Pulse Amplification in Dispersion-Decreasing Fibers with Symbolic Computation

The pulse amplification in the dispersion-decreasing fiber （DDF） is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrfdinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametric conditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.     

Nonsingular terminal sliding mode approach applied to synchronize chaotic parameters and systems with unknown nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.     

High power nano-LiMn2Oa cathode materials with high-rate pulse discharge capability for lithium-ion batteries＊

Nano-LiMn2O4 cathode materials with nano-sized particles are synthesized via a citric acid assisted sol-gel route. The structure, the morphology and the electrochemical properties of the nano-LiMn204 are investigated. Compared with the micro-sized LiMn2O4, the nano-LiMn2O4 possesses a high initial capacity （120 mAh/g） at a discharge rate of 0.2 C （29.6 mA/g）. The nano-LiMn2O4 also has a good high-rate discharge capability, retaining 91% of its capacity at a discharge rate of 10 C and 73~ at a discharge rate of 40 C. In particular, the nano-LiMn2O4 shows an excellent high-rate pulse discharge capability. The cut-off voltage at the end of 50-ms pulse discharge with a discharge rate of 80 C is above 3.40 V, and the voltage returns to over 4.10 V after the pulse discharge. These results show that the prepared nano-LiMn2O4 could be a potential cathode material for the power sources with the capability to deliver very high-rate pulse currents.     

Characterization of zirconium thin films deposited by pulsed laser deposition

Zirconium(Zr) thin films deposited on Si(100) by pulsed laser deposition(PLD) at different pulse repetition rates are investigated. The deposited Zr films exhibit a polycrystalline structure, and the X-ray diffraction(XRD) patterns of the films show the α Zr phase. Due to the morphology variation of the target and the laser–plasma interaction, the deposition rate significantly decreases from 0.0431 /pulse at 2 Hz to 0.0189 /pulse at 20 Hz. The presence of droplets on the surface of the deposited film, which is one of the main disadvantages of the PLD, is observed at various pulse repetition rates. Statistical results show that the dimension and the density of the droplets increase with an increasing pulse repetition rate. We find that the source of droplets is the liquid layer formed under the target surface. The dense nanoparticles covered on the film surface are observed through atomic force microscopy(AFM). The root mean square(RMS) roughness caused by valleys and islands on the film surface initially increases and then decreases with the increasing pulse repetition rate.The results of our investigation will be useful to optimize the synthesis conditions of the Zr films.     

Multi-crack imaging using nonclassical nonlinear acoustic method

Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy （NEWS） method with a time-reversal （TR） mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress-strain relation is established with Preisach-Mayergoyz （PM） model in crack zone. Pulse inversion （PI） and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR- NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation （NEWS） added to the existing phases （NEWS and TR）. In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.     

Statistical properties of the photoelectron energy spectrum generated by an intense laser pulse and a continuous X-ray

This study shows that the photoelectron energy spectrum generated by an intense laser pulse in the presence of a continuous X-ray has interesting and useful statistical properties. The total photoionization production is linearly propor- tional to the time duration of the laser pulse and the square of the beam size. The spectral double energy-integration is an intrinsic value of the laser-assisted X-ray photoionization, which linearly depends on the laser intensity and which quantita- tively reflects the strengths of the laser-field modulation and the quantum interference between photoelectrons. The spectral energy width also linearly depends on the laser intensity. These linear relationships suggest new methods for the in-situ measurement of laser intensity and pulse duration with high precision.     

N-Soliton Solutions of General Nonlinear Schrodinger Equation with Derivative

The bilinear equation of the genera/nonlinear Schrodinger equation with derivative （GDNLSE） and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative （DNLSE） and its multisoliton solutions are given by reduction.     

Exact Solutions to Short Pulse Equation

In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation.     

Memristance controlling approach based on modification of linear M–q curve

The memristor has broad application prospects in many fields, while in many cases, those fields require accurate impedance control. The nonlinear model is of great importance for realizing memristance control accurately, but the im- plementing complexity caused by iteration has limited the actual application of this model. Considering the approximate linear characteristics at the middle region of the memristance-charge （M-q） curve of the nonlinear model, this paper pro- poses a memristance controlling approach, which is achieved by linearizing the middle region of the M-q curve of the nonlinear memristor, and establishes the linear relationship between memristances M and input excitations so that it can realize impedance control precisely by only adjusting input signals briefly. First, it analyzes the feasibility for linearizing the middle part of the M-q curve of the memristor with a nonlinear model from the qualitative perspective. Then, the lin- earization equations of the middle region of the M-q curve is constructed by using the shift method, and under a sinusoidal excitation case, the analytical relation between the memristance M and the charge time t is derived through the Taylor series expansions. At last, the performance of the proposed approach is demonstrated, including the linearizing capability for the middle part of the M-q curve of the nonlinear model memristor, the controlling ability for memristance M, and the influence of input excitation on linearization errors.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.     

Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

We obtain the integrable relation for the one-dimensional nonlinear Schrodinger equations which describes the dynamics of a Bos-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.     

A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f（ξ）, is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Soliton Solutions and Bilinear B/icklund Transformation for Generalized Nonlinear Schr6dinger Equation with Radial Symmetry

Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B~cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.     

Optimal design of a 7 T highly homogeneous superconducting magnet for a Penning trap

A Penning trap system called Lanzhou Penning Trap（LPT） is now being developed for precise mass measurements at the Institute of Modern Physics（IMP）.One of the key components is a 7 T actively shielded superconducting magnet with a clear warm bore of 156 mm.The required field homogeneity is 3 × 10-7 over two 1 cubic centimeter volumes lying 220 mm apart along the magnet axis.We introduce a two-step method which combines linear programming and a nonlinear optimization algorithm for designing the multi-section superconducting magnet.This method is fast and flexible for handling arbitrary shaped homogeneous volumes and coils.With the help of this method an optimal design for the LPT superconducting magnet has been obtained.     

Synchronization of the fractional-order generalized augmented Lii system and its circuit implementation

In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.     

Design on a highly birefringent and nonlinear photonic crystal fiber in the C waveband

In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.     

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves.When a laser or electron beam passes through a dense plasma,hot low density electron populations can be generated to alter the wave damping/growth rate.In this paper,we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found.The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized(r,q)distribution function,which is the generalized form of the kappa and Maxwellian distribution functions.In the limiting case of r=0 and q→∞,it reduces to the classical Maxwellian distribution function,and when r=0 and q→κ+1,it reduces to the kappa distribution function.     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

Digital structured light （SL） profilometry is increasingly used in three-dimensional （3D） measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector-camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method.