By means of the reductive perturbation method, three types
of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP)
equations are derived from the baroclinic potential vorticity (BPV)
equation, including the modified KP (mKP) equation, standard KP equation
and cylindrical KP (cKP) equation. Then some solutions of
generalized cKP and KP equations with certain conditions are given
directly and a relationship between the generalized mKP equation and
the mKP equation is established by the symmetry group direct method
proposed by Lou et al. From the relationship and the solutions
of the mKP equation, some solutions of the generalized mKP equation can be
obtained. Furthermore, some approximate solutions of the baroclinic
potential vorticity equation are derived from three types of
generalized KP equations.

This paper is devoted to studying the El Ni?o
mechanism of atmospheric physics. The existence and asymptotic
estimates of periodic solutions for its model are obtained by
employing the technique of upper and lower solution, and using
the continuation theorem of coincidence degree theory.

An evolutionary prisoner's dilemma game is investigated on
two-layered complex networks respectively representing interaction
and learning networks in one and two dimensions. A parameter q is
introduced to denote the correlation degree between the two-layered
networks. Using Monte Carlo simulations we studied the effects of
the correlation degree on cooperative behaviour and found that the
cooperator density nontrivially changes with q for different
payoff parameter values depending on the detailed strategy updating
and network dimension. An explanation for the obtained results is
provided.

The complete band gaps (CBGs) of shallow water waves
propagating over bottoms with periodically drilled holes are
investigated numerically by the plane wave expansion method. Four
different patterns are considered, containing triangular, square,
hexagonal and circular cross-sectioned holes arranged into
triangular lattices. Results show that the width of CBGs can be
changed by adjusting the orientation of noncircular holes and the
effect of hole shape on the width of the maximal CBGs is discussed.

This paper introduces Bohmian mechanics (BM) into the
intense laser-atom physics to study high-order harmonic generation.
In BM, the trajectories of atomic electron in an intense laser field can
be obtained with the Bohm--Newton equation. The power spectrum with the
trajectory of an atomic electron is calculated, which is found to be irregular.
Next, the power spectrum associated with an atom
ensemble from BM is considered, where the power spectrum becomes
regular and consistent with that from quantum mechanics. Finally,
the reason of the generation of the irregular spectrum is discussed.

By virtue of the completeness of Wigner operator and Weyl
correspondence we construct a general equation for deriving pure
state density operators. Several important examples are considered
as the applications of this equation, which shows that our approach
is effective and convenient for deducing these entangled state
representations.

The influence of parameters such as the strength and
frequency of a periodic driving force on the tunneling dynamics is
investigated in a symmetric triple-well potential. It is shown that
for some special values of the parameters, tunneling could be
enhanced considerably or suppressed completely. Quantum fluctuation
during the tunneling is discussed as well and the numerical results
are presented and analysed by virtue of Floquet formalism.

Using the momentum space representation, we solve the
Klein--Gordon equation in one spatial dimension for the case of mixed
scalar and vector linear potentials in the context of deformed
quantum mechanics characterized by a finite minimal uncertainty in
position. The expressions of bound state energies and the associated
wave functions are exactly obtained.

The photodetachment of a hetero-nuclear diatomic molecular
negative ion is studied by using a two-centre model. An analytic
formula is presented for the electron flux distribution of a
heteronuclear diatomic molecular negative ion. Taking HF^{-} as
an example, we calculated the electron flux distributions of this
ion for various detached electron energies. The results show that
the electron flux distributions exhibit oscillatory structures,
which are caused by the interference effect between the two nuclei.
Besides, the laser light polarization also has a great influence on
the electron flux distribution. The oscillation amplitude is the
largest when the laser polarization is parallel to the z-axis;
when the laser polarization is perpendicular to the z-axis, the
oscillation almost vanishes. This study provides a new understanding
of the photodetachment of a heteronuclear diatomic molecular
negative ion.

A criterion for he tquantum teleportation of an arbitrary
N-particle state via a 2N-particle quantum channel is presented
by introducing a term of the ``judgment operator''. Using the
criterion, not only the qualitative judgment of the possibility of
successful teleportation can be made but also the quantitative
calculation of the probability of successful teleportation can be
explicitly given. In addition, a new genuine four-qubit entangled
state is proposed, which could not belong to the category of
previously known states under stochastic local operations and
classical communication.

In the paper ({\em Phys. Rev.} 2006 A {\bf 74} 062320)
Agrawal {\em et al}. have introduced a kind of W-class state which
can be used for the quantum teleportation of single-particle state
via a three-particle von Neumann measurement, and they thought that
the state could not be used to teleport an unknown state by making
two-particle and one-particle measurements. Here we reconsider the
features of the W-class state and the quantum teleportation process
via the W-class state. We show that, by introducing a unitary
operation, the quantum teleportation can be achieved
deterministically by making two-particle and one-particle
measurements. In addition, our protocol is extended to the process
of teleporting two-particle state and splitting information.

In this paper, the entanglement of two moving atoms
induced by a single-mode field via a three-photon process is
investigated. It is shown that the entanglement is dependent on the
category of the field, the average photon number N, the number p
of half-wave lengths of the field mode and the atomic initial state.
Also, the sudden death and the sudden birth of the entanglement are
detected in this model and the results show that the existence of the
sudden death and the sudden birth depends on the parameter and the
category of the mode field. In addition, the three-photon process is a higher
order nonlinear process.

The security of the quantum secure deterministic communication
scheme [{\it Chin. Phys.} {\bf16} (2007) 2549] is reexamined. A
security loophole is pointed out. Taking advantage of this loophole,
an eavesdropper can steal all the secret messages without being
detected by an intercept-and-resend attack strategy. Furthermore, a
possible improvement on this protocol is presented. It makes the
modified protocol secure against this kind of attack.

The energy--momentum tensor, which is coordinate-independent, is
used to calculate energy, momentum and angular momentum of two
different tetrad fields. Although, the two tetrad fields reproduce
the same space--time their energies are different. Therefore, a
regularized expression of the gravitational energy--momentum tensor
of the teleparallel equivalent of general relativity (TEGR), is
used to make the energies of the two tetrad fields equal. The
definition of the gravitational energy--momentum is used to
investigate the energy within the external event horizon. The
components of angular momentum associated with these space--times
are calculated. In spite of using a static space--time, we get
a non-zero component of angular momentum! Therefore, we derive
the Killing vectors associated with these space--times using the
definition of the Lie derivative of a second rank tensor in the
framework of the TEGR to make the picture more clear.

In this paper, we propose a simple model that can generate
small-world network with community structure. The network is
introduced as a tunable community organization with parameter r,
which is directly measured by the ratio of inter- to intra-community
connectivity, and a smaller r corresponds to a stronger community
structure. The structure properties, including the degree
distribution, clustering, the communication efficiency and
modularity are also analysed for the network. In addition, by using
the Kuramoto model, we investigated the phase synchronization on
this network, and found that increasing the fuzziness of community
structure will markedly enhance the network synchronizability;
however, in an abnormal region (r ≤ 0.001), the network has even
worse synchronizability than the case of isolated communities (r =
0). Furthermore, this network exhibits a remarkable
synchronization behaviour in topological scales: the oscillators of
high densely interconnected communities synchronize more easily, and
more rapidly than the whole network.

We investigate phase diffusion of a two-component
Bose--Einstein condensates prepared initially in arbitrary coherent
spin state |θ_{0},φ_{0}|. Analytical expression of the
phase-diffusion time is presented for θ_{0}～π/2 case. In
comparison with the symmetrical case (i.e., θ_{0}=π/2), we
find that the diffusion process becomes slow due to the reduced
atom number variance.

Molecular motors are proteins or protein complexes which
function as transporting engines in biological cells. This paper
models the tether between motor and its cargo as a symmetric linear
potential. Different from Elston and Peskin's work for which
performance of the system was discussed only in some limiting cases,
this study produces analytic solutions of the problem for general
cases by simplifying the transport system into two physical states,
which makes it possible to discuss the dynamics of the motor--cargo
system in detail. It turns out that the tether strength between
motor and cargo should be greater than a threshold or the motor will
fail to transport the cargo, which was not discussed by former
researchers yet. Value of the threshold depends on the diffusion
coefficients of cargo and motor and also on the strength of the
Brownian ratchets dragging the system. The threshold approaches a
finite constant when the strength of the ratchet tends to infinity.

This paper investigates the stochastic resonance (SR)
phenomenon induced by the multiplicative periodic signal in a cancer
growth system with the cross-correlated noises and time delay. To
describe the periodic change of the birth rate due to the periodic
treatment, a multiplicative periodic signal is added to the system.
Under the condition of small delay time, the analytical expression
of the signal-to-noise ratio R_{\rm SNR} is derived in the
adiabatic limit. By numerical calculation, the effects of the
cross-correlation strength \lambda and the delay time \tau on
R_{\rm SNR} are respectively discussed. The existence of a peak in
the curves of R_{\rm SNR} as a function of the noise intensities
indicates the occurrence of the SR phenomenon. It is found that
\lambda and \tau play opposite role on the SR phenomenon, i.e.,
the SR is suppressed by increasing \lambda whereas it is enhanced
with the increase of \tau, which is different from the case where
the periodic signal is additive.

In this paper, a learning control approach is applied to
the generalized projective synchronisation (GPS) of different
chaotic systems with unknown periodically time-varying parameters.
Using the Lyapunov--Krasovskii functional stability theory, a
differential-difference mixed parametric learning law and an
adaptive learning control law are constructed to make the states of
two different chaotic systems asymptotically synchronised. The
scheme is successfully applied to the generalized projective
synchronisation between the Lorenz system and Chen system. Moreover,
numerical simulations results are used to verify the effectiveness
of the proposed scheme.

This paper introduces the concept of
hierarchical-control-based output synchronization of coexisting
attractor networks. Within the new framework, each dynamic node is
made passive at first utilizing intra-control around its own arena.
Then each dynamic node is viewed as one agent, and on account of
that, the solution of output synchronization of coexisting attractor
networks is transformed into a multi-agent consensus problem, which
is made possible by virtue of local interaction between individual
neighbours; this distributed working way of coordination is coined
as inter-control, which is only specified by the topological
structure of the network. Provided that the network is connected and
balanced, the output synchronization would come true naturally via
synergy between intra and inter-control actions, where the
rightness is proved theoretically via convex composite Lyapunov
functions. For completeness, several illustrative examples are
presented to further elucidate the novelty and efficacy of the
proposed scheme.

By introducing an additional state feedback into a
three-dimensional autonomous chaotic attractor Lü system, this
paper presents a novel four-dimensional continuous autonomous
hyper-chaotic system which has only one equilibrium. There are only
8 terms in all four equations of the new hyper-chaotic system, which
may be less than any other four-dimensional continuous autonomous
hyper-chaotic systems generated by three-dimensional (3D) continuous
autonomous chaotic systems. The hyper-chaotic system undergoes Hopf
bifurcation when parameter c varies, and becomes the 3D modified
Lü system when parameter k varies. Although the hyper-chaotic
system does not undergo Hopf bifurcation when parameter k varies,
many dynamic behaviours such as periodic attractor, quasi periodic
attractor, chaotic attractor and hyper-chaotic attractor can be
observed. A circuit is also designed when parameter k varies and
the results of the circuit experiment are in good agreement with those
of simulation.

This paper studies the stability of the fractional order
unified chaotic system. On the unstable equilibrium points, the
``equivalent passivity'' method is used to design the nonlinear
controller. With the definition of fractional derivatives and
integrals, the Lyapunov function is constructed by which it is
proved that the controlled fractional order system is stable. With
Laplace transform theory, the equivalent integer order state
equation from the fractional order nonlinear system is obtained, and the
system output can be solved. The simulation results validate the
effectiveness of the theory.

In the case where the knowledge of goal states is not known, the controllers
are constructed to stabilize unstable steady states for a coupled dynamos
system. A delayed feedback control technique is used to suppress chaos to
unstable focuses and unstable periodic orbits. To overcome the topological
limitation that the saddle-type steady state cannot be stabilized, an
adaptive control based on LaSalle's invariance principle is used to control
chaos to unstable equilibrium (i.e. saddle point, focus, node, etc.). The
control technique does not require any computer analysis of the system
dynamics, and it operates without needing to know any explicit knowledge of
the desired steady-state position.

A new stability theory of nonlinear dynamic systems is
proposed, and a novel adaptive synchronisation method is presented
for fractional-order chaotic and hyperchaotic systems based on the
theory described in this paper. In comparison with previous methods,
not only is the present control scheme simple but also it employs
only one control strength, converges very fast, and it is also
suitable for a large class of fractional-order chaotic and
hyperchaotic systems. Moreover, this scheme is analytical and simple
to implement in practice. Numerical and circuit simulations are
used to validate and demonstrate the effectiveness of the method.

The existence of two types of generalized synchronisation
is studied. The model considered here includes three bidirectionally
coupled chaotic systems, and two of them denote the driving systems,
while the rest stands for the response system. Under certain
conditions, the existence of generalised synchronisation can be
turned to a problem of compression fixed point in the family of
Lipschitz functions. In addition, theoretical proofs are proposed to
the exponential attractive property of generalised synchronisation
manifold. Numerical simulations validate the theory.

The impulsive synchronization problem of two identical
chaotic ratchets
is investigated in this paper.
We demonstrate that the impulsive method to control directed
transport is applicable when there are multiple co-existing
attractors in phase space transporting particles in different
directions. Numerical simulations are carried out to illustrate the
effectiveness of the proposed method.

Modeling time headways between vehicles has attracted
increasing interest in the traffic flow research field recently,
because the corresponding statistics help to reveal the intrinsic
interactions governing the vehicle dynamics. However, most previous
micro-simulation models cannot yield the observed log-normal
distributed headways. This paper designs a new car-following model
inspired by the Galton board to reproduce the observed time-headway
distributions as well as the complex traffic phenomena. The
consistency between the empirical data and the simulation results
indicates that this new car-following model provides a reasonable
description of the car-following behaviours.

Ce^{3+}-doped yttrium lanthanum oxide
(Y_{0.9}La_{0.1})_{2}O_{3} transparent ceramics is fabricated
with nanopowders and sintered in H_{2} atmosphere. The spectral
properties of Ce:(Y_{0.9}La_{0.1})_{2}O_{3} transparent
ceramics are investigated. There appear two characteristic
absorption peaks of Ce^{3+} ions at 230~nm and 400~nm,
separately. It is found that Ce^{3+} ions can efficiently
produce emission at 384~nm from (Y_{0.9}La_{0.1})_{2}O_{3}
transparent ceramic host, while the emission is completely quenched
in Re_{2}O_{3} (Re=Y, Lu, La) host materials.

This paper uses the classical ensemble method to study the
double ionization of a 2-dimensional (2D) model helium atom
interacting with an elliptically polarized laser pulse. The classical
ensemble calculation demonstrates that the ratio of double to single
ionization decreases with the increasing ellipticity of the driving
field. The classical scenario shows that there are hardly any e--e
recollisions with the circularly polarized laser pulse. The double
ionization probability is studied for linearly and circularly
polarized laser pulses. The classical numerical results are
consistent with the semiclassical rescattering mechanism and in
agreement with the experimental results and the quantum calculations
qualitatively.

This paper uses a nonperturbative scattering theory to
study photoelectron angular distributions of homonuclear diatomic
molecules irradiated by circularly polarized laser fields. This
study shows that the nonisotropic feature of photoelectron angular
distributions is not due to the polarization of the laser field but
the internuclear vector of the molecules. It suggests a method to
measure the molecular orientation and the internuclear distance of
molecules through the measurement of photoelectron angular
distributions.

We present a valence orbital method of calculating
high-order harmonic generation from a diatomic molecule with arbitrary
orientation by using a space rotation operator. We evaluate the
effects of each valence orbital on harmonic emissions from N_{2}
and O_{2} molecules in detail separately. The calculation
results confirm the different properties of harmonic yields from
N_{2} and O_{2} molecules which are well consistent with available
experimental data. We observe that due to the orientation dependence
of \sigma and \pi orbitals, the bonding orbital (\sigma
_{2pz} )^2 of N_{2} determines the maximum of harmonic emission
when the molecular axis of N_{2} is aligned parallel to the laser
vector, and the magnitude of the high harmonic signal gradually
weakens with the orientation angle of molecular axis increasing. But
for O_{2} molecule the antibonding orbitals (\pi _{2py}^\ast )^1
and (\pi _{2pz}^\ast )^1 contribute to the maximum of harmonic
yield when O_{2} is aligned at 45^{\circ} and bonding orbitals
(\pi _{2py} )^2 and (\pi _{2pz} )^2 slightly influence the
orientation angle of maximum of harmonic radiation not exactly at
45^{\circ}.

We demonstrated two experimental methods of producing and
guiding pulsed atomic beams on chip. One is to trap atoms first in a
U-type magneto-optical trap on the chip, then transfer them to the
magnetic guide field and push them simultaneously by a continuous
force from the power imbalance of the magneto-optical trap laser
beams hence the pulsed cold atom beams are produced and move along
the magnetic guide to the destination. The other is to trap atoms
directly by a H-type magneto-optical trap, then push them to make
them move along the magnetic guide field, thus high rate cold atom
beams can be produced and guided on the chip.

Employing the two-state model and the time-dependent wave
packet method, we have investigated the influences of the parameters of the intense
femtosecond laser field on the evolution of the wave packet, as well
as the population of ground and double-minimum electronic states of
the NaRb molecule. For the different laser wavelengths, the evolution of
the wave packet of 6{ }^1\Sigma ^ + state with time and
internuclear distance is different, and the different laser
intensity brings different influences on the population of the
electronic states of the NaRb molecule. One can control the evolutions
of wave packet and the population in each state by varying the laser
parameters appropriately, which will be a benefit for the light
manipulation of atomic and molecular processes.

We have developed a computer code for {\em ab initio}
the variational configuration interaction calculation of the electronic
structure of atoms via variationally optimized Lagurre type
orbitals, treating the orbital effective charges as variational
parameters. Excited states of the same symmetry, in order to avoid
the inherent restrictions of the standard method of
Hylleraas--Unheim and MacDonald, are computed variationally by
minimizing the recently developed minimization functionals for
excited states. By computing, at the minimum, the one-electron
density and the probability distribution of the two-electron angle,
and the most probable two-electron angle, we investigate the atomic
states of the carbon atom. We show that, without resorting to the
(admittedly unproven) concept of hybridization, as an intrinsic
property of the atomic wave function, the most probable value of the
two-electron angle is around the known angles of carbon bonding,
i.e. either 109^\circ or 120^\circ or 180^\circ, depending on
each low-lying state of the bare carbon atom.

Clusters traverse a gas and collide with gas particles.
The gas particles are absorbed, and the clusters become hosts. If
the clusters are size-selected, the number of guests will be Poisson
distributed. We review this by showcasing four laboratory procedures
that all rely on the validity of the Poisson model. The effects of a
statistical distribution of the clusters' sizes in a beam of
clusters are discussed. We derive the average collision rates.
Additionally, we present Poisson mixture models that also involve
standard deviations. We derive the collision statistics for common
size distributions of hosts and also for some generalizations
thereof. The models can be applied to large noble gas clusters
traversing doping gas. While outlining how to fit a generalized
Poisson to the statistics, we still find even these Poisson models
to be often insufficient.

In recent years, linear fractal sea surface models have
been developed for the sea surface in order to establish an
electromagnetic backscattering model. Unfortunately, the sea surface
is always nonlinear, particularly at high sea states. We present a
nonlinear fractal sea surface model and derive an electromagnetic
backscattering model. Using this model, we numerically calculate the
normalized radar cross section (NRCS) of a nonlinear sea surface.
Comparing the averaged NRCS between linear and nonlinear fractal
models, we show that the NRCS of a linear fractal sea surface
underestimates the NRCS of the real sea surface, especially for sea
states with high fractal dimensions, and for dominant ocean surface
gravity waves that are either very short or extremely long.

A very simple technique, by which both the magnitude and
the sign of nonlinear refraction can be determined through using
only one single pulse and beam with a phase object, is presented.
Using this technique, only the transmittance of an aperture in the
far field is investigated. We study the nonlinear refraction of the
carbon disulfide by using the presented technique with 21~ps pulses
at a wavelength of 532~nm as a test.

A simple method is applied to calculating the optical
path difference (OPD) of a plane parallel uniaxial plate with an
arbitrary optical axis direction. Then, the theoretical expressions
of the OPD and lateral displacement (LD) of Savart polariscope under
non-ideal conditions are obtained exactly. The variations of OPD and
LD are simulated, and some important conclusions are obtained when
the optical axis directions have an identical tolerance of \pm
1^{{\circ}}. An application example is given that the tolerances of
optical axis directions are gained according to the spectral
resolution tolerances of the stationary polarization interference
imaging spectrometer (SPIIS). Several approximate formulae are
obtained for explaining some conclusions above. The work provides a
theoretical guidance for the optic design, crystal processing,
installation and debugging, data analysis and spectral
reconstruction of the SPIIS.

Under the quadratic approximation of the Rytov's phase
structure function, this paper derives the general closed-form
expressions for the mean-squared width and the angular spread of
partially coherent beams in turbulence. It finds that under a
certain condition different types of partially coherent beams may
have the same directionality as a fully coherent Gaussian beam in
free space and also in atmospheric turbulence if the angular spread
is chosen as the characteristic parameter of beam directionality. On
the other hand, it shows that generally, the directionality of
partially coherent beams expressed in terms of the angular spread is
not consistent with that in terms of the normalized far-field
average intensity distribution in free space, but the consistency
can be achieved due to turbulence.

The femtosecond temporal speckle field of a random medium is
studied theoretically and experimentally. Femtosecond temporal
speckle arises from the interference of multiple randomly scattered
electric fields. The femtosecond temporal speckle field is measured with
a cross-correlation frequency-resolved optical gating method. The
spatial average of the speckle field yields a smooth transmitted
profile. The speckle field is a circular complex Gaussian variable
because the scattered light beams from different trajectories have
no correlation with each other. The field and the intensity profiles
of individual speckle spots fluctuate randomly in time. The ensemble
average of the temporal intensity profiles converges, thereby
yielding the photon travel time probability distribution
function.

Truncation manipulation is a simple but effective way to
improve the intensity distribution properties of the phase-locked
Gaussian beam array at the receiving plane. In this paper, the
analytical expression for the propagation of the phase-locked truncated
Gaussian beam array in a turbulent atmosphere is obtained based on
the extended Huygens--Fresnel principle. Power in the
diffraction-limited bucket is introduced as the beam quality factor
to evaluate the influence of different truncation parameters. The
dependence of optimal truncation ratio on the number of beamlets,
the intensity of turbulence, propagation distance and laser
wavelength is calculated and discussed. It is revealed that the
optimal truncation ratio is larger for the laser array that contains
more lasers, and the optimal truncation ratio will shift to a larger
value with an increase in propagation distance and decrease in
intensity of atmosphere turbulence. The optimal truncation ratio is
independent of laser wavelength.

This paper demonstrates the influence of external optical
feedback on the polarization state of longitudinal modes in
quasi-isotropic microchip Nd:YAG lasers. Under optical feedback, the
polarization state of longitudinal modes in quasi-isotropic lasers
relies strongly on the intracavity anisotropy loss and mode
competition. When the intracavity anisotropy loss is small, external
optical feedback can cause polarization switching and strong mode
competition between two orthogonal linearly polarized eigenstates of
one laser longitudinal mode, which leads to the distortion of laser
intensity modulation waveform. The polarization switching is
independent of the initial external cavity length. By increasing the
intracavity anisotropy loss, one polarization eigenstate can be
suppressed and the laser works in single-polarization state. A
theoretical analysis based on the compound cavity model is
presented, which is in good agreement with the experimental results.
The results offer guidance to the development of laser feedback
interferometers.

We present the numerical and experimental study on
the coherent beam combining of fibre amplifiers by means of simulated
annealing (SA) algorithm. The feasibility is validated by the Monte
Carlo simulation of correcting static phase distortion using SA
algorithm. The performance of SA algorithm under time-varying phase
noise is numerically studied by dynamic simulation. It is revealed
that the influence of phase noise on the performance of SA algorithm
gets stronger with an increase in amplitude or frequency of phase
noise; and the laser array that contains more lasers will be more
affected from phase noise. The performance of SA
algorithm for coherent beam combining is also compared with a widely
used stochastic optimization algorithm, i.e., the stochastic
parallel gradient descent (SPGD) algorithm. In a proof-of-concept
experiment we demonstrate the coherent beam combining of two 1083~nm
fibre amplifiers with a total output power of 12~W and 93%
combining efficiency. The contrast of the far-field coherently
combined beam profiles is calculated to be as high as 95%.

This paper reports that in the quantization of
electromagnetic field in the dielectrics, the wave equation with
regard to the Green function is analytically solved by a direct integral
method for a quadratic continuous nonlinear absorptive dielectric
medium. The quantization of the electromagnetic field in such a
nonlinear absorptive dielectric is carried out for which the
material dielectric function is assumed as a separable variable about
the frequency and the space coordinate. The vacuum field
fluctuations for different spatial continuous variations of
dielectric function are numerically calculated, which shows that the
present result is self-consistent.

A system consisting of two atoms interacting with a
two-mode vacuum is considered, where each atom is resonant with the
two cavity modes through two different competing transitions. The
effect of mode--mode competition on the atom--atom entanglement is
investigated. We find that the entanglement between the two atoms
can be induced by the mode--mode competition. For the initial atomic
state |\varPsi(0)\rangle, whether the atoms are initially
separated or entangled, a large or even maximal entanglement between
them can be obtained periodically by introducing the mode--mode
competition. For the initial atomic state |\varPhi(0)\rangle, the
strong mode--mode competition can prevent the two atoms entangled
initially from suffering entanglement sudden death; besides, it
makes them in a more stable and longer-lived entanglement than in
the non-competition case.

By using the algebraic dynamical approach, an atom--field
bipartite system in mixed state is employed to investigate the
partial entropy change and the entanglement in a cavity filled with
Kerr medium. The effects of different nonlinear intensities are
studied. One can find that the Kerr nonlinearity can reduce the
fluctuation amplitudes of the partial entropy changes and the
entanglement of the two subsystems, and also influence their
periodic evolution. Meanwhile, increasing the Kerr nonlinear
strength can convert the anti-correlated behaviour of the partial
entropy change to the positively correlated behaviour. Furthermore,
the entanglement greatly depends on the temperature. When the
temperature or the nonlinear intensity increases to a certain value,
the entanglement can be suppressed greatly.

We show that incoherently coupled soliton pairs can
exist in nonlocal Kerr-type nonlinear media. Such
solitons can propagate in bright--bright, dark--dark, and gray--gray
configurations. When the nonlocal nonlinearity is absent, these
bright--bright and dark--dark soliton pairs are those observed
previously in local Kerr-type nonlinear media. Our analysis
indicates that for a self-focusing nonlinearity the intensity full
width half maximum (FWHM) of the bright--bright pair components
increases with the degree of nonlocality of the nonlinear response,
whereas for a self-defocusing nonlinearity the intensity FWHM of the
dark--dark and gray--gray pair components decreases with the
increase in the degree of nonlocality of the nonlinear response. The
stability of these soliton pairs has been investigated numerically
and it has been found that they are stable.

Holographic parameters and photobleaching kinetics of the
photopolymers with five different amine photoinitiators are studied.
The maximum values of diffraction efficiency, photobleaching
coefficient and quantum yield follow the sequence: Triethanolamine
(TEA)> Diethanolamine (DEA)> Ethanolamine (EA)> Triethylamine
(TETN)> Diethylamine (DETN). The holographic capabilities of
photopolymer performances are determined by the number of functional
groups in the amine molecular structure. There is an optimum
proportion of the photoinitiator, the photosensitizer and the
monomer in the test of holographic parameters with different amine
concentrations. The maximum diffraction efficiency is 59.26\%,
sensitivity is 1.72\times 10^{ - 3}~cm^{2}/mJ, and the maximum
refractive modulation index is 4.64\times 10^{ - 4}.

By utilizing the electrorheological effect,
three-dimensional colloidal crystals can be produced, whose lattice
structure can be changed from the body-centered-tetragonal lattice
to other lattices under the application of electric fields. This
paper calculates photonic band structures of such crystals with
lattice structure transformation, and demonstrates the existence of
complete band gaps for some intermediate lattices. Thus, it becomes
possible to use the electrorheological effect to achieve photonic
crystals with desired photonic gap properties resulting from tunable
structures.

We report the near-stoichiometric Ti:LiNbO_{3} strip
waveguides fabricated by vapour transport equilibration (VTE) at
1060~^{\circ}C for 12 h and co-diffusion of 4--8~\mu m wide,
115-nm thick Ti-strips. Optical studies show that these waveguides
are monomode at 1.5~\mu m and have losses of 1.3 and 1.1~dB/cm for
the TM and TE modes, respectively. In the waveguide width/depth
direction, the mode field follows a Gauss/Hermite--Gauss profile.
A secondary ion mass spectrometry study reveals that the Ti profile
follows a sum of two error functions along the width direction and a
complementary error function in the depth direction. Micro-Raman
analysis shows that the Li-composition in the depth direction
also follows a complementary error function. The mean Li/Nb ratio in
the waveguide layer is about 0.98. The inhomogeneous Li-composition
profile results in a varied substrate index in the guiding layer,
and the refractive index profile in the guiding layer is given.

This paper presents the effects of density difference on
the three-dimensional (3D) distribution of random mixed packing. The
random mixed packing dynamics of particles of two different
densities are simulated. The initial state is homogeneous, but the
final packing state is inhomogeneous. The segregation phenomenon
(inhomogeneous distribution) is also observed. In the final state,
the top layers are composed of mostly light particles. The several
layers beneath the top contain more heavy particles than light
particles. At the bottom, they also contain more heavy particles
than light particles. Furthermore, at both the top and the bottom,
particle clustering is observed. The current study also analyses the
cause of this inhomogeneity in detail. The main cause of this
phenomenon is the velocity difference after collision of these two
types of particles induced by the density difference. The present
study reveals that even if particles were perfectly mixed, the
packing process would lead to the final inhomogeneous mixture. It
suggests that special treatment may be required to get the true
homogeneous packing.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The behaviours of ionization and shock propagation in
radiatively heated material is crucial for the understanding of
indirect drive inertial confinement fusion as well as some
astrophysics phenomena. In this work, radiation field with a peak
temperature of up to 155 eV was generated in a gold cavity heated by
four laser beams on the SG-II laser system and was used to irradiate
a plastic foam cylinder at one end. The radiatively ablated foam
cylinder was then backlighted side-on by x-ray from a
laser-irradiated Ti disk. By observing the transmission decrease due
to the shock compression of the foam cylinder, the trajectories of shock
front were measured, and from the onset of the intense thermal
emission from the side of the cylinder, the propagations of
the ionization front were also observed on the same shot. The
experimental measurements were compared to predictions of the
radiation hydrodynamics code Multi-1D and reasonable agreements were
found.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

This paper reports that a large amount of Mn-doped ZnO
nanorods have been synthesized through thermal evaporation. The
morphologies and properties are studied with x-ray diffraction,
a scanning electron microscope, transmission electron microscope and
Raman spectroscope. The results indicate that the manganese atoms
occupy the zinc vacancies in the wurtzite lattice of ZnO without
forming secondary phases. The exact manganese content has been
studied by the x-ray fluorescence spectrum. Meanwhile, the magnetic moment
versus temperature result proves that the as-prepared Mn-doped ZnO
nanorods show ferromagnetic properties at temperatures as high as
400~K. These studies provide a good understanding of the origin of
magnetic properties in diluted magnetic semiconductors.

Mo-doped SnO_{2} (MTO) nanowires are synthesized by an
in-situ doping chemical vapour deposition method. Raman scattering
spectra indicate that the lattice symmetry of MTO nanowires lowers
with the increase of Mo doping, which implies that Mo ions do enter
into the lattice of SnO_{2} nanowire. Ultraviolet-visible diffuse
reflectance spectra show that the band gap of MTO nanowires
decreases with the increase of Mo concentration. The
photoluminescence emission of SnO_{2} nanowires around 580~nm at
room temperature can also be controlled accurately by Mo-doping, and
it is extremely sensitive to Mo ions and will disappear when the
atomic ratio reaches 0.46%.

A series of big single crystals of BaFeFe_{2-x}Ni_{x}As_{2} have been prepared by the FeAs self-flux method,
with nominal nickel doping x = 0--0.12. The dimensions of the
cleaved crystals are over 10~mm along ab plane and ～ 2~mm
in maximum along the c direction. The measurements of x-ray
diffraction, electrical resistance and magnetic property are carried
out on the crystals. For the undoped parent compound
BaFe_{2}As_{2}, both resistance and magnetization data display
an anomaly associated with spin density wave and/or structural phase
transition, with the transition temperatures at ～ 138~K. For
Ni-doped BaFe_{2-x}Ni_{x}As_{2} crystals, the
superconducting critical temperature T_{c} ranges from 4.3~K
for x=0.06 sample to 20~K for the optimally doped x=0.10
crystal.

By using the molecular dynamic simulation method with a
fourth-order Runge--Kutta algorithm, a two-dimensional dc- and
ac-driven Frenkel--Kontorova (FK) model with a square symmetry
substrate potential for a square lattice layer has been investigated
in this paper. For this system, the effects of many different
parameters on the average velocity and the static friction force
have been studied. It is found that not only the amplitude and
frequency of ac-driven force, but also the direction of the external
driving force and the misfit angle between two layers have some
strong influences on the static friction force. It can be concluded
that the superlubricity phenomenon appears easily with a larger ac
amplitude and lower ac frequency for some special direction of the
external force and misfit angle.

The interpenetrating network structure provides an interesting avenue to novel materials. Locally resonant phononic
crystal (LRPC) exhibits excellent sound attenuation performance based on the periodical arrangement of sound wave scatters.
Combining the LRPC concept and interpenetrating network glassy structure, this paper has developed a new material which can achieve a wide band underwater strong acoustic absorption. Underwater absorption coefficients of different samples were measured by the pulse tube. Measurement results show that the new material possesses excellent underwater acoustic effects in a wide frequency range.Moreover, in order to investigate impacts of locally resonant units,some defects are introduced into the sample. The experimental result and the theoretical calculation both show that locally resonant units being connected to a network structure play an important role in achieving a wide band strong acoustic absorption.

We have performed the first-principles linear response calculations of the lattice dynamics, thermal equation of state and
thermodynamical properties of hcp Os metal by using the plane-wave pseudopotential method. The thermodynamical properties are deduced from the calculated Helmholtz free energy by taking into account the electronic contribution and lattice vibrational contribution. The phonon frequencies at Gamma point are consistent with experimental
values and the dispersion curves at various pressures have been determined. The calculated volume, bulk modulus and their pressure derivatives as a function of temperature are in excellent agreement with the experimental results. The calculated specific heat indicates that the electronic contribution is important not only at very low temperatures but also at high temperatures due to the electronic thermal excitation. The calculated Debye temperature at a very low temperature is in good agreement with experimental values and drops to a constant until 100~K.

Under harmonic approximation, this paper discusses the
linear dispersion relation of the one-dimensional chain. The existence
and evolution of discrete breathers in a general one-dimensional
chain are analysed for two particular examples of soft (Morse) and
hard (quartic) on-site potentials. The existence of discrete
breathers in one-dimensional and two-dimensional Morse lattices is
proved by using rotating wave approximation, local anharmonic
approximation and a numerical method. The localization and amplitude
of discrete breathers in the two-dimensional Morse lattice with on-site
harmonic potentials correlate closely to the Morse parameter a and
the on-site parameter к.

Cu thin films are deposited on p-type Si (100) substrates
by magnetron sputtering at room temperature. The interface reaction
and atomic diffusion of Cu/SiO_{2}/Si (100) systems are studied by
x-ray diffraction (XRD) and Rutherford backscattering spectrometry
(RBS). Some significant results can be obtained. The onset
temperature of interdiffusion for Cu/SiO_{2}/Si(100) is 350~℃.
With the annealing temperature increasing, the interdiffusion
becomes more apparent. The calculated diffusion activation energy is
about 0.91 eV. For the Cu/SiO_{2}/Si (100) systems copper
silicides are not formed below an annealing temperature of 350~℃.
The formation of the copper silicides phase is observed when the
annealing temperature arrives at 450~℃.

In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical
buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We_{1},~We_{2},~We_{3} and We_{4}, which distinguish five different kinds of bubble behaviours. It is also
found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We >We_{2}, the bubble will not reach a steady shape, and in this case
it will not rise with a constant speed. The mechanism of the above
phenomena has been analysed theoretically and numerically.

This paper proposes a controlled particle deposition model
for cluster growth on the substrate surface and then presents exact
results for the cluster (island) size distribution. In the system,
at every time step a fixed number of particles are injected into the
system and immediately deposited onto the substrate surface. It
investigates the cluster size distribution by employing the
generalized rate equation approach. The results exhibit that the
evolution behaviour of the system depends crucially on the details
of the adsorption rate kernel. The cluster size distribution can
take the Poisson distribution or the conventional scaling form in
some cases, while it is of a quite complex form in other cases.

The reconstructed structure of Cu (100) surface induced by
atomic N adsorption is studied by using scanning tunneling
microscopy (STM). The 2D structure of copper boundary between
neighbouring N covered islands is found to be sensitive to the
growth conditions, e.g. N^{+} bombardment time and annealing
temperature. The copper boundary experiences a transition from
nano-scale stripe to nano-particle when the substrate is
continuously annealed at 623~K for a longer time. A well-defined
copper-stripe network can be achieved by precisely controlling the
growth conditions, which highlights the possibility of producing new
templates for nanofabrication.

This paper reports that Al_{1-x}In_{x}N epilayers
were grown on GaN template by metalorganic chemical vapor deposition
with an In content of 7%--20%. X-ray diffraction results indicate
that all these Al_{1-x}In_{x}N epilayers have a relatively low
density of threading dislocations. Rutherford
backscattering/channeling measurements provide the exact
compositional information and show that a gradual variation in
composition of the Al_{1-x}In_{x}N epilayer happens along the
growth direction. The experimental results of optical reflection
clearly show the bandgap energies of Al_{1-x}In_{x}N
epilayers. A bowing parameter of 6.5~eV is obtained from the
compositional dependence of the energy gap. The cathodoluminescence
peak energy of the Al_{1-x}In_{x}N epilayer is much lower than its
bandgap, indicating a relatively large Stokes shift in the Al_{1-x}In_{x}N sample.

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

The structural, elastic constants and anisotropy of
RuB_{2} under pressure are investigated by first-principles
calculations based on the plane wave pseudopotential density
functional theory method within the local density approximation
(LDA) as well as the generalized gradient approximation (GGA) for
exchange and correlation. The results accord well with the available
experimental and other theoretical data. The elastic constants,
elastic anisotropy, and Debye temperature \varTheta as a function
of pressure are presented. It is concluded that RuB_{2} is brittle
in nature at low pressure, whereas it becomes ductile at higher
pressures. An analysis for the calculated elastic constant has been
made to reveal the mechanical stability of RuB_{2} up to 100~GPa.

The influencing range of a vacancy defect in a zigzag
single-walled nanotube is characterized with both structural
deformation and variation in bandstructure. This paper proposes a
microscopic explanation to relate the structural deformation to the
bandstructure variation. With an increasing defect density, the
nanotubes become oblate and the energy gap between the deep
localized gap state and the conducting band minimum state decreases.
Theoretical results shed some light on the local energy gap
engineering via vacancy density for future potential applications.

Current--voltage measurements obtained from lead zirconate
titanate/nickel bilayered hollow cylindrical magnetoelectric
composite showed that a sinusoidal current applied to the copper
coil wrapped around the hollow cylinder circumference induces
voltage across the lead zirconate titanate layer thickness. The
current--voltage coefficient and the maximum induced voltage in lead
zirconate titanate at 1~kHz and resonance (60.1~kHz) frequencies
increased linearly with the number of the coil turns and the applied
current. The resonance frequency corresponds to the
electromechanical resonance frequency. The current--voltage
coefficient can be significantly improved by optimizing the
magnetoelectric structure geometry and/or increasing the number of
coil turns. Hollow cylindrical lead zirconate titanate/nickel
structures can be potentially used as current sensors.

Sol--gol method was employed to synthesize Mg doped ZnO
films on Si substrates. The annealing temperature-dependent
structure and optical property of the produced samples were studied.
An interesting result observed is that increasing Mg concentration
in the studied samples induces the full width at half maximum (FWHM)
of their near-band-edge (NBE) emission decrease and the defect
related emission of the corresponding sample suppresses drastically.
The possible mechanism of the observed result is discussed.

The p and s-polarized surface plasmon polaritons (SPPs) of symmetric and asymmetric slabs formed arbitrarily by four types of conventional materials: dielectrics, negative dielectric permittivity materials, negative magnetic permeability materials, and left-handed materials are comprehensively analysed. The existence regions, dispersion relations, and excitation of SPPs in different frequency regions are investigated in detail. For symmetric slabs, the numbers and the frequency positions of surface polariton branches are quite different. At the same time, the pairs
of the p or s-polarized SPP branches occur in the same frequency range. For asymmetric slabs, the SPP branches in mid- and high-frequency ranges are greatly different. In addition, the slab thickness has a great effect on SPPs of asymmetric and symmetric slabs. The attenuated total reflection spectra for the cases of p and s polarizations in these slabs are also calculated.

Taking account of the electron--electron (hole) and
electron--hole interactions, the tunneling processes of the main
quantum dot (QD) Coulomb-coupled with a second quantum dot embedded
in n--n junction have been investigated. The eighteen resonance
mechanisms involved in the tunneling processes of the system have
been identified. It is found that the tunneling current depends
sensitively on the electron occupation number in the second quantum
dot. When the electron occupation number in the second dot is tiny,
both the tunneling current peaks and the occupation number plateaus
in the main QD are determined by the intra-resonance mechanism. The
increase of the electron occupation number in the second dot makes
the inter-resonance mechanism participate in the transport processes.
The competition between the inter and intra resonance mechanisms
persists until the electron occupation number in the second dot
reaches around unity, leading to the consequence that the
inter-resonance mechanisms completely dominate the tunneling
processes.

Deep levels in Cds/CdTe thin film solar cells have a
potent influence on the electrical property of these devices. As an
essential layer in the solar cell device structure, back contact is
believed to induce some deep defects in the CdTe thin film. With the
help of deep level transient spectroscopy (DLTS), we study the deep
levels in CdS/CdTe thin film solar cells with Te:Cu back contact.
One hole trap and one electron trap are observed. The hole trap H1,
localized at E_{v}+0.128~eV, originates from the vacancy of Cd
(V_{Cd}. The electron trap E1, found at E_{c}-0.178~eV,
is considered to be correlated with the interstitial Cu_{i}^{=}
in CdTe.

By using a model Hamiltonian with competing antiferromagnetic (AFM) spin density wave (SDW) and d-wave
superconductivity orders, the effect of next-nearest-neighbour (nnn)
hopping on spin and charge structures in high-temperature
superconductors is investigated at finite temperatures. For an
optimally doped sample, we find that the AFM order magnitude in the
vortex core is firstly enhanced and then suppressed, accompanied
with a ``positively → negatively → positively" charged vortex structure transition with increasing nnn
hopping strength, which implies that the AFM order is unnecessarily
bounded to an electron-rich vortex core. In addition, a charge
ordering pattern with four negatively charged peaks localized in a
small region is also found around the vortex core centre without net
charge. Recent scanning-tunneling-microscopy experimental
observations of the checkerboard structure are hopefully
understood.

This paper reports that the polycrystalline
Si_{0.965}Mn_{0.035}:B films have been prepared by cosputtering
deposition followed by rapid thermal annealing for crystallization.The polycrystalline thin films consist of two ferromagnetic phases.The low temperature ferromagnetic phase with Curie temperature (T_{c}) of about 50~K is due to the Mn_{4}Si_{7} phase in the films, while the high temperature one (T_{c}～ 250~K) is resulted from the incorporation of Mn into silicon. The films are treated by boron plasma excited with the approach of microwave plasma enhanced chemical vapor deposition for 40 minutes. After plasma treatment, it is observed that no extra magnetic phases or magnetic complexes exist in the films, while both the high temperature saturation magnetization and the hole concentration in the films increase. The obvious correlation between the magnetic properties and the electrical properties of the polycrystalline Si_{0.965}Mn_{0.035}:B films suggests that the hole carriers
play an important role in Si:Mn diluted magnetic semiconductors.

This paper reports that Zn_{0.97}Mn_{0.03}O thin films
have been prepared by radio-frequency sputtering technology followed
by rapid thermal processing in nitrogen and oxygen ambient
respectively. Magnetic property investigation indicates that the
films are ferromagnetic and that the Curie temperature (T_{c}) is over
room temperature. It is observed that the saturation magnetization
of the films increases after annealing in nitrogen ambience but
decreases after annealing in oxygen. Room temperature
photoluminescence spectra indicate that the amount of defects in the
films differs after annealing in the different ambiences. This
suggests that the ferromagnetism in Zn_{0.97}Mn_{0.03}O films is
strongly related to the defects in the films.

This paper numerically investigates the magnetoelastic
instability in the S = 1/2 {XXZ} rings containing finite spins N
with antiferromagnetic nearest-neighbour ({NN}) and next-nearest
neighbour ({NNN}) coupling. It finds that, as the {NN} anisotropy
Δ_{1} equals the {NNN} anisotropy \varDelta_{2}, there
exists a critical {NNN} coupling strength J_{2}^{c}(≈0.5), at which the systems always locate in dimerized phase for
arbitrary large spring constant. As Δ_{1} \ne
Δ_{2}, the values of J_{2}^{\rm c} are dependent on N
and the difference of (Δ_{1}-\varDelta_{2}).

A series of Nb^{5+} codoped red long afterglow
phosphors CaTi_{1-x}Nb_{x}O_{3}:Pr _{0.002}^{3+} (0
≤ x ≤ 0.05) is prepared by a solid state reaction method. Their
photoluminescence, phosphorescence and thermoluminescence are
investigated. The results indicate that codoping Nb^{5+} can
improve the photoluminescence and phosphorescence property of
CaTiO_{3}:Pr^{3+} significantly. When 3-mol% Nb^{5+} is
codoped, the emission intensity of CaTiO_{3}:Pr^{3+} is
enhanced twice, while the afterglow time is extended from 10 min to
about 40 min. Thermoluminescence results reveal that the trapping
level of CaTiO_{3}:Pr^{3+} is reduced from 0.82~eV to 0.62~eV
by codoping Nb^{5+}. The effect of Nb^{5+} doping on
enhancing the photoluminescence intensity and afterglow time of
CaTiO_{3}:Pr^{3+} is discussed.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Based on a recently formulated unified theory of coherence
and polarization, a method is described to study turbulence-induced
changes in the polarization, the coherence and the spectrum of
partially coherent electromagnetic beams on propagation. The
electromagnetic Gaussian Schell-model beam is taken as a typical
example of partially coherent electromagnetic beams, and the
closed-form expressions for the degree of polarization, the degree
of coherence and the spectrum of electromagnetic Gaussian
Schell-model beams propagating through atmospheric turbulence are
derived in the quadratic approximation of Rytov's phase structure
function. Some interesting results are obtained, which are
illustrated by numerical examples and are explained in physics.

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