The EI Ni?o and Southern Oscillation (ENSO) is an interannual
phenomenon involved in the tropical Pacific sea--air interactions. In
this paper, an asymptotic method of solving nonlinear equations for
the ENSO model is proposed. And based on a class of oscillator of the
ENSO model and by employing the method of homotopic mapping, the
approximate solution of equations for the corresponding ENSO model
is studied. It is proved from the results that homotopic method can
be used for analysing the sea surface temperature anomaly in the
equatorial Pacific of the sea--air oscillator for the ENSO model.

Based on some known facts of integrable models, this paper proposes
a new (2+1)-dimensional bilinear model equation. By virtue of the
formal series symmetry approach, the new model is proved to be
integrable because of the existence of the higher order symmetries.
The Lie point symmetries of the model constitute an infinite
dimensional Kac--Moody--Virasoro symmetry algebra. Making use of the
infinite Lie point symmetries, the possible symmetry reductions of
the model are also studied.

This paper studies the Lie symmetries and Noether conserved
quantities of discrete mechanical systems with variable mass. The
discrete Euler--Lagrange equation and energy evolution equation are
derived by using a total variational principle. The invariance of
discrete equations under infinitesimal transformation groups is
defined to be Lie symmetry. The condition of obtaining the Noether
conserved quantities from the Lie symmetries is also presented. An
example is discussed for applications of the results.

This paper analyses bright and dark spatial self-similar waves
propagation and collision in graded-index nonlinear waveguide
amplifiers with self-focusing and self-defocusing Kerr
nonlinearities. It finds an appropriate transformation for the first
time such that the nonlinear Schr\"odinger equation (NLSE) with
varying coefficients transform into standard NLSE. It obtains
one-solitonlike, two-solitonlike and multi-solitonlike self-similar
wave solutions by using the transformation. Furthermore, it analyses
the features of the self-similar waves and their collisions.

In this paper, we consider the macroscopic quantum tunnelling and
self-trapping phenomena of Bose--Einstein condensates (BECs) with
three-body recombination losses and atoms feeding from thermal cloud
in triple-well potential. Using the three-mode approximation, three
coupled Gross--Pitaevskii equations (GPEs), which describe the
dynamics of the system, are obtained. The corresponding numerical
results reveal some interesting characteristics of BECs for
different scattering lengths. The self-trapping and quantum
tunnelling both are found in zero-phase and \pi-phase modes.
Furthermore, we observe the quantum beating phenomenon and the
resonance character during the self-trapping and quantum tunnelling.
It is also shown that the initial phase has a significant effect on
the dynamics of the system.

Utilizing the generalized measurement described by positive
operator-valued measure, this paper comes up with a protocol for
teleportation of an unknown multi-particle entangled
(GHZ) state with a certain
probability. The feature of the present protocol is to weaken
requirement for the quantum channel initially shared by sender and
receiver. All unitary transformations performed by receiver are
summarized into a formula. On the other hand, this paper explicitly
constructs the efficient quantum circuits for implementing the
proposed teleportation by means of universal quantum logic
operations in quantum computation.

Remote quantum-state discrimination is a critical step for the
implementation of quantum communication network and distributed
quantum computation. We present a protocol for remotely implementing
the unambiguous discrimination between nonorthogonal states using
quantum entanglements, local operations, and classical
communications. This protocol consists of a remote generalized
measurement described by a positive operator valued measurement
(POVM). We explicitly construct the required remote POVM. The remote
POVM can be realized by performing a nonlocal controlled-rotation
operation on two spatially separated qubits, one is an ancillary
qubit and the other is the qubit which is encoded by two
nonorthogonal states to be distinguished, and a conventional local
Von Neumann orthogonal measurement on the ancilla. The particular
pair of states that can be remotely and unambiguously distinguished
is specified by the state of the ancilla. The probability of
successful discrimination is not optimal for all admissible pairs.
However, for some subset it can be very close to an optimal value in
an ordinary local POVM.

We propose feasible schemes for preparation of all five-atom graph
states by cavity quantum electrodynamics (QED). Our schemes require
only the atom--cavity interaction with a large detuning which is
available in current experiment so that these schemes are within the
reach of the current technology.

By using the theory of cavity QED, we study the system in which a
two-level atom interacts with a cavity in the case of large detuning.
Through the selective detecting of atomic state, Schr\"{o}dinger cat
states and entangled coherent states are easily generated. When the
atom is driven by a weak classical field and the cavity field is in
the Schr\"{o}dinger cat state, we study the conditions of generating
the Fock states and the maximal success probability. The maximal
success probability in our scheme is larger than the previous one.

The entanglement in one-dimensional random XY spin systems where
the impurities of exchange couplings and the external magnetic
fields are considered as random variables is investigated by solving
the different spin--spin correlation functions and the average
magnetization per spin. The entanglement dynamics near particular
locations of the system is also studied when the exchange couplings
(or the external magnetic fields) satisfy three different
distributions (the Gaussian distribution, double-Gaussian
distribution, and bimodal distribution). We find that the
entanglement can be controlled by varying the strength of external
magnetic field and the distributions of impurities. Moreover, the
entanglement of some nearest-neighbouring qubits can be increased
for certain parameter values of the three different distributions.

This paper presents recurrence spectra of highly excited lithium
atoms with M = 1 state in parallel electric and magnetic fields at
a fixed scaled energy \varepsilon = - 0.03. Short-ranged potentials
including ionic core potential and centrifugal barrier are taken into
account. Their effects on the states and photo-absorption spectrum
are analysed in detail. This demonstrates that the geometric
features of classical orbits are of special importance for
modulations of the spectral pattern. Thus the weak polarization as
well as the reduction of correlation of electrons induced by
short-ranged potentials give rise to the recurrence spectra of
lithium M = 1 atoms more compact than that of the M = 0 one,
which is in good agreement with the experimental prediction.

This paper proposes a scheme to teleport an arbitrary mixture of
diagonal states of multiqutrit via classical correlation and
classical communication. To teleport an arbitrary mixture of
diagonal states of N qutrits, N classically correlated pairs of
two qutrits are used as channel. The sender (Alice) makes Fourier
transform and conditional gate (i.e., XOR^{(3)} gate) on her
qutrits and does measurement in appropriate computation bases. Then
she sends N ctrits to the receiver (Bob). Based on the received
information, Bob performs the corresponding unitary transformation
on his qutrits and obtains the teleported state. Teleportation of an
arbitrary mixture of diagonal states of multiqudit is also
discussed.

After briefly introducing Akhtarshenas, concurrence vector and
subvector for describing many-body entanglement, we investigate the
entanglement formation for a system which contains three bodies, i.e.
two identical atoms and a single-model cavity field, in the
Tavis--Cummings model by calculating the concurrences. The results
show that the coupling strength between two atoms, the decay cavity
and the atomic spontaneous emission can change the entanglement of
formation according to different modes: these factors destroy
periodicity and symmetry of all concurrences, and that the coupling
strength of two atoms does not change the peak value of concurrence
(C), but the strength of decay cavity and the atomic spontaneous
emission decline in the peak value of concurrence (C) and the
latter is more serious than the former under the same strengths. The
concurrence vector and subvector are a useful measure of entanglement
for a pure state of the many-body system, in that it can give novel
pictures about the entanglements for the entire system and between
its inner bodies.

Extending Parikh and Wilczek's work to the non-stationary black hole,
we study the Hawking radiation of the non-stationary Kerr black hole
by the Hamilton--Jacobi method. The result shows that the radiation
spectrum is not purely thermal and the tunnelling probability is
related to the change of Bekenstein--Hawking entropy, which gives a
correction to the Hawking thermal radiation of the black hole.

This paper studies integration of a higher-order differential
equation which can be reduced to a second-order ordinary differential
equation. The solution of the second-order equation can be obtained
by the Noether method and the Poisson method. Then the solution of
the higher-order equation can be obtained by integrating the solution
of the second-order equation.

This paper derives the Hawking flux from the Schwarzschild black
hole with a global monopole by using Robinson and Wilczek's method.
Adopting a dimensional reduction technique, it can describe the
effective quantum field in the (3+1)-dimensional global monopole
background by an infinite collection of the (1+1)-dimensional
massless fields if neglecting the ingoing modes near the horizon,
where the gravitational anomaly can be cancelled by the
(1+1)-dimensional black body radiation at the Hawking temperature.

Recently, a number of efforts are underway to investigate
inter-vehicle communications (IVC). This paper studies the
instantaneous information propagation behaviours based on IVC in
three different traffic situations (free flow, synchronized flow and
stop-and-go waves) in a cellular automaton model. It is shown that
different behaviours appear in stop-and-go waves from those in free
flow and synchronized flow. While the distribution of Multi-hop
Communication Distance (MhCD) is either exponential or uniform in
free flow and synchronized flow, the distribution of MhCD is either
exponential or with a single peak in stop-and-go waves.

The adaptive coupled synchronization method for non-autonomous
systems is proposed. This method can avoid estimating the value of
coupling coefficient. Under the uniform Lipschitz assumption, we
derive the asymptotical synchronization for a general coupling ring
network with N identical non-autonomous systems, even when N is
large enough. Strict theoretical proofs are given. Numerical
simulations illustrate the effectiveness of the present method.

This paper deals with the exponential stability of
impulsive Takagi--Sugeno fuzzy systems with delay. Impulsive control
and delayed fuzzy control are applied to the system, and the
criterion on exponential stability expressed in terms of linear
matrix inequalities (LMIs) is presented.

Based on passive theory, this paper studies a hybrid chaotic
dynamical system from the mathematics perspective to implement the
control of system stabilization. According to the Jacobian matrix of
the nonlinear system, the stabilization control region is gotten.
The controller is designed to stabilize fast the minimum phase
Lorenz--Chen chaotic system after equivalently transforming from
chaotic system to passive system. The simulation results show that
the system not only can be controlled at the different equilibria,
but also can be transformed between the different chaotic
attractors.

In this paper the decrease in the Hurst exponent of human gait with
aging and neurodegenerative diseases was observed by using an
improved rescaled range (R/S) analysis method. It indicates that
the long-range correlations of gait rhythm from young healthy people
are stronger than those from the healthy elderly and the diseased.
The result further implies that fractal dynamics in human gait will
be altered due to weakening or impairment of neural control on
locomotion resulting from aging and neurodegenerative diseases. Due
to analysing short-term data sequences rather than long datasets
required by most nonlinear methods, the algorithm has the
characteristics of simplicity and sensitivity, most importantly, fast
calculation as well as powerful anti-noise capacities. These findings
have implications for modelling locomotor control and also for
quantifying gait dynamics in varying physiologic and pathologic
states.

Stochastic period-doubling bifurcation is explored in a forced
Duffing system with a bounded random parameter as an additional weak
harmonic perturbation added to the system. Firstly, the biharmonic
driven Duffing system with a random parameter is reduced to its
equivalent deterministic one, and then the responses of the
stochastic system can be obtained by available effective numerical
methods. Finally，numerical simulations show that the phase of the
additional weak harmonic perturbation has great influence on the
stochastic period-doubling bifurcation in the biharmonic driven
Duffing system. It is emphasized that, different from the
deterministic biharmonic driven Duffing system, the intensity of
random parameter in the Duffing system can also be taken as a
bifurcation parameter, which can lead to the stochastic
period-doubling bifurcations.

Based on the phase state reconstruction of welding current in
short-circuiting gas metal arc welding using carbon dioxide as
shielding gas, the approximate entropy of welding current as well as
its standard deviation has been calculated and analysed to
investigate their relation with the stability of electric arc and
welding process. The extensive experimental and calculated results
show that the approximate entropy of welding current is
significantly and positively correlated with arc and welding process
stability, whereas its standard deviation is correlated with them
negatively. A larger approximate entropy and a smaller standard
deviation imply a more stable arc and welding process, and vice
versa. As a result, the approximate entropy of welding current
promises well in assessing and quantifying the stability of electric
arc and welding process in short-circuiting gas metal arc welding.

This paper presents a method used to the numeral eddy current sensor
modelling based on the genetic neural network to settle its
nonlinear problem. The principle and algorithms of genetic neural
network are introduced. In this method, the nonlinear model
parameters of the numeral eddy current sensor are optimized by
genetic neural network (GNN) according to measurement data. So the
method remains both the global searching ability of genetic algorithm
and the good local searching ability of neural network. The nonlinear
model has the advantages of strong robustness, on-line modelling and
high precision. The maximum nonlinearity error can be reduced to
0.037{\%} by using GNN. However, the maximum nonlinearity error is
0.075$^{ }${\%} using the least square method.

Angular distributions of pions and kaons produced in heavy ion
collisions at the low-energy end of high energies (1--2\,A GeV) have
been investigated by using a multisource ideal gas model. The model
covers the expansions and movements of the emission sources, and it
is related to the collective flows. By using the analytic expression
and the Monte Carlo method, the azimuthal and polar angle
distributions of mesons are calculated by the model and compared
with the experimental data of the KaoS Collaboration.

The values of effective breeding coefficient K_{eff} in a
reactor core of nuclear power plant are calculated for different
values of parameters (core structure, fuel assembly component) by
using the Monte Carlo method. The obtained values of K_{eff}
are compared and analysed, which can provide theoretical basis for
reactor design.

This paper presents an analytical description for the growth of the
projected emittance (here just referred to the transverse emittance)
based on the concept of the slice emittance in an RF photoinjector.
In the RF photoinjector, the slice emittance undergoes small changes,
but the projected emittance changes significantly even in the drift
space after the injector. Carefully adjusting the parameters of the
RF photoinjector, which usually means emittance compensation, the
projected emittance can be minimized to the value of the slice
emittance. The relation between slice emittance and projected
emittance is explained in this paper. An emittance function, which
shows such a relation, is also introduced. A model about the
emittance growth in the RF photoinjector is established, which
accords with the particle simulation results by using the code ASTRA.
The condition to minimize the emittance is also given by using the
emittance function, which means the emittance compensation in the RF
photoinjector.

Based on the obtained energy values of 1s$^{2}n$p ($n \le $ 9) states
for lithium-like systems from $Z$=11 to 20 (by the authors of this
paper: Hu M H and Wang Z W 2004 \textit{Chin. Phys.} \textbf{13}
662), this paper determines the quantum defects, as slowly varying
function of energy, of this Rydberg series. Using them as input, it
can predict the energies of any highly excited states below the
ionization threshold for this series according to the quantum defect
theory. The regularities of variation for quantum defects of the
series along this isoelectronic sequence are physically analysed and
discussed. The screening parameters, which are equal to the effective
screening charge of the core-electrons, are also obtained.

This paper analyses the heteronuclear Cosy Revamped by Asymmetric
Z-gradient Echo Detection pulse sequence. General theoretical
expressions of the pulse sequence with arbitrary flip angles were
derived by using dipolar field treatment and signals originating from
heteronuclear intermolecular single-quantum coherences (iSQCs) in
highly-polarized two spin-1/2 systems were mainly discussed in order
to find the optimal flip angles. The results show that signals from
heteronuclear iSQCs decay slower than those from intermolecular
double-quantum coherences or intermolecular zero-quantum coherences.
Magical angle experiments validate that the signals are from
heteronuclear iSQCs and insensitive to the imperfection of
radio-frequency flip angles. All experimental observations are in
excellent agreement with theoretical predictions. The
quantum-mechanical treatment leads to similar predictions to the
dipolar field treatment.

This paper observes the parametric excitation on atom chip by
measuring the trap loss when applying a parametric modulation. By
modulating the current in chip wires, it modulates not only the trap
frequency but also the trap position. It shows that the strongest
resonance occurs when the modulation frequency equals to the trap
frequency. The resonance amplitude increases exponentially with
modulation depth. Because the Z-trap is an anharmonic trap, there
exists energy selective excitation which would cause parametric
cooling. We confirm this effect by observing the temperature of atom
cloud dropping.

The flow is assumed to be potential, and a boundary integral method
is used to solve the Laplace equation for the velocity potential to
investigate the shape and the position of the bubble. A 3D code to
study the bubble dynamics is developed, and the calculation results
agree well with the experimental data. Numerical analyses are
carried out for the interaction between multiple bubbles near the
free surface including in-phase and out-of-phase bubbles. The
calculation result
shows that the bubble period increases with the
decrease of the distance between bubble centres because of the
depression effect between multiple bubbles. The depression has no
relationship with the free surface and it is more apparent for
out-of-phase bubbles. There are great differences in dynamic
behaviour between the in-phase bubbles and the out-of-phase bubbles
due to the depression effect. Furthermore, the interaction among
eight bubbles is simulated with a three-dimensional model, and the
evolving process and the relevant physical phenomena are presented.
These phenomena can give a reference to the future work on the power
of bubbles induced by multiple charges exploding simultaneously or
continuously.

This paper presents a self-consistent nonlinear theory of the
current and energy modulations when an electron beam propagates
through an inductively-loaded wide gap cavity. The
integro-differential equations are obtained to describe the
modulation of the beam current and kinetic energy. A relativistic
klystron amplifier (RKA) model is introduced, which uses an
inductively-loaded wide gap cavity as an input cavity. And a
numerical code is developed for the extended model based on the
equations, from which some relations about the modulated current and
modulated energy are numerically given.

This paper derives the closed-form expressions for nonparaxial phase
flipped Gaussian (PFG) beams propagating in free space, through a
knife edge and an aperture, which enable us to study nonparaxial
propagation properties of PFG beams and to compare nonparaxial
results with paraxial ones. It is found that the $f$ parameter,
offsetting distance of the knife edge and truncation parameter
affect the nonparaxial beam propagation properties. Only under
certain conditions the paraxial approximation is applicable. The
results are illustrated by numerical examples.

In this paper a novel method is proposed to determine the cell
parameters including the twist angle, optic retardation and rubbing
direction of twisted-nematic liquid crystal displays (TNLCD) by
rotating the TNLCD. It is a single-wavelength method. Because using
subtraction equation of transmittance as curve fitting equation, the
influence of the light from environment and the absorption by
polarizer, the sample of TNLCD and analyser on the transmittance is
eliminated. Accurate results can also be obtained in imperfect
darkness. By large numbers of experiments, we found that not only the
experimental setup is quite simple and can be easily adopted to be
carried out, but also the results are accurate.

Since the complete correction of all five monochromatic Seidel
aberrations for a singlet lens with random shape or a two-thin-lens
system is unprocurable merely by using the conventional
positive-index materials both in theory and practice, this paper
proposes that when one or both of the two lenses is/are made from
negative-index materials, an imaging system composed of a pair of
spherical thin lenses is possible to form a real image, in air, free
from all five monochromatic Seidel aberrations. The calculated
numerical solutions to the structural parameters of such lens
systems possessing superior performance are provided and examples of
them are illustrated for the given combinations of the two lenses'
refractive indices, including an ultimately-remote imaging system.

The statistics of polarization in electromagnetic waves or target
vector has been studied deeply, generally using Stokes parameters.
Unfortunately, all the data-processing includes the assumption that
the sampling data are independent of time, without a consideration
of the time coherence of the polarization data, such as
instantaneous Stokes parameters. In this paper, the definitions of
the instantaneous coherent polarization function and polarimetric
spectrum are presented for the first time, which shows the
coherences of the instantaneous Stokes parameters in both time and
frequency domain, even in spatial coherence. The new formula of
definition can be extended to spatial propagation coherence, both in
free space or any linear medium.

This paper proposes a scheme for the implementation of $1 \to 3$
optimal phase-covariant quantum cloning with trapped ions. In the
present protocol, the required time for the whole procedure is short
due to the resonant interaction, which is important in view of
decoherence. Furthermore, the scheme is feasible based on current
technologies.

A system consisting of two different atoms interacting with a
two-mode vacuum, where each atom is resonant only with one cavity
mode, is considered. The effects of dipole--dipole ({dd})
interaction between two atoms on the atom--atom entanglement and
mode--mode entanglement are investigated. For a weak {dd}
interaction, when the atoms are initially separable,
the entanglement between them can be induced by the {dd}
interaction, and the entanglement transfer between the atoms and the
modes occurs efficiently; when the atoms are initially entangled,
the entanglement transfer is almost not influenced by the {dd}
interaction. However, for a strong {dd} interaction, it is difficult
to transfer the entanglement from the atoms to the modes, but the
atom--atom entanglement can be maintained when the atoms are
initially entangled.

We study the colour-locked twin-noisy-field correlation effects in
the fifth-order nonlinear susceptibility of ultrafast polarization
beats in a cascade four-level system. More importantly, the
fifth-order phase-sensitive heterodyne detection of ultrafast
polarization beats has been exploited. The fifth-order nonlinear
optical response can be controlled and modified through the
colour-locked correlation of twin noisy fields. Thus, this method
with the phase dispersion information is a good way to measure the
real and imaginary parts of the fifth-order nonlinear
susceptibility.

We address the existence of surface solitons at an interface in a
defocusing cubic medium with an imprinted one-dimensional ($1$D)
composite Bessel optical lattice. This setting is composed of two
Bessel lattices with different orders and different modulation
depths, separated beside both sides of an interface. Stability
analysis and numerical propagation simulations prove that solitons
supported by the model are dynamically stable in the entire domain
of their existence. The order of lattice determines the shape of
soliton, and the amplitude of soliton depends on the lattice
modulation depth. The experimental realization of the scheme is also
proposed. Our results may provide another effective way of
controlling the shapes of surface solitons and thus their evolutions
by introducing a new freedom degree.

High nonlinear microstructure fibre (HNMF) is preferred in nonlinear
fibre optics, especially in the applications of optical parametric
effects, due to its high optical nonlinear coefficient. However,
polarization dependent dispersion will impact the nonlinear optical
parametric process in HNMFs. In this paper, modulation instability
(MI) method is used to measure the polarization dependent dispersion
of a piece of commercial HNMF, including the group velocity
dispersion, the dispersion slope, the fourth-order dispersion and
group birefringence. It also experimentally demonstrates the impact
of the polarization dependent dispersion on the continuous wave
supercontinuum (SC) generation. On one axis MI sidebands with
symmetric frequency detunings are generated, while on the other axis
with larger MI frequency detuning, SC is generated by soliton
self-frequency shift.

Taking into account ultra-fast carrier dynamics, this paper models
640\,Gbit/s wavelength conversion scheme based on nonlinear
polarization rotation (NPR) in a single semiconductor optical
amplifier (SOA) and investigates the performance of this kind of
wavelength conversion scheme in detail. In this model, two carrier
temperature equations are introduced to substitute two energy
density equations, which reduce the complexity of calculation in
comparison with the previous model. The temporary gain and phase
shift dynamics induced by ultra-short optical pulses are numerically
simulated and the simulated results are qualitatively in good
agreement with reported experimental results. Simulated results show
that non-inverted and inverted 640\,Gbit/s wavelength conversions
based on NPR are achieved with clear open eye diagrams. To further
investigate the performance of the non-inverted wavelength
conversion scheme, the dependence of output extinction ratio (ER) on
some key parameters used in simulation is illustrated. Furthermore,
simulated analyses show that high performance non-inverted
wavelength conversion based on NPR can be achieved by using a
red-shifted filtering scheme.

We investigate the energy exchange between (3+1)D colliding
spatiotemporal solitons (STSs) in dispersive media with
cubic--quintic (CQ) nonlinearity by numerical simulations. Energy
exchange between two (3+1)D head on colliding STSs caused by their
phase difference is observed, just as occurring in other optical
media. Moreover, energy exchange between two head-on colliding STSs
with different speeds is firstly shown in the CQ and saturable media.
This phenomenon, we believe, may arouse some interest in the future
studies of soliton collision in optical media.

This paper investigates the photorefractive properties of iron doped
lithium niobate with different [Li]/[Nb] ratios. The experimental
results show two photorefractive centres for iron doped
near-stoichiometric lithium niobate crystal. Besides Fe$^{2 + }$ and
Fe$^{3 + }$ ions, small polarons and bipolarons are considered as
another photoactive centre.

A photonic crystal fibre Brillouin laser based on fibre Bragg
grating Fabry--Perot cavity is presented. A highly nonlinear
photonic crystal fibre 25\,m in length is used as Brillouin gain
medium and fibre Bragg grating Fabry--Perot cavity is chosen in
order to enhance the laser conversion efficiency and suppress the
higher-order Stokes waves. The laser reaches the threshold at input
power of 35\,mW, and the experimental laser conversion efficiency
achieves 18{\%} of the input power of 140\,mW and does not show
higher-order Stokes waves. A photonic crystal fibre Brillouin laser
with shorter fibre length and lower threshold is experimentally
realized.

By considering higher-order effects, the properties of self-similar
parabolic pulses propagating in the microstructured fibre amplifier
with a normal group-velocity dispersion have been investigated. The
numerical results indicate that the higher-order effects can badly
distort self-similar parabolic pulse shape and optical spectrum, and
at the same time the peak shift and oscillation appear, while the
pulse still reveals highly linear chirp but grows into asymmetry. The
influence of different higher-order effects on self-similar parabolic
pulse propagation has been analysed. It shows that the
self-steepening plays a more important role. We can manipulate the
geometrical parameters of the microstructured fibre amplifier to gain
a suitable dispersion and nonlinearity coefficient which will keep
high-quality self-similar parabolic pulse propagation. These results
are significant for the further study of self-similar parabolic pulse
propagation.

In this paper, bendloss characteristics of an optical fibre are
investigated in detail, and the results show that the resonator with
a smaller ring radius, wider free spectrum range (FSR), higher
fineness ($f$) and quality-factor ($Q$) can be achieved by using
microfibres. Based on the improved fused taper technique, a
high-quality microfibre with 5\,$\mu$m radius has been fabricated,
and an all-fibre micro-ring resonator with a radius of only
500\,$\mu$m is realized using self-coiling coupling method. The
good-resonant characteristic makes the all-fibre device be expected
to avoid bendloss and connection loss associated with planar
waveguide integration.

This paper solves the three-dimensional Navier--Stokes equation by a
fractional-step method with the Reynolds number Re$_\tau $=194 and
the rotation number $N_\tau $=0--0.12. When $N_\tau $ is less than
0.06, the turbulence statistics relevant to the spanwise velocity
fluctuation are enhanced, but other statistics are suppressed. When
$N_\tau $ is larger than 0.06, all the turbulence statistics
decrease significantly. Reynolds stress budgets elucidate that
turbulence kinetic energy in the vertical direction is transferred
into the streamwise and spanwise directions. The flow structures
exhibit that the bursting processes near the bottom wall are ejected
toward the free surface. Evident change of near-surface streak
structures of the velocity fluctuations are revealed.

The three-dimensional (3D) lattice Boltzmann models, 3DQ15, 3DQ19 and
3DQ27, under different wall boundary conditions and lattice
resolutions have been investigated by simulating Poiseuille flow in a
circular cylinder for a wide range of Reynolds numbers. The 3DQ19
model with improved Fillippova and Hanel (FH) curved boundary
condition represents a good compromise between computational
efficiency and reliability. Blood flow in an aortic arch is then
simulated as a typical haemodynamic application. Axial and secondary
fluid velocity and effective wall shear stress profiles in a
180$^\circ$ bend are obtained, and the results also demonstrate that
the lattice Boltzmann method is suitable for simulating the flow in
3D large-curved vessels.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

A Cherenkov-type terahertz electromagnetic radiation is revealed,
which results efficiently from the collective effects in the
time-domain of ultrafast pulsed electron current produced by
ultrafast intense laser--plasma interaction. The emitted pulse
waveform and spectrum, and the dependence of laser pulse parameters
on the structure of the radiation field are investigated numerically.
The condition of THz radiation generation in this regime and
Cherenkov geometry of the radiation field are studied analytically.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Different In/Ge(001) nanostructures have been obtained by annealing
the samples at 320\du\ with different coverages of In. Annealing a
sample with a critical coverage of 2.1 monolayer of In, different
In/Ge(001) nanostructures can be obtained at different temperatures.
It is found that thermal annealing treatments first make In atoms
form elongated Ge{\{}103{\}}-faceted In-clusters, which will grow
wider and longer with increasing temperature, and finally cover the
surface completely.

In this paper, a rotational invariant of interaction energy between
two biaxial-shaped molecules is assumed and in the mean field
approximation, nine elastic constants for simple distortion patterns
in biaxial nematics are derived in terms of the thermal average
$\langle {D_{mn}^{(l)} } \rangle \langle {D_{{m}'{n}'}^{({l}')} }
\rangle $, where $D_{mn}^{(l)} $ is the Wigner rotation matrix. In
the lowest order terms, the elastic constants depend on coefficients
$\Ga$, ${\Ga'}$, $\lambda $, order parameters $\bar {Q}_0 = Q_0
\langle {D_{00}^{(2)} } \rangle + Q_2 \langle {D_{02}^{(2)} + D_{0 -
2}^{(2)} } \rangle $ and $\bar {Q}_2 = Q_0 \langle {D_{20}^{(2)} }
\rangle + Q_2 \langle {D_{22}^{(2)} + D_{2 - 2}^{(2)} } \rangle $.
Here $\Ga $ and ${\Ga'}$ depend on the function form of molecular
interaction energy $v_{j'j''j} ( {r_{12} } )$ and probability
function $f_{k'k''k} ( {r_{12} } )$, where $r_{12} $ is the distance
between two molecules, and $\lambda $ is proportional to temperature.
$Q_0 $ and $Q_2 $ are parameters related to multiple moments of
molecules. Comparing these results with those obtained from
Landau--de Gennes theory, we have obtained relationships between
coefficients, order parameters used in both theories. In the special
case of uniaxial nematics, both results are reduced to a degenerate
case where $K_{11} = K_{33}$.

Non-volatile memory based on TiN nanocrystal (TiN--NC) charge storage
nodes embedded in SiO$_{2}$ has been fabricated and its electrical
properties have been measured. It was found that the density and size
distribution of TiN--NCs can be controlled by annealing temperature.
The formation of well separated crystalline TiN nano-dots with an
average size of 5\,nm is confirmed by transmission electron
microscopy and x-ray diffraction. x-ray photoelectron spectroscopy
confirms the existence of a transition layer of TiN$_{x}$O$_{y}$/SiON
oxide between TiN--NC and SiO$_{2}$, which reduces the barrier height
of tunnel oxide and thereby enhances programming/erasing speed. The
memory device shows a memory window of 2.5\,V and an endurance cycle
throughout 10$^{5}$. Its charging mechanism, which is interpreted
from the analysis of programming speed (d$V_{\rm th}$/d$t$) and the
gate leakage versus voltage characteristics ($I_{\rm g}$ vs $V_{\rm
g})$, has been explained by direct tunnelling for tunnel oxide and
Fowler--Nordheim tunnelling for control oxide at programming voltages
lower than 9V, and by Fowler--Nordheim tunnelling for both the oxides
at programming voltages higher than 9\,V.

This paper simulates the dendrite growth process during
non-isothermal solidification in the Al--Cu binary alloy by using the
phase-field model. The heat transfer equation is solved
simultaneously. The thermodynamic and kinetic parameters are directly
obtained from existing database by using the Calculation of Phase
Diagram (CALPHAD) method. The effects of the latent heat and
undercooling on the dendrite growth, solute and temperature profile
during the solidification of binary alloy are investigated. The
results indicate that the dendrite growing morphologies could be
simulated realistically by linking the phase-field method to CALPHAD.
The secondary arms of solidification dendritic are better developed
with the increase of undercooling. Correspondingly, the tip speed and
the solute segregation in solid--liquid interface increase, but the
tip radius decreases.

The weak classical light excitations in many semiconductor quantum
dots have been chosen as important solid-state quantum systems for
processing quantum information and implementing quantum computing.
For strong classical light we predict theoretically a novel phase
transition as a function of magnitude of this classical light from
the deformed to the normal phases in resonance case, and the
essential features of criticality such as the scaling behaviour,
critical exponent and universality are also present in this paper.

The fusion temperature as a function of pressure for carbon
tetrachloride, chloroform, bromoform and silicon tetrachloride at
pressures up to 3500MPa has been determined. The experimental data
were fitted by the equation $T_{{\rm fus}} = T_0 (1 + \Delta p / a_1
)^{a_2 }\exp ( - a_3 \Delta p)$ and the changes of the molar
enthalpy and molar internal energy on fusion were calculated using
the parameters of the fitted equation. Comparisons with the data
from the literature show that the experimental data, parameters of
fitted equations, changes of the molar enthalpy and molar internal
energy are reliable.

The spread of perfluoropolyether (PFPE) droplets on solid surfaces
has been measured from the top-down view through a microscope system.
Effects of substrates, molecular weight and end-group functionality
on spreading of the PFPE droplets have been studied experimentally
and the results were compared with those by molecular dynamics (MD)
simulations. Silicon wafer and diamond-like carbon (DLC) substrates
were used to study the effect of substrates on spreading. Two types
of PFPE, Z-dol and Z-tetraol, with the same chain structure and
various molecular weights (2000 and 4000\,g/mol) were employed in
experiments. Effect of molecular weight has been investigated through
comparing the spreading of Z-dol 2000 and Z-dol 4000, and it is found
that the increase of molecular weight will decrease the mobility of
PFPE. Comparison between spreading of Z-dol and Z-tetraol of the same
molecular weight proved that functional end group plays a significant
role on the spreading of PFPE, which confirmed the MD simulation
results.

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

We have investigated in detail the influence of defect on the
focusing of electromagnetic waves in a two-dimensional
photonic-crystal flat lens by using the finite-difference
time-domain method. The result shows that many focusings can be
observed at the symmetrical positions when a defect is introduced
into the lens. Furthermore, the wave-guides in the lens can confine
the transmission wave effectively and improve the quality of the
focusing.

This paper reports the preparation of antimony doped tin oxide
crystalline powders by chemical coprecipitation method. The influence
of sintering temperature and the sintering retention time on the
thermal infrared emissivity is analysed. The thermal infrared
reflectivity is measured and the optimum doping concentration is
proposed.

This paper studies quantum diffusion in semi-infinite
one-dimensional periodic lattice and quasiperiodic Fibonacci
lattice. It finds that the quantum diffusion in the semi-infinite
periodic lattice shows the same properties as that for the infinite
periodic lattice. Different behaviour is found for the semi-infinite
Fibonacci lattice. In this case, there are still $C(t)\sim t^{ -
\delta }$ and $d(t)\sim t^{\beta }$. However, it finds that $0 <
\delta < 1$ for smaller time, and $\delta = 0$ for larger time due
to the influence of surface localized states. Moreover, $\beta $ for
the semi-infinite Fibonacci lattice is much smaller than that for
the infinite Fibonacci lattice. Effects of disorder on the quantum
diffusion are also discussed.

A series of metamorphic high electron mobility transistors (MMHEMTs)
with different V/III flux ratios are grown on GaAs (001) substrates
by molecular beam epitaxy (MBE). The samples are analysed by using
atomic force microscopy (AFM), Hall measurement, and low temperature
photoluminescence (PL). The optimum V/III ratio in a range from 15
to 60 for the growth of MMHEMTs is found to be around 40. At this
ratio, the root mean square (RMS) roughness of the material is only
2.02 nm; a room-temperature mobility and a sheet electron density
are obtained to be 10610.0cm$^{2}$/(V$\cdot$s) and 3.26$\times
$10$^{12}$cm$^{ - 2}$ respectively. These results are equivalent to
those obtained for the same structure grown on InP substrate. There
are two peaks in the PL spectrum of the structure, corresponding to
two sub-energy levels of the In$_{0.53}$Ga$_{0.47}$As quantum well.
It is found that the photoluminescence intensities of the two peaks
vary with the V/III ratio, for which the reasons are discussed.

The crystal structure and the superconductivity for samples Mg(B_{1-x}C_{x})_{2} (0 \le x \le 0.09) prepared by a hybrid microwave
synthesis have been investigated. The starting material B_{10}C is
also obtained by using the microwave method. The carbon can
distribute uniformly in the Mg(B_{1-x}C_{x})_{2} samples
because boron and carbon are mixed on an atomic scale in the staring
material B_{10}C. The dependences of both lattice parameters and
superconducting transition temperature T_{c} on carbon content
accord with those reported in the literature. The upper critical
field H_{c2} at 20K can be enhanced from about 4.3T for
x=0 to 10\,T for x=0.05. The critical current density J_{c}
of Mg(B_{0.95}C_{0.05})_{2} is 1.05×10^{4}A/cm^{2} at
20K and 1T.

In this paper magnetization remanence curves were studied for
nanocrystalline Pr_{8}Fe_{87}B_{5}, Pr_{12}Fe_{82}B_{6}
and Pr_{15}Fe_{77}B_{8}. Initially the sample was at remanence
following saturation along $z$-axis. After rotating the magnet by
$5n$ degrees (n=0, 1, ..., 18) a field H was applied along
$z$-axis and then decreased to zero, and the remanence J_{r}^{n} $ was
measured as a function of $H$. The curves were compared with those
calculated based on the nucleation of reverse domain model and domain
wall pinning model. The latter model succeeds in simulation much
better than the former, and it is concluded that the magnetization
reversal is dominated by domain wall pinning for all the samples. The
nucleation mechanism contribution, while remains small, increases
with the increase of Pr content.

This paper synthesizes the Sr$_{2}$SiO$_{4}$\,:\,Eu$^{2 + }$
phosphor by high temperature solid-state reaction. The emission
spectrum of Sr$_{2}$SiO$_{4}$\,:\,Eu$^{2 + }$ shows two bands
centred at 480 and 547\,nm, which agree well with the calculation
values of emission spectrum, and the location of yellow emission of
Sr$_{2}$SiO$_{4}$\,:\,Eu$^{2 + }$ is influenced by the Eu$^{2 + }$
concentration. The excitation spectrum for 547\,nm emission has two
bands at 363 and 402\,nm. The emission spectrum of white light
emitting diodes (w-LEDs) based on Sr$_{2}$SiO$_{4}$\,:\,Eu$^{2 + }$
phosphor + InGaN LED was investigated.

This paper investigates the interaction between transient wave and
non-stationary and non-conservative basic flow. An interaction
equation is derived from the zonally symmetric and non-hydrostatic
primitive equations in Cartesian coordinates by using the
Momentum--Casimir method. In the derivation, it is assumed that the
transient disturbances satisfy the linear perturbation equations and
the basic states are non-conservative and slowly vary in time and
space. The diabatic heating composed of basic-state heating and
perturbation heating is also introduced. Since the theory of
wave--flow interaction is constructed in non-hydrostatic and
ageostrophic dynamical framework, it is applicable to diagnosing the
interaction between the meso-scale convective system in front and
the background flow.
It follows from the local interaction equation that the local
tendency of pseudomomentum wave-activity density depends on the
combination of the perturbation flux divergence second-order in
disturbance amplitude, the local change of basic-state
pseudomomentum density, the basic-state flux divergence and the
forcing effect of diabatic heating. Furthermore, the tendency of
pseudomomentum wave-activity density is opposite to that of
basic-state pseudomomentum density. The globally integrated
basic-state pseudomomentum equation and wave-activity equation
reveal that the global development of basic-state pseudomomentum is
only dominated by the basic-state diabatic heating while it is the
forcing effect of total diabatic heating from which the global
evolution of pseudomomentum wave activity results. Therefore, the
interaction between the transient wave and the non-stationary and
non-conservative basic flow is realized in virtue of the basic-state
diabatic heating.

The electron capture timescale may be shorter than hydrodynamic
timescale in inner iron core of core-collapse supernova according to
a recent new idea. Based on the new idea, this paper carries out a
numerical simulation on supernova explosion for the progenitor model
Ws15M$_{\odot}$. The numerical result shows that the size of
proto-neutron star has a significant change (decrease about 20{\%}),
which may affects the propagation of the shock wave and the final
explosion energy.

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