Table of contents

We study the order reduction method of the rotational relativistic Birkhoffian equations. For a rotational relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the rotational relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. An example is given to illustrate the application of the result.

The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by the entrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shown that the coherent soliton structures may be dromions, solitoffs, etc.

We report on our model study of stochastic resonance in the stock market using numerical simulation and analysis. In the model, we take the interest rate as the external signal, the randomness of traders' behaviour as the noise and the stock price as the output. With computer simulations, we find that the system demonstrates a characteristic of stochastic resonance as noise intensity varies. An analytical explanation is proposed.

An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.

By using the generalized cell mapping digraph (GCMD) method, we study bifurcations governing the escape of periodically forced oscillators in a potential well, in which a chaotic saddle plays an extremely important role. In this paper, we find the chaotic saddle and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property, that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins. The chaotic saddle in the Wada fractal boundary, by colliding with a chaotic attractor, leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system. We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary, particularly concentrating on its discontinuous bifurcations (metamorphoses). We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries. After a final escape bifurcation, there only exists the attractor at infinity; a chaotic saddle with a beautiful pattern is left behind in phase space.

In this paper, we present a secure communication method for a high-power information signal based on chaotic masking. In the transmitter, an adaptive controller is adopted to pick up the change of the information signal and to inject the controller's error into the transmitting system. At the same time, the information is directly added to the chaotic signal in transmission to drive the receiving system. In the receiver, another adaptive controller is used to maintain chaotic synchronization of the transmitting and receiving systems and to recover the information signal. Since the synchronization error is independent from the information signal, the power of the information signal can be equivalent to that of the chaotic signal and the frequency of the information signal can be set within the range of the principal frequencies of the chaotic signal. The results of theoretical analysis and numerical simulation show that the presented method not only enhances the degree of security of low-dimensional chaotic systems but also significantly improves the signal-to-noise ratio at the receiving end.

In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg-de Vries equation and modified Korteweg-de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.

We have constructed a scanning low-T_c superconducting quantum interference device (SQUID) microscope, in which the SQUID is mounted on the lower end of a copper rod and cooled to liquid helium temperature. There is a 65µm thick sapphire window under the SQUID. The sample at room temperature underneath the window can be scanned to produce magnetic images. The microscope has a spatial resolution of 100-150µm and a magnetic field sensitivity of 3-60pT/√ Hz in a magnetically unshielded environment. We have used this scanning SQUID microscope to measure various room temperature samples.

For heavy meson systems, we study the heavy quark potential, which emerges from the effective dilaton-gluon coupling inspired from the superstring theory. We put emphasis on the new confinement generating mechanism of this potential through the investigation of the spin-averaged energy levels of the heavy meson systems. By using a unified approach to the solutions of the Schrödinger and the spinless Salpeter equations, we can examine in a realistic way the effects of using a relativistic kinetic energy. The obtained results agree favourably with other predictions and the relativistic equation can better account for the observed energy levels.

We present a technology for diagnosing the D-T fusion process by detecting capture γ-rays. This technology provides an alternative route to diagnosing the D-T reaction process when a great deal of heavy Z materials surrounds the D-T region. A very important aspect of this paper is to focus on the methods of shielding low-energy γ-rays whose radiation intensity is 10⁶ times higher than that of the capture γ-rays. Another aspect is about how to distinguish signal from noise. The result of a 50/1 signal-to-noise ratio indicates that the designed double-magnetic spectrograph is very successful for diagnosing the D-T fusion reaction process.

The absolute optical oscillator strength density spectra of nitric oxide in the energy region of 5.0-22.0 eV have been measured by a high-resolution fast-electron energy loss spectrometer. With the calculated results obtained by the multiscattering self-consistent-field method and channel characteristics, the strongly overlapped spectra in the energy region of 7.5-9.3 eV have been analysed and the corresponding partially vibrationally resolved optical oscillator strengths have been estimated from the experimental spectra.

We report on a new experimental result to generate dark hollow beams by using a geometric optical method. We propose two new methods to produce focused and localized hollow laser beams by using π-phase plates. Using Monte Carlo simulations, we have studied the Sisyphus cooling of alkali atoms in pyramidal hollow beam gravito-optical traps. We discuss some potential applications of the dark hollow beams in atom optics and the preparation of an all optically-cooled and optically-trapped atomic Bose-Einstein condensation (BEC). Our research shows that an ultracold atomic sample with a temperature of ~2µK can be obtained in the pyramidal hollow beam dipole trap and an all optical-type BEC may be realized in a far blue-detuned, hollow beam trap.

A simple model has been developed to describe the Zeeman patterns of far-infrared laser magnetic resonance spectra of the monobromomethyl radical CH₂Br observed at 447.3 and 671.1µm. A satisfactory agreement between the experimental spectra of the radical and their simulation with this simple model has been achieved. This approach can be used to gain further information about the structure and the spectrum of this interesting radical.

We have investigated the dispersive properties of tunnelling-induced transparency in asymmetric double quantum well structures where two excited states are coupled by resonant tunnelling through a thin barrier in a three-level system of electronic subbands. The intersubband transitions exhibit high dispersion at zero absorption, which leads to the slow light velocity in this medium as compared with that in vacuum (c=3×10⁸). The group velocity in a specific GaAs/AlGaAs sample is calculated to be v_g=c/4.30. This structure can be used to compensate for the dispersion and energy loss in fibre optical communications.

When micrometre-sized polymer particles were added into a dye-doped pendant drop that acted as a quasi-two-dimensional circular resonator, we found a blueshift of the peak wavelength of its lasing spectrum. The lasing output was also enhanced by the particles. The spectral blueshift was explained by a model of dye lasing in a circular cavity. The model includes losses of the scattering particles, medium absorption and radiation leakage. An optimum particle density for maximum lasing output was deduced. The results are consistent with our experimental findings.

Using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm plasma. It is found that the inclusion of ion temperature in the equation modifies the nature of the ion-acoustic wave stability and the soliton structures. The effects of ion plasma temperature on the modulational stability and ion-acoustic wave properties are investigated in detail.

A correction of Walsh's method for bulk sound velocity calculation for shocked porous materials is accomplished based on the Wu-Jing thermodynamic equation of state. The corrected bulk velocities for solid and porous samples with low porosities are in good agreement with the corresponding experimental data published previously. On the basis of this corrected equation, the influence of thermoelectrons on the bulk velocity of shocked materials is discussed in detail at pressures of 50, 70 and 200 GPa. Some interesting phenomena are revealed, which seem to be the unique features of a dynamic-pressure-loading process and could not be found in static experiments.

The virial theorem in refined Thomas-Fermi-Dirac theory for the interior of atoms in a solid is given and proven.

We report on the reversible, electrical and optical switching on silver 3-phenyl-1-ureidonitrile complex thin films. The films can switch from a high impedance state to a low impedance state with an applied electric field at the threshold of 3.5×10⁷V/m. Furthermore, the films can be switched back to the original state by treating the samples at about 80 °C. The optical recording is fulfilled using a semiconductor laser with a wavelength of 780 nm. Erasure can be accomplished by bulk heating or by the laser working with the power beneath the threshold. No loss of the organic was found in the experiments. This material may have a potential application in ultrahigh data density storage.

We study the quantum dynamics of a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We demonstrate that under the weak damping, the collapse-revival phenomena can exist in this system. We also demonstrate that the revivals of oscillations are sensitive to the initial coherent field and the damping rate of the single-mode quantized field.