The form invariance of Appell equations of holonomic mechanical systems under the infinitesimal transformations of groups is studied. The definition and the criterion of the form invariance of Appell equations are given. This form invariance can lead to a conserved quantity under certain conditions.

The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.

Within the framework of quantum dynamical theory, we present a new method to control the quantum statistics of an atom laser by applying a powerful input light. Differing from the case in the rotating wave approximation, the non-classical properties can appear in the output atom laser beam with the evolution of time. By choosing a suitable phase of the input light, it is capable of realizing a steady and brighter output of coherent atom laser.

Based on the hydrodynamic energy transport model, immunity from the hot-carrier effect in deep-sub-micron grooved-gate p-channel metal-oxide-semiconductor field-effect transistors (PMOSFETs) is analysed. The results show that hot carriers generated in grooved-gate PMOSFETs are much smaller than those in planar ones, especially for the case of channel lengths lying in the deep-sub-micron and super deep-sub-micron regions. Then, the hot-carrier generation mechanism and the reason why grooved-gate MOS devices can suppress the hot-carrier effect are studied from the viewpoint of physical mechanisms occurring in devices. It is found that the highest hot-carrier generating rate is at a medium gate bias voltage in three stress areas, similar to conventional planar devices. In deep-sub-micron grooved-gate PMOSFETs, the hot-carrier injection gate current is still composed mainly of the hot-electron injection current, and the hole injection current becomes dominant only at an extremely high gate voltage. In order to investigate other influences of the hot-carrier effect on the device characteristics, the degradation of the device performance is studied for both grooved-gate and planar devices at different interface states. The results show that the drift of the device electrical performance induced by the interface states in grooved-gate PMOSFETs is far larger than that in planar devices.

The positive parity collective states in the even-even ^{100}Pd-^{116}Pd isotopes are studied in the framework of the interacting boson model. A schematic Hamiltonian capable of describing their spectra and transition is used. It is found that the spectra can be well described by a U(5) plus SU(3) perturbation interaction. As the valence neutron number changes, the structure of the isotopes shows regular patterns of change. In the meantime, the behaviour of 0^{+}_{2} can also be partially described by the model.

In the absence of the requirements of the Lamb-Dicke limit and rotating wave approximation, we semi-classically investigate the dynamics of a trapped ultra-cold ion in the standing-wave laser, with the consideration of the time-dependent potential and pseudo-potential of the Paul trap. The specific calculations show that the larger the Lamb-Dicke parameter η and the Rabi frequency Ω, the greater the difference between the dynamics in the time-dependent potential and the pseudo-potential.

Based on the second-order coherence function, we have studied a phase-conjugate ultrafast modulation spectroscopy due to the interference between the fifth- and fifth-order optical polarizations in cascade three-level Doppler-broadened system. It is found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The beat signal depends on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field only affect higher than second-order coherence functions, they have little influence on the general temporal modulation behaviour of the beat signal. The cases that pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases the overall accuracy for the energy-level difference measurement is determined by the homogeneous linewidths of the optical transitions. Finally, the spatial modulation behaviour of the beat signal has also been discussed.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The nonlinear effect of ponderomotive force of high-frequency ion motion on the low-frequency motion of ions coupling with the dust density fluctuation is investigated. The nonlinear localized structure described by Zakharov equations and nonlinear Schr?dinger equation in dusty plasma are obtained. Envelope solitons for high-frequency ion motion and the dust density cavitons are also obtained and discussed.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Conditions for a self-organized formation of ordered hexagonal structure in anodic alumina were investigated, using oxalic or sulphuric acid as an electrolyte. Highly-ordered nanopore arrays with pore densities of 9×10^{9}-6.5×10^{10}cm^{-2} and high aspect ratios over 3000 were fabricated by a two-step anodization process. The array exhibits characteristics analogous to a two-dimensional polycrystalline structure of a few micrometres in size. The interpore distance can be controlled by changing the electrolyte and/or the applied voltage. The formation mechanism of ordered arrays is consistent with a previously proposed mechanical stress model, i.e., the repulsive forces between neighbouring pores at the metal/oxide interface promote the formation of hexagonally ordered pores during the oxidation process.

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

The effect of radial thickness on the thermal conductivity of a free standing wire is investigated. The thermal conductivity is evaluated using the Boltzmann equation. A simple expression for the reduction in conductivity due to the increase of boundary scattering is presented. A comparison is made between the experimental results of indium wires and the theoretical calculations. It is shown that this decrease of conductivity in wires is smaller than that in film where heat flux is perpendicular to the surface.

Numerical study of the influence of the distribution of pinning centres on the dynamics of a two-dimensional vortex system is performed. The superconductor sample has a periodic structure with a pinned region of length L_{p} and an unpinned region of length L_{x}-L_{p} along the direction of driving force (Lorentz force). Results show that, at zero temperature, the critical force F_{c} increases with the increase of L_{p}, indicating that the homogeneity of pinning centres helps to enhance the critical electric current of the superconductor. At large driving forces, vortex static channels form in the pinned region even for L_{p}x.

By using Brown-York quasilocal energy theory we calculate the quasilocal energy of a stationary axisymmetic EMDA black hole and explore the universality of Martinez's conjecture in string theory. We show that the energy is positive and monotonically decreases to the ADM mass at spatial infinity, and the Martinez's conjecture, the Brown-York quasilocal energy at the outer horizon reduces to twice its irreducible mass, is still valid for stationary axisymmetric EMDA black hole. From the result we also find that the Kerr-Sen spacetime keeps up with Martinez's conjecture. This is different from the Bose-Naing result that the quasilocal energy of the Kerr-Sen spacetime does not approach the Martinez's conjecture.

On the basis of the beaming model, we have derived a relation between the observed polarization (P^{ob}) and Doppler-corrected optical magnitude (m^{corr}), log P^{ob}=0.4(1-k) m^{corr}+C. We tested the correlation between P^{ob} and mcorr. The main results are as follows: (1) for both high and low states, there are strong correlations between Pob and mcorr for 29 RBLs with well-observed polarization and Doppler factor, where mcorr=mob+(3+α)logδ/0.4, and δ is the optical Doppler factor; (2) no correlation exists between Pob and the observed optical magnitude, mob, for the 29 RBLs in high state, but there is a close correlation for the 29 RBLs in low state; (3) however, there is an obvious anti-correlation between Pob and mcorr for 35 XBLs with good simultaneous observation data. Our results show that (i) a new difference in polarization is found between RBLs and XBLs; (ii) this difference in polarization between RBLs and XBLs seems really to be physical differences.}

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