We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.

Using the wave packet theory, we obtain all the solutions of the weakly damped nonlinear Schr?dinger equation. These solutions are the static solution, and solutions of planar wave, solitary wave, shock wave and elliptic function wave and chaos. The bifurcation phenomenon exists in both steady and non-steady solutions. The chaotic and periodic motions can coexist in a certain parametric space region.

We propose a scheme for teleporting an unknown atomic state. In order to realize the teleportation to any node in a quantum communication network, an n-atom Greenberger-Horne-Zeilinger (GHZ) state is needed, which is utilized as the quantum channel. From this n-atom GHZ state, two-node entanglement of processing and receiving teleported states can be obtained through the quantum logic gate manipulation. Finally, for the unequally weighted GHZ state, probabilistic teleportation is shown.

In this paper, the Arnowitt-Deser-Misner (ADM) constraint equations are naturally derived in two different ways. One method is to construct a one-parametric gravitational action in the Lorentzian spacetime. Hence, the one-parametric ADM constraint equations can be obtained. The other method is to apply the double complex function method to Einstein-Hilbert gravitational fields in Hamiltonian formulation. Therefore the double ADM constraint equations can be obtained, in which the well-known ADM constraint equations are included as a special case.

A numerical scheme is developed to simulate electro-osmotic flow and mass transport in a microchannel which includes a 180° turn. The model has been used to predict the behaviour of electro-osmotically driven flows. The detailed structure of the flow field in a microchannel in combination with species mass diffusion can explain the concentration dispersion introduced by a 180° turn. The results of our simulations agree both qualitatively and quantitatively with experimental observation. It is demonstrated that an improved electro-osmotic force model could simulate the electrokinetically driven flow well without making detailed calculations of the electric charge density distribution within the electrical double layer. Additionally, because this model applies forces to the liquid as opposed to imposing local velocities, it should also be appropriate for use where pressure gradients exist in the flow field.

A novel tracking control and synchronization method is proposed based upon sampled-data feedback. This method can make a chaotic system approach any desired smooth orbit and synchronize the driving system and the response system, both in the same structure and in diverse structures. Finally, a numerical simulation with a Lorenz system is provided for the purpose of illustration and verification.

We investigate theoretically the temperature effects on the evolution of both bright and dark screening-photovoltaic optical spatial solitons in biased photovoltaic-photorefractive crystals in the case of neglecting the diffusion process. For a stable bright or dark screening-photovoltaic soliton originally formed in a crystal at a given temperature, when the crystal temperature changes, it will evolve into another stable screening-photovoltaic soliton if the change is quite small, whereas it will become unstable or break down if the temperature change is large enough. The spatial shape of a stable screening-photovoltaic soliton can be reshaped by appropriately adjusting the crystal temperature.

Electromagnetically-induced transparency is observed in a three-level multi-V-type system in cesium vapour at room temperature. The absorption property is measured and the hyperfine structures of atomic states can be determined. The results of the experiment agree with the theoretical analysis.

Sputtering yields and kinetic energy distributions (KED) of Al atomic ions ejected from a pure aluminium sample under MeV silicon ion bombardment were simulated with the molecular dynamic method. Since the electronic energy loss S_{e} is much higher than the nuclear energy loss S_{n} when the incident ion energy is as high as several MeV, the S_{e} effect was also taken into consideration in the simulation. It was found that the simulated sputtering yield fits well with the experimental data and the electronic energy loss has a slight effect at incident ion energies higher than 4 MeV. The simulated secondary ion KED spectrum is a little lower in the peak energy and narrower in the peak width than that in the experiment.

There is a type of nodal surface imposed by symmetry on wavefunctions. These surfaces are crucial to the ordering of low-lying states. Based on an analysis of this type of surface and based on existing theoretical results, the feature of the low-lying spectrum of the He-tetramer is studied, and the candidates of bound states and narrow resonances are suggested.

We discuss the formation of matter structures in the Universe, and show that spherical Higgs bosonic membranes were possibly produced homogeneously in the early Universe and expanded rapidly. After a period of evolution, the composition of the membranes began to change, the massive particles replaced the imaginary Higgs bosons through the Higgs mechanism, while the energy came from the Universe expansion. After that, the membranes reduced their speed and broke into pieces, which became the seeds of matter structures. It is proven that microscopic principles may affect the formation of large-scale structures, and the formation of structures such as cosmic foam is also possible.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

We have used optical emission spectroscopy to characterize the high-voltage pulsed discharge of ammonia. Ammonia was highly dissociated in the discharge at low pressures. More atomic nitrogen was generated as compared to the discharge of nitrogen gas at the same pressure of 0.8kPa. We discuss the elimination of the oxygen impurity in the ammonia discharge, and we estimate the time-dependent atomic excitation temperature and the electron density from the measured spectra.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.

Molybdenum ions are implanted into aluminium with high ion flux and high dose at elevated temperatures of 200℃, 400℃ and 500℃. Due to the high temperature and high flux of vacancies and interstitial atoms, the atom diffusion and chemical effects are enhanced during the ion implantation. The effects increase with increasing ion flux and dose, so that new phase formation and phase transition emerge noticeably. X-ray diffraction analysis shows that when the aluminium is implanted with Mo ions at a low ion flux (25μA/cm^{2}), the Al_{5}Mo alloy is formed. The atomic ratio of Mo/Al of the Al_{5}Mo phase is close to 20%. When the aluminium is implanted with Mo ions at a high ion flux (50μA/cm^{2}), the phase transition from Al_{5}Mo to Al_{12}Mo appears, and the latter is dominant, which is determined to be the final phase. The ratio of Mo/Al in Al_{12}Mo is 7.7%. Rutherford backscattering spectroscopy indicates also that the Mo/Al atom ratio is ～7% to ～8% in Mo-implanted aluminium. The atomic ratios of the constituents in Al_{5}Mo and Al_{12}Mo are of stoichiometric composition for these alloys. The thicknesses of the Al_{12}Mo alloy layers for Mo-implanted Al with ion doses of 3×10^{17}/cm^{2} and 1×10^{18}/cm^{2} are 550nm and 2000nm, respectively. The pitting corrosion potential V_{p} increases obviously. It is clear that due to the formation of Al_{12}Mo alloy layer, the pitting corrosion resistance is enhanced.

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

A new type of partial-dielectric-loaded helical groove slow-wave structure (SWS) for millimetre wave travelling wave tube (TWT) is presented in this paper. The radio-frequency characteristics including the dispersion properties, the longitudinal electric field distribution and the beam-wave coupling impedance of this structure are analysed. The results show that the dispersion of the helical groove circuit is weakened, the phase velocity is reduced and the position of the maximum E_{z} is moved from the mouth to the inside of the groove after partially filling the dielectric materials in the helical groove SWS. Therefore, the dielectric-loaded helical groove SWS is suitable for a multi-beam TWT with broad band and high gain.

The in-plane electrical resistivity and thermoelectric power have been measured on single crystals of La_{2-x}Ba_{x}CuO_{4} at around x=0.125. The room temperature resistivity and thermopower have their maximum values at x=0.125, indicating that the carrier concentration is the minimum and the carriers are most strongly localized at x=0.125. The observed semiconductor-like behaviour can be well described by the weak-localized quasi-two-dimensional state. The steep rise in electric resistivity of the sample at x=0.125 below 70K is attributed to the formation of static stripe-order of holes and spins, which are pinned by the low-temperature tetragonal (LTT) structure, as discovered in La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4}. The temperature dependence of electric resistivity below 70K is still well described by the formula ρ∝ lnT. A definite change in the slope of thermopower is observed at the low-temperature orthorhombic-LTT structural phase transition temperature. The origin of the 1/8 anomaly is discussed in the text.

We have found phase separation in La_{0.45}Sr_{0.55}MnO_{3-δ} (LSMO) by means of electron spin resonance, magnetic force microscopy (MFM) and magnetic measurements. Ferromagnetic and antiferromagnetic phases can coexist at low temperatures, and ferromagnetic and paramagnetic phases coexist when the temperature lies between the Néel and Curie temperatures. The size and shape of the ferromagnetic phases (the minority phases) was first observed directly from MFM images. It is suggested that the phase separation in LSMO is not the charge segregation type, but an electroneutral type due perhaps to the nonuniform distribution of oxygen vacancies.

In this paper, the crystallization behaviour of amorphous Ge_{2}Sb_{2}Te_{5} thin films is investigated using differential scanning calorimetry), x-ray diffraction and optical transmissivity measurements. It is indicated that only the amorphous phase to face-centred-cubic phase transformation occurs during laser annealing of the normal phase-change structure, which is a benefit for raising the phase-change optical disk's carrier-to-noise ratio (CNR). For amorphous Ge_{2}Sb_{2}Te_{5} thin films, the crystallization temperature is about 200℃ and the melting temperature is 546.87℃. The activation energy for the crystallization, E_{a}, is 2.25eV. The crystallization dynamics for Ge_{2}Sb_{2}Te_{5} thin films obeys the law of nucleation and growth reaction. The sputtered Ge_{2}Sb_{2}Te_{5} films were initialized by an initializer unit. The initialization conditions have a great effect on the reflectivity contrast of the Ge_{2}Sb_{2}Te_{5} phase-change optical disk.