is developed using the example of second-harmonic generation. One of the layers forming a period is assumed to have nonlinear polarization. The theory is an improved perturbation theory based on the Green theorem. The phase-matching conditions for interacting waves are shown to correspond to dimensional resonances for individual layers or for the structure period. The interaction efficiency is maximum at passband edges for the case of resonance for the entire period. For this resonance, the phase-matching conditions are met for a frequency spectrum rather than for a single frequency. This feature makes it possible to convert spectra from one frequency range to another.     

Spin wave mode excited by spin-polarized current in a magnetic nanocontact is a standing self-localized wave bullet

We demonstrate that the lowest threshold of spin-wave excitation in an in-plane magnetized magnetic nanocontact driven by spin-polarized current is achieved for a nonlinear self-localized spin-wave mode-standing spin-wave bullet--stabilized by current-induced nonlinear dissipation. This nonlinear mode has a nonpropagating evanescent character, is localized in the region comparable with the contact radius, and has a frequency that is lower than the frequency of the linear ferromagnetic resonance. The threshold current and generated frequency at the threshold theoretically calculated for this mode are in quantitative agreement with experiment.