The one-dimensional time-independent Schrödinger equation is transformed into a Hamiltonian canonical equation by means of the Legendre transformation, then the symplectic schemes and a new shooting method extended to the eigenvalues of the Schrödinger equation. The method is applied to the calculations of one-dimensional harmonic oscillator, an anharmonic oscillator and the hydrogen atom. The numerical results are in good agreement with the exact ones.

Using the basic ingredient of supersymmetry, we present a general procedure for the treatment of quantum states having nonzero angular momenta.

A scheme is proposed to implement a universal quantum cloning machine with atoms trapped in an optical cavity. In the scheme the atoms are always populated in the two ground states and the cavity remains in the vacuum state. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay.

By numerically analysing the entropy of entanglement of the output state from a Mach--Zehnder interferometer for the two-mode squeezed vacuum state input, it is found that if the internal phase shift of the interferometer is adjusted to the value of 0 or π, the entangling characteristic of the input state is efficiently preserved at the output. If the internal phase shift is tuned to the value of π, the two-mode squeezed vacuum state is completely disentangled at the output of the setup. If the internal phase shift deviates from the above values, the input state is degraded into a partially entangled output state. Based on these results, a method for optically realizing the entanglement preservation, entanglement degradation, and disentanglement via the interferometer is obtained.

Complete synchronization of coupled Hindmarsh--Rose (HR) neurons with a ring structure is studied. The criterion for complete synchronization of coupled neurons with the ring structure is obtained through the stability analysis of the linearized synchronization error system. Numerical simulation is given to test the criterion for a system with three coupled HR neurons.

Introducing an explicit expression of gauge transformation turning the spin in linear order of spectral parameter in the first Lax pair into the third axis in spin space, we derive the required Hamiltonian
ensities for the spin chain with the easy axis, easy plane, and full anisotropy, respectively.

Catastrophic phenomena such as earthquakes, avalanches, and critical points in the stock market are hard to predict. Recently, Xia et al. [Pure Appl. Geophys. 159(2002)2491] showed that a geometrical system near catastrophic rupture presents a general critical sensitivity: the system becomes significantly sensitive near the catastrophe transition. Here we report that the phenomenon of critical sensitivity also exists in small-world network systems. With the increase of the small-world rewiring probability p, from the regular network p=0 to the random one p=1, the system performs more sensitively before the critical point while remaining in better organization through the evolutional progress, and the prediction threshold P_s performs more in advance. The concept of critical sensitivity can be applied to other complex network systems.

Based on the Dyson-Schwinger approach, we propose a new method for calculating vacuum susceptibilities. As an example, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is presented.

The total reaction cross sections (TRCSs) of ²⁹S+²⁸Si have been measured at intermediate energies. An obvious enhancement in TRCS of ²⁹S is observed as compared with its neighbouring nuclei. The TRCSs of ²⁹S+²⁸Si are calculated with the modified Glauber theory in the optical limit and few-body approaches. The different factor d as a possible measure of halo appearance is deduced from the experimental and theoretical data. It is well accepted that ²⁷P is a proton halo nucleus. Although not as anomalous as ²⁷P, the different factor d of ²⁹S is obviously larger than that of its neighbouring isotones of N=13. This result indicates that a moderate proton halo may exist in ²⁹S nucleus. We calculate the total reaction cross sections for ²⁹S with the modified Glauber theory as a function of incident energy and compare the results with those for ²⁷Si which is a core nucleus of ²⁹S. The measured TRCSs of ²⁷Si+²⁸Si can be described to be satisfactory by the modified Glauber theory of the optical limit approach. Although a diffused nuclear density distribution is used, the theories still inadequately predict the experimental TRCSs of ²⁹S+²⁸Si, which further indicates the possibility of proton halo in²⁹S.

Considering the nuclear motion, we present the nonrelativistic ground energy of a helium atom by using a simple effective variational wavefunction with a flexible parameter k. Based on the result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338a.u. with the relative error 0.00034%.

Synthesis and photoelectric properties of a high soluble zinc phthalocyanine--epoxy derivative are investigated. The derivative can be solubilized in convenient solvents, such as CH₃OH, CH₃CH₂OH and H₂O. The fluorescence and UV-visible analyses indicate that the ZnPc--epoxy derivative still maintains the plane structure which comes from Zn(4,4^',4^'',4^''' -ta)Pc and the derivative has obvious up-conversion luminescence in room temperature. The up-conversion luminescence can be explained by the selection rule depending on the two-photon absorption.

Radiative lifetime measurements were performed by time-resolved laser-induced fluorescence (LIF) technique for eight even-parity levels of the astrophysically important ion Er⁺ over the energy range from 33753 to 55317 cm^-1. Free erbium ions were generated by a laser-induced plasma. A narrow bandwidth UV laser pulse (1ns) was employed to populate selectively the short-lived upper levels, and the lifetime value were evaluated from the time-resolved fluorescence signals. The lifetimes reported fall in the range of 3-35ns with the experimental accuracy 5-8%.

Using the R-matrix method, we carry out theoretical calculations for recombination line λ 8794Å(3d'-3p') of C_II, which is important to estimate the abundances of carbon in planetary nebulae. Our calculations are based on three sets of target orbital basis, through which we elucidate the electron correlation and static polarization effects in the dielectronic recombination processes.

We study high-order harmonic generation (HHG) in an intense laser pulse when the initial state is prepared as a coherent superposition of the ground and first excited states. By examining the populations of these states for different laser intensity regions, the role of the excited state in the harmonic generation process can be identified. We also find that high conversion efficiency and high cutoff frequency of HHG can be achieved if the intensity of the laser pulse is high enough to cause considerable ionization of the first excited state but not sufficient to ionize the ground state.

A novel tri-branched copolymer is synthesized to show strong two-photon absorption and intense two-photon absorption induced fluorescence emission under the excitation of the femtosecond laser pulses at wavelength of 800nm. The dynamics of the excited state was measured by the pump-probe technique. In a one-colour pump-probe experiment at 800nm, there was an ultrafast transient absorption, followed by other two relaxation processes. The two-photon absorption process could be one origin for this ultrafast photoabsorption signal, which was further proven by two-colour pump--probe experiments. The other two decaying processes in the transient absorption dynamics have lifetime of about 15ps and 129ps, which reflect the intraband vibrational relaxation and the decay of two-photon excited state, respectively.

Electron scattering from spherical polyatomic molecules in the intermediate and high energy range is studied by employing the developed semi-empirical formula for electron scattering from simple diatomic molecules. The total cross sections of electron scattering from CF₄ and CCl₄ are obtained over the incident energy range 30-5000eV. The quantitative total cross sections are compared with the measurements and with the other calculations wherever available including the results derived from the additivity rule model and the correlated optical potential [Chin. Phys. Lett. 21 (2004) 474], and good agreement is obtained over the incident energy range 30--5000eV. It is shown that the calculations derived from the semi-empirical formula are much closer to the measurements than other calculations. Finally, some quantitative information of the single Yukawa potential is also obtained.

Electron correlation in triple differential cross sections for ionization of atomic hydrogen by electron impact is analysed for the case of coplanar asymmetric geometry within the framework of the two-potential formulae. Based on the approximations of projectile and faster-electron plane wave, the transition matrix element is analytically expressed to be a product of two factors: the correlation factor of two electrons in the final channel and the structure-scattering factor. The contribution of both the factors to the angular distribution of the triple differential cross section is calculated. The present results are compared with the experimental data and the other theoretical calculations for the incident energy of 150eV.

We investigate the nonlinear blind equalization for volume holographic data storage channel. Base on the recurrent neural network channel model, we describe a novel blind equalizer for the volume holographic data storage system to improve the bit error rate and hence to make the storage densities achievable. The experimental results also indicate that a significant improvement in the bit error rate to 2.55×10³ is possible with the nonlinear blind equalization.

Following the recent proposal by Solano E et al. [Phys. Rev. Lett. 87 (2001) 060402] a procedure is proposed to generate arbitrary discrete multicomponent motional coherent and squeezed coherent states of N trapped ions by additionally using a dispersive bichromatic interaction in a long-living and fast way. In this procedure, two lasers in the Raman configuration are tuned quasiresonant and resonant with N two-level ions under different conditions, respectively. Furthermore, we show how the idea can be used for the generation of two-mode SU(2) Schrödinger cat states for the vibrational motion of a single ion trapped in a two-dimensional harmonic potential.

A theoretical approach is proposed to deal with the detuning between the atom and cavity field in the one-photon mazer. Our starting point is to find a conserved quantity, which is characteristic of the atom plus field system. Resorting to this characteristic conserved quantity, we separate the Hamiltonian into two independent parts and then solve the Schrödinger equation of quantum scattering of an incident cold atom. We investigate the detuning effects on the one-photon induced emission probability and obtain some distinct results in contrast to the previous work.

Resonance peak spectral splitting (RPSS) in the intensity modulation of a hybrid soliton pulsed source, where fibre Bragg gratings are used as an external cavity, can be suppressed by introducing a suitable linear chirp rate in a Gaussian apodized grating. Antireflection-coated reflectivity and gain suppression factor does not strongly affect the RPSS.

Gain spectra and corresponding optical signal-to-noise ratio (OSNR) for bi-directional multi-pump Raman amplifiers are optimized and compared. Numerical results exhibit that, for optimizing bi-directional multi-pump configurations, there are multiple global maxima for signal gain spectra, and different bi-directional pump cases have different gain ripple and noise performance. Bi-directionally pumping schemes with suitable pump spectra can obviously decrease the gain ripple and equalize the OSNR tilt in comparison with pure backward pumping schemes.

Novel lead-bismuthate glasses with low OH concentration have been obtained in the Bi₂O₃-PbO-SrO system. The role of the different components in the glass formation has been explored from the density, refractive index measurements, indicating that the physical properties are mainly affected by Bi₂O₃ and PbO contents. The densities and refractive indices of these glasses are in the ranges of 7.639--7.699g/cm³ and 2.47--2.94, respectively. A wide transmitting window from visible to infrared (IR) regions and good thermal stability for some compositions of these glasses have been observed, which make them appealing candidates for different optical applications such as upconverting phosphors, new laser materials, optical waveguides and crystal-free fibre drawing.

Relying on the huge group velocity dispersion available in photonic crystal (PC) waveguides, we observe the formation of both Bragg grating solitons and gap solitons in nonlinear PC waveguides in numerical experiments. Also, we indicate the potential applications of optical solitons in optical limiting, optical delay, and pulse compression and the feasibility of observing optical solitons in practical experiments.

The self-adaptive focusing of the time reversal in anisotropic media is studied theoretically and experimentally. It is conducted for the compressional wave field in the cubic crystal silicon. The experimental result is in agreement with our theoretical analysis. The focusing gain and the displacement distributions of the time reversal field are analysed in detail. It is shown that the waves from different elements of the transducer array arrive at the original place of the source simultaneously after the time reversal operation. The waveform distortions caused by the velocity anisotropy can automatically be compensated for after the time reversal processing.

We present a systematical numerical study of the effects of adiabatic exponent γ on Richtmyer--Meshkov instability (RMI) driven by cylindrical shock waves, based on the γ model for the multi-component problems and numerical simulation with high-order and high-resolution method for compressible Euler equations. The results show that the RMI of different γ across the interface exhibits different evolution features with the case of single γ. Moreover, the large γ can hold back the development of nonlinear structures, such as spikes and bubbles.

The instantaneous and time-averaged statistic characteristics of the sub-grid scale (SGS) turbulent kinetic energy and SGS dissipation in a backward-facing step turbulent flow have been studied by large eddy simulation. The SGS turbulent kinetic energy and SGS turbulent dissipation vary in different flow regions and decrease with the flow developing spatially. The fluid molecular dissipation shares about 14% to 28% of the whole dissipation.

The molecular dynamics simulation method is applied to investigate the rarefied gas flow in a submicron channel with surface roughness which is modelled by an array of triangle modules. The boundary conditions are found to be determined not only by the Knudsen number but also the roughness, which implies that the breakdown of the Maxwell slip model under the conditions that the surface roughness is comparable to the molecular mean free path. The effects of the rarefaction and the surface roughness on the boundary conditions and the flow characteristics are strongly coupled. The flow friction increases with increasing roughness and with decreasing Knudsen number.

Populations of the 249 levels belonging to the ground configuration 3s²3p⁶3d¹⁰ and those of single excitations of a 3d, 3p or 3s electron to the orbitals of n=4 and 5 have been calculated for nickel-like samarium at temperatures from 300 to 1600eV and at densities from 10²⁰ to 10²²cm^-3. The gain coefficients for possible x-ray laser lines are also determined under these plasma conditions. The possible laser lines are transitions from levels (3d^-1_3/24d_3/2)₀ and (3d^-1_5/24d_5/2)₀ to levels (3d^-1_3/24p_1/2)₁, (3d^-1_5/24p_3/2)₁ and (3d^-1_3/24p_3/2)₁. The favourable plasma condition for x-ray lasers is at the temperature of about 800eV and at the density of approximately 5.0×10²¹cm^-3.

Based on the recent progress in the spherical torus approach (ST), it is meaningful to revisit the possibility of establishing D-³ He fusion reactor using both the ST and the tokamak scaling. Fundamental requirements then are obtained and some important issues are discussed. The wall reflection of the synchrotron radiation is very important for a good reactor merit.

Highly oriented Ag(TCNQ) nanowires have been prepared on Si(111) wafer at 100°C by the vapour-transport reaction between silver and TCNQ without any other catalyst. X-ray diffraction analysis shows that the composition and crystal structure of the obtained nanostructure were Ag(TCNQ) crystalline. Most Ag(TCNQ) nanowires were grown uniformly and vertically on the substrate with diameters ranging from 50 to 300nm and the lengths measuring from 2 to 50μm by scanning electron microscopy. Ag particles were observed on the substrate from pure thin Ag film heated under the same conditions as used in synthesizing the nanowires. Nucleation and short Ag(TCNQ) nanowires were prepared by controlling the reaction time, providing direct evidence of the growth mechanism in a nanometre scale. The growth process was explained according to the vapour--liquid--solid model. The gradient of temperature and the densely distributed Ag particles may contribute to the vertically aligned growth. These results will be helpful for the controllable synthesis of
Ag(TCNQ) nanowires.

The atomic, binding and electronic structures of very thin Zr chains are studied by the first-principles density-functional method. The present calculations reveal that zirconium can form planar chains in zigzag, dimer and ladder structures. The zigzag geometry has two minima. The most stable geometry is the zigzag one with a unit cell rather close to equilateral triangles with four nearest neighbours. The other stable zigzag structure has a wide bond angle and allows for two nearest neighbours. An intermediary structure has the ladder geometry and is formed by two strands. The dimer structure is also found to be more stable than the truly linear chain. All these planar geometries are more favourable energetically than the linear chain. We also show that by going from Zr bulk to a Zr chain, the characters of bonding do not change significantly.

The current-voltage (I--V) characteristics of In/p-Si Schottky barrier diodes have been determined in the temperature range 100--300K and have been interpreted based on the assumption of a Gaussian distribution of barrier heights due to barrier height inhomogeneities that prevail at the metal- semiconductor interface. The evaluation of the experimental I--V data reveals a decrease of zero-bias barrier height but an increase of ideality factor n with decreasing temperature. The inhomogeneities are considered to have Gaussian distribution with a mean zero-bias barrier height of 0.630eV and standard deviation of 0.083V at zero bias. Furthermore, the mean barrier height and the Richardson constant values were obtained to be 0.617eV and 20.71A K^-2 cm^-2, respectively, by means of the modified Richardson plot, (I₀/T²) - (q²σ_s0/2k²T²) versus 1000/T.

A series of new Er³⁺/Yb³⁺-codoped 70TeO₂--5Li₂O--(25-x)B₂O₃--xGeO₂ (TLBG, x=0, 5, 10, 15, 20mol%) glasses are prepared. The thermal stability and spectroscopic properties of TLBG glasses are studied. It is found that these glasses have the better thermal stability ((T_x-T_g)>150 °C) compared with 75TeO₂--20ZnO--5Na₂O (TZN) glass. The fluorescence full width at half maximum (FWHM) is about 77nm, while the emission intensity and the quantum efficiency of the ⁴I_13/2 level of Er³⁺ increase with the increasing GeO₂ content. The maximum quantum efficiency and stimulated emission cross-section of Er³⁺ calculated from the McCumber theory are 93.82% and 9.0×10^-21cm², respectively. The products of FWHM and σ^peak_e of Er³⁺ in TLBG glasses are larger than those in other reported glasses. The obtained data indicate that this kind of TLBG glasses is a promising candidate host material for Er³⁺-doped broadband amplifiers.

The Fano resonance of a quantum wire (QW) with a side-coupled quantum dot (QD) is investigated. The QD has multilevel and is in the Coulomb blockade regime. We show that there are two aspects in contribution to asymmetric Fano dip line shape of conductance: (1) the quantum interference between the resonant level and non-resonant levels, (2) the asymmetric electron occupation of levels in the two sides of a resonant level in the QD. The smearing of the asymmetry of the dip structure with the increasing temperature is partially attributed to fluctuation of electron state in the QD.

Possibility of coexistence of ferromagnetism (FM) and superconductivity (SC) in UGe₂ based on a two-parameter model in an anisotropic quasi-two-dimensional system is discussed with both singlet s-wave and triplet p-wave SCs. It is emphasized that the coexistence of FM and singlet s-wave SC is energetically high among all possible states, while the coexistence of FM and triplet p-wave SC is energetically favourable among all possible states. Furthermore, we find that the magnetization dependence of the SC energy gap is nonmonotonic, which may explain the experimental result discovered in UGe₂ .

La_0.14Pr_0.56Sr_0.3MnO₃/SrTiO₃ and La_0.7Ca_0.3MnO₃/Gd_0.7Ca_0.3MnO₃ multilayers have been fabricated by using pulsed laser deposition. The insulator--metal transition temperatures of the multilayers decrease with the decreasing thickness of the ferromagnetic layers. It is confirmed from the experiment and analysis that a non-ferromagnetic insulating region exists near the interface, which could not be attributed to the roughness of the growth surfaces and disorder of the ferromagnetic layers.

We investigate the electrical properties of Sm-doped Bi_4-xSm_xTi₃O₁₂ (BST) ceramics prepared by a conventional electroceramic technique. The x-ray diffraction analysis reveals the Bi-layered perovskite structure in all samples. The SEM micrographs show randomly oriented and plate-like morphology. For the samples with x=0.4 and 1.0, the current--voltage characteristics exhibit negative differential resistance behaviour and the P--V hysteresis loops are characterized by large leakage current, whereas for the samples with x=0.6 and 0.8, the current--voltage characteristics show simple ohmic behaviour and the P--V hysteresis loops are of the saturated and undistorted hysteresis. The remanent polarization and coercive field of the BST ceramic with x=0.8 are above 32μC/cm² and 70kV/cm, respectively.

Cubic perovskite-related ceramic CaCu₃Ti₄O₁₂ has a very high dielectric constant larger than 10000 in the kilohertz frequency region. It is almost constant in the 100--600K region. The ceramic compounds were prepared by conventional solid-state reaction at different sintering temperatures 1040°C(C04),1060°C(C06), 1080°C(C08), and 1100°C(C10). Impedance spectroscopy on CaCu_sTi₄O₁₂ ceramics demonstrates that they are electrically heterogeneous and consist of semi-conducting grains with insulating grain boundaries. It is shown that C06 is the most suitable one for device applications. Surface observation and analysis of the grain-boundary-grained structure were carried out by using scanning electron microscopy, which confirms that the samples have clearly different crystal grain sizes and C06 has a larger grain size of about 20μm. Compared to the dielectric relaxation spectroscopy, the mechanical relaxation spectroscopy on C06 was performed and a mechanical loss peak was found, which was attributed to the thermally activated behaviour being immanent in the grains.

Polycrystalline Bi₄Ti₃O₁₂ thin films were prepared on fused quartz substrates by pulsed laser deposition. The films were crystallized in the orthorhombic layer perovskite structure confirmed by x-ray diffraction and Raman spectroscopy. The two broad Raman bands centred at 57 and 93cm^-1 at 300K break up into clusters of several sharp Raman peaks at 90K. The temperature dependence of Raman spectra indicates the occurrence of monoclinic distortion of orthorhombic structure at low temperature in the as-prepared Bi₄Ti₃O₁₂ thin films.

Single transient cavitation bubble with luminescence has been generated in pure glycerin by using the 'tube arrest' method. The analyses of high-speed photograph and light emission data suggest that the light emission would be a single bubble sonoluminescence. The luminescence pulse width is observed to vary from sub nanosecond to about 30ns. The width and intensity of luminescence pulses increases with the height of the liquid column height and decreases with the liquid temperature.

GaN films are grown on Si(111) with low-temperature GaN (LT-GaN) layers as buffer layers by hydride vapour phase epitaxy (HVPE). The deposition temperature of the LT-GaN layers is changed from 400 to 900°C. When the LT-GaN layer is deposited at 600°C, GaN films show only c-oriented GaN (0002) and have the band edge emission at 365nm with no yellow luminescence bands. The results indicate that the LT-GaN layer can effectively block the unexpected Si etching by reactive gas during the GaN growth. However, the surface roughness of these GaN films grown on Si(111) is larger than that of GaN films on c-plane sapphire.

Solid-state electrolyte LiI(CH₃OH)₄-I₂ is used in dye-sensitized solar cells (DSSCs). The DSSCs using only the LiI(CH₃OH)₄-I₂ electrolyte show very poor performance due to the quick crystal growth of LiI(CH₃OH)₄. In order to improve the performance of DSSCs, we prepare a composite electrolyte by adding SiO₂ nano-particles and an ionic liquid, 1-methyl-3-ethylimidazolium iodide, into the original solid-state electrolyte. High efficiency of 4.3% is achieved by applying this composite electrolyte to DSSCs.

We report a systematical study on the molecular beam epitaxy growth and optical property of (GaAs_1-xSb_x/In_y Ga_1-yAs)/GaAs bilayer quantum well (BQW) structures. It is shown that the growth temperature of the wells and the sequence of layer growth have significant influence on the interface quality and the subsequent photoluminescence (PL) spectra. Under optimized growth conditions, three high-quality (GaAsSb_0.29/In_0.4GaAs)/GaAs BQWs are successfully fabricated and a room temperature PL at 1314nm is observed. The transition mechanism in the BQW is also discussed by photoluminescence and photoreflectance measurements. The results confirm experimentally a type-II band alignment of the interface between the GaAsSb and InGaAs layers.

Performance of dye-sensitized solar cells can be improved by treating the nanoporous TiO₂ films with titanium tetrachloride (TiCl₄) aqueous solution. We explore the reason why the performance of dye-sensitized solar cells is enhanced by this method. It is found that the effect of TiCl₄ treatment not only reduces the films surface area and improves the electronic contact, but also enhances the binding of N719 with the TiO₂ films surface.

Monte Carlo simulation is used to explore the effects of the Eley-Rideal (ER) process on the phase diagram of the Langmuir--Hinshelwood (LH) type monomer--dimer (CO--O₂) catalytic reaction on the surface and subsurface of a body-centred cubic structure, which extends to only two layers in the z-direction. The dimer (O₂) is adsorbed in such a way that it takes one surface site whereas the second site is from the subsurface. For this mechanism, an interesting situation develops. The production rate of CO₂ is found to be consistent with experiment. The qualitative trend of the surface oxygen coverage is not consistent with the experimental situation in one model while it is found to be consistent with that in another model, i.e. the coverage of surface oxygen decreases slowly with increase of concentration of CO (yCO). Moreover, the production of CO₂ can be predicted in the form of a mathematical relation.

We report the experimental results of a large-aperture biased semi-insulating GaAs photoconductive dipole antenna, with a gap of 3mm between two Au/Ge/Ni electrodes, triggered by 800nm Ti--sapphire laser pulses with 82MHz repetition rate. A direct comparison is made between insulated GaAs dipole antenna with a Si₃N₄ layer and bare GaAs dipole antenna. Both the current in the antenna and the radiation amplitude present as linear to the exciting power when the applied voltage is fixed. The Si₃N₄ insulated GaAs dipole antenna can hold higher biased voltage than a normal GaAs dipole antenna; its terahertz radiation generation efficiency is significantly higher than that of a normal GaAs dipole antenna.

An InGaN multiple-quantum-well (MQW) violet-light-emitting diode (LED) is grown by low-pressure metalorganic chemical vapour deposition. It is found that photoluminescence wavelength of the InGaN MQW violet LED is lengthened with increasing growth temperature and with the increasing trimethylindium flow of the InGaN wells. The electroluminescence peak wavelength of the violet LED are about 401nm with full width at half maximum of 14nm, and the output power in injection current of 20mA at room temperature is 4.1mW.

We present an approximate method for calculating the thermoelectric efficiency. The method has a high precision and is applicable to almost all of the thermoelectric devices. The expression for the thermoelectric efficiency we obtained does not involve the position variable, so the calculations are simplified greatly.

Electrowetting-on-dielectric (EWOD) controls directly the wettability of liquids on the solid surface by applying an electric potential to the microelectrode array under the dielectric layer. A prototype of the EWOD droplet actuator is put forward, consisting of Si used as the substrate of the microelectrode array, Si₃N₄ film as the dielectric layer and fluorocarbon polymer (p-C:F) film deposited by plasma enhanced chemical vapour deposition (PECVD) as the hydrophobic layer. The p-C:F film was uniform and compact, and the contact angle of deionized water on the p-C:F film reached $110 °. The actuator successfully actuated deionized droplets surrounded in silicone oil at the voltage of 35V.

The scale-free power-law behaviour of the statistics of the download frequency of publications has been reported, for the first time to our knowledge. The data of the download frequency of publications are taken from a well-constructed web page in the field of economic physics (http://www.unifr.ch/econophysics/). The Zipf-law analysis and the Tsallis entropy method were used to fit the download frequency. It was found that the power-law exponent of rank-ordered frequency distribution is γ～0.38±0.04, which is consistent with the power-law exponent α～3.37±0.45 for the cumulated frequency distributions. The preferential attachment model of Barabasi and Albert network has been used to explain the download network.

We divide various fat-tailed degree distributions of real-world networks into five classes based on careful examination of experimental data. By taking account of the mechanism of addition and deletion of nodes in the growing network model with and without preferential attachment respectively, we obtain all the five classes of degree distributions, which is believed to shed some light on the dynamics of formation of complex network systems.

An analytical expression for the jet power extracted from the disc (JPEFD) is derived based on an equivalent circuit in black hole magnetosphere with a mapping relation between the radial coordinate of the disc and that of unknown astrophysical load. It turns out that this JPEFD is comparable with two other JPEFDs derived in the Poynting flux and hydrodynamic regimes, respectively. In addition, the relative importance of this JPEFD relative to the Blandford--Znajek power is discussed. It is shown that the BZ power is generally dominated by the JPEFD except in some extreme cases. Furthermore, we show that the JPEFD derived in our model can be well fitted with the jet power of 3C 273.

As is well known, the exact evolution equation of the curvature perturbation plays a very important role in investigation of the inflation power spectrum of the flat universe. However, the corresponding exact extension for the non-flat universes has not yet been given clearly. Interest in the non-flat, specially closed, universes has been aroused recently. The need for this extension is pressing. We start with the most elementary physical consideration and obtain finally this exact evolution equation of the curvature perturbation for the non-flat universes, as well as the evolutionary controlling parameter and the exact expression of the variable mass in this equation. We approximately perform a primitive and immature analysis on the power spectrum of non-flat universes. This analysis shows that the exact evolution equation of the curvature perturbation for the non-flat universes is very complicated, and we need to carry out many numerical and analytic works for this new equation in the future to judge whether the universe is flat or closed by comparison of theories with observations.