The weakly nonlinear boundary value problem of wave propagation in an optical fibre (for the transverse electric mode, for example) is formulated and a modified linear solution is obtained. It is shown that a self-consistent theory of fibre optics should be weakly nonlinear. The mode of critical refraction that does not exist in the linear theory is obtained, showing that it is a mode consisting of resonance modes. It is shown that the signal carriers in a long fibre are of resonance modes, not normal modes. Some experimental data are given for comparison with the theoretical predictions, and the agreement seems satisfactory.

In this paper, we present a general approach to the construction of conservation laws for generalized classical dynamical systems. Firstly, we give the definition of integrating factors and, secondly, we study in detail the necessary conditions for the existence of conserved quantities. Then we establish the conservation theorem and its inverse for the Hamilton's canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics. Finally, we give an example to illustrate the application of the results.

Seeking a travelling wave solution of the classical Boussinesq system and making an ansatz for the solution, we obtain a nonlinear system of algebraic equations. We solve the system using an effective algorithm and then two general explicit solutions are obtained which are of physical interest.

We propose two schemes for teleporting an unknown state. In our schemes, a three-particle Greenberger－Horne－Zeilinger state is used as a quantum channel. We show that the probabilistic teleportation of an unknown quantum state can be realized.

We propose two schemes for teleporting an arbitrary three-particle state. In the first scheme, a two-particle state and a three-particle entangled state (both non-maximally entangled states) are used as quantum channels, while in the second scheme, three non-maximally entangled particle pairs are employed as quantum channels. We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations. Their success probabilities and the classical communication costs are different.

A parametrically excited oscillator with strong nonlinearity, including van der Pol and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt－Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_{m}/B_{0} in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.

Close coupling calculations have been carried out for rotational excitations in He－H_{2} collisions with symmetric isotopic substitution (He－H_{2}, D_{2}, T_{2}) and asymmetric isotopic substitution (He－HD, HT, DT). Cross sections have been obtained at the incidence energy of 0.3eV. Based on the calculations, the effect of isotopic substitution on atom－diatom collisions is discussed.

We propose the formation mechanism of the body-centred regular tetrahedral structure of the He^{+}_{5} cluster. The total energy curve for this structure has been calculated by using a modified arrangement channel quantum mechanics method. The result shows that a minimal energy of -13.9106 a.u. occurs at a separation of 1.14a_{0} between the nucleus at the centre and nuclei at the apexes. Therefore we obtain the binding energy of 0.5202 a.u. for this structure. This means that the He^{+}_{5} cluster may be stable with a high binding energy in a body-centred regular tetrahedral structure.

A virtual probe is a novel immaterial tip based on the near-field evanescent wave interference and small aperture diffraction, which can be used in near-field high-density optical data storage, nano-lithography, near-field optical imaging and spectral detection, near-field optical manipulation of nano-scale specimen, etc. In this paper, the formation mechanism of the virtual probe is analysed, the evanescent wave interference discussed theoretically, and the sidelobe suppression by small aperture is simulated by the three-dimensional finite-difference time-domain method. The simulation results of the optical distribution of the near-field virtual probe reveal that the transmission efficiency of the virtual probe is 10^{2}－10^{4} times higher than that of the nano-aperture metal-coated fibre probe widely used in near-field optical systems. The full width at half maximum of the peak, in other words, the size of virtual probe, is constant whatever the distance in a certain range so that the critical nano-separation control in the near-field system can be relaxed. We give an example of the application of the virtual probe in ultrahigh-density optical data storage.

We have investigated the position-dependent dynamics of a trapped ion in a standing wave laser by transforming it to the Jaynes－Cummings-type system under the Lamb－Dicke limit. A variety of novel phenomena are exhibited, e.g. periodic collapse and revival features and long-time scaled revivals of the ionic inversion, depending on its position in the standing wave. Our result provides a way of producing a system equivalent to the two-photon Jaynes－Cummings model in the trapped ion system, with its exact periodicities.

We demonstrate a new kind of instability of the external cavity semiconductor laser. In some parameter regimes, the external cavity system will produce short and strong optical pulses in aperiodic intervals. This instability also shows low-frequency characteristics.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The conformation of polystyrene in the anti-solvent process of supercritical fluids (compressed CO_{2} + polystyrene + toluene) has been studied by small angle x-ray scattering with synchrotron radiation as an x-ray source. Coil-to-globule transformation of the polystyrene chain was observed with the increase of the anti-solvent CO_{2} pressure; i.e. polystyrene coiled at a pressure lower than the cloud point pressure (P_{c}) and turned into a globule with a uniform density at pressures higher than P_{c}. Fractal behaviour was also found in the chain contraction, and the mass fractal dimension increased with increasing CO_{2} pressure.

In the work reported in this paper, we have used a low-temperature scanning tunnelling microscope (LT-STM) system to manipulate accurately single atoms. We show how we can use a LT-STM to image and modify a bulk Ag(111) surface and manipulate Ag atoms from substrate and evaporated adsorbates on Ag(111) substrates. We present a synergistic combination of STM-induced modification and ordered arrays of nanometre-scale structures. In particular, we demonstrate the ability to modify Ag atomic nanometre structures on the Ag(111) substrate, and some English letters and a Chinese character can be written by single Ag atoms coming from the substrate and evaporated adsorbates on Ag(111). In this way, we supply an effective basis to explore the fundamental physical properties of a nanometre structure and to develop nanotechnology with a `bottom-up' approach.

Silicon nanowires have been grown by the thermal decomposition of silane via the vapour－liquid－solid (VLS) mechanism. Three different stages of VLS growth (eutectic alloy formation, crystal nucleation and unidirectional growth) were studied separately using a scanning electron microscope and a high-resolution transmission electron microscope. Very short silicon nanowires prepared under particular conditions provide direct evidence of the VLS mechanism on a nanometre scale. Our results will be very helpful for the controllable synthesis of Si nanowires.

The universality principle of the free energy density functional and the ‘test particle' trick by Percus are combined to construct the approximate free energy density functional or its functional derivative. Information about the bulk fluid radial distribution function is integrated into the density functional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum density functional theory.

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

Based on the free-electron approximation, we investigate the effect of the ferromagnetic metal layer on the tunnelling magnetoresistance (TMR) and tunnelling conductance (TC) in the double magnetic tunnel junctions (DMTJs) of the structure NM/FM/I(S)/NM/I(S)/FM/NM, where FM, NM and I(S) represent the ferromagnetic metal, nonmagnetic metal and insulator (semiconductor), respectively. The FM, I(S) and inner NM layers are of finite thickness, while the thickness of the outer NM layer is infinite. The calculated results show that, due to the spin-dependent interfacial potential barriers caused by electronic band mismatch between the various magnetic and nonmagnetic layers, the dependences of the TMR and TC on the thicknesses of the FM layers exhibit oscillations, and a much higher TMR can be obtained for suitable thicknesses of FM layers.

Numerical and analytical results are presented for the magnetic ordering in a bond-diluted spin-1/2 and spin-1 mixed transverse Ising system with a single-ion anisotropy on a honeycomb lattice. Special emphasis is placed on the magnetic ordering under the bond dilution and percolation threshold. We discuss in detail the influence of transverse fields of different sublattices on the normal magnetic ordering and on the magnetic ordering induced by single-ion anisotropy. We find that the magnetic ordering of a system exhibits an explicit difference when receiving the transverse field. This phenomenon has not been revealed in previous reports.

A novel read-only super-resolution optical disc structure (substrate/mask layer/dielectric layer) is proposed in this paper. By using a Si thin film as the mask layer, the recording pits with a diameter 380nm and a depth 50nm are read out on the dynamic measuring equipment; the laser wavelength α is 632.8nm and the numerical aperture is 0.40. In the course of reproduction, the laser power is 5mW and the rotation velocity of the disc is 4m·s^{-1}. The optimum thickness of the Si thin film is 18nm and the signal-to-noise ratio is 32dB.

The mechanism of carrier transport in organic light-emitting devices is numerically studied, on the basis of trapped-charge-limited conduction with an exponential trap distribution. The spatial distributions of the electrical potential, field and carrier density in the organic layer are calculated and analysed. Most carriers are distributed near the two electrodes, only a few of them are distributed over the remaining part of the organic layer. The carriers are accumulated near the electrodes, and the remaining region is almost exhausted of carriers. When the characteristic energy of trap distribution is greater than 0.3 eV, it leads to a reduction of current density. In order to improve the device efficiency, organic materials with minor traps and low characteristic energy should be chosen. The diffusion current is the dominant component near the injection electrode, whereas the drift current dominates the remaining region of the organic layer.

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