Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.

In this paper we first discuss the asymptotic behaviours of solitary impulses in reaction-diffusion equations of Oregonator under the equal, single and double diffusion conditions, respectively. Then we obtain the asymptotic equations of motion of wavetrains for this model by a superposition of solitary impulses, and finally we analyse the stability of wavetrains.

In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.^{[1-4]} Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.

With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.^{[1,2]} The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.^{[3,4]} With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.

Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.

We study the synchronizing sensitive errors of chaotic systems for adding other signals to the synchronizing signal. Based on the model of the Henon map masking, we examine the cause of the sensitive errors of chaos synchronization. The modulation ratio and the mean square error are defined to measure the synchronizing sensitive errors by quality. Numerical simulation results of the synchronizing sensitive errors are given for masking direct current, sinusoidal and speech signals, separately. Finally, we give the mean square error curves of chaos synchronizing sensitivity and three-dimensional phase plots of the drive system and the response system for masking the three kinds of signals.

In this paper we adopt a new approach－the evolutionary algorithm based on cell division operation－to deal with ground-state energies of double-electron systems. This algorithm is based on the evolution of sets and can incorporate other search algorithms. Firstly, we make a search for several good subsets of solution space at the same time. Then, we make a fine search in the neighbourhood of some better points obtained in the first step to determine the final optimal results. In addition, the cell division enables the solution subspaces to become smaller and smaller, and thus increase the convergence speed. We have tested this approach on double-electron systems in magnetic fields, and the results obtained have shown that it can improve not only the efficiency but also the accuracy of the calculations compared with other methods.

Ab initio calculations of the rate coefficients for dielectronic recombination (DR) of Co-like Ag and Ta ions are performed based on Cowan's quasi-relativistic multi-configuration Hartree－Fock code. Co-like (3s ^{2}3p^{6}3d^{10})^{-1} configurations and Ni-like (3s^{2}3p^{6}3d^{10})^{-2}4l4l' autoionization configurations are included in the present calculation. Because of the extensive distribution of autoionization state energy levels, the DR rate coefficients cannot be reproduced or interpolated by a simple analytical formula, such as the Burgess－Merts formula, or the Hagelstein approximation. We propose to use multi-set Hagelstein parameters, which is convenient in practice and can reproduce well the ab initio calculated DR rate coefficients.

We have designed a spatially quantized diffractive optical element (DOE) for controlling the beam profile in a three-dimensional space with the help of the simulated annealing (SA) algorithm. In this paper, we investigate the annealing schedule and the neighbourhood which are the deterministic parameters of the process that warrant the quality of the SA algorithm. The algorithm is employed to solve the discrete stochastic optimization problem of the design of a DOE. The objective function which constrains the optimization is also studied. The computed results demonstrate that the procedure of the algorithm converges stably to an optimal solution close to the global optimum with an acceptable computing time. The results meet the design requirement well and are applicable.

A continuous-wave laser oscillation was demonstrated with a Yb-doped fluorapatite (FAP) crystal pumped with a 905 nm Ti:sapphire laser. The output characteristics for different output couplers were investigated. A maximum power of 67mW at a 1043nm wavelength was obtained with 10% output coupler, pumped by a Ti:sapphire laser with 910mW power. This corresponds to a slope efficiency of 26.5%.

Optical limiting (OL) properties of two phthalocyanines were investigated by using picosecond laser pulses at 532nm. The relative ratios k of the absorption cross section of the first singlet excited state to that of the ground state were approximately obtained by the analysis of the experimental results in which the reverse saturable absorption model of the three-energy-level scheme was employed. A significant comparison with fullerene C_{60} was presented for OL. The OL mechanisms have been analysed in detail.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

A statistical mechanical variational theory and an improved van der Waals one-fluid model have been used to compute the equation of state of fluid He+H_{2} mixtures with different H_{2}:He compositions under high pressure. The first-order quantum correction is included. Comparing the present results with Monte Carlo simulations indicates that the quantum corrections for calculating the thermodynamic properties become increasingly important at lower temperatures.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

In this paper we have calculated the variations of the gap Δ'(0,d) and transition temperature T'_{c} in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical d_{c}, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'_{c} decreases and Δ'(0,d)/k_{B}T'_{c}≤πe_{-γ} in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes Δ'(0,d)/k_{B} T'_{c}>πe_{-γ} in even numbers of electrons.

In this paper we use a numerical method to study the quantum effect of dynamical localization on the supercurrent in a mesoscopic Josephson junction driven by a periodically external electromagnetic field. We find that the charge is localized effectively when the ratio of the field magnitude and the field frequency equal some critical values, and in these cases the amplitude of the oscillation of the supercurrent will remain constant.

The demagnetization process for a Nd_{2}Fe_{14}B grain covered by an α-Fe layer was studied by use of the finite element technique of micromagnetics. μ_{0}_{i}H_{c} decreases with the increase of α-Fe layer thickness t. With the increase of t from 0 to 6nm, μ_{0}_{i}H_{c} decreases from ～7 T to ～3.5 T when the angle between the applied field and the c-axis of the Nd_{2}Fe_{14}B grain is 0.5° and from ～4 T to ～1.5 T when the angle is 30° or 60°. The effect is only slightly affected by the angle between the α-Fe layer and the field direction.

This paper studies the upconversion luminescence phenomenon of the Ho,Yb co-doped oxyfluoride vitroceramics. There is one group of strong upconversion luminescence lines positioned at 536.5nm, 18639cm^{-1}; 540.5nm, 18501cm^{-1}; 544.0nm, 18399cm^{-1}, which is easily identified as the transitions of ^{5}S_{2}→^{5}I_{8}. There are other splendid upconversion luminescence lines, which are ^{5}S_{2}→^{5}I_{7},^{5}F_{5}→^{5}I_{8},^{5}G_{6}→^{5}I_{8}, (^{5}G^{3}G)_{5} →^{5}I_{8},(^{3}F^{3}H^{5}G)_{4}→^{5}I_{7},^{5}G_{4}→^{5}I_{8} and (^{5}G^{3}H)_{5}→^{5}I_{8}. It is also found that an interesting kind of upconversion cooperative radiation fluorescence comes from a kind of coupling state of clusters consisting of two Yb^{3+} ions.

We present the experimental results of the magnetic viscosity, demagnetization curve and recoil loop for isotropic nanocrystalline Pr_{12}Fe_{82}B_{6} ribbons prepared by melt-spinning. The thermal fluctuation field, activation volume and irreversible demagnetization are discussed. The coercivity mechanism is mainly determined by the inhomogeneous nucleation rather than a simple nucleation of reverse domain.

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