Video solitons in a dispersive transmission line with the nonlinear capacitance of a p-n junction

Possible types of low-frequency electromagnetic solitary waves in a dispersive LC transmission line with a quadratic or cubic capacitive nonlinearity are investigated. The fourth-order nonlinear wave equation with ohmic losses is derived from the differential-difference equations of the discrete line in the continuum approximation. For a zero-loss line, this equation can be reduced to the nonlinear equation for a transmission line, the double dispersion equation, the Boussinesq equations, the Korteweg-de Vries (KdV) equation, and the modified KdV equation. Solitary waves in a transmission line with dispersion and dissipation are considered.     

Nonlinear dispersion in the process of quasistationary excitation of plasma waves

A quasistationary problem of Lengmuir wave excitation by external sources in uniform plasma is considered. It is established that energy is transferred from external sources to the wave if during its excitation the wave phase velocity changes in addition to an increase in the wave amplitude. A nonlinear dispersion equation for the plasma wave of finite amplitude excited by the external sources is derived. The nonlinear contribution of this dispersion equation is caused not only by an increase in the wave amplitude but also by the wave frequency shift.     

一类非线性相对转动系统的组合谐波分岔行为研究

针对一类具有非线性刚度、非线性阻尼的非线性相对转动系统, 应用耗散系统的拉格朗日原理建立在组合谐波激励作用下非线性相对转动系统的动力学方程. 构造李雅普诺夫函数, 分析相对转动系统的稳定性, 研究自治系统的分岔特性. 应用多尺度法求解相对转动系统的非自治系统在组合激励作用下的分岔响应方程. 最后采用数值仿真方法, 通过分岔图、时域波形、相平面图、Poincaré截面图等研究外扰激励、系统阻尼、 非线性刚度对相对转动系统经历倍周期分岔进入混沌运动的影响. 关键词： 相对转动 组合激励 分岔 混沌     

Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.     

Observation of the Bose condensation of excitonic molecules in CdSe

It is observed that excitonic molecules in CdSe exhibit the Bose condensation when excitation is given at 1.8–4.2 K by pico-second light pulses from a mode-locked glass laser. Strong evidence is provided by the appearance of an extremely sharp luminescence line produced from the excitonic molecules condensed to the k = 0 state.     

A nonlinear theory of laser noise and coherence. I

We consider the interaction of a set of atoms at random lattice sites with a decaying resonator mode. The optical transition is supposed to possess a homogeneously broadened Lorentzian line. The pumping is taken into account explicitly as a stochastic process. After elimination of the atomic coordinates a second order nonlinear differential equation for the light amplitude is found. In between excitation collisions this equation can be solved exactly if the resonator width is large as compared to all other frequency differences. In contrast to linear theories there exists a marked threshold. Below it the amplitude decreases after each excitation exponentially and the linewidth turns out to be identical with those of previous authors (for instanceWagner andBirnbaum), if specialized to large cavity width. Above the threshold the light amplitude converges towards a stable value, whereas the phase undergoes some kind of undamped diffusion process. We then consider the general case with arbitrary cavity width. If the general equation of motion of the light amplitude is interpreted as that of a particle moving in two dimensions, it becomes clear that also in this case the amplitude oscillates above threshold around a stable value which is identical with that determined in previous papers byHaken andSauermann neglecting laser noise. This stable value may, however, undergo shifts, if there are slow systematic changes of the cavity width, inversion etc. On the other hand the phase still fluctuates in an undamped way. After splitting off the phase factor the equations can be linearized and solved explicitly. With these solutions simple examples of correlation functions are calculated in a semiclassical way, thus yielding expressions for the line width above threshold. The results can also be used to evaluate from first principles correlation functions for different laser beams. As an example the complex degree of mutual coherence of two laser beams is determined. It vanishes if one of the lasers is still below threshold and its value is close to unity well above threshold for observation times small compared to the inverse laser linewidth.     

On the initial-boundary value problems for soliton equations

We present a novel approach to solving initial-boundary value problems on the segment and the half line for soliton equations. Our method is illustrated by solving a prototypal and widely applied dispersive soliton equation—the celebrated nonlinear Schroedinger equation. It is well known that the basic difficulty associated with boundaries is that some coefficients of the evolution equation of the (x) scattering matrix S(k, t) depend on unknown boundary data. In this paper, we overcome this difficulty by expressing the unknown boundary data in terms of elements of the scattering matrix itself to obtain a nonlinear integrodifferential evolution equation for S(k, t). We also sketch an alternative approach in the semiline case on the basis of a nonlinear equation for S(k, t), which does not contain unknown boundary data; in this way, the “linearizable” boundary value problems correspond to the cases in which S(k, t) can be found by solving a linear Riemann-Hilbert problem.     

Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory

In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.     

M-shaped asymmetric nonlinear oscillator for broadband vibration energy harvesting: Harmonic balance analysis and experimental validation

Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is validated experimentally, analytically, and numerically. As compared to the 3 dB bandwidth of the corresponding linear system with the same linear damping ratio, the M-shaped oscillator offers 3200, 5600, and 8900 percent bandwidth enhancement at the root-mean-square base excitation levels of 0.03g, 0.05g, and 0.07g, respectively. The M-shaped configuration can easily be exploited in piezoelectric and electromagnetic energy harvesting as well as their hybrid combinations due to the existence of both large strain and kinetic energy regions. A demonstrative case study is given for electromagnetic energy harvesting, revealing the importance of higher harmonics and the need for multi-term harmonic balance analysis for predicting the electrical power output accurately.     

近共振区超短强激光脉冲激发的等离子体尾波场

 用一维相对论粒子模拟研究了相对论超短强激光脉冲在等离子体中传播时激发的尾波场,初步获得了近共振区尾波场的峰值幅度随激光脉冲宽度变化的特点,发现在近共振区等离子体波激发出现增强。通过准静态近似下尾波激发的一维非线性方程数值求解,并与粒子模拟结果比较,得到了该非线性方程的适用范围：当激光脉冲宽度小于等离子体波波长的4倍时,该方程所得结果与粒子模拟结果一致;而当激光脉冲宽度大于该数值时,该方程不再适用。     

Nonequilibrium phenomena in damaged media and their effects on the elastic properties

Concrete, particularly if damaged, exhibits a peculiar nonlinear elastic behavior, which is mainly due to the coupling between nonequilibrium and nonlinear features, the two of which are intrinsically connected. More specifically, the formulation of a constitutive equation able to properly predict the dynamic behavior of damaged concrete is made difficult by the concomitant presence of two mechanisms: The modification of the microstructure of the medium and the transition to a new elastic state caused by a finite amplitude excitation (conditioning). Memory of that new state is kept when the excitation is removed, before relaxation back to the original elastic state takes place. Indeed, besides accounting for linear and nonlinear parameters, a realistic constitutive equation to be used in reliable prediction models should take into account nonequilibrium effects. Specific parameters, sensitive to finite amplitude excitations, should be introduced to provide information about conditioning effects. In this paper, experimental results indicating that nonlinearity of damaged concrete is memory-dependent will be presented and the implications of such findings in the development of physical models, with relevant outcomes for the characterization of hysteretical features, will be discussed.     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincar map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrödinger equation.     

Laser-induced spectral broadening and hole-burning in rare earth doped crystals and coherent optical spectroscopy for frequency upconversion

The excitation spectra for linear fluorescence and for frequency upconversion are recorded in Er³⁺ doped crystal Er:YAG. An excitation induced spectral broadening and hole-burning are shown to appear at the resonant frequency of the linear fluorescence excitation spectrum, where the upconversion is simultaneously enhanced. Rate equation analysis is applied to model the optical pumping processes in the crystal. We present evidence that the induced resonance broadening and hole-burning are the result of excitation competition between the linear absorption and the excited state absorption. Femtosecond pulse pairs are applied to excite the linear and nonlinear frequency conversion, resulting in coherent controlled branching ratio between the linear and nonlinear frequency conversion. The experimental reasults are in good agreement with the numerical evaluation based on optical Bloch equation. PACS 78.47.+p; 42.65.Re; 78.20.Ci     

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

Dynamics and interaction of pulses in the modified Manakov model

The two-component vector nonlinear Schrödinger equation, with mixed signs of the nonlinear coefficients, is considered. This equation is integrable by the inverse scattering transform method. The evolution of a single pulse and interaction of pulses are studied. It is shown that the dynamics of a single pulse is reduced to the scalar nonlinear Schrödinger equation of focusing or defocusing type, depending on the initial parameters. It is found that the interaction of pulses results in the appearance of additional solitons and bound states of several solitons. The asymptotic field profile in the non-soliton regime is also obtained.     

Pure odd-order oscillators with constant excitation

In this paper the excited vibrations of a truly nonlinear oscillator are analyzed. The excitation is assumed to be constant and the nonlinearity is pure (without a linear term). The mathematical model is a second-order nonhomogeneous differential equation with strong nonlinear term. Using the first integral, the exact value of period of vibration i.e., angular frequency of oscillator described with a pure nonlinear differential equation with constant excitation is analytically obtained. The closed form solution has the form of gamma function. The period of vibration depends on the value of excitation and of the order and coefficient of the nonlinear term. For the case of pure odd-order-oscillators the approximate solution of differential equation is obtained in the form of trigonometric function. The solution is based on the exact value of period of vibration. For the case when additional small perturbation of the pure oscillator acts, the so called ‘Cveticanin's averaging method’ for a truly nonlinear oscillator is applied. Two special cases are considered: one, when the additional term is a function of distance, and the second, when damping acts. To prove the correctness of the method the obtained results are compared with those for the linear oscillator. Example of pure cubic oscillator with constant excitation and linear damping is widely discussed. Comparing the analytically obtained results with exact numerical ones it is concluded that they are in a good agreement. The investigations reported in the paper are of special interest for those who are dealing with the problem of vibration reduction in the oscillator with constant excitation and pure nonlinear restoring force the examples of which can be found in various scientific and engineering systems. For example, such mechanical systems are seats in vehicles, supports for machines, cutting machines with periodical motion of the cutting tools, presses, etc. The examples can be find in electronics (electromechanical devices like micro-actuators and micro oscillators), in music instruments (hammers in piano), in human voice producing folds (voice cords), etc.     

Functional quantum statistics of light propagation in a two-level system

The functional Fokker-Planck formalism developed in a preceding paper is applied to the problem of a radiation field propagating in a medium, which contains resonant two-level atoms. Besides the electromagnetic field also the medium is described by continuous space dependent fields. We give the masterequation and transform it into ac-number functional differential equation for a characteristic functional. This equation is reduced considerably by the projection onto one dimension and the introduction of the diffusion approximation. It forms a solid basis for the study of all types of light propagation in resonant media including classical and quantum noise. We give an approximate solution of this equation by considering the problem of an externally pumped optical transmission line, in the case that saturation effects are absent. The spectral function of the electric field strength is obtained which describes a statistical mixture of photons with the quasiparticles of the polarization field. It shows the onset of a condensation of the quasiparticles into a single state. Self excitation of the transmission line is obtained at a certain threshold of the atomic inversion. This threshold is characterized by a finite occupation number of one single quasiparticle state. The influence of a finite length of the transmission line is briefly considered.     

Acoustic Solit on in One-Dimensional Ferromagnetic Systems

The local nonlinear excitation caused by the magnon-phonon interactions as an anisotropic source of nonlinearity is studied. The nonlinear equation for the Schrodinger probability amplitude of spin motion is given, and its soliton solutions are obtained in a weak coupling approximation. The existence conditions are discussed. It is shown that the soliton excitation energy can be less than a one-magnon state and a gap appears in the energy spectrum. The effect of the magnon-rnagnon interactions on the local acouitic soliton excitation is also discussed.     

Local 2PPE-yield enhancement in a defined periodic silver nanodisk array

Well-prepared periodic arrays of silver nanoparticles are investigated by means of linear and non-linear photoemission electron microscopy. The structures show homogeneous photoemission for UV excitation in the linear photoemission regime whereas striking inhomogeneities are mapped in the case of the nonlinear (2 photon) excitation using ultrashort 400 nm laser pulses. A detailed analysis enables to assign these inhomogeneities to defect induced electron momentum transfer processes only effective for the 2 photon excitation process. We propose this mechanism to be of relevance for the appearance of so-called hot spots in nonlinear photoemission as identified in other 2PPE studies in the past. Furthermore, the complementarity between all-optical studies and nonlinear photoemission studies of localized surface plasmons in nanoparticles is discussed.