Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota－Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota－Satsuma equations.

Solving Klein－Gordon equation with equal ring-shaped harmonic oscillator scalar and vector potentials, we obtain the exact normalized bound-state wavefunction and energy equation.

The order reduction method of the rotational relativistic Birkhoffian equations is studied. For a rotational relativistic Birkhoffian system, the cyclic integrals can be found by using the perfect differential method. Through these cyclic integrals, the order of the system can be reduced. If the rotational relativistic Birkhoffian system has a cyclic integral, then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept. An example is given to illustrate the application of the results.

In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.

The dual-ring erbium-doped fibre laser shows a hyperchaotic behaviour under some conditions. The hyperchaotic behaviour can be well controlled to enter into periodicity by modulating the pumping in one of the two rings. The period is different for different modulation index at the same modulation frequency, or for different modulation frequency at the same modulation index.

Our theoretical study on UH^{2+}( X^4Σ) using a density functional method shows that its potential energy curve has both minimum and maximum, which is the so-called "energy trapped" molecules. This sort of potential maximum is mainly caused by Coulomb repulsion. We have proposed the perturbation effect of ionic charges to explain the existence of the potential maximum for diatomic ions, and derived an analytic potential energy function has been derived, and the force constants and spectroscopic data are obtained. Finally, the vertical ionization potential for UH^{2+} has been calculated as well.

Using the many-body perturbation theory, we have calculated the photoionization cross section of 3p and 3d subshells of the neutral manganese, and discussed the second-order ground-state correlation and random-phase approximation correlations in detail. This is the first theoretical calculation for manganese as far as we know. Our calculated results are more consistent with the experimental results than those given by other methods in the literature.

We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged time-dependent local density approximation scheme, which is solved directly in the time domain without any linearization. As an example we consider the simple Na_{2} cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.

Starting from the Maxwell's equation, and using the resonant-dipole equation together with the multilevel rate equations which take the effects of energy relaxation into consideration, we have derived a more realistic numerical model of the chirped pulse amplification for an ultra-broad band width laser amplifier. Numerical simulations of this model show that both the intensity profile and the energy fluence of the amplified chirped pulse are closely connected with the two relaxation effects: the relaxation of the thermalization among the components of the laser multiplets and the depletion of the lower laser level. The results are valuable for the design of ultra-broad bandwidth chirped pulse amplification lasers.

Using density matrix equation, we calculate analytically as well as numerically the effect of the four-wave mixing (FWM) field on electromagnetically induced transparency (EIT) in the rubidium 5S_{1/2}-5P_{3/2}-5D_{5/2} Λ-type system with a two-photon probe field. The calculated results are in good agreement with Fulton's experimental results in 1995 Phys. Rev. A 52 2302.

We proposed a four-level system to explore the quantum interference effects on optical amplification. We found that the gain of the probe, including positions and values of gain peaks, can be adjusted by changing the coherent field and the incoherent pumping. At the same time, we can also modify the absorption profile of electromagnetically induced transparency by the incoherent pump. The results provide a method to flatten the gain of Erbium-doped fibre amplifiers.

Pattern formation is closely related to system boundary conditions in nonlinear dynamic systems, apart from the system control parameters. To avoid complexity, system boundary conditions are usually considered to be infinite or periodic, and the initial conditions spatially homogeneous. But it is not always the case in real situations, or sometimes periodic boundary conditions are not exact. To show the important and interesting boundary effects in real pattern formation, we suggest a simple universal boundary condition in a typical optical pattern formation system. Numerical simulations of the passive optical system show that pattern characteristics such as distribution symmetry, peak number, structure strength, evolution course and stability are all greatly influenced by the system boundary conditions.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

A one-dimensional cellular automaton is defined without the critical gradient rule (Δh>Δh_c) which is essential to the existence of avalanches in self-organized criticality (SOC) models. Instead, only the local diffusion rule is used, however, the characteristics of SOC, such as the bursty behaviour, power-law decay in fluctuation spectra, self-similarity over a broad range of scales and long-time correlations, are still observed in these numerical experiments. This numerical model is established to suggest that the bursty events and the incremental diffusion observed universally in fusion experiments do not necessarily imply the submarginal dynamics.

Electron energy distribution function (EEDF) is a key parameter of plasmas, which is directly proportional to the second derivative of the probe I-V characteristics. Because of an amplifying effect of unavoidable noises in the experimental probe I-V curves during the derivation process, the experimental I-V curves should be smoothed before performing the numerical derivation. This paper investigates the effect of adjustable factors used in the smoothing process on the deduced second derivative of the I-V curves, and an optimum group of the adjustable factors is selected to make the rms deviation of the smoothed I-V curves from the measured curves less than 1%. A simple differentiation circuit is designed and used to measure the EEDF parameter straightforwardly. It is the first time, so far as we know, to measure the EEDF parameters simultaneously by means of both numerical and circuit derivative methods under the same discharge conditions and on the same discharge equipment. The deviation between two groups of mean electron energy E and electron density n_e obtained by the above different methods is within about 7%. This apparently improves the reliability of the measurements of the EEDF parameters.

The results of the investigation on the space-charge limiting current for a spherical-cathode diode in the non-relativistic situation are presented in this paper. The results show that the current enhancement factor equals the square of E-field enhancement factor on the cathode surface. The generated space-charge limiting current is deduced. In the case of a pin-shaped-cathode diode, the space-charge limiting current is also obtained, indicating that the current is independent of the geometric parameters of the diode. Analyses of the shielding effects and the conditions for generation of the uniform space-charge limiting beam show that, for pin-arrayed cathodes, the distance between pins should be in the range from 1.2D to 1.5D, where D is the distance between the two electrodes.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The small-angle x-ray scattering (SAXS) resulting from a non-ideal two-phase system having sharply defined phase boundaries but with micro-fluctuations of electron density within any phase shows a positive deviation from Debye's theory. We have found a simple method suitable for fitting the slit-smeared SAXS data and correcting the positive deviation. The validity of this procedure is tested on porous ZrO_2 xerogel prepared using the sol-gel process.

By using the phase-field approach, we have simulated the directional growth of alloys in undercooled molten states under the isothermal and nonisothermal conditions. The influences of the isothermal approximation on simulation results are discussed. We found that for undercooling greater than 25K, the isothermal approximation overestimates the interface growth velocity and reduces a critical velocity for an absolute stable planar interface, thus in this simulation, the interface morphology shows the plane-cell-plane transition with increasing initial undercooling of the melt, and the planar interface obtained under a large undercooling is absolutely stable. Whereas in the nonisothermal simulation, only plane-cell transition occurs in the same range of the initial undercoolings of the melt, and the planar interface tends to be destabilized and evolve into cells.

Atomic hydrogen assisted molecular beam epitaxy (MBE) is a novel type of epitaxial growth of nanostructures. The GaAs (311)A surface naturally forms one-dimensional step arrays by step bunching along the direction of 〈-233〉 and the space period is around 40nm. The step arrays extend over several μm without displacement. The InGaAs quantum wire arrays are grown on the step arrays as the basis. Our results may prompt further development of more uniform quantum wire and quantum dot arrays.

Since Tetsujiro Kubo indirectly found the spontaneous polarization of tourmaline through absorbing copper ions in copper sulfate aqueous solutions in 1980s, there is no other evidence to demonstrate the existence of the spontaneous polarization in tourmaline. It was found that after a tourmaline particle was bombarded by electron beams, a spot appeared on the surface of the sample, and that one half of the spot was brighter than the other half under scanning electron microscope. After tourmaline was treated for 2 h at 1223K and then bombarded by electron beams, the bombardment spot did not appear because the crystal structure of tourmaline is destroyed. The existence of the bombardment spot accounts for the spontaneous polarization. The shape and brightness of the bombardment spot not only shows the existence of a surface electric field induced by spontaneous polarization, but also the relation with the direction of the crystal plane of tourmaline.

We have studied the dynamic process of interactions between a DNA chain and a histone octamer by numerical simulations. It is found that DNA indeed may wrap around the histone octamer about two turns as in the actual situations. The simulation shows that the interaction potential between DNA and histone is a key factor for the wrapping of DNA, and the temperature is also an important parameter in the process.

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