An easy and general way to access more complex soliton phenomena is introduced in this paper. The collision process between two solitons of the KdV equation is investigated in great detail with this novel approach, which is different from the sophisticated method of inverse scattering transformation. A more physical and transparent picture describing the collision of solitons is presented.

Using the extended homogeneous balance method, we have obtained abundant exact solution structures of a (2+1)-dimensional integrable model, the Nizhnik－Novikov－Veselov equation. By means of leading order terms analysis, the nonlinear transformations of the Nizhnik－Novikov－Veselov equation are given first, and then some special types of single solitary wave solution and multisoliton-like solutions are constructed.

The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik－Novikov－Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation.

By introducing the double spacetime manifold, the double gamma matrices and Dirac spinors, the action of the Dirac spinoral fields is doubled. Furthermore, the double coupling of the Dirac fields to the Ashtekar gravitational fields is studied.

Frequency catastrophe is found in a cell Ca^{2+} nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

In the spring-block models of earthquakes, one of the key factors is the dynamic friction term which determines the complexity of the faulting process. Generally, two kinds of friction, namely velocity-dependent friction and slip-dependent friction, are used in the modelling. But until now there has still been a lack of information on which kind of friction term is more suitable for modelling the phenomenology of earthquakes. Based on the numerical studies of Shaw (1998 Bull. Seismol. Soc. Am. 88 1457), we have examined the ratio of the broadband radiated energy and the scalar seismic moment of shallow earthquakes worldwide from 1987 to 1998. The result shows that for earthquakes with strike-slip mechanisms, velocity-dependent friction seems to be predominant, while for thrust and normal events, slip-dependent friction seems predominant. This suggests that in the spring-block models for earthquakes, the type of focal mechanism has to be accounted for, and different types of earthquakes require different dynamic friction terms in the corresponding spring-block model.

Piezoresistive cantilevers with dimensions of 200×50×1.8μm^{3} have been fabricated from polycrystalline silicon using reactive ion etching (RIE) and back etching processes. Full Wheatstone bridges have been designed symmetrically on-chip, with two resistors placed on the cantilevers and two resistors on the substrate. The differential measurements of the two cantilevers can reduce the thermal shift of the signal in the system and the external noise in the laboratory. The characteristics of the fabricated cantilevers have been analysed by measuring the noise and the sensitivity. The measured noise spectra show that the 1/f noise is the dominant noise source at low frequencies. With the linear relation between 1/f noise and bias voltages, the Hooge factor (α) was calculated to be 0.0067. The 1/f noise was explained in terms of a lattice scattering model, which occurs in the depletion region of the grains. The displacement sensitivity of the cantilevers ((ΔR)/Rz^{-1}) was calculated to be 1×10^{-6}nm^{-1} by measuring the resistance change and the vertical deflection of the cantilever. The gauge factor of the piezoresistive cantilever was calculated to be 19. At a 3 V bias voltage and 1000 Hz measurement bandwidth, 1 nm of minimum detectable deflection has been obtained.

In this paper, we obtain the eigenstates and the eigenvalues of the Hamiltonians of the trigonometric SU(N) Gaudin model based on the quasi-classical limit of the trigonometric SU(N) chain with the periodic boundary condition. By using the quantum inverse scattering method, we also obtain the eigenvalues of the generating function of the trigonometric SU(N) Gaudin model.

The Stark effects of the Rydberg states in the alkaline-earth atoms are studied theoretically. Using a method similar to the treatment of alkali atoms, the properties of the Stark states of Mg, Ca, Sr and Ba atoms in the regions far away from the perturbers are investigated. The Stark maps for Mg (n=16, M=0), Ca (n=10, M=0), Sr (n=12, M=0) and Ba (n=13, |M|=0,1) are presented. Topics such as the general methods of calculation, the treatment of fine structure, and the structure of level anti-crossings are discussed. The comparison between the theoretical and experimental Stark maps is satisfactory.

We adopt a dynamical algebraic approach to study the system of a two-level atom moving in a quantized travelling light field and a gravitational field with a multiphoton interaction. The exact solution of the system is obtained and used to discuss the influence of the gravitational field on the collapses and revivals of atomic population, sub-Poissonian statistics.

The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell--Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2π pulse. The spectrum of the 4π pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.

An optical pulse autocorrelator for rapid and slow scanning is described in this paper. Using an audio loudspeaker on one arm, an interferometric rapid-scanning signal of the output from a high-repetition laser oscillator is obtained. However, by adjusting the positions of the mirrors and using a step-motor on another arm, the intensity autocorrelation function of the output from a low-repetition laser amplifier can be easily measured. Using all-reflecting optics and an adequate nonlinear crystal, the whole instrument is very compact and has been used to measure sub-20 fs light pulses in both configurations with excellent agreement. In the slow-scanning configuration, a pulse train as long as 500ps has been determined. Using this autocorrelator, the home-made JIGUANG-I CPA laser facility was characterized for its pulse duration evolution.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Lattice dynamical calculations of ice VIII have been carried out by using a slightly modified set of force constants obtained recently for ice Ih (Li J C and Ross D K 1993 Nature 365 327). A weak interaction was introduced between the two interpenetrated sublattices in the ice VIII structure. The calculated results for H_{2}O and D_{2}O ice VIII are in reasonable agreement with the measured inelastic neutron scattering spectra. The eigenvectors of phonon modes in the range of translational and librational bands have been studied in order to understand the properties of the vibrational modes. It is found that the third peak at 26.7meV in the translation results from weak hydrogen bond interactions, and the first peak (14.7meV) is much higher than it is in ice Ih (～7.1meV), which is partially due to the interactions between the two sublattices.

Lattice dynamical calculations have been carried out for ice II based on the force field constructed for ice Ih. In order to fully understand ice II inelastic neutron scattering spectra, the decomposed phonon density of states was shown mode by mode. Calculated results have shown that the hydrogen bond force constant between the six-molecule rings is significantly weaker, 75eV/nm^{2}, compared with the force constant, 220eV/nm^{2}, within the rings. Inelastic neutron scattering spectra of clathrate hydrate H_{2}O+He are almost the same as ice II. This means that the absorption of He atoms cannot affect the bond strengths of the ice II host lattice. Based on the force field model for ice II, the van der Waals interactions between water molecules and helium atoms are considered. The results obtained are consistent with experimental data. Lattice dynamical calculations have been carried out for ice II using seven rigid pairwise potentials. It was found that MCY makes the stretching and bending interactions in ice II too weak and makes the O-O bond length too long (～5%), thus its lattice densities are obviously lower than other potential lattices or experimental values.

Self-assembled Ge islands were grown on Si(100) substrate by Si_{2}H_{6}-Ge molecular beam epitaxy. After being subjected to chemical etching, it is found that the photoluminescence from the etched Ge islands became more intense and shifted to the higher-energy side compared to that of the as-deposited Ge islands. This behaviour was explained by the effect of chemical etching on the morphology of the Ge islands. Our results demonstrate that chemical etching can be a way to change the luminescence property of the as-deposited islands.

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

The magnetocaloric effect in polycrystalline of Pr_{1-x}Sr_{x}MnO_{3} (x=0.33, 0.43, 0.50) has been investigated. A large magnetic entropy change (7.1J/kgK) was discovered in Pr_{0.5}Sr_{0.5}MnO_{3} under a low magnetic field of 1T at charge-ordered state transition temperature (161K). The physical mechanism is related to a drastic magnetization change at a temperature where the field-induced magnetic, electron and structural phase transitions occur (from the antiferromagnetic charge-ordered state to the ferromagnetic charge-disordered state).

Measurements were performed using the positron annihilation technique associated with physical metallurgical techniques for several engineering alloys containing fine precipitates. It is shown that positron annihilation is an effective method to detect fine precipitates, providing a sound basis for a further intense research of these.

In the spacetime of a charged spinning black hole, the distribution of particle energy levels has been studied. Near the event horizon of such a black hole a crossing of the particle energy levels exists, which leads to the occurrence of non-thermal radiation of the black hole. This quantum effect is non-thermal and also different from those of the Kerr and Kerr－Newman black holes.

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