Traveling-wave solution of non-linear coupled reaction diffusion equation arising in mathematical chemistry

A simple analytical approach to find the traveling-wave solution for a set of two coupled non-linear reaction diffusion equations is reported. An exact analytical solution for traveling-waves of the Fisher equations with a general non-linearity is found. The boundary value, the boundedness and the stability of the solution are discussed. This technique is straight forward to use involving minimal algebra. Use of the method for selected case is demonstrated.     

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: Internal resonance activation,reduced-order models and nonlinear normal modes

Resonant multi-modal dynamics due to planar 2:1 internal resonances in the non-linear, finite-amplitude, free vibrations of horizontal/inclined cables are parametrically investigated based on the second-order multiple scales solution in Part I [1] (in press). The already validated kinematically non-condensed cable model accounts for the effects of both non-linear dynamic extensibility and system asymmetry due to inclined sagged configurations. Actual activation of 2:1 resonances is discussed, enlightening on a remarkable qualitative difference of horizontal/inclined cables as regards non-linear orthogonality properties of normal modes. Based on the analysis of modal contribution and solution convergence of various resonant cables, hints are obtained on proper reduced-order model selections from the asymptotic solution accounting for higher-order effects of quadratic nonlinearities. The dependence of resonant dynamics on coupled vibration amplitudes, and the significant effects of cable sag, inclination and extensibility on system non-linear behavior are highlighted, along with meaningful contributions of longitudinal dynamics. The spatio-temporal variation of non-linear dynamic configurations and dynamic tensions associated with 2:1 resonant non-linear normal modes is illustrated. Overall, the analytical predictions are validated by finite difference-based numerical investigations of the original partial-differential equations of motion.     

Geometrically non-linear transverse vibrations of C-S-S-S and C-S-C-S rectangular plates

This paper is concerned with a new improved formulation of the theoretical model previously developed by Benamar et al. based on Hamilton's principle and spectral analysis, for the geometrically non-linear vibrations of thin structures. The problem is reduced to a non-linear algebraic system, the solution of which leads to determination of the amplitude-dependent fundamental non-linear mode shapes, the frequency parameters, and the non-linear stress distributions. The cases of C-S-C-S and C-S-S-S rectangular plates are examined, and the results obtained are in a good qualitative and quantitative agreement with the previous available works, based on various methods. In order to obtain explicit analytical solutions for the first non-linear mode shapes of C-S-C-S RP² and C-S-S-S RP, which are expected to be very useful in engineering applications and in further analytical developments, the improved version of the semi-analytical model developed by El Kadiri et al. For beams and fully clamped rectangular plates, has been slightly modified, and adapted to the above cases, leading to explicit expressions for the higher basic function contributions, which are shown to be in a good agreement with the iterative solutions, for maximum non-dimensional vibration amplitude values up to 0.75 and 0.6 for the first non-linear mode shapes of C-S-C-S RP and C-S-S-S RP, respectively.     

Experimental study of non-linear energy pumping occurring at a single fast frequency

Experimental verification of passive non-linear energy pumping in a two-degree-of-freedom system comprising a damped linear oscillator coupled to an essentially non-linear attachment is carried out. In the experiments presented the non-linear attachment interacts with a single linear mode and, hence, energy pumping occurs at a single ‘fast’ frequency in the neighborhood of the eigenfrequency of the linear mode. Good agreement between simulated and experimental results was observed, in spite of the strongly (essentially) non-linear and transient nature of the dynamics of the system considered. The experiments bear out earlier predictions that a significant fraction of the energy introduced directly to a linear structure by an external impulsive (broadband) load can be transferred (pumped) to an essentially non-linear attachment, and dissipated there locally without spreading back to the system. In addition, the reported experimental results confirm that (a) non-linear energy pumping in systems of coupled oscillators can occur only above a certain threshold of the input energy, and (b) there is an optimal value of the energy input at which a maximum portion of the energy is absorbed and dissipated at the NES.     

Non-linear normal modes,invariance, and modal dynamics approximations of non-linear systems

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation.     

Non-isothermal Decomposition Mechanism and Kinetics of LiClO4 in Nitrogen

The non-isothermal decomposition kinetics of LiClO4 in flow N2 atmosphere was studied.TG-DTA curves show that the decomposition proceeded through two well-defined steps below 900°C,and the mass loss was in agreement with the theoretica1 value.XRD profile demonstrates that the product of the thermal decomposition at 500°C is LiCl.For the decomposition kinetics study,the activation energies calculated with the Friedman method were considered as the initial values for non-linear regression and were used for verifying the correctness of the fitted models.The decomposition process was fitted by a two-step consecutive reaction:extended Prout-Tompkins equation[Bna,f (α) is (1?α)nα a] followed by a 1th order reaction(F1).The activation energies were (215.6±0.2) and (251.6±3.6) kJ/mol,respectively.The exponentials n and a for Bna reaction were (0.25±0.05) and (0.795±0.005),respectively.The reaction types and activation energies were in agreement with those obtained from the isothermal method,but the exponentials were optimized for better fitting and prediction.     

Effect of CdS nanoparticles on fluorescence from Sm doped SiO2 glass

Sm³⁺ doped CdS nanoparticles have been prepared by sol-gel method. The effect of annealing temperatures and doping concentrations of CdS on the photoluminescence spectra of Sm³⁺ were studied. From the measurement of its optical absorption, three phenomenological Judd-Ofelt intensity parameters (Ω₂, Ω₄, and Ω₆) have been computed and used to parameterize the radiative properties. The influences of CdS on Sm³⁺ ions were studied by fluorescence spectroscopy. The fluorescence spectra revealed that the emission intensity of samarium increased considerably in the presence of CdS nanoparticles. The evaluation of radiative properties of Sm³⁺ containing CdS showed that the ⁴G_5/2→⁶H_7/2 transition in silica matrix had the potential to be a laser transition.     

Multi-wavelength operation of LD side-pumped Nd:YAG laser

A dual-wavelength laser at 1064 nm and 1319 nm is obtained by a single Nd:YAG crystal rod. On the basis of 1064 nm and 1319 nm dual-wavelength laser installation, the second harmonic waves at 532 nm and 660 nm can be achieved by using non-linear frequency conversion technology. When 1064 nm and 1319 nm lasers oscillate simultaneously, the maximum output power is 30.5 W and 8.78 W, respectively. When the 1319 nm laser is restrained, we obtain a 35.6 W maximum output power at 1064 nm and by contrary 11.2 W at 1319 nm. The maximum output powers of 532 nm and 660 nm lasers are 5.34 W and 1.353 W when oscillating simultaneously. With one of them restrained, the maximum output power is 6.72 W at 532 nm and 1.90 W at 660 nm. The optimum repetition rate of the acousto-optic Q-switch is 10.5 KHz and 20.5 KHz for 532 nm and 660 nm lasers, respectively. The optical-to-optical conversion efficiency from the fundamental waves to the harmonic waves is 17.5% and 15.4%. The instability is less than 2%.     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

Non-linear buckling for the surface rectangular delamination of laminated piezoelectric shells

An analytical method is presented to study the non-linear buckling characteristic of rectangular local delamination near the surface of fiber-reinforced piezoelectric lamination shells under coupled mechanical and electric loads. The stacking sequence of fiber reinforced lamination shells with piezoelectric layers is considered as symmetry, but the stacking sequence of rectangular local delamination sub-shells is arbitrary. Based on the nonlinear displacement mode of delaminated sub-shells, the effects of electric fields, the geometrical, physical parameters and stacking sequences of piezoelectric laminated shells on the non-linear local buckling for rectangular delamination near the surface of piezoelectric laminated base-shells are solved.