Based on the algebraic graph theory, the networked multi-agent
continuous systems are investigated. Firstly, the digraph (directed
graph) represents the topology of a networked system, and then a
consensus convergence criterion of system is proposed. Secondly, the
issue of stability of multi-agent systems and the consensus
convergence problem of information states are all analysed.
Furthermore, the consensus equilibrium point of system is proved to
be global and asymptotically reach the convex combination of initial
states. Finally, two examples are taken to show the effectiveness of
the results obtained in this paper.

Based on the adaptive network, the feedback mechanism and interplay
between the network topology and the diffusive process of
information are studied. The results reveal that the adaptation of
network topology can drive systems into the scale-free one with the
assortative or disassortative degree correlations, and the
hierarchical clustering. Meanwhile, the processes of the information
diffusion are extremely speeded up by the adaptive changes of
network topology.

Based on the definition of higher-order adiabatic invariants of a
mechanical system, a new type of adiabatic invariants，i.e.
generalized Lutzky adiabatic invariants, of a disturbed holonomic
nonconservative mechanical system are obtained by investigating the
perturbation of Lie symmetries for a holonomic nonconservative
mechanical system with the action of small disturbance. The
adiabatic invariants and the exact invariants of the Lutzky type of
some special cases, for example, the Lie point symmetrical
transformations, the special Lie symmetrical transformations, and
the Lagrange system, are given. And an example is given to
illustrate the application of the method and results.

We propose a scheme to effectively generate a four-photon
path-entangled number state [the NOON state i.e.
\dfrac{1}{\sqrt{2}}(\vert N,0\rangle+\vert 0,N\rangle)] for the
demonstration of four-photon de Broglie wavelength. Our scheme
requires only linear optical elements, photon detectors and
post-selections which are all within the reach of current
technology.

The entanglement dynamics of system, where atoms A and B interact
with single mode cavity fields a and b respectively, is
studied. The interaction between atom A and cavity a may be
described by using the typical Jaynes--Cummings model, while that
between the atom B and cavity b filled with a Kerr medium is of a
two-photon process. For a certain initial atom entanglement state,
there is an entanglement sudden death effect between the two atoms.
The Kerr medium in the cavity b can effectively prevent the
undesirable entanglement sudden death from occurring. Also, from the
viewpoint of the population dynamics, we discuss why the Kerr
medium can do so.

The mixedness of the $N$-qubit quantum states with exchange symmetry
has been studied, and the results show that the linear entropy of
the single qubit reduced density matrix (RDM), which can describe
the mixedness, is completely determined by the expectation values
$\langle S_z \rangle $ and $\langle S_\pm \rangle $ for both the
pure and the mixed states. The mixedness of the pure states can be
used to describe the bipartite entanglement, as an example we have
calculated the mixedness of the Dicke state and the spin squeezed
Kitagawa--Ueda state. For the mixed states, we determine the
mixedness properties of both the ground states and the thermal
states in mean-field clusters of spin-1/2 particles interacting via
the anisotropy Heisenberg XXZ interaction, and found for the
ferromagnetic case ($J < 0)$, the mixedness will approximate to the
pairwise entanglement when the anisotropic parameter ${\it\Delta }>
{\it\Delta }_{\rm c} $.

We investigate a planar ion chip design with a two-dimensional array
of linear ion traps for scalable quantum information processing.
Qubits are formed from the internal electronic states of trapped
$^{40}$Ca$^{+}$ ions. The segmented electrodes reside in a single
plane on a substrate and a grounded metal plate separately, a
combination of appropriate rf and DC potentials is applied to them
for stable ion confinement. Every two adjacent electrodes can
generate a linear ion trap in and between the electrodes above the
chip at a distance dependent on the geometrical scale and other
considerations. The potential distributions are calculated by using
a static electric field qualitatively. This architecture provides a
conceptually simple avenue to achieving the microfabrication and
large-scale quantum computation based on the arrays of trapped ions.

A Hauser--Ernst-type extended hyperbolic complex linear system given
in our previous paper [Gao Y J 2004 {\it Chin. Phys.} {\bf 13} 602]
is slightly modified and used to develop a new inverse scattering
method for the stationary axisymmetric Einstein--Maxwell theory with
multiple Abelian gauge fields. The reduction procedures in this
inverse scattering method are found to be fairly simple, which makes
the inverse scattering method be fine and effective in practical
application. As an example, a concrete family of soliton solutions
for the considered theory is obtained.

In this paper, an empirical investigation is presented, which
focuses on unveiling the universality of connectivity correlations
in three spaces (the route space, the stop geographical space and
bus-transferring space) of urban bus-transport networks (BTNs) in
four major cities of China. The underlying features of the
connectivity correlations are shown in two statistical ways. One is
the correlation between the (weighted) average degree of all the
nearest neighbouring vertices with degree $k$, ($K^w_{nn}(k)$)
$K_{nn}(k)$, and $k$, and the other is the correlations between the
assortativity coefficient $r$ and, respectively, the network size
$N$, the network diameter $D$, the averaged clustering coefficient
$C$, and the averaged distance $\lan l\ran$. The obtained results
show qualitatively the same connectivity correlations of all the
considered cities under all the three spaces.

A new one-way hash function based on the unified chaotic system is
constructed. With different values of a key parameter, the unified
chaotic system represents different chaotic systems, based on which
the one-way hash function algorithm is constructed with three round
operations and an initial vector on an input message. In each round
operation, the parameters are processed by three different chaotic
systems generated from the unified chaotic system. Feed-forwards are
used at the end of each round operation and at the end of each
element of the message processing. Meanwhile, in each round
operation, parameter-exchanging operations are implemented. Then,
the hash value of length 160 bits is obtained from the last six
parameters. Simulation and analysis both demonstrate that the
algorithm has great flexibility, satisfactory hash performance, weak
collision property, and high security.

In this paper, a new four-dimensional autonomous hyperchaotic system
is designed for generating complex chaotic signals. In the design,
its parameters are selected according to the requirements for chaos
and hyperchaos. The hyperchaotic nature is verified theoretically by
using the bifurcation analysis and demonstrated experimentally by
the implementation of an analogue electronic circuit. Moreover, the
Field Programmable Gate Array (FPGA) technology is applied to
implementing a continuous system in a digital form by using a chip
of Altera Cyclone II EP2C35F484C8. The digital sequence generated
from the FPGA device is observed in our experimental setup.

A universal adaptive generalized functional synchronization approach
to any two different or identical chaotic systems with unknown
parameters is proposed, based on a unified mathematical expression
of a large class of chaotic system. Self-adaptive parameter law and
control law are given in the form of a theorem. The synchronization
between the three-dimensional R\"{o}ssler chaotic system and the
four-dimensional Chen's hyper-chaotic system is studied as an
example for illustration. The computer simulation results
demonstrate the feasibility of the method proposed.

Fountain codes provide an efficient way to transfer information over
erasure channels like the Internet. LT codes are the first codes fully
realizing the digital fountain concept. They are asymptotically
optimal rateless erasure codes with highly efficient encoding and
decoding algorithms. In theory, for each encoding symbol of LT
codes, its degree is randomly chosen according to a predetermined
degree distribution, and its neighbours used to generate that
encoding symbol are chosen uniformly at random. Practical
implementation of LT codes usually realizes the randomness through
pseudo-randomness number generator like linear congruential method.
This paper applies the pseudo-randomness of chaotic sequence in the
implementation of LT codes. Two Kent chaotic maps are used to
determine the degree and neighbour(s) of each encoding symbol. It is
shown that the implemented LT codes based on chaos perform better
than the LT codes implemented by the traditional pseudo-randomness
number generator.

In this paper, a practical impulsive lag synchronization scheme for
different chaotic systems with parametric uncertainties is proposed.
By virtue of the new definition of synchronization and the theory of
impulsive differential equations, some new and less conservative
sufficient conditions are established to guarantee that the error
dynamics can converge to a predetermined level. The idea and
approach developed in this paper can provide a more practical
framework for the synchronization between identical and different
chaotic systems in parameter perturbation circumstances. Simulation
results finally demonstrate the effectiveness of the method.

In this paper, the dissipative and the forced terms of the Duffing
equation are considered as the perturbations of nonlinear
Hamiltonian equations and the perturbational effect is indicated by
parameter $\varepsilon $. Firstly, based on the gradient-Hamiltonian
decomposition theory of vector fields, by using splitting methods,
this paper constructs structure-preserving algorithms (SPAs) for the
Duffing equation. Then, according to the Liouville formula, it
proves that the Jacobian matrix determinants of the SPAs are equal
to that of the exact flow of the Duffing equation. However,
considering the explicit Runge--Kutta methods, this paper finds that
there is an error term of order $p$+1 for the Jacobian matrix
determinants. The volume evolution law of a given region in phase
space is discussed for different algorithms, respectively. As a
result, the sum of Lyapunov exponents is exactly invariable for the
SPAs proposed in this paper. Finally, through numerical experiments,
relative norm errors and absolute energy errors of phase
trajectories of the SPAs and the Heun method (a second-order
Runge--Kutta method) are compared. Computational results illustrate
that the SPAs are evidently better than the Heun method when
$\varepsilon $ is small or equal to zero.

This paper reports that the Tm$^{3 + }$:Lu$_{2}$SiO$_{5}$ (Tm:LSO)
crystal is grown by Czochralski technique. The room-temperature
absorption spectra of Tm:LSO crystal are measured on a b-cut sample
with 4 at.{\%} thulium. According to the obtained Judd--Ofelt
intensity parameters $\Om _{2}$=9.3155$\times $10$^{ - 20
}$\,cm$^{2}$, $\Om_{4}$=8.4103$\times $10$^{ - 20 }$\,cm$^{2}$,
$\Om_{6}$=1.5908$\times $10$^{ - 20 }$\,cm$^{2}$, the fluorescence
lifetime is calculated to be 2.03\,ms for $^{3}$F$_{4} \to
{}^{3}$H$_{6}$ transition, and the integrated emission cross section
is 5.81$\times $10$^{ - 18 }$\,cm$^{2}$. Room-temperature laser
action near 2\,$\mu $m under diode pumping is experimentally
evaluated in Tm:LSO. An optical-optical conversion efficiency of
9.1{\%} and a slope efficiency of 16.2{\%} are obtained with
continuous-wave maximum output power of 0.67\,W. The emission
wavelengths of Tm:LSO laser are centred around 2.06\,$\mu $m with
spectral bandwidth of $\sim $13.6\,nm.

By using Darboux transformation, this paper studies analytically the
nonlinear dynamics of a one-dimensional growing Bose--Einstein
condensate (BEC). It is shown that the growing model has an
important effect on the amplitude of the soliton in the condensates.
In the absence of the growing model, there exhibits the stable
alternate bright solitons in the condensates. In the presence of the
growing model, the obtained results show that the amplitude of the
bright soliton decreases (increases) for the BEC growing coefficient
$\Om<0$ $(\Om
>0)$. Furthermore, we propose experimental protocols to manipulate
the amplitude of the bright soliton by varying the scattering length
via the Feshbach resonance in the future experiment.

A chemical vapour deposition (CVD) diamond film detector was
prepared and the main characteristics for pulsed proton detection
were studied at Beijing Tandem Accelerator. The result shows that
the charge collection efficiency of the detector increases with
increasing electric field intensity and reaches to 9.44{\%} at
5\,V/$\mu $m with the charge collection distance of 15.9\,$\mu $m.
The relationship between the sensitivity of the detector and proton
energy is consistent with the Monte Carlo (MC) simulation result.
Its plasma time for a pulse with 4.85$\times $10$^{5}$ protons is
11.2ns. The dose threshold for onset of damage under 9MeV proton
irradiation in the detector is about 10$^{13}$\,cm$^{ - 2}$. All of
the results show that a CVD diamond detector has fast time response
and high radiation hardness, and can be used in pulsed proton
detection.

This paper proposes a hybrid method based on the forward--backward
method (FBM) and the reciprocity theorem (RT) for evaluating the
scattering field from dielectric rough surface with a 2D target
above it. Here, the equivalent electric/magnetic current densities
on the rough surface as well as the scattering field from it are
numerically calculated by FBM, and the scattered field from the
isolated target is obtained utilizing the method of moments (MOM).
Meanwhile, the rescattered coupling interactions between the target
and the surface are evaluated employing the combination of FBM and
RT. Our hybrid method is first validated by available MOM results.
Then, the functional dependences of bistatic and monostatic
scattering from the target above rough surface upon the target
altitude, incident and scattering angles are numerically simulated
and discussed. This study presents a numerical description for the
scattering mechanism associated with rescattered coupling
interactions between a target and an underlying randomly rough
surface.

In this paper, a new type of resonant Brewster filters (RBF) with
surface relief structure for the multiple channels is first
presented by using the rigorous coupled-wave analysis and the
$S$-matrix method. By tuning the depth of homogeneous layer which is
under the surface relief structure, the multiple channels phenomenon
is obtained. Long range, extremely low sidebands and multiple
channels are found when the RBF with surface relief structure is
illuminated with Transverse Magnetic incident polarization light
near the Brewster angle calculated with the effective media theory
of sub wavelength grating. Moreover, the wavelengths of RBF with
surface relief structure can be easily shifted by changing the depth
of homogeneous layer while its optical properties such as low
sideband reflection and narrow band are not spoiled when the depth
is changed. Furthermore, the variation of the grating thickness does
not effectively change the resonant wavelength of RBF, but have a
remarkable effect on its line width, which is very useful for
designing such filters with different line widths at desired
wavelength.

Based on the second-order moments, this paper derives an analytical
expression of the $M^{2}$ factor of four-petal Gaussian beam. The
results show that the $M^{2}$ factor is only determined by the beam
order $n$. The corresponding numerical calculations are also given.
As the beam order increases, the augment of $M^{2}$ factor is
disciplinary. As the expression of $M^{2}$ factor is expressed in
series form and becomes more complicated, a new concise formula of
$M^{2}$ factor is also presented by using curve fitting of numerical
calculations. When $3 \le n \le 200$, the maximum error rate of
fitting formula will not exceed 2.6{\%} and the average error rate
is 0.28{\%}. This research is helpful to the applications of
four-petal Gaussian beam.

This paper studies the light scattering and adsorption of
nanocrystalline TiO$_2$ porous films used in dye-sensitized solar
cells composed of anatase and/or rutile particles by using an
optical four-flux radiative transfer model. These light properties
are difficult to measure directly on the functioning solar cells and
they can not be calculated easily from the first-principle
computational or quantitative theoretical evaluations. These
simulation results indicate that the light scattering of 1--25\,nm
TiO$_{2}$ particles is negligible, but it is effective in the range
of 80 and 180\,nm. A suitable mixture of small particles (10\,nm
radius), which are resulted in a large effective surface, and of
larger particles (150\,nm radius), which are effective light
scatterers, have the potential to enhance solar absorption
significantly. The rutile crystals have a larger refractive index
and thus the light harvest of the mixtures of such larger rutile and
relatively small anatase particles is improved in comparison with
that of pure anatase films. The light absorption of the 10\,$\mu$m
double-layered films is also examined. A maximal light absorption of
double-layered film is gotten when the thickness of the first layer
of 10\,nm-sized anatase particles is comparable to that of the
second larger rutile layer.

This paper reports that the central position of the reflected and
transmitted beams of a nonlinear polarized light beam at the
interface between two media undergoes transverse shifts. It presents
a solution to the problem of transverse shift of a non-uniformly
polarized paraxial light beam transmitting through interfaces
between two homogeneous media by using a two-form amplitude and an
extension matrix to represent the vector angular spectrum of a
three-dimensional (3D) light beam. It derives general formula for
the transverse shift of the transmitted beam, and discusses the
shift of a well-collimated beam transmitting through an interface
between two homogeneous media and a thin dielectric slab.

In this paper, a scheme is proposed for remote state preparation (RSP) with
cavity quantum electrodynamics (QED). In our scheme, two observers share
two-atom nonmaximally entangled state as quantum channels and can realize
remote preparation of state of an atom. We also propose a generalization for
remote preparation of $N$-atom entangled state by ($N$+1)-atom {GHZ-like} state ($N \ge 2)$.
By this scheme, one single-atom projective measurement is enough for the RSP
of a qubit or $N$-atom entangled state, and the probability of success for RSP is
unity. Furthermore, we have considered the case where observers use {W-like} state as
quantum channels to realize RSP of a qubit. We compare our scheme with
existing ones.

In this paper, we accomplish the teleportation of an unknown
three-particle maximally entangled $W$ state by using a spin-path
entangled quantum channel which may be realized experimentally based
on the advanced theory and technique in Bose--Einstein condensate
(BEC) of molecule, micro-fabricated wave guide and simple quantum
logic gate. Similarly, we can make an arbitrary $n$-particle entangled
Greenberger--Horne--Zeilinger (GHZ) state ($n\ge 4$) teleported
through this kind of quantum channel. It may have important
applications due to its resource-economic and practical features.

This paper studies the propagation effect in a closed lambda-type
three-level atomic system with Doppler broadening. It is shown that,
Doppler broadening due to atomic motion and propagation effect
associated with driving field depletion along the active medium
decreases obviously the gain and output of the lasing without
inversion (LWI); the relative phase between the probe and driving
fields has a remarkable modulation role to the propagation effect on
LWI when Doppler broadening presents; by choosing suitable value of
the relative phase, we can get the largest gain and output of LWI.

In this paper, we present an approach to generating arbitrary
symmetric Dicke states with distant trapped ions and linear optics.
Distant trapped ions can be prepared in the symmetric Dicke states
by using two photon-number-resolving detectors and a polarization
beam splitter. The atomic symmetric Dicke states are robust against
decoherence, for atoms are in a metastable level. We discuss the
experimental feasibility of our scheme with current technology.
Finally, we discuss the classification of arbitrary $n$-qubit
symmetric Dicke states under statistical local operation and
classical communication and prove the existence of $[n/2]$
inequivalent classes of genuine entanglement of $n$-qubit symmetric
Dicke states.

This paper describes the interaction between two spatial modes of
the optical fields with a single atom trapped inner coupled
double-cavity. Theoretical derivation and numerical simulation with
the experimental available parameters show that photon--photon
switching and $\pi $ phase shift of single photons may be achieved
with current experimental technology. As the probe and control
fields are in different spatial modes, the system is superior for
implementing cavity QED-based photonic quantum networks.

The photoluminescence (PL) of nanocrystal present in porous silicon
shifts from the near infrared to the ultraviolet depending on the
size when the surface is passivated with Si-H bonds. After
oxidation, the centre wavelength of PL band is pinned in a region of
700--750\,nm and its intensity increases obviously. Calculation
shows that trap electronic states appear in the band gap of a
smaller nanocrystal when Si = O bonds or Si--O--Si bonds are formed.
The changes in PL intensity and wavelength can be explained by both
quantum confinement and trap states in an oxidation layer of
nanocrystal. In the theoretical model, the most important factor in
the enhancement and the pinning effects of PL emission is the
relative position between the level of the trap states and the level
of the photoexcitation in the silicon nanocrystal.

We have made a gain-switched all-solid-state quasi-continuous-wave
(QCW) tunable Ti:sapphire laser system, which is pumped by a 532\,nm
intracavity frequency-doubled Nd:YAG laser. Based on the theory of
gain-switching and the study on the influencing factors of the
output pulse width, an effective method for obtaining high power and
narrow pulse width output is proposed. Through deliberately
designing the pump source and the resonator of the Ti:sapphire
laser, when the repetition rate is 6\,kHz and the length of the
cavity is 220\,mm, at an incident pump power of 22\,W, the tunable
Ti:sapphire laser from 700 to 950\,nm can be achieved. It has a
maximum average output power of 5.6\,W at 800\,nm and the pulse
width of 13.2\,ns, giving an optical conversion efficiency of
25.5{\%} from the 532\,nm pump laser to the Ti:sapphire laser.

A theoretical model for calculating spontaneous and stimulated
Brillouin scattering(SBS) spectra is described. An empirical formula
for the Stokes output spectral linewidth, a function of spontaneous
Brillouin linewidth and the exponential gain coefficient, is
obtained by the calculated data fitting. The formula holds true for
two cases involving pump undepletion and depletion. The lineshape
change from spontaneous to highly pump-depleted SBS spectra is also
investigated. The result shows that for the pump power below the SBS
threshold, the Stokes output spectral lineshape evolves from
Lorentzian to approximately Gaussian as the pump power increases.
For the pump power near or beyond the threshold, the SBS spectrum is
in the form of a steady Gaussian profile, and the spectral linewidth
comes to a certain value about 7 times narrower than the spontaneous
one. The theoretical results are experimentally demonstrated by
using several common liquid media.

In a biased dissipative photovoltaic--photorefractive system, this
paper investigates the temperature effect on the evolution and the
self-deflection of the dissipative holographic
screening-photovoltaic (DHSP) solitons. The results reveal that, the
evolution and the self-deflection of the bright and dark DHSP
solitons are influenced by the system temperature. At a given
temperature, for a stable DHSP soliton originally formed in the
dissipative system, it attempts to evolve into another DHSP soliton
when the temperature change is appropriately small, whereas it will
become unstable or break down if the temperature departure is large
enough. Moreover, the self-deflection degree of the solitary beam
centre increases as temperature rises in some range, while it is
decided by the system parameters and is slight under small-signal
condition. The system temperature can be adjusted to change the
formation and the self-deflection of the solitary beam in order to
gain certain optical ends. In a word, the system temperature plays a
role for the DHSP solitons in the dissipative system.

Two kinds of fabricated hollow-core photonic crystal fibres
(HC-PCFs) are studied using finite element method (FEM) because the
structures of the fibres are special. Normalized transmission
spectra and transverse intensity distribution of the modes are
calculated and measured. And the dispersion characteristics of these
two kinds of HC-PCFs were analysed from 400\,nm to 800\,nm.
Simulated and measured results show that the special structure could
affect the properties of HC-PCFs. By comparing the simulated values
with the measured results, it can be clarified that FEM is feasible
and accurate for analysing photonic crystal fibres whose structures
are irregular and complex.

The numerical results obtained by Rayleigh--Plesset (R-P) equation
failed to agree with the experimental Mie scattering data of a
bubble in water without inappropriately increasing the shear
viscosity and decreasing the surface tension coefficient. In this
paper, a new equation proposed by the present authors (Qian and
Xiao) is solved. Numerical solutions obtained by using the symbolic
computation program from both the R-P equation and the Qian-Xiao
(Q-X) equation clearly demonstrate that Q-X equation yields best
results matching the experimental data (in expansion phase). The
numerical solutions of R-P equation also demonstrate the oscillation
of a bubble in water depends strongly upon the surface tension and
the shear viscosity coefficients as well as the amplitude of driving
pressure, so that the uniqueness of the numerical solutions may be
suspected if they are varied arbitrarily in order to fit the
experimental data. If the bubble's vibration accompanies an energy
loss such as the light radiation during the contract phase, the
mechanism of the energy loss has to be taken into account. We
suggest that by use of the bubble's vibration to investigate the
state equations of aqueous solutions seem to be possible. We also
believe that if one uses this equation instead of R-P equation to
deal with the relevant problems such as the `phase diagrams for
sonoluminescing bubbles', etc., some different results may be
expected.

To study theoretically the relationship between the differential
interference angle and the scattering angle in collisional quantum
interference (CQI), we have investigated the differential
interference angle of the atom--diatomic [case(a)] molecule system in
detail. For the $^2{\it \Pi} $ electronic state in Hund's case
(a), the degree of the differential interference is also discussed.
The differential interference angles of NO($X{ }^2{\it \Pi})$ are
calculated quantitatively for the rotational energy transfer in
Hund's case (a) induced by collision with He, Ne and Ar atoms. The
method to calculate the differential interference angle is
presented. Several factors that affect the differential interference
angle are investigated. Finally the variation of the differential
interference angle with the impact parameter and relative velocity
is discussed.

Two-step excitation and ionization processes are used to detect Sm
atoms in many excited states populated with tunable lasers. The
wavelength of the first laser is tuned to the resonances from the Sm
4f$^{6 }$6s$^{2}$ ${}^7F_{J}$ ($J$=0--6) states to many odd-parity
states with different electronic configurations, where the atoms are
detected by photoionization process using an ultraviolet laser with
a wavelength of 355\,nm. Precise measurements on the energy level
and intensity for many Sm 4f$^{6}$ 6s6p and 4f$^{5}$5d6s$^{2}$
states have been carried out. In a theoretical analysis on the
spectral data, such as peak position, relative intensity, many
transitions can be identified as the resonances from the Sm 4f$^{6
}$6s$^2$ $^7F_{J }$ ($J$=0--6) states to the atomic states with
4f$^{6 }$6s6p and 4f$^{5}$5d6s$^{2}$ electronic configurations.
This work also reports many spectral data on the
odd-parity states that cannot be found in the literature.

We have studied theoretically and numerically the enhanced cooling
of a V-type three-level atom in a high-finesse optical cavity and
shown that the cooling rate can be increased by one order of
magnitude over that of a two-level atom, and the momentum amplitude
tends to a stationary state much smaller than that of a two-level
atom. We have further shown that the cooling rate can be
significantly improved by using feedback and a time-dependent pump.

This paper studies the multiphoton resonant ionization by two-colour
laser pulses in the hydrogen atom by solving the time-dependent
Schr\"odinger equation. By fixing the parameters of fundamental
laser field and scanning the frequency of second laser field, it
finds that the ionization probability shows several resonance peaks
and is also much larger than the linear superposition of
probabilities by applying two lasers separately. The enhancement of
the ionization happens when the system is resonantly pumped to the
excited states by absorbing two or more colour photons
non-sequentially.

We propose a promising scheme to decelerate a CW molecular beam by
using a red-detuned quasi-cw semi-Gaussian laser beam (SGB). We
study the dynamical process of the deceleration for a CW deuterated
ammonia (ND$_{3})$ molecular beam by Monte-Carlo simulation method.
Our study shows that we can obtain a ND$_{3}$ molecular beam with a
relative average kinetic energy loss of about 10{\%} and a relative
output molecular number of more than 90{\%} by using a single
quasi-cw SGB with a power of 1.5kW and a maximum optical well depth
of 7.33mK.

This paper constructs the interaction potential of the SH($X^{2}{\it
\Pi})$ radical by using the coupled-cluster
singles-doubles-approximate-triples theory combining the
correlation-consistent quintuple basis set augmented with the
diffuse functions, aug-cc-pV5Z, in the valence range. Employing the
potential, it accurately determines the spectroscopic parameters.
The present $D_{\e}$, $R_{\e}$, \textit{$\omega $}$_{\e}$,
\textit{$\omega $}$_{\e}$\textit{$\chi $}$_{\e}$, \textit{$\alpha
$}$_{\e}$ and $B_{\e}$ values are of 3.7767\,eV, 0.13424\,nm,
2699.846\,cm$^{ - 1}$, 47.7055\,cm$^{ - 1}$, 0.2639\,cm$^{ - 1}$ and
9.4414\,cm$^{ - 1}$, respectively, which are in excellent agreement
with those obtained from the measurements. A total of 19
vibrational states has been found when $J$ = 0 by solving the radial
Schr\"{o}dinger equation of nuclear motion. The complete vibrational
levels, classical turning points, initial rotation and centrifugal
distortion constants when $J$ = 0 are reported for the first time,
which are in good accord with the experimental results. The total
and various partial-wave cross sections are computed for the elastic
collisions of sulfur and hydrogen in their ground states at low
temperatures when two atoms approach each other along the
SH($X^{2}{\it \Pi} )$ potential energy curve. Over the impact energy
range from 1.0$\times $10$^{ - 11}$ to 1.0$\times $10$^{ - 4}$ a.u.,
eight shape resonances have been found in the total elastic cross
sections. For each shape resonance, the resonant energy is
accurately calculated. Careful investigations have pointed out that
these resonances result from the $l$ = 0, 1, 2, 3, 4, 6, 7, 8
partial-wave contributions.

This paper studies the equilibrium geometries and electronic
properties of Be$_{n}$ and Be$_{n}$Li clusters, up to $n$=15, by
using density-functional theory(DFT) at B3LYP/6--31G(d) level. The
lowest-energy structures of Be$_{n}$ and Be$_{n}$Li clusters were
determined. The results indicate that a single lithium impurity
enhances the stability and chemical reactivity of the beryllium
clusters. It finds that the geometries of the host clusters change
significantly after the addition of the lithium atom for $n \ge $8.
The lithium impurity prefers to be on the periphery of beryllium
clusters, and occupies vertex sites. Both Be$_{4}$Li, Be$_{9}$Li,
and Be$_{13}$Li were found to be particularly stable with higher
average binding energy, local peaks of second-order energy
difference and fragmentation energies. For all the Be$_{n}$Li
clusters studied, we found charge transfers from the Li to Be site
and co-existence of covalent and metallic bonding characteristics.

This paper reports that an analytic method is used to calculate the
load responses of the two-wire transmission line excited by a
plane-wave directly in the time domain. By the frequency-domain
Baum--Liu--Tesche (BLT) equation, the time-domain analytic solutions
are obtained and expressed in an infinite geometric series.
Moreover, it is shown that there exist only finite nonzero terms in
the infinite geometric series if the time variate is at a finite
interval. In other word, the time-domain analytic solutions are
expanded in a finite geometric series indeed if the time variate is
at a finite interval. The computed results are subsequently compared
with transient responses obtained by using the frequency-domain BLT
equation via a fast Fourier transform, and the agreement is
excellent.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

This paper investigates the interaction of a small number of modes
in the two-fluid Kelvin--Helmholtz instability at the nonlinear
regime by using a two-dimensional hydrodynamic code. This
interaction is found to be relatively long range in wave-number
space and also it acts in both directions, i.e.~short wavelengths
affect long wavelengths and vice versa. There is no simple
equivalent transformation from a band of similar modes to one mode
representing their effective amplitude. Three distinct stages of
interaction have been identified.

Both high and low frequency relaxation oscillations have been
observed in an argon capacitive discharge connected to a peripheral
grounded chamber through a slot with dielectric spacers. The
oscillations, observed from time-varying optical emission of the
main discharge chamber, show, for example, a high frequency
(46\,kHz) relaxation oscillation at 100\,mTorr, with an absorbed
power near the peripheral breakdown, and a low frequency
(2.7--3.7\,Hz) oscillation, at a higher absorbed power. The high
frequency oscillation is found to ignite a plasma in the slot, but
usually not in the periphery. The high frequency oscillation is
interpreted by using an electromagnetic model of the slot impedance,
combined with the circuit analysis of the system including a
matching network. The model is further developed by using a parallel
connection of variable peripheral capacitance to analyse the low
frequency oscillation. The results obtained from the model are in
agreement with the experimental observations and indicate that a
variety of behaviours are dependent on the matching conditions.

This paper studies three types of coaxial slow wave structures
(SWSs): (1) with ripples on both the inner and outer conductors; (2)
with ripples on the outer conductor and smooth on the inner one; and
(3) with ripples on the inner conductor and smooth on the outer one.
The frequencies, coupling impedances, time growth rates and
beam-wave interaction efficiencies of the three types of coaxial
SWSs are obtained by theoretical analysis. Moreover, the
relativistic Cerenkov generators (RCGs) with the three types of
coaxial SWSs are simulated with a fully electromagnetic
particle-in-cell code, and the results verify the theoretical
analysis. It is proved that the RCG with double-rippled coaxial SWS
has the highest conversion efficiency and the shortest starting
time.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

In this work, a bridge density functional approximation (BDFA)
(\wx{J. Chem. Phys.} 112, 8079 (2000)) for a non-uniform hard-sphere
fluid is extended to a non-uniform hard-core repulsive Yukawa (HCRY)
fluid. It is found that the choice of a bulk bridge functional
approximation is crucial for both a uniform HCRY fluid and a
non-uniform HCRY fluid. A new bridge functional approximation is
proposed, which can accurately predict the radial distribution
function of the bulk HCRY fluid. With the new bridge functional
approximation and its associated bulk second order direct
correlation function as input, the BDFA can be used to well
calculate the density profile of the HCRY fluid subjected to the
influence of varying external fields, and the theoretical
predictions are in good agreement with the corresponding simulation
data. The calculated results indicate that the present BDFA captures
quantitatively the phenomena such as the coexistence of solid-like
high density phase and low density gas phase, and the adsorption
properties of the HCRY fluid, which qualitatively differ from those
of the fluids combining both hard-core repulsion and an attractive
tail.

This paper investigates the morphology and crystallization
properties of the two crystalline phases of pentacene grown by
thermal evaporation on p$^+$-Si substrates at room temperature by
the methods of atomic force microscopy and x-ray diffraction. This
kind of substrate induces a thin film phase and a triclinic phase
which are formed directly onto p$^+$-Si substrates and constitute a
layer consisting of faceted grains with a step height between
terraces of 15.8\,{\AA} (1\,\AA=0.1\,nm) and 14.9\,{\AA},
respectively. Above the critical thickness of the thin film phase,
lamellar structures are found with an increasing fraction with the
increase of the film thickness. When the film thickness is fixed,
the fraction of lamellar structures increases with the increase of
annealing temperature. These lamellar structures are identified as
the second phase with a interplanar distance of 14.9\,{\AA}
corresponding to the pentacene triclinic phase. Furthermore, the
thin film phase consisting of several micrometre sized uniformly
oriented grains at an annealing temperature of less than
80${^\circ}$C and a deposition rate of 0.6\,{\AA}/s is observed.

This paper reports that a simple chemical vapour deposition method
has been adopted to fabricate large scale, high density boron
nanocones with thermal evaporation of B/B$_{2}$O$_{3}$ powders
precursors in an Ar/H$_{2}$ gas mixture at the synthesis temperature
of 1000--1200$^{\circ}$C. The lengths of boron nanocones are several
micrometres, and the diameters of nanocone tops are in a range of
50--100\,nm. transmission electron microscopy and selected area
electron diffraction indicate that the nanocones are single
crystalline $\alpha $-tetragonal boron. The vapour--liquid--solid
mechanism is the main formation mechanism of boron nanocones. One
broad photoluminescence emission peak at the central wavelength of
about 650 nm is observed under the 532 nm light excitation. Boron
nanocones with good photoluminescence properties are promising
candidates for applications in optical emitting devices.

In the present work, a Cz--Silicon wafer is implanted with helium
ions to produce a buried porous layer, and then thermally annealed
in a dry oxygen atmosphere to make oxygen transport into the
cavities. The formation of the buried oxide layer in the case of
internal oxidation (ITOX) of the buried porous layer of cavities in
the silicon sample is studied by positron beam annihilation (PBA).
The cavities are formed by 15\,keV He implantation at a fluence of
$2\ti 10^{16}$\,cm$^{ - 2}$ and followed by thermal annealing at
673\,K for 30 min in vacuum. The internal oxidation is carried out
at temperatures ranging from 1073 to 1473\,K for 2\,h in a dry
oxygen atmosphere. The layered structures evolved in the silicon are
detected by using the PBA and the thicknesses of their layers and
nature are also investigated. It is found that rather high
temperatures must be chosen to establish a sufficient flux of oxygen
into the cavity layer. On the other hand high temperatures lead to
coarsening the cavities and removing the cavity layer finally.

By means of the Glauber's coherent state method combined with
multiple-scale method, this paper investigates the localized modes
in a quantum one-dimensional Klein--Gordon chain and finds that the
equation of motion of annihilation operator is reduced to the
nonlinear Schr\"{o}dinger equation. Interestingly, the model can
support both bright and dark small amplitude travelling and
non-travelling nonlinear localized modes in different parameter
spaces.

A numerical method for simulating the motion and deformation of an
axisymmetric bubble or drop rising or falling in another infinite
and initially stationary fluid is developed based on the volume of
fluid (VOF) method in the frame of two incompressible and immiscible
viscous fluids under the action of gravity, taking into
consideration of surface tension effects. A comparison of the
numerical results by this method with those by other works indicates
the validity of the method. In the frame of inviscid and
incompressible fluids without taking into consideration of surface
tension effects, the mechanisms of the generation of the liquid jet
and the transition from spherical shape to toroidal shape during the
bubble or drop deformation, the increase of the ring diameter of the
toroidal bubble or drop and the decrease of its cross-section area
during its motion, and the effects of the density ratio of the two
fluids on the deformation of the bubble or drop are analysed both
theoretically and numerically.

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

Ag adsorptions at 0.25--3 monolayer (ML) coverage on a perfect
TiC(001) surface and at 0.25\,ML coverage on C vacancy are
separately investigated by using the pseudopotential-based density
functional theory. The preferential adsorption sites and the
adsorption-induced modifications of electronic structures of both
the substrate and adsorbate are analysed. Through the analyses of
adsorption energy, ideal work of separation, interface distance,
projected local density of states, and the difference electron
density, the characteristic evolution of the adatom-surface bonding
as a function of the amount of deposited silver is studied. The
nature of the Ag/TiC bonding changes as the coverage increases from
0.25 to 3\,MLs. Unlike physisorption in an Ag/MgO system, polar
covalent component contributes to the Ag/TiC interfacial adhesion in
most cases, however, for the case of 1--3\,ML coverage, an
additional electrostatic interaction between the absorption layer
and the substrate should be taken into account. The value of ideal
work of separation, 1.55\,J/m$^{2}$, for a 3-ML-thick adlayer
accords well with other calculations. The calculations predict that
Ag does not wet TiC(001) surface and prefers a three-dimensional
growth mode in the absence of kinetic factor. This work reports on a
clear site and coverage dependence of the measurable physical
parameters, which would benefit the understanding of Ag/TiC(001)
interface and the analysis of experimental data.

The electronic, optical and thermodynamic properties of ZnS in the
zinc-blende (ZB) and wurtzite (WZ) structures are investigated by
using the plane-wave pseudopotential density functional theory
(DFT). The results obtained are consistent with other
theoretical results and the available experimental data. When the
pressures are above 20.5 and 27\,GPa, the ZB-ZnS and the WZ-ZnS are
converted into indirect gap semiconductors, respectively. The
critical point structure of the frequency-dependent complex
dielectric function is investigated and analysed to identify the
optical transitions. Moreover, the values of heat capacity $C_{V}$
and Debye temperature {$\Th$} at different pressures and
different temperatures are also obtained successfully.

This paper reports on a method of assembling semiconducting ZnO
nanowires onto a pair of Au electrodes to construct a
metal--semiconductor--metal (MSM) structure by dielectrophoresis and
studying on its electrical characteristics by using current-voltage
($I-V$) measurements. An electronic model with two back to back
Schottky diodes in series with a semiconductor of nanowires was
established to study the electrical transport of the MSM structures.
By fitting the measured $I-V$ characteristics using the proposed
model, the parameters of the Schottky contacts and the resistance of
nanowires could be acquired. The photoelectric properties of the MSM
structures were also investigated by analysing the measurements of
the electrical transports under various light intensities. The
deduced results demonstrate that ZnO nanowires and their Schottky
contacts with Au electrodes both contribute to photosensitivity and
the MSM structures with ZnO nanowires are potentially applicable for
photonic devices.

A theoretical investigation on the surface plasmon polariton in a
gold cylindrical nanocable is presented. By solving a complete set
of Maxwell's equations in the nanocable (with a $50$\,nm radius gold
nanocore, 10--300\,nm silica layer, and 30--200\,nm gold nanocladding), the dispersion relations on the optical frequency and on
the silica thickness are discussed. When the silica thickness varies
from $50$ to $250$\,nm, at a fixed wavelength, the strong coupling
between the gold nanocore and the nanocladding leads to a
symmetric-like surface mode and an antisymmetric-like surface mode
in the nanocable. The transformation between the surface mode and
the waveguide mode in this structure is also investigated. The
results will be helpful for understanding the surface waves in the
subwavelength structures.

The magnon energy band in a four-layer ferromagnetic superlattice is
studied by using the linear spin-wave approach and Green's function
technique. It is found that three modulated energy gaps exist in the
magnon energy band along $K_{x }$ direction perpendicular to the
superlattice plane. The spin quantum numbers and the interlayer
exchange couplings all affect the three energy gaps. The magnon
energy gaps of the four-layer ferromagnetic superlattice are
different from those of the three-layer one. For the four-layer
ferromagnetic superlattice, the disappearance of the magnon energy
gaps $\Delta \omega _{12} $, $\Delta \omega _{23} $ and $\Delta
\omega _{34} $ all correlates with the symmetry of this system. The
zero energy gap $\Delta \omega _{23}$ correlates with the symmetry
of interlayer exchange couplings, while the vanishing of the magnon
energy gaps $\Delta \omega _{12} $ and $\Delta \omega _{34} $
corresponds to a translational symmetry of $x$-direction in the
lattice. When the parameters of the system deviate from these
symmetries, the three energy gaps will increase.

The growth of Mn$_{5}$Ge$_{3}$ ultrathin films with different
thicknesses, prepared by solid phase epitaxy, is studied. The
results of scanning tunnelling microscopy and low energy electron
diffraction studies show that the film can be formed and it is
terminated with a ($\sqrt 3\times \sqrt 3$) R$30^\circ$ surface
reconstruction when the thickness of Mn exceeds 3 monolayers. The
magnetic properties show that the Curie temperature is about 300\,K
and the $T^{2}$-dependent behaviour is observed to remain up to
220\,K.

The magnetic properties of exchange coupled composite (ECC) media
that are composed of perpendicular magnetic recording media FePt--MgO
and two kinds of soft layers have been studied by using an x-ray
diffractometer, a polar Kerr magneto-optical system (PMOKE) and a
vibrating sample magnetometer (VSM). The results show that ECC media
can reduce the coercivities of perpendicular magnetic recording
media FePt--MgO. The ECC media with granular-type soft layers have
weaker exchange couplings between magnetic grains and the
magnetization process, for ECC media of this kind mainly follow the
Stoner--Wohlfarth model.

Multiferroic NiFe_{2}O_{4}--BaTiO_{3} (BTO) bilayered
thin films are epitaxially grown on (001) Nb-doped SrTiO$_{3}$ (STO)
substrates by pulsed-laser deposition (PLD). Different growth
sequences of NFO and BTO on the substrate yield two kinds of
epitaxial heterostructures with (001)-orientation, i.e.
(001)-NFO/(001)-BTO/substrate and (001)-BTO/(001)-NFO/substrate.
Microstructure studies from x-ray diffraction (XRD) and electron
microscopies show differences between these two heterostructures,
which result in different multiferroic behaviours. The
heterostructured composite films exhibit good coexistence of both
ferroelectric and ferromagnetic properties, in particular, obvious
magnetoelectric (ME) effect on coupling response.

By adjusting the pressure grads in the stage of formation of the
shock wave, a successful prompt explosion process has been
numerically simulated through a progenitor model of 15Msolar, in
which the effects of pressure grads on various convections,
including the Rayleigh--Taloy (R-T) convection, the lepton driven
convection and the negative entropy grads driven convection, in an
inner core are analysed. The simulation results show that the
increase of the pressure grads in the inner core region may cause a
powerful convection, which causes energy transfer from the inner
core to the shock wave rapidly and efficiently.