The differential equations of motion of a relativistic variable mass system are given. By using the invariance of the differential equations under the infinitesimal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built, and the structure equation and the conserved quantity of the Lie symmetries are obtained. Then the inverse problem of the Lie symmetries is studied. The corresponding Lie symmetries are found according to a known conserved quantity. An example is given to illustrate the application of the result.

In this paper, we extend the well-known direct method proposed by Clarkson and Kruskal for finding similarity reductions of partial differential equations. It follows that some new similarity reductions of the generalized Burgers equation, such as travelling wave reduction, logarithmic reduction, power reduction, rational fractional reduction, etc, are derived, in which some of these cannot be obtained solely by using the direct method. The similarity reductions obtained are interpreted by the nonclassical symmetry Lie group.

We establish the double complex Ashtekar gravitational theory with the cosmological term. In particular, by performing the 3+1 decomposition of the double Ashtekar action containing the cosmological term to pass on the Hamiltonian framework, the double Ashtekar constraint equations are derived, which respectively correspond to Lorentzian and Euclidean gravity.

In this paper we discuss the reality conditions for Lorentzian and Euclidean gravity in the Ashtekar formulation by introducing a double conformal transformation. We generalize Marugan's results and demonstrate that the values of the double conformal factor have to be either real or double complex numbers. Either Lorentzian or Euclidean gravitational theory is up to the different values of the double conformal factor. Furthermore, the reality conditions of Lorentzian and Euclidean gravitational theory can be expressed in a unified way by use of the double complex function method.

In this paper, we present a general M?bius inversion transform formula for hcp lattices. This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy. Also, the three-body interaction among atoms in the lattices can be taken into account in the method. This method gives a useful means to obtain interatomic interactions in the interatomic force model. The method has been applied to zinc, and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions. It is found that, by properly considering a three-body interaction, one can acquire satisfactory results.

With the application of a Wigner function description of a two-mode squeezed state, we study a protocol of continuous variable entanglement swapping in a noisy quantum channel. Assuming that the two initial entangled states are coupled with the same environment, we analyse the quantum state emerging from the swapping and obtain the inseparable condition for the output correlation. It is found that there is more noise resulting from the entanglement swapping than from the direct transmission, no matter what values of displacement gain are chosen.

We have studied theoretically constructive interference via collision-aided radiative excitation in an open four-level system using a density matrix approach. The four-level system consists of a Λ-type three-level quantum-beat configuration driven by one laser field and a fourth level coupled by a vacuum mode. It is shown that through the incoherent process (collision), coherence between widely-separated doublets and subsequent constructive interference can be realized. We analyse the effects of the collision-induced coherent and incoherent decay rates, laser intensity, and energy separation of the doublets on the interference. Meanwhile, the constructive interference between the two transition pathways 3P_{1/2}-4D and 3P_{3/2}-4D via equal-frequency hybrid excitation and collision-aided radiative excitation in an Na_{2}-Na system is experimentally observed. A good agreement between the theoretical and experimental results is obtained.

In this paper, we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres. Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion, while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion. Moreover, there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression. Redshifted initial chirp is helpful to the pulse compression, while blueshifted chirp is detrimental to the pulse compression. There is also an optimal chirp parameter to reach maximum pulse compression. The optimal pulse compression for TOD parameters under different N-order solitons is also found.

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_{inv}(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_{nz}. E has a minimum as L_{nz} increases up to the maximum no matter what the values of P, M and ε. The E～ L_{nz} curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).

The dephasing time of a positron in the total field associated with a laser pulse in a plasma J28is studied numerically. It is shown that the dynamics of the positron is quite different from that of an electron due to the electrostatic potential in the body of the pulse. The dephasing time of the positron increases with the pulse length and decreases with the pulse intensity nonlinearly. In the long pulse case (L》λ_{p}) the dephasing time is proportional to the pulse length. These results provide a scientific basis for experiments to observe the positron acceleration scheme, and may be important to the physics of laser-article interactions in multi-component plasmas.

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

The superconducting transition of a YBCO film was measured by a MPMS-5 superconducting quantum interference device magnetometer, using a zero-field cooling process. The experimental results have shown that there are positive magnetic moment and positive peak on the M－T curve. We have proven that these anomalous behaviours are due to measurement error, but not phase transition. We have proposed a simple formula to explain and to calculate quantitatively these anomalous behaviours. It was found that, provided dH>0.59H_{p} (dH is the inhomogeneous field of the remnant field, H_{p} is the fully penetrated field of the measured sample), the experimental results will be positive, not negative. If dH≥2H_{p}, the experimental results will be symmetrical to their real negative values. From the M－T curve, which has positive moment and positive peak below T_{c} (superconducting transition temperature), we found a new possible method to obtain H_{p} of the measured sample.

A transverse ferromagnetic spin-1 system with a random single-ion anisotropy is considered in the framework of an Ising model. The effective field theory and decoupling approximation are applied to the derivation of the expressions of magnetizations for a honeycomb lattice. Special emphasis is placed on the critical properties of the system. New critical properties are obtained in a certain range of single-ion anisotropy, random concentration, and transverse field. We discuss in detail the influence of the random concentration and transverse field on the critical properties. Some phenomena have not been discovered in previous reports. Detailed descriptions of the phase transition and magnetization curves are presented.

Based on the translational invariance of a medium, a new theorem has been proposed and proved rigorously: the depth distributions of the deposited energy, momentum and ion range must be infinitely differentiable functions in amorphous or polycrystalline infinite targets by ion bombardment, if these functions exist. The origin of the "discontinuity", derived by Dr Glazov in 1995 in J. Phys.: Condens. Matter 7 6365, has been analysed in detail. For the power cross section, neglecting electronic stopping, the linear transport equations determining the depth distribution functions of the deposited energy and momentum (by taking the threshold energy into account) have been solved asymptotically. An important formula derived by Dr Glazov has been confirmed and generalized. The results agree with the new theorem.