We investigate the one-dimensional
nonlinear Schr\"{o}dinger equation with a perturbation of polynomial
type. The approximate symmetries and approximate symmetry reduction
equations are obtained with the approximate symmetry perturbation
theory.

According to the conjecture based on some known facts of integrable
models, a new (2+1)-dimensional supersymmetric integrable bilinear
system is proposed. The model is not only the extension of the known
(2+1)-dimensional negative Kadomtsev--Petviashvili equation but also
the extension of the known (1+1)-dimensional supersymmetric
Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro
symmetries and the related symmetry reductions of the model are
obtained. Furthermore, the traveling wave solutions including
soliton solutions are explicitly presented.

This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation. Under the suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, using the stretched variable and the composing expansion method the boundary layer is constructed; finally, using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed.

Through analysing the exact solution of some nonlinear
models, the role of the variable separating method in solving
nonlinear equations is discussed. We find that rich solution
structures of some special fields of these equations come from the
nonzero seed solution. However, these nonzero seed solutions is
likely to result in the divergent phenomena for the other field
component of the same equation. The convergence and the
signification of all field components should be discussed when
someone solves the nonlinear equation using the variable separating
method.

We study evolutionary prisoner's dilemma game on adaptive
networks where a population of players co-evolves with their
interaction networks. During the co-evolution process, interacted
players with opposite strategies either rewire the link between them
with probability $p$ or update their strategies with probability
$1-p$ depending on their payoffs. Numerical simulation shows that
the final network is either split into some disconnected communities
whose players share the same strategy within each community or forms
a single connected network in which all nodes are in the same
strategy. Interestingly, the density of cooperators in the final
state can be maximised in an intermediate range of $p$ via the
competition between time scale of the network dynamics and that of
the node dynamics. Finally, the mean-field analysis helps to
understand the results of numerical simulation. Our results may
provide some insight into understanding the emergence of cooperation
in the real situation where the individuals' behaviour and their
relationship adaptively co-evolve.

A form invariance and a conserved quantity of the generalised Birkhoffian system are studied.
Firstly, a definition and a criterion of the form invariance are given. Secondly, through the form invariance,
a new conserved quantity can be deduced. Finally,
an example is given to illustrate the application of the result.

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii--Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states $\cos \theta \left\vert 00\right\rangle +\sin \theta \left\vert 11\right\rangle $ and $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $ at zero temperature. The influences of Dzyaloshinskii--Moriya interaction $D$, anisotropic parameter $\varDelta$ and environment coupling strength $\gamma$ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii--Moriya interaction $D$ acts on the time evolution of entanglement only when the initial state is $\cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle $. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii--Moriya interaction $D$, depends on the anisotropic parameter $\varDelta$ and the environment coupling strength $\gamma$.

By introducing the $s$-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within $s$-ordered product of operators (which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases). The $s$-ordered operator expansion (denoted by $\circledS \cdots \circledS)$ formula of density operators is derived, which is $$\rho=\frac{2}{1-s}\int \frac{\d^2\beta}{\pi}\left \langle -\beta \right \vert \rho \left \vert \beta \right \rangle \circledS \exp \Big\{ \frac{2}{s-1}\left( s|\beta|^{2}-\beta^{\ast}a+\beta a^{\dagger}-a^{\dagger}a\right) \Big\} \circledS.$$ The $s$-parameterized quantization scheme is thus completely established.

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

We demonstrate that the $n$-partite continuous-variable entanglement can be unconditionally prepared among $n$ parties that share no common past, from $n$ two-mode squeezed states. Both GHZ-like and cluster-like states can be generated for any nonzero squeezing in the entangled sources. An application of the resulting multipartite entangled state to a teleportation network is illustrated.

Based on $\chi $-type entangled states and the two-step protocol [Deng F G, Long G L and Liu X S 2003 {\it Phys. Rev.} A {\bf68} 042317], a quantum secret sharing protocol of secure direct communication based on $\chi$-type entangled states $\vert \chi ^{00}\rangle _{3214} $ is proposed. Using some interesting entanglement properties of this state, the agent entirety can directly obtain the secret message from the message sender only if they collaborate together. The security of the scheme is also discussed.

A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.

By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker--Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.

It is an important problem in chaos theory whether an
observed irregular signal is deterministic chaotic or stochastic. We
propose an efficient method for distinguishing deterministic chaotic
from stochastic time series for short scalar time series. We first
investigate, with the increase of the embedding dimension, the
changing trend of the distance between two points which stay close
in phase space. And then, we obtain the differences between Gaussian
white noise and deterministic chaotic time series underlying this
method. Finally, numerical experiments are presented to testify the
validity and robustness of the method. Simulation results indicate
that our method can distinguish deterministic chaotic from
stochastic time series effectively even when the data are short and
contaminated.

In this paper the fault tolerant synchronization of two
chaotic systems based on fuzzy model and sample data is investigated.
The problem of fault tolerant synchronization is formulated to study
the global asymptotical stability of the error system with the fuzzy
sampled-data controller which contains a state feedback controller
and a fault compensator. The synchronization can be achieved no
matter whether the fault occurs or not. To investigate the stability
of the error system and facilitate the design of the fuzzy
sampled-data controller, a Takagi--Sugeno (T--S) fuzzy model is
employed to represent the chaotic system dynamics. To acquire the
good performance and produce less conservative analysis result, a
new parameter-dependent Lyapunov--Krasovksii functional and a relaxed
stabilization technique are considered. The stability conditions
based on linear matrix inequality are obtained to achieve the fault
tolerant synchronization of the chaotic systems. Finally, a
numerical simulation is shown to verify the results.

In this paper, new delay-dependent stability criteria
for asymptotic stability of neural networks with time-varying delays are derived.
The stability conditions are represented in terms of linear matrix
inequalities (LMIs)
by constructing new Lyapunov--Krasovskii
functional. The proposed functional has an augmented quadratic form with states as well as the
nonlinear function to consider the sector and the slope constraints.
The less conservativeness of the proposed stability criteria can be guaranteed
by using convex properties of the nonlinear function which satisfies the sector and slope bound.
Numerical examples are presented to show the effectiveness of the proposed
method.

In this study an adaptive arithmetic coder is embedded in the Baptista-type chaotic cryptosystem for implementing secure data compression. To build the multiple lookup tables of secure data compression, the phase space of chaos map with a uniform distribution in the search mode is divided non-uniformly according to the dynamic probability estimation of plaintext symbols. As a result, more probable symbols are selected according to the local statistical characters of plaintext and the required number of iterations is small since the more probable symbols have a higher chance to be visited by the chaotic search trajectory. By exploiting non-uniformity in the probabilities under which a number of iteration to be coded takes on its possible values, the compression capability is achieved by adaptive arithmetic code. Therefore, the system offers both compression and security. Compared with original arithmetic coding, simulation results on Calgary Corpus files show that the proposed scheme suffers from a reduction in compression performance less than 12{\%} and is not susceptible to previously carried out attacks on arithmetic coding algorithms.

The dynamical behaviours of valley current controlled buck
converter are studied by establishing its corresponding discrete
iterative map model in this paper. Time-domain waveforms and phase
portraits of valley current controlled buck converter are obtained
by Runge--Kutta algorithm through a piecewise smooth switching
model. The research results indicate that the valley current
controlled buck converter exhibits rich nonlinear phenomena, and it
has routes to chaos through period-doubling bifurcation and
border-collision bifurcation in a wide parameter range. Interesting
inverse nonlinear behaviours compared with peak current controlled
buck converter are observed in the valley current controlled buck
converter. Analysis and simulation results are verified by
experimental results.

The denoising problem of impure chaotic signals is
addressed in this paper. A method based on sparse representation is
proposed, in which the random frame dictionary is generated by a
chaotic random search algorithm. The numerical simulation shows the
proposed algorithm outperforms those recently reported alternative
denoising methods.

This paper studies how random phase (namely,
noise-perturbed phase) effects the dynamical behaviours of
a simple model of power system which operates in a
stable regime far away from chaotic behaviour in the absence of
noise. It finds that when the phase perturbation is weak, chaos is
absent in power systems. With the increase of disturbed intensity
$\sigma$, power systems become unstable and fall into chaos as
$\sigma$ further increases. These phenomena imply that random phase
can induce and enhance chaos in power systems. Furthermore, the
possible mechanism behind the action of random phase is addressed.

A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.

This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh--Nagumo cells with self-sustained oscillation via Hopf bifurcation. When the coupling strength of the active variable decreases to a critical value, wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence. Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.

In this paper, we propose the distributed predictive
control strategies of spiral wave in cardiac excitable media. The
modified FitzHugh--Nagumo model was used to express the cardiac
excitable media approximately. Based on the control-Lyapunov theory,
we obtained the distributed control equation, which consists of a
positive control-Lyapunov function and a positive cost function.
Using the equation, we investigate two kinds of robust control
strategies: the time-dependent distributed control strategy and the
space-time dependent distributed control strategy. The feasibility
of the strategies was demonstrated via an illustrative example, in
which the spiral wave was prevented to occur, and the possibility
for inducing ventricular fibrillation was eliminated. The strategies
are helpful in designing various cardiac devices. Since the second
strategy is more efficient and robust than the first one, and the
response time in the second strategy is far less than that in the
first one, the former is suitable for the quick-response control
systems. In addition, our spatiotemporal control strategies,
especially the second strategy, can be applied to other cardiac
models, even to other reaction-diffusion systems.

This paper uses the two-dimensional Brusselator model to
study reflection and refraction of chemical waves. It presents some
boundary conditions of chemical waves, with which occurence of
observed phenomena at interface as refraction and reflection of
chemical waves can be interpreted. Moreover, the angle of reflection
may be calculated by using the boundary conditions. It finds that
reflection and refraction of chemical waves can occur simultaneously
even if plane wave goes from a medium with higher speed to a medium
with lower speed, provided the incident angle is larger than the
critical angle.

Dynamical behaviour of the one-dimensional complex
Ginzburg--Landau equation (CGLE) with finite system size $L$ is
investigated, based on numerical simulations. By varying the system
size and keeping other system parameters in the defect turbulence
region (defect turbulence in large $L$ limit), a number of
intermittencies new for the CGLE system are observed in the
processes of pattern formations and transitions while the system
dynamics varies from a homogeneous periodic oscillation to strong
defect turbulence.

Since ramp is an important composition of traffic system
and there often exist multi ramps in a traffic system, the number of
ramps can have great effects on main road traffic and produce some
complex phenomena. In this paper, we employ the model presented by
Tang \textit{et al}. [2009 {\em Communications in Theoretical
Physics} {\bf 51}({1}) 71] to further study the effects of the number
of on-ramps on the stability of traffic flow on a ring road. The
numerical results show that this model can reproduce some complex
traffic phenomena resulting from multi on-ramps on the ring road and
the effects of the number of on-ramps on traffic flow, but the
phenomena and the effects are both related to the initial density of
the main road.

Recently, Shi {\it et al.} [2008 {\it Phys. Lett.} A
{\bf372} 5922] have studied the dynamical response of the kinetic
Ising model in the presence of a sinusoidal oscillating field and
presented the dynamic phase diagrams by using an effective-field
theory (EFT) and a mean-field theory (MFT). The MFT results are in
conflict with those of earlier work of Tom\'{e} and de Oliveira,
[1990 {\it Phys. Rev.} A {\bf41} 4251]. We calculate the dynamic
phase diagrams and find that our results are similar to those of
earlier work of Tom\'{e} and de Oliveira; hence the dynamic phase
diagrams calculated by Shi {\it et al.} are incomplete within both
theories, except the low values of frequencies for the MFT
calculation. We also investigate the influence of external field
frequency ($\omega$) and static external field amplitude ($h_{0})$
for both MFT and EFT calculations. We find that the behaviour of the
system strongly depends on values of $\omega$ and $h_{0}$.

We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite being widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.

In this paper, we consider multi-agent consensus problems
in a decentralised fashion. The interconnection topology graph among
the agents is switching and undirected. The agent dynamics is
expressed in the form of a double integrator model. Two different
cases are considered in this study. One is the leader-following case
and the other is leaderless case. Based on graph theory and common
Lyapunov function method, some sufficient conditions are obtained
for the consensus stability of the considered systems with the
neighbour-based feedback laws in both leader-following case and
leaderless case respectively. Finally, two numerical examples are
given to illustrate the obtained results.

The periodic impact force induced by tip-sample contact in
tapping mode atomic force microscope (AFM) gives rise to
non-harmonic response of a micro-cantilever. These non-harmonic
signals contain the full characteristics of tip-sample interaction.
A complete theoretical model describing the dynamical behaviour of
tip--sample system was developed in this paper. An analytic formula
was introduced to describe the relationship between time-varying
tip--sample impact force and tip motion. The theoretical analysis
and numerical results both show that the time-varying tip--sample
impact force can be reconstructed by recording tip motion. This
allows for the reconstruction of the characteristics of the
tip--sample force, like contact time and maximum contact force. It
can also explain the ability of AFM higher harmonics imaging in
mapping stiffness and surface energy variations.

By applying systematically enlarged multi-configuration
Dirac--Fock wavefunction, the transitions for electric-dipole
allowed (E1) and forbidden (E2, M1 and M2) lines are studied among
4f pair coupling and low-lying configurations for singly ionized
nitrogen. Most important effects of relativity, electron
correlation, the rearrangement of electron density, Breit
interaction, and quantum electrodynamic effects are included in the
computation. Then, allowed (E1) and forbidden (E2, M1 and M2)
transition probabilities of 4f for N$^{+}$ are obtained and compared
with experimental results. Good agreement with available
experimental results is found and most of data of 4f are presented
for the first time.

Equilibrium internuclear separations, harmonic frequencies
and potential energy curves (PECs) of HCl($X^{1}\Sigma ^{ + })$
molecule are investigated by using the highly accurate valence
internally contracted multireference configuration interaction
(MRCI) approach in combination with a series of
correlation-consistent basis sets in the valence range. The PECs are
all fitted to the Murrell--Sorbie function, and they are used to
accurately derive the spectroscopic parameters ($D_{\rm e}$,
$D_{0}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm e}$ and $B_{\rm
e})$. Compared with the available measurements, the PEC obtained at
the basis set, aug-cc-pV5Z, is selected to investigate the
vibrational manifolds. The constants $D_{0}$, $D_{\rm e}$, $R_{\rm
e}$, $\omega_{\rm e}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm
e}$ and $B_{\rm e}$ at this basis set are 4.4006~eV, 4.5845~eV,
0.12757~nm, 2993.33~cm$^{ - 1}$, 52.6273~cm$^{ - 1}$, 0.2981~cm$^{ -
1}$ and 10.5841~cm$^{ - 1}$, respectively, which almost perfectly
conform to the available experimental results. With the potential
determined at the MRCI/aug-cc-pV5Z level of theory, by numerically
solving the radial Schr\"{o}dinger equation of nuclear motion in the
adiabatic approximation, a total of 21 vibrational levels are
predicted. Complete vibrational levels, classical turning points,
inertial rotation and centrifugal distortion constants are
reproduced, which are in excellent agreement with the available
Rydberg--Klein--Rees data. Most of these theoretical vibrational
manifolds are reported for the first time to the best of our
knowledge.

The four-level model of laser-induced collisional energy
transfer (LICET) for ion--ion collision system is established based
on the time-dependent Schr\"{o}dinger equation for the electron
dynamics, through which the equations of motion of the probability
amplitudes and cross section of the collision system are obtained.
Numerical calculations are performed for the Ca$^+$--Sr$^+$ system,
with the results showing that the peak of the LICET spectrum appears
at a resonant frequency of the transfer laser. The magnitude of the
obtained collision cross section is in the order of
$10^{-16}$~cm$^2$, and is comparable to that obtained in atomic
systems, which indicates the validity of the established four-level
model.

This paper is devoted to the study of polarization
properties, scattering properties and propagation properties of
global positioning system (GPS) scattering signal over the rough sea
surface. To investigate the polarization and the scattering
properties, the scattering field and the bistatic scattering
coefficient of modified Kirchhoff approximation with using the
tapered incident wave is derived in detail. In modeling the
propagation properties of the GPS scattering signal in the
evaporation duct, the initial field of parabolic equation
traditionally computed by the antenna pattern with using fast
Fourier transform (FFT) is replaced by the GPS scattering field. And
the propagation properties of GPS scattering signal in the
evaporation duct with different evaporation duct heights and
elevation angles of GPS are discussed by the improved discrete mixed
Fourier transform with taking into account the sea surface
roughness.

To study the electromagnetic (EM) backscatter
characteristics of freak waves at moderate incidence angles, we
establish an EM backscattering model for freak waves in
(1+1)-dimensional deep water. The nonlinear interaction between
freak waves and Bragg short waves is considered to be the basic
hydrodynamic spectra modulation mechanism in the model. Numerical
results suggest that the EM backscattering intensities of freak
waves are less than those from the background sea surface at
moderate incidence angles. The normalised radar cross sections
(NRCSs) from freak waves are highly polarisation dependent, even at
low incidence angles, which is different from the situation for
normal sea waves; moreover, the NRCS of freak waves is more
polarisation dependent than the background sea surface. NRCS
discrepancies between freak waves and the background sea surface
with using horizontal transmitting horizomtal (HH) polarisation are
larger than those with using vertical transmitting vertical (VV)
polarisation, at moderate incident angles. NRCS discrepancies
between freak waves and background sea surface decreases with the
increase of incidence angle, in both HH and VV polarisation radars.
As an application, in the synthetic-aperture radar (SAR) imaging of
freak waves, we suggest that freak waves should have extremely low
backscatter NRCSs for the freak wave facet with the strongest slope.
Compared with the background sea surface, the freak waves should be
darker in HH polarisation echo images than in VV echo images, in SAR
images. Freak waves can be more easily detected from the background
sea surface in HH polarisation images than in VV polarisation
images. The possibility of detection of freak waves at low incidence
angles is much higher than at high incidence angles.

Backscattered fields from one-dimensional time-varying
Gerstners sea surface are calculated utilising the second-order
small slope approximation. It is well known that spectral properties
of the backscattered echoes relate to the velocity of the small
elementary scatterers on sea surface profiles. Therefore, modeling
Doppler spectra from the ocean requires an accurate description of
the sea surface motion. The profile of nonlinear Gerstners sea
surface shows vertical-skewness of sea waves, it is sharper at the
crest and flatter at the trough than linear waves, and its maximum
slope position is closer to the crest than to the trough.
Furthermore, the horizontal component of the small elementary
scatterers orbit velocity on the sea surface, which yields
noticeable influence on Doppler spectra, can be obtained
conveniently by Gerstners sea surface model. In this study, the
characteristics of Doppler spectra of backscattered fields from
time-varying Gerstners sea surface are investigated and the
dependences of the Doppler frequency and the Doppler bandwidth on
the parameters, such as the wind speed, the radar frequency, the
incident angle, etc. are discussed. It is shown that the Doppler
bandwidth of microwave scattered fields from Gerstners sea surface
is considerably broadened. For the case of high frequency
backscattered fields, the values of the higher-order spectrum peaks
are larger than those obtained by linear sea surface.

The enhancement characteristics of the local field in the
surface plasmon nanocavities are investigated numerically. The
cavity is constructed by placing a defect structure in the
thickness-modulated metal--insulator--metal waveguide Bragg gratings.
The characteristic impedance based transfer matrix method is used to
calculate the transmission spectra and the resonant wavelength of
the cavities with various geometric parameters. The
finite-difference time-domain method is used to obtain the field
pattern of the resonant mode and validate the results of the
transfer matrix method. The calculation and simulation results
reveal the existence of resonant wavelength shift and intensity
variation with structural parameters, such as the modulation period
of the gratings, the length and the width of the defect structure.
Both numerical analysis and theoretical interpretation on these
phenomena are given in details.

Guided-mode resonance in a diffraction band of multilayer
dielectric gratings may lead to a catastrophic result in laser
system, especially in the ultrashort pulse laser system, so the
inhibition of guided-mode resonance is very important. In this paper
the characteristics of guided-mode resonance in multilayer
dielectric grating are studied with the aim of better understanding
the physical process of guided-mode resonance and designing a
broadband multilayer dielectric grating with no guided-mode
resonance. By employing waveguide theory, all guided-wave modes
appearing in multilayer dielectric grating are found, and the
incident conditions, separately, corresponding to each guided-wave
mode are also obtained. The electric field enhancement in multilayer
dielectric grating is shown obviously. Furthermore, from the
detailed analyses on the guided-mode resonance conditions, it is
found that the reduction of grating period would effectively avoid
the appearing of guided-mode resonance. And the expressions for
calculating maximum periods, which ensure that no guided-mode
resonance occurs in the requiring broad angle or wavelength range,
are first reported. The above results calculated by waveguide theory
and Fourier mode method are compared wit each other, and they are
coincident completely. Moreover, the method that relies on waveguide
theory is more helpful for understanding the guided-mode resonance
excited process and analyzing how each parameter affects the
characteristic of guided-mode resonance. Therefore, the effects of
multilayer dielectric grating parameters, such as period, fill
factor, thickness of grating layer, {\it et al.}, on the guided-mode
resonance characteristic are discussed in detail based on waveguide
theory, and some meaningful results are obtained.

In this paper, the relation between spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters. And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams. Theoretical analysis shows that correlation vortices are linearly polarized singularities. The results are illustrated by numerical examples.

Phase properties of the even and odd circular states are
studied within the Hermitian phase formalism of Pegg and Barnett.
Exact analytical formulas for the distribution function and the
variance of the phase operator are obtained and used to examine
whether or not the even and odd circular states exhibit
photon-number squeezing and phase squeezing.

We numerically simulate three-photon absorption spectra in a three-coupled-quantum-well nanostructure interacting with a pump field, a coherent coupling field, and a probe field. We find that the three-photon absorption spectra can be dramatically influenced due to the intensities of the coupling field and pump field changing under the three-photon resonance condition. The effect of the frequency detuning of the pump field on the three-photon absorption spectra is also discussed. The study in our case is much more practical than the study in the case of its atomic counterpart in the sense of flexible design and the wide adjustable parameters. Thus it may open up some new possibilities for technological applications in optoelectronics and solid-state quantum information science.

Through picture of dressed states, this paper investigates
the spontaneous emission spectrum from a microwave-driven
three-level atom embedded in a double-band photonic crystals. The
physical dynamics of the phase dependent phenomenon is analysed by
comparing two models `upper level coupling' and `lower level
coupling'. When the phase is changed from 0 to $\pi$, the variety of
spontaneous emission spectra from either of the two models are
inverse to each other, in which the relative height and width of
peaks are determined by the density of states in photonic crystals.

A novel Whispering--Gallery--Mode (WGM) fibre laser,
emitting linearly polarised three-colour light, is demonstrated by
pumping and gain coupling with evanescent waves. The pump light is
longitudinally coupled into a bare optical fibre immersed in a dye
solution of lower refractive index. The dye molecules around the
bare fibre are excited by the evanescent waves of pump light when
they propagate along the fibre in a total internal reflection. When
the pump beam within the fibre is a meridian beam, the WGM lasing
emission from the fibre laser is a linearly polarised transverse
electric wave, while it is a mixed wave of the linearly polarised
transverse electric and magnetic waves if the pump beam is a skew
beam within the fibre. Because the excited molecules are located
within the evanescent field of WGM, a good spatial overlap between
the dye gain and the evanescent field leads to a high pumping
efficiency and a longer gain distance along the fibre. Once the bare
fibre is inserted into three glass capillaries filled with Rhodamine
6G, 610 and 640 dye solutions, respectively, WGM laser oscillations
at the wavelengths of 567--575, 605--614 and 656--666~nm occur
simultaneously, and a linearly polarised three-colour lasing
emission is achieved in a single optical fibre.

A 7.8-$\mu $m surface emitting second-order distributed
feedback quantum cascade laser (DFB QCL) structure with metallized
surface grating is studied. The modal property of this structure is
described by utilizing coupled-mode theory where the coupling
coefficients are derived from exact Floquet--Bloch solutions of
infinite periodic structure. Based on this theory, the influence of
waveguide structure and grating topography as well as device length
on the laser performance is numerically investigated. The optimized
surface emitting second-order DFB QCL structure design exhibits a
high surface outcoupling efficiency of 22{\%} and a low threshold
gain of 10~cm$^{ - 1}$. Using a {$\pi $} phase-shift in the centre
of the grating, a high-quality single-lobe far-field radiation
pattern is obtained.

A corner-pumped type is a new pumping type in the
diode-pumped all-solid-state lasers, which has the advantages of
high pump efficiency and favourable pump uniformity. A highly
efficient corner-pumped Nd:YAG/YAG composite slab laser is
demonstrated in this paper. The maximal continuous-wave output power
of the 1064~nm laser is up to 18.57~W with a slope efficiency and an
optical-to-optical conversion efficiency of 44.9{\%} and 39.8{\%},
respectively. Inserting an acousto-optic $Q$-switch in the cavity,
the highest average output power of the quasi-continuous wave
1064~nm laser of 6.73~W is obtained at a repetition rate of
9.26~kHz. The experimental results show that a corner-pumped type is
a kind of feasible schedules in the design of diode-pumped
all-solid-state lasers with low or medium output powers.

We report on the microstructure formation in Foturan glass, induced by 1~kHz, 120 femtosecond laser irradiation. It is found that the line-shaped filamentation, not void array tends to be formed in this glass. This is different from our previous experimental results in fused silica and BK7 glasses. A possible mechanism Ag$^+$ captures the free electrons generated by laser, is proposed to explain the observed phenomena.

This paper studies the propagation of dipole solitons in
highly nonlocal medium by using the variational method. It finds
that the dipole solitons will be stable when the input power obeys a
restrict value. When the incident power does not satisfy the stable
conditions, the nonlocal accessible dipole solitons will undergo
linear harmonic oscillation. It shows such evolution behaviours in
detail.

We report on the generation of a high energy and long
pulse for pumping optical parametric chirped-pulse amplification
(OPCPA) by a high-birefringence photonic crystal fibre (HB-PCF) and
a laser-diode-pumped regenerative chirped pulse amplifier. Using the
femtosecond pump pulse centred at 815~nm, a 1064~nm soliton pulse is
produced in the HB-PCF. After injecting it into an Nd:YAG
regenerative amplifier with the glass etalons, a narrow-band
amplified pulse with an energy of $\sim $4~mJ and a duration of 235
ps is achieved at a repetition rate of 10~Hz, which is suitable for
being used as a pump source in the 800~nm OPCPA system.

Holographic dark (bright) screening solitons are predicted
in one dimension for a series circuit consisting of two
photorefractive crystals connected electronically by electrode leads
in a chain with a voltage source. Each crystal can support a
holographic screening soliton. The two solitons are known
collectively as a separate holographic screening soliton pair with
three types: bright--bright, bright--dark and dark--dark. The
numerical results show that the two solitons in a soliton pair can
affect each other through a light-induced current and their coupling
can affect their spatial profiles under the limit in which the
optical wave has a spatial extent much less than the width of the
crystal.

We study the ultraslow optical solitons in a resonant
three-level atomic system via electromagnetically induced
transparency under a density-matrix (DM) approach. The results of
linear and nonlinear optical properties are compared with those
obtained by using an amplitude variable (AV) approach. It is found
that the results for both approaches are the same in the linear
regime if the corresponding relations between the
population-coherence decay rates in the DM approach and the
energy-level decay rates in the AV approach are appropriately
imposed. However, in the nonlinear regime there is a small
difference for the self-phase modulation coefficient of the
nonlinear Schr\"{o}dinger equation that governs the time evolution
of probe pulse envelope. All analytical predicts are checked by
numerical simulations.

Group velocity (GV) of eigenmode is a crucial parameter to
explain the extraordinary phenomena about light propagation in
photonic crystals (PhCs). To study relationships between group
velocity and symmetry of PhCs, a new general expression of GV in
PhCs made up of non-dispersive material is introduced. Based on
this, the GVs of eigenmodes of PhCs, especially those of degenerate
eigenmodes at highly symmetric points in the first Brillouin zone,
are discussed. Some interesting results are obtained. For example,
the summation of degenerate eigenmodes' GVs is invariant under the
operations of wave vector ${{\bm K}}$-group $M_{{\bm K}} $. In
addition, some numerical results are presented to verify them.

Research on the underwater target scattering can provide
important theoretical support for target detection. The scattering
model of cylindrical shell is established in this paper. It is found
that the forward target strength is much stronger and varies with
angles of incident wave less significantly than backward target
strength. The received forward signal strength fluctuates with the
target moving due to the interference between direct signal and
scattering signal, which is most significant when target approaches
the baseline. An experiment is carried out in an anechoic tank to
validate the scattering model. The method of acquisiting forward
scattering in the tank is proposed. The forward and the backward
target strengths are achieved by using the pulse compression
technology, and they are about 3dB less than the modeling results.
The forward scattering phenomena of quiescent and moving target are
measured, which are similar to modeling results with different
target types.

This article proposes a finite element model (FEM) for
predicting the acoustic scattering from an encapsulated microbubble
near rigid boundary. The validity of the model is first examined by
comparing the acoustic nonlinear response of a free microbubble with
that obtained by the Church model. Then this model is used to
investigate the effect of the rigid boundary on acoustic scattering
signals from microbubble. The results indicate that the resonance
frequency decreases while the oscillation amplitude increases as the
microbubble approaches the rigid boundary. In addition, the
fundamental component of the acoustic scattering signal is enhanced
compared with that of the free microbubble.

A spherical cap radiator is one of the important parts of
an underwater wide-beam imaging system. The back radiation of a
traditional spherical cap radiator, which is composed of a vibrating
cap and a rigid baffle, is strong and its far-field directivity
function may fluctuate in big amplitude in the vicinity of the polar
axis. These shortcomings complicate the processing of the reflective
waves received for imaging the targets. In this study, the back
radiation is weakened by adding an acoustic soft material belt
between the vibrating cap and the rigid baffle. And the fluctuation
mentioned above is lowered remarkably by dividing the spherical cap
radiator into many annuluses and a relatively smaller spherical cap,
and by controlling the phase retardations of all elements
appropriately. Furthermore, the numerical experiments are carried
out by the finite element method (FEM) to prove the validity of the
above methods.

We propose a new concept, the centre of energy, to study
energy diffusion and heat conduction in one-dimensional hard-point
model. For diatom model, we find an anomalous energy diffusion as
$\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is
independent of initial condition and mass rate. The present model
can be viewed as the model composed by independent quasi-particles,
the centre of energy. In this way, heat current can be calculated.
Based on theory of dynamic billiard, the divergent exponent of heat
conductivity is estimated to be $\alpha=0.33$, which is confirmed by
a simple numerical calculation.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Forward fast protons are generated by the
moderate-intensity
laser--foil interaction. Protons with maximum energy 190~keV are
measured by using magnetic spectrometer and CR-39 solid state
track detectors along the direction normal to the rear surface.
The experimental results are also modeled by the particle-in-cell
method, investigating the time-varying electron temperature and
the rear sheath field. The temporal and spatial structure of the
sheath electrical field, revealed in the simulation, suggests that
these protons are accelerated by target normal sheath acceleration
(TNSA) mechanism.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

This paper reports that the high-quality Co-doped ZnO
single crystalline films have been grown on $a$-plane sapphire
substrates by using molecular-beam epitaxy. The as-grown films show
high resistivity and non-ferromagnetism at room temperature, while
they become good conductive and ferromagnetic after annealing in the
reducing atmosphere either in the presence or absence of Zn vapour.
The x-ray absorption studies indicate that all Co ions in these
samples actually substituted into the ZnO lattice without formatting
any detectable secondary phase. Compared with weak ferromagnetism
(0.16~$\mu _{\rm B}$/Co$^{2 + })$ in the Zn$_{0.95}$Co$_{0.05}$O
single crystalline film with reducing annealing in the absence of Zn
vapour, the films annealed in the reducing atmosphere with Zn vapour
are found to have much stronger ferromagnetism (0.65~$\mu _{\rm
B}$/Co$^{2 + })$ at room temperature. This experimental studies
clearly indicate that Zn interstitials are more effective than
oxygen vacancies to activate the high-temperature ferromagnetism in
Co-doped ZnO films, and the corresponding ferromagnetic mechanism is
discussed.

The interaction between a wedge disclination dipole and a
crack emanating from a semi-elliptic hole is investigated. Utilising
the complex variable method, the closed form solutions are derived
for complex potentials and stress fields. The stress intensity
factor at the tip of the crack and the image force acting on the
disclination dipole center are also calculated. The influence of the
morphology of the blunt crack and the position of the disclination
dipole on the shielding effect to the crack and the image force is
examined in detail. The results indicate that the shielding or
anti-shielding effect to the stress intensity factor increases when
the wedge disclination dipole approaches the tip of the crack. The
effects of the morphology of the blunt crack on the stress intensity
factor of the crack and the image force are very significant.

The radiation effects of the metal-oxide-semiconductor
(MOS) and the bipolar devices are characterised using 8~MeV protons,
60~MeV Br ions and 1~MeV electrons. Key parameters are measured {\it
in-situ} and compared for the devices. The ionising and nonionising
energy losses of incident particles are calculated using the Geant4
and the stopping and range of ions in matter code. The results of
the experiment and energy loss calculation for different particles
show that different incident particles may give different
contribution to MOS and bipolar devices. The irradiation particles,
which cause larger displacement dose within the same chip depth of
bipolar devices at a given total dose, would generate more severe
damage to the voltage parameters of the bipolar devices. On the
contrary, the irradiation particles, which cause larger ionising
damage in the gate oxide, would generate more severe damage to MOS
devices. In this investigation, we attempt to analyse the
sensitivity to radiation damage of the different parameter of the
MOS and bipolar devices by comparing the irradiation experimental
data and the calculated results using Geant4 and SRIM code.

We perform a first-principles simulation to study the
electronic and optical properties of wurtzite Zn$_{1 - x}$Cu$_{x}$O.
The simulations are based upon the Perdew--Burke--Ernzerhof form of
generalised gradient approximation within the density functional
theory. Calculations are carried out in different concentrations.
With increasing Cu concentration, the band gap of Zn$_{1 -
x}$Cu$_{x}$O decreases due to the shift of valence band. The
imaginary part of the dielectric function indicates that the optical
transition between O 2p states in the highest valence band and Zn 4s
states in the lowest conduction band shifts to the low energy range
as the Cu concentration increases. Besides, it is shown that the
insertion of Cu atom leads to redshift of the optical absorption
edge. Meanwhile, the optical constants of pure ZnO and
Zn$_{0.75}$Cu$_{0.25}$O, such as loss function, refractive index and
reflectivity, are discussed.

An improved multiple car-following model is proposed by
considering the arbitrary number of preceding cars, which includes
both the headway and the velocity difference of multiple preceding
cars. The stability condition of the extended model is obtained by
using the linear stability theory. The modified Korteweg--de Vries
equation is derived to describe the traffic behaviour near the
critical point by applying the nonlinear analysis. Traffic flow can
be also divided into three regions: stable, metastable and unstable
regions. Numerical simulation is accordance with the analytical
result for the model. And numerical simulation shows that the
stabilisation of traffic is increasing by considering the
information of more leading cars and there is unavoidable effect on
traffic flow from the multiple leading cars' information.

This paper provides an investigation of the phase
transition and spalling characteristic induced during shock loading
and unloading in the pure iron and the FeMnNi alloy. The impact for
the pure iron is symmetric and with same-thickness for both the
flyer and the target plate. It is found that an abnormal multiple
spalling happens in the pure iron sample as the pressure exceeds the
$\alpha -\varepsilon $ transition threshold of 13 GPa. In the
symmetric and same-thickness impact and reverse impact experiments
of the FeMnNi alloy, two abnormal tension regions occur when the
pressure exceeds the $\alpha -\varepsilon $ transition threshold of
6.3~GPa, and the reverse phase transition $\varepsilon -\alpha $
begins below 4.2~GP. The experimental process is simulated
successfully from the non-equilibrium mixture phase and Boettger's
model. Such abnormal spalling phenomena are believed to relate to
the shocked $\alpha -\varepsilon $ phase transition. The possible
reasons for the abnormal multiple spalling, which occurs during the
symmetric and same-thickness impact experiments of pure iron and
FeMnNi alloy, are discussed.

The string model for the glass transition can quantitatively describe the universal $\alpha $-relaxation in glassformers, including the average relaxation time, the distribution function of the relaxation time, and the relaxation strength as functions of temperature. The string relaxation equation (SRE) of the model, at high enough temperatures, simplifies to the well-known single particle mean-field Debye relaxation equation, and at low enough temperatures to the well-known Rouse--Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the special initial condition (SIC) of the SRE, i.e. for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics, was solved exactly. It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model, i.e. for stochastically spatially configurating strings, as will be described in separate publications.

This paper performs the two-dimensional, soft-sphere
molecular dynamics simulations to study the granular segregation in
a binary granular mixture with the same size but different density
in the container with the sawtooth base under horizontal vibration.
The segregation phase diagram is presented in the
acceleration-frequency space. When the acceleration is high enough
to result in relative motions of the particles, the system can be in
various states (mixed state, vertical and horizontal segregation
state), which depend on both acceleration and frequency. Due to the
sawtooth base there is stratified flow effect besides density
effect. The density effect raises the light particles. The
stratified flow drives the particles in the upper levels to the
right and the particles in the lower particles to the left, those
fact results in the appearance of the left segregation state. The
left segregation state can be changed to the right segregation by
changing the shape of the sawtooth. As the vibration frequency
increases, the stratified flow effect becomes weaker and weaker, so
at high vibration frequencies the vertical segregation state appears
instead of the left segregation state.

ZnO micro/nano complex structure films, including reticulate papillary nodes, petal-like and flake-hole, have been self-assembled by a hydrothermal technique at different temperatures without metal catalysts. The wettability of the above film surfaces was modified with a simple coating of heptadecafluorodecyltrimethoxy-silane in toluene. After modifying, the surface of ZnO film grown at 50~${^\circ}$C was converted from superhydrophilic with a water contact angle lower than 5$^{\circ}$ to superhydrophobic with a water contact angle of 165$^{\circ}$. Additionally, the surface of reticulate papillary nodes ZnO film grown at 100~${^\circ}$C had excellent superhydrophobicity, with a water contact angle of 173$^{\circ}$ and a sliding angle lower than 2$^{\circ}$. Furthermore, the water contact angle on the surface of petal-like and flake-hole ZnO films grown at 150~${^\circ}$C and 200~${^\circ}$C were found to be 140$^{\circ}$ and 120$^{\circ}$, respectively. The wettability for the samples was found to depend strongly on the surface morphology which results from the growth temperature.

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

Icosahedral iron clusters are synthesized and
characterized in our group by using experimental methods. But the
measurements of magnetic properties still face difficulties: the
sizes of the clusters and the amount of product. Therefore
theoretical methods are employed to study these issues. In this
paper, icosahedral iron clusters containing 13, 55, 147, 309 atoms
are calculated by {\em ab initio} techniques. After the structural
relaxation, the magnetism of the clusters is found to be similar to
that of face centred cubic (FCC) iron with stronger ferromagnetism
on surface. But the central atom of each cluster is exceptional,
which has a smaller magnetic moment. We also study the electronic
structural properties in the clusters for the better explanation of
the magnetism. It is suggested that in small clusters, the magnetic
properties still depend on the local structural arrangement.

This paper performs atomic simulations of the nucleation
and growth of Xe bubble in UO$_{2}$ at 1600~K. The bubble growth was
simulated up to the bubble containing 50 Xe atoms. The Xe atoms were
added directly to the bubble one by one, followed by a relaxation of
the system for several picoseconds. The simulations estimated the
bubble pressure and radius at different Xe concentrations. The
results indicate that the bubble pressure drops with the increasing
Xe/U and bubble size at low Xe concentration, while the pressure
will increase with the Xe/U ratio at high Xe concentration. The
swelling of the system associated with the bubble growth was also
obtained. Finally, the recovery of the damaged structure was
investigated.

A hexagon pitch carbon nanotube (CNT) array vertical to
the normal gate of cold cathode field emission displayer (FED) is
simulated by solving the Laplace equation. The calculated results
show that the normal gate causes the electric field around the CNT
tops to be concentrated and emission electron beam become a column.
The field enhancement factor and the emission current intensity step
up greatly compared with those of diode structure. Emission current
density increases rapidly with the decrease of normal-gate aperture.
The gate voltage exerts a critical influence on the emission
current.

Within the framework of the Floquet theorem, we have
investigated single-electron photon-assisted tunneling in a
double-well system using the transfer matrix technique. The
transmission probability displays satellite peaks on the both sides
of main resonance peaks and these satellite peaks originate from
emission or absorption photons. The single-electron resonance
tunneling can be control through changing applied harmonically
potential positions, such as driven potential in wells, in barriers,
or in whole double-well system. This advantage should be useful in
the optimization of the parameters of a transmission device.

Comparative study of high and low temperature AlN
interlayers and their roles in the properties of GaN epilayers
prepared by means of metal organic chemical vapour deposition on
(0001) plane sapphire substrates is carried out by high resolution
x-ray diffraction, photoluminescence and Raman spectroscopy. It is
found that the crystalline quality of GaN epilayers is improved
significantly by using the high temperature AlN interlayers, which
prevent the threading dislocations from extending, especially for
the edge type dislocation. The analysis results based on
photoluminescence and Raman measurements demonstrate that there
exist more compressive stress in GaN epilayers with high temperature
AlN interlayers. The band edge emission energy increases from
3.423~eV to 3.438~eV and the frequency of Raman shift of $E_{2
}$(TO) moves from 571.3~cm$^{ - 1}$ to 572.9~cm$^{ - 1}$ when the
temperature of AlN interlayers increases from 700~$^{\circ}$C to
1050~$^{\circ}$C. It is believed that the temperature of AlN
interlayers effectively determines the size, the density and the
coalescence rate of the islands, and the high temperature AlN
interlayers provide large size and low density islands for GaN
epilayer growth and the threading dislocations are bent and
interactive easily. Due to the threading dislocation reduction in
GaN epilayers with high temperature AlN interlayers, the approaches
of strain relaxation reduce drastically, and thus the compressive
stress in GaN epilayers with high temperature AlN interlayers is
high compared with that in GaN epilayers with low temperature AlN
interlayers.

This paper reports a procedure of soft x-ray lithography
for the fabrication of organic crossbar structure. Electron beam
lithography is employed to fabricate the mask for soft x-ray
lithography, with direct writing technology to lithograph positive
resist, polymethyl methacrylate on the polyimide film. Then Au is
electroplated on the polyimide film. Hard contact mode exposure is
used in x-ray lithography to transfer the graph from the mask to the
wafer. The 256-bits organic memory is achieved with the critical
dimension of 250~nm.

This paper studies the effects of silane back diffusion in
the initial plasma ignition stage on the properties of
microcrystalline silicon ($\mu $c-Si:H) films by Raman spectroscopy
and spectroscopic ellipsometry, through delaying the injection of
SiH$_{4}$ gas to the reactor before plasma ignition. By comparing
with standard discharge condition, delayed SiH$_{4}$ gas condition
could prevent the back diffusion of SiH$_{4}$ from the reactor to
the deposition region effectively, which induced the formation of a
thick amorphous incubation layer in the interface between bulk film
and glass substrate. Applying this method, it obtains the
improvement of spectral response in the middle and long wavelength
region by combining this method with solar cell fabrication.
Finally, results are explained by modifying zero-order analytical
model, and a good agreement is found between model and experiments
concerning the optimum delayed injection time.

This paper studies the quantum conductance properties of
three-terminated carbon nanotube Y-junctions, which are built by
connecting three (5,5) single-walled carbon nanotubes. The results
show that the quantum conductance at the Fermi energy oscillates
periodically with the junction's size, and the number of oscillating
periodic layers is 3 which is the same as that in the two terminated
$(10,0)/m(5,5)/(10,0)$ junctions. Moreover, this Y-junction with
different size exhibits obvious different distribution of electron
current in the two drain branches, called shunt valve effect of
electronic current. Thus the degree of this effect can be controlled
and modulated directly by constructing the three branches' sizes or
the distribution of defect. The results show in detail that the
difference between the two drain currents can be up to two times for
some constructions with special sizes. In addition, the uniform
distribution of defects in the Y-junction leads to lower quantum
conductance than that of other defect configurations.

For a mesoscopic radio frequency superconducting quantum
interference device (rfSQUID), at a degeneracy point, the system
reduces to a quantum two-state system which can be used as a flux
qubit. When the noise environment is equivalent to a harmonic
oscillators bath, by virtue of an operator-norm measure for the
short time decoherence, this paper investigates the initial
decoherence of the flux qubit operating in the ohmic noise
environment and illustrates its property by means of the numerical
evaluation.

Ge and Si p-channel metal--oxide--semiconductor
field-effect-transistors (p-MOSFETs) with hafnium silicon oxynitride
(HfSiON) gate dielectric and tantalum nitride (TaN) metal gate are
fabricated. Self-isolated ring-type transistor structures with two
masks are employed. W/TaN metal stacks are used as gate electrode
and shadow masks of source/drain implantation separately.
Capacitance--voltage curve hysteresis of Ge metal--oxide--semiconductor
(MOS) capacitors may be caused by charge trapping centres in
GeO$_{x}$ ($1

Current transport mechanism in Ni-germanide/n-type Ge
Schottky diodes is investigated using current--voltage
characterisation technique with annealing temperatures from 300~\duto 500~\du. Based on the current transport model, a simple method to
extract parameters of the NiGe/Ge diode is presented by using the
$I$--$V$ characteristics. Parameters of NiGe/n-type Ge Schottky
diodes fabricated for testing in this paper are as follows: the
ideality factor $n$, the series resistance $R_{\rm s}$, the
zero-field barrier height $\phi _{\rm b0}$, the interface state
density $D_{\rm it}$, and the interfacial layer capacitance $C_{\rm
i}$. It is found that the ideality factor $n$ of the diode increases
with the increase of annealing temperature. As the temperature
increases, the interface defects from the sputtering damage and the
penetration of metallic states into the Ge energy gap are
passivated, thus improving the junction quality. However, the
undesirable crystallisations of Ni-germanide are observed together
with NiGe at a temperature higher than 400~\du. Depositing a very
thin ($\sim $1~nm) heavily Ge-doped $n^{+}$ Ge intermediate layer
can improve the NiGe film morphology significantly.

Interface roughness strongly influences the performance
of germanium metal--organic--semiconductor field effect transistors
(MOSFETs). In this paper, a 2D full-band Monte Carlo simulator is
used to study the impact of interface roughness scattering on
electron and hole transport properties in long- and short- channel
Ge MOSFETs inversion layers. The carrier effective mobility in the
channel of Ge MOSFETs and the in non-equilibrium transport
properties are investigated. Results show that both electron and
hole mobility are strongly influenced by interface roughness
scattering. The output curves for 50~nm channel-length double gate n
and p Ge MOSFET show that the drive currents of n- and p-Ge MOSFETs
have significant improvement compared with that of Si n- and
p-MOSFETs with smooth interface between channel and gate dielectric.
The $82\%$ and $96\%$ drive current enhancement are obtained for the
n- and p-MOSFETs with the completely smooth interface. However, the
enhancement decreases sharply with the increase of interface
roughness. With the very rough interface, the drive currents of Ge
MOSFETs are even less than that of Si MOSFETs. Moreover, the
significant velocity overshoot also has been found in Ge MOSFETs.

The crystal structure, magnetic and magnetocaloric
characteristics of the pseduo ternary compounds of
Tb$_{5}$Ge$_{2-x}$Si$_{2-x}$Mn$_{2x}$ (0 $\leq $ 2$x$ $\leq$ 0.1)
were investigated by x-ray powder diffraction and magnetization
measurements. The x-ray powder diffraction results show that all
compounds preserve the monoclinic phase as the majority phase and
all the synthesized compounds were observed to be ferromagnetic from
magnetization measurements. Magnetic phase transitions were
interpreted in terms of Landau theory. Maximum isothermal magnetic
entropy change value
(20.84~J\,$\cdot$\,kg$^{-1}$\,$\cdot$\,K$^{-1}$) was found for
Tb$_{5}$Ge$_{1.95}$Si$_{1.95}$Mn$_{0.1}$ at around 123~K in the
magnetic field change of 5~T.

The interaction and its variation between magnetic grains
in two kinds of magnetic recording tapes are investigated by
first-order reversal curves (FORC) and the $\delta M$ method. The
composition and microstructure of the samples are characterised by
x-ray diffraction and scanning electron microscope. The FORC diagram
can provide more accurate information of the interaction and its
variation, but the $\delta M$ curves cannot. The positive
interaction field and the large variation of the interaction field
have opposite effects on the $\delta M$ curve.

This paper investigates the capacitance--voltage
($C$--$V$) characteristics of F doping SiCOH low dielectric constant
films metal--insulator--semiconductor structure. The F doping SiCOH
films are deposited by decamethylcyclopentasiloxane (DMCPS) and
trifluromethane (CHF$_{3})$ electron cyclotron resonance plasmas.
With the CHF$_{3}$/DMCPS flow rate ratio from 0 to 0.52, the
positive excursion of $C$--$V$ curves and the increase of flat-band
voltage $V_{\rm FB}$ from $-6.1$~V to 32.2~V are obtained. The
excursion of $C$--$V$ curves and the shift of $V_{\rm FB}$ are
related to the change of defects density and type at the Si/SiCOH
interface due to the decrease of Si and O concentrations, and the
increase of F concentration. At the CHF$_{3}$/DMCPS flow rate ratio
is 0.12, the compensation of F-bonding dangling bond to Si dangling
bond leads to a small $V_{\rm FB}$ of 2.0~V.

We present a detailed theoretical analysis on the
possibilities and conditions for negative permeability and negative
refraction occuring in the magnetic materials with both pronounced
magnetic and dielectric responses to electromagnetic waves. The
results indicate that the permeability is always positive for
$\de=(2q+0.5)\pi$ ($\de$ is the initial phase difference of magnetic
components $h_{x}$ and $h_{y }$ of incident electromagnetic wave,
$q$ is integer), which means that it is difficult to realize
negative refraction. However, for $\de=2q\pi, \de=(2q+1)\pi$, or
$\de=(2q-0.5)\pi$, the negative permeability occurs at some range of
free procession frequency, which means that the refraction can
become negative under certain conditions. Further analysis reveals
that for general positive permittivity there are various
opportunities for realizing the negative refraction provided that
some requirements are met. One concludes also that the refractive
index for $\de=2q\pi$ case is similar to $\de=(2q+1)\pi$. The only
difference between two cases of $\de=2q\pi$ and $\de=(2q+1)\pi$ is
that the $x$-direction for $\de=2q\pi$ corresponds to the
$y$-direction for $\de=(2q+1)\pi$, and the $y$-direction for
$\de=2q\pi$ corresponds to the $x$-direction for $\de=(2q+1)\pi$.
The results are valuable for designing and analysing the complex
negative refraction of magnetic materials.

The leakage current of GaN Schottky barrier ultraviolet
photodetectors is investigated. It is found that the photodetectors
adopting undoped GaN instead of lightly Si-doped GaN as an active
layer show a much lower leakage current even when they have a higher
dislocation density. It is also found that the density of Ga
vacancies in undoped GaN is much lower than in Si-doped GaN. The Ga
vacancies may enhance tunneling and reduce effective Schottky
barrier height, leading to an increase of leakage current. It
suggests that when undoped GaN is used as the active layer, it is
necessary to reduce the leakage current of GaN Schottky barrier
ultraviolet photodetector.

Novel Y$_{1 - x - y}$VO$_{4}$:$x$Dy$^{3 + }$, $y$Bi$^{3 +
}$ ($0.01 \le x \le 0.05, 0 \le y \le 0.20$) phosphors for light
emitting diode (LED) were successfully synthesised by solid-state
reaction. The calculation results of electronic structure show that
YVO$_{4}$ has a direct band gap with 3~eV at $G$. The top of the
valence band is dominated by O 2p state and the bottom of the
conduction band is mainly composed of O 2p and V 3d states. An
efficient yellow emission under near-ultraviolet (365 nm) excitation
is observed. Compared with the pure YVO$_{4}$:Dy$^{3 + }$ samples,
the Dy$^{3 + }$, Bi$^{3 + }$ co-doped samples show a more intensive
emission peak (at 574~nm) and a new broad emission band
(450--770~nm), due to the $^{4}F_{9 / 2}-{}^{6}H_{13 / 2 }$
transition of Dy$^{3 + }$ and the emission of the VO$_{4}^{3 -
}-$Bi$^{3 + }$ complex respectively. The optimum chromaticity index
of Y$_{1 - x - y}$VO$_{4}$:$x$Dy$^{3 + }$, $y$Bi$^{3 + }$ ($0.01 \le
x \le 0.05, 0 \le y \le 0.20$) is (0.447, 0.497), which indicates
that YVO$_{4}$:Dy$^{3 + }$, Bi$^{3 + }$ has higher colour saturation
than the commercial phosphor YAG: Ce$^{3 + }$. The effects of
concentration of Dy$^{3 + }$, Bi$^{3 + }$, electric states and the
photoluminescence properties are discussed in details.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Using the theory of nonlinear interactions between long and short waves, a nonlinear fractal sea surface model is presented for a one dimensional deep sea. Numerical simulation results show that spectra intensity changes at different locations (in both the wave number domain and temporal-frequency domain), and the system obeys the energy conservation principle. Finally, a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed.

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