Using the φ-mapping method and topological current theory, we study the inner structure of disclination points in three-dimensional liquid crystals. By introducing the strength density and the topological current of many disclination points, it is pointed out that the disclination points are determined by the singularities of the general director field and they are topologically quantized by the Hopf indices and Brouwer degrees.

The behaviour of electrons during electron-assisted chemical vapour deposition of diamond is investigated using Monte Carlo simulation. The electron energy distribution and velocity distribution are obtained over a wide range of reduced field E/N (the ratio of the electric field to gas molecule density) from 100 to 2000 in units of 1Td=10^{-17}Vcm^{2}. Their effects on the diamond growth are also discussed. The main results obtained are as follows. (1) The velocity profile is asymmetric for the component parallel to the field. The velocity distribution has a peak shift in the field direction. Most electrons possess non-zero velocity parallel to the substrate. (2) The number of atomic H is a function of E/N. (3) High-quality diamond can be obtained under the condition of E/N from 50 to 800Td due to sufficient atomic H and electron bombardment.

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo－Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff－Birkhoff－D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given.

In this paper we present the variational equations of constrained Birkhoffian systems and study their solution. It is proven that, under some conditions, a particular solution of variational equations can be obtained by using a first integral. At the end of the paper, an example is given to illustrate the application of the results.

Chaotic behaviour in a second-order autonomous Birkhoff system with a heteroclinic circle under weakly periodic perturbation is studied using the Melnikov method. The equations of heteroclinic orbits and the criteria for chaos are given. One example is also presented to illustrate the application of the results.

Noether's theory of a rotational relativistic variable mass system is studied. Firstly, Jourdain's principle of the rotational relativistic variable mass system is given. Secondly, on the basis of the invariance of the Jourdain's principle under the infinitesimal transformations of groups, Noether's theorem and its inverse theorem of the rotational relativistic variable mass system are presented. Finally, an example is given to illustrate the application of the result.

By making use of the theoretical framework presented by Bostroem (K. J. Bostroem, LANL quant-ph/0009052), we generalize the standard quantum information theory of block messages with fixed block length to the variable one. We show that the states belonging to a sufficiently large Hilbert space are the highly distinguishable states. We also consider the collection states (product states of more than one qubit state) and seek a "pretty good measurement"(PGM) with measurement vectors to improve the mutual information. The average mutual information over random block-message ensembles with variable block length n is discussed in detail.

A new approach to the numerical solution of normal mode problems in underwater acoustics is presented, in which the corresponding normal mode problem is transformed to the problem of solving a dynamic system. Three applications are considered: (1) the broad band normal mode problem; (2) the range-dependent problem with perturbation proportional to the range parameter; and (3) the evolution of the normal mode with environmental parameters. A numerical simulation for a broad band problem is performed, and the calculated eigenvalues have good agreement with those obtained by the standard normal mode code KRAKAN.

We have investigated the interaction of an electromagnetic (EM) wave with a standing gravitational wave (GW) in an external static magnetic field, and obtained concrete forms of first-order perturbative EM energy fluxes. Unlike the propagating properties of the "left-circular" and "right-circular" waves of the tangential perturbative energy fluxes around the symmetrical axis, the radial perturbative energy fluxes are expressed as the outgoing and imploding waves to the symmetrical axis. We also examine several physical examples and show that this effect can produce very small but nonvanishing radial perturbative photon fluxes. This may be useful for EM detection of the high-frequency relic GWs of the GHz region in quintessential inflationary models.

We have obtained a k-quantum nonlinear Jaynes－Cummings model for two trapped ions interacting with laser beams resonant to the kth red side-band of the centre-of-mass mode, far from the Lamb－Dicke regime. The exact analytic solution shows the existence of quantum collapses and revivals of the occupation of two atoms.

Using the adiabatic approximation and adiabatic variational approximation with an effective potential, the total energies and the equilibrium internuclear separations of H_{2}^{+} ion in states σ_{g}, π_{u}, δ_{g}, φ_{u}, γ_{g}, η_{u} in strong magnetic fields have been calculated. Our results reproduced those obtained by Vincke and Baye (Vincke M and Baye D 1985 J. Phys. B: At. Mol. Phys. 18 167), which are considered the most reliable. We found a basic function with better convergence than the Landau functions.

A single microscopic magnetic trap for neutral atoms using planar current-carrying wires was proposed and studied theoretically by Weinstein et al. In this paper, we propose three structures of composite current-carrying wires to provide 1D, 2D and 3D arrays of microscopic magnetic traps for cold alkali atoms. The spatial distributions of magnetic fields generated by these structures are calculated and the field gradient and curvature in each single microtrap are analysed. Our study shows that arrays of microscopic magnetic traps can be used to provide 1D, 2D or 3D atomic magnetic lattices, and even to realize 1D, 2D and 3D arrays of magneto-optical traps, and so on.

The laser-induced fluorescence excitation spectrum of the A^{2}Σ^{－}X^{2}Π_{3/2} transition of CuO in the 540－620nm region has been studied, where the CuO molecule was produced by using the technique of dc discharge reaction under a supersonic condition. We have recorded and rotationally analysed the 0－0, 1－0, 2－0 and 3－0 bands. The rotational constants of the upper state A^{2}Σ^{-} were determined and vibrational constants improved. In addition, the lifetime measurement for the A^{2}Σ^{-} state was carried out under the collision-free condition, and the lifetimes obtained are 469±2, 456±2, 488±3 and 490±4ns for v'=0, v'=1, v'=2 and v'=3 levels, respectively.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

A novel pulsed rapid thermal processing (PRTP) method has been used for realizing solid-phase crystallization of amorphous silicon films prepared by plasma-enhanced chemical vapour deposition. The microstructure and surface morphology of the crystallized films were investigated using x-ray diffraction and atomic force microscopy. The results indicate that PRTP is a suitable post-crystallization technique for fabricating large-area polycrystalline silicon films with good structural quality, such as large grain size, small lattice microstrain and smooth surface morphology on low-cost glass substrates.

We have investigated the morphology and microstructure of carbon nanotubes and nanoparticles in cathode deposits prepared by self-sustained arc discharge. Scanning electron microscopy images indicate that there are two regions exhibiting different morphologies on the top surface of the cathode deposits. In the central region, there is a triangular pattern of spots with a diameter up to 100μm, which consists of carbon nanotubes and nanoparticles. In the fringe region, carbon nanotubes and nanoparticles are distributed randomly. In addition, carbon nanotubes in the central region have a larger inner diameter, compared with those in the fringe region. The outer diameter distribution of tubes in the central region is narrower than that of tubes in the fringe region, while the former has a smaller peak value than the latter. For the nanoparticles, they exhibit a different behaviour from the tubes existing in the same region. The difference between the microstructure of tubes or particles in the two regions is attributed to the different temperatures and temperature gradients during their formation.

A method in which nanometre-thick film deposition was alternated with hydrogen plasma annealing (layer-by-layer method) was applied to fabricate hydrogenated amorphous carbon films in a conventional plasma-enhanced chemical vapour deposition system. It was found that the hydrogen plasma treatment could decrease the hydrogen concentration in the films and change the sp^{2}/sp^{3} ratio to some extent by chemical etching. Blue photoluminescence was observed at room temperature, as a result of the reduction of sp^{2} clusters in the films.

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

New experimental evidence that a switch controls the reduction of the heme a_{3}－Cu_{B} binuclear centre has been observed in the N_{2}-dried thin film of purified cytochrome oxidase. When immersing the enzyme film into the acid phosphate buffer with extremely low concentration of dithionite, a spectrum was given to show a reduction of heme a with no electrons resting on Cu_{A}. By increasing dithionite, electrons could be accumulated gradually on Cu_{A}, but the binuclear centre still remains in the oxidized state. When the accumulation of electrons on Cu_{A} and/or heme a exceeded a threshold, a turnover of reduction of the binuclear centre and oxidation of heme a occurred abruptly. This switch-like action is pH-dependent.