This paper establishes a new isospectral problem. By making use of
the Tu scheme, a new integrable system is obtained. It gives
integrable couplings of the system obtained. Finally, the Hamiltonian
form of a binary symmetric constrained flow of the system obtained is
presented.

Many real-world networks have the ability to adapt themselves in
response to the state of their nodes. This paper studies controlling
disease spread on network with feedback mechanism, where the
susceptible nodes are able to avoid contact with the infected ones by
cutting their connections with probability when the density of
infected nodes reaches a certain value in the network. Such feedback
mechanism considers the networks' own adaptivity and the cost of
immunization. The dynamical equations about immunization with
feedback mechanism are solved and theoretical predictions are in
agreement with the results of large scale simulations. It shows that
when the lethality $\alpha$ increases, the prevalence decreases more
greatly with the same immunization $g$. That is, with the same cost,
a better controlling result can be obtained. This approach offers an
effective and practical policy to control disease spread, and also
may be relevant to other similar networks.

In this paper Lou's direct perturbation method is applied to the
perturbed coupled nonlinear Schr\"{odinger equations to obtain
their asymptotical solutions, which include not only the zero-order
solutions but also the first-order modifications. Based on the
asymptotical solutions, the effects of perturbations on soliton
parameters and the collision between two solitons are then discussed
in brief. Furthermore, we directly simulate the perturbed coupled
nonlinear Schr\"{odinger equations by split-step Fourier method to
check the validity of the direct perturbation method. It turns out
that our analytical results are well supported by the numerical
calculations.

This paper obtains some solutions of the 5th-order mKdV equation
by using the exponential--fraction trial function method, such
as solitary wave solutions, shock wave solutions and the hopping
wave solutions. It successfully shows that this method may be
valid for solving other nonlinear partial differential
equations.

Some new exact solutions of the Burgers--Fisher equation and
generalized Burgers--Fisher equation have been obtained by using the
first integral method. These solutions include exponential function
solutions, singular solitary wave solutions and some more complex
solutions whose figures are given in the article. The result shows
that the first integral method is one of the most effective
approaches to obtain the solutions of the nonlinear partial
differential equations.

The well-posedness of the initial-boundary value problem of the time-varying
linear electromagnetic field in a multi-medium region is investigated.
Function spaces are defined, with Faraday's law of
electromagnetic induction and the initial-boundary conditions considered
as constraints. Gauss's
formula applied to a multi-medium region is used to derive
the energy-estimating
inequality. After converting the initial-boundary conditions into
homogeneous ones and analysing the characteristics of an operator introduced
according to the total current law, the existence, uniqueness and stability
of the weak solution to the initial-boundary value problem of
the time-varying linear electromagnetic field are proved.

In this paper the bulk exciton polaritons in ternary mixed crystals
(TMCs) are investigated in
the Born--Huang approximation. The numerical results of the polariton
frequencies as functions of the wave-vector and the compositions for ternary
mixed crystals Al$_{x$Ga$_{1 - x$As, Cd$_{x$Zn$_{1 - x$Se, and
Al$_{x$Ga$_{1 - x$N are obtained and discussed. The new dispersion
characteristics for exciton--polaritons in TMC systems are found in
comparison with binary crystals. The splitting of the two branches of
exciton--polariton frequencies varies nonlinearly with the composition of
TMCs and has a minimum in the long-wavelength range.

A density matrix is usually obtained by solving the Bloch equation,
however only a few Hamiltonians' density matrices can be analytically
derived. The density matrix for two interacting particles with
kinetic coupling is hard to derive by the usual method due to this
coupling; this paper solves this problem by using the bipartite
entangled state representation.

Based on the techniques of the quantum remote state preparation via
a deterministic way, this paper proposes a quantum communication
scheme to distribute the secret messages in two phases, i.e., the
carrier state checking phase and the message state transmitting
phase. In the first phase, the secret messages are encoded by the
sender using a stabilizer quantum code and then transmitted to the
receiver by implementing three CNOT gates. In the second phase, the
communicators check the perfectness of the entanglement of the
transmitted states. The messages can be distributed to the receiver
even if some of the transmitted qubits are destroyed.

In this paper a scheme for controlled teleportation of arbitrary
high-dimensional unknown quantum states is proposed by using the generalized
Bell-basis measurement and the generalized Hadamard transformation. As two
special cases, two schemes of controlled teleportation of an unknown
single-qutrit state and an unknown two-qutrit state are investigated in
detail. In the first scheme, a maximally entangled
three-qutrit state is used as the quantum channel, while in the second
scheme, an entangled two-qutrit state and an entangled three-qutrit state are
employed as the quantum channels. In these schemes, an unknown qutrit state
can be teleported to either one of two receivers, but only one of them can
reconstruct the qutrit state with the help of the other. Based on the case
of qutrits, a scheme of controlled teleportation of an unknown qudit state
is presented.

In the context of microwave cavity QED, this paper proposes a new scheme for
teleportation of an arbitrary pure state of two atoms. The scheme is very
different from the previous ones which achieve the integrated state
measurement, it deals in a probabilistic but simplified way. In the scheme,
no additional atoms are involved and thus only two atoms are required to be
detected. The scheme can also be used for the teleportation of arbitrary pure
states of many atoms or two-mode cavities.

We have considered two distant mesoscopic superconducting quantum
interference device (SQUID) rings A and B in the presence of two-mode
nonclassical state fields and investigated the correlation of the
supercurrents in the two rings using the normalized correlation
function $C_{\rm AB}$. We show that when the parameter $\alpha$ is
very small for the separable state with the density matrix $\hat
{\rho } = (\left| {\alpha , - \alpha } \right\rangle \left\langle
{\alpha , - \alpha } \right| + \left| { - \alpha ,\alpha }
\right\rangle \left\langle { - \alpha ,\alpha } \right|) / 2$ and
entangled coherent state (ECS) $\left| u \right\rangle = N_1 (\left|
{\alpha , - \alpha } \right\rangle + \left| { - \alpha ,\alpha }
\right\rangle )$ fields, the dynamic behaviours of the normalized
correlation function $C_{\rm AB}$ are similar, but it is quite
different for the entangled coherent state $\left| {u}'
\right\rangle = N_2 (\left| {\alpha , - \alpha } \right\rangle -
\left| { - \alpha ,\alpha } \right\rangle )$ field. When the
parameter $\alpha $ is very large, the dynamic behaviours of $C_{\rm
AB}$ are almost the same for the separable state, entangled coherent
state $\left| u \right\rangle $ and $\left| {u}' \right\rangle $
fields. For the two-mode squeezed vacuum state field the maximum of
$C_{\rm AB}$ increases monotonically with the squeezing parameter
$r$, and as $r \to \infty $, $C_{\rm AB} \to 1$. This means that the
supercurrents in the two rings A and B are quantum mechanically
correlated perfectly. It is concluded that not all the quantum
correlations in the two-mode nonclassical state field can be
transferred to the supercurrents; and the transfer depends on the
state of the two-mode nonclassical state field prepared.

This paper studies the Josephson-like tunnelling in two-component
Bose--Einstein condensates coupled with microwave field,
which is in respond to various attractive and repulsive atomic interaction
under the various aspect ratio of trapping potential. It is very
interesting to find that the dynamic of Josephson-like tunnelling can
be controlled from fast damped oscillations to nondamped oscillation,
and relative number of atoms changes from asymmetric occupation to
symmetric occupation correspondingly.

This paper presents a realistic scheme for the teleportation of
coherent states in which a two-mode squeezed vacuum state serves as
the quantum channel and the position-sum and momentum-difference of
two local modes serve as the measuring observables. The average
fidelity of the teleportation of coherent states is derived for
finite squeezing parameters and it turns out that fidelity greater
than 1/2 cannot be achieved by using a classical channel alone and
the probability distribution of the measurement result is a Gaussian
distribution around the unknown parameter of the input coherent
state with a width given by the squeezing parameter.

Network motifs hold a very important
status in genetic regulatory networks. This paper aims to analyse
the dynamical property of the network motifs in genetic regulatory
networks. The main result we obtained is that the dynamical
property of a single motif is very simple with only an
asymptotically stable equilibrium point, but the combination of
several motifs can make more complicated dynamical properties
emerge such as limit cycles. The above-mentioned result shows that
network motif is a stable substructure in genetic regulatory
networks while their combinations make the genetic regulatory
network more complicated.

In this paper the stochastic resonance (SR) is studied in an overdamped linear system
driven by multiplicative noise and additive quadratic noise. The exact
expressions are obtained for the first two moments and the correlation
function by using linear response and the properties of the dichotomous noise.
SR phenomenon exhibits in the linear system. There are three different forms
of SR: the bona fide SR, the conventional SR and SR in the broad sense.
Moreover, the effect of the asymmetry of the multiplicative noise on the
signal-to-noise ratio (SNR) is different from that of the additive noise and
the effect of multiplicative noise and additive noise on SNR is different.

We have studied sharp peak landscapes of the Eigen model from a
new perspective about how the quasispecies are distributed in the
sequence space. To analyse the distribution more carefully, we bring
in two tools. One tool is the variance of Hamming distance of the
sequences at a given generation. It not only offers us a different
avenue for accurately locating the error threshold and illustrates
how the configuration of the distribution varies with copying
fidelity $q$ in the sequence space, but also divides the copying
fidelity into three distinct regimes. The other tool is the
similarity network of a certain Hamming distance $d_{0}$, by which we
can gain a visual and in-depth result about how the sequences
are distributed. We find that there are several local similarity optima
around the centre (global similarity optimum) in the distribution of
the sequences reproduced near the threshold. Furthermore, it is
interesting that the distribution of clustering coefficient $C(k)$
follows lognormal distribution and the curve of clustering
coefficient $C$ of the network versus $d_{0}$ appears to be linear
near the threshold.

In this paper, generalized synchronization of two
different chaotic dynamical systems is investigated. An active control is
adopted to construct a response system which synchronizes with a given drive
system for a function relation. Based on rigorous analysis, the error system
is asymptotically stable at the equilibrium. Numerical simulations
illustrate the effectiveness of the proposed theory.

This paper proposes a method to achieve projective synchronization of
the fractional order chaotic Rossler system. First, construct the
fractional order Rossler system's corresponding approximate integer
order system, then a control method based on a partially linear
decomposition and negative feedback of state errors is utilized on
the new integer order system. Mathematic analyses prove the
feasibility and the numerical simulations show the effectiveness of
the proposed method.

In this paper, one-state on--off intermittency and two-state on--off
intermittency are generated in two five-dimensional continuum systems
respectively. In each system, a two-dimensional subsystem is driven by the
R\"{o}ssler chaotic system. The parameter conditions under which the on--off
intermittency occurs are discussed in detail. The statistical property of
the intermittency is investigated. It is shown that the distribution of the
laminar phase duration time follows a power law with an exponent of
$-3/2$, which is
a signature of on--off intermittency. Moreover, the phenomenon of
intermingled basins is observed when attractors in the two symmetric
invariant subspaces are stable. We provide an effective way to generate
on--off intermittency based on a chaotic system, which
is important for
application and theoretical study.

The paper is concerned with adaptive tracking problem for a class of
chaotic system with time-varying uncertainty, but bounded by norm
polynomial. Based on adaptive technique, it proposes a novel
controller to asymptotically track the arbitrary desired bounded
trajectory. Simulation on the Rossler chaotic system is performed
and the result verifies the effectiveness of the proposed method.

In this paper the nonlinear dynamical behaviour of a quantum cellular neural network (QCNN)
by coupling Josephson circuits was investigated and it was shown that the
QCNN using only two of them can cause the onset of chaotic oscillation. The
theoretical analysis and simulation for the two Josephson-circuits-coupled
QCNN have been done by using the amplitude and phase as state variables. The
complex chaotic behaviours can be observed and then proved by calculating
Lyapunov exponents. The study provides valuable information about QCNNs for
future application in high-parallel signal processing and novel chaotic
generators.

This paper reports on the canard phenomenon occurring in a
rheodynamic model of cardiac pressure pulsations. By singular
perturbation techniques the corresponding parameter value at which
canards exist is obtained. The physiological significance of canards
in this model is given.

Spiral waves have been controlled by generating target waves with a
localized inhomogeneity in the oscillatory medium. The competition between
the spiral waves and target waves is discussed. The effect of the localized
inhomogeneity size has also been studied.

A semiclassical method based on the closed-orbit theory is applied to
analysing the dynamics of photodetached electron of H$^- $ in the
parallel electric and magnetic fields. By simply varying the magnetic
field we reveal spatial bifurcations of electron orbits at a fixed
emission energy, which is referred to as the fold caustic in
classical motion. The quantum manifestations of these singularities
display a series of intermittent divergences in electronic flux
distributions. We introduce semiclassical uniform approximation to
repair the electron wavefunctions locally in a mixed phase space and
obtain reasonable results. The approximation provides a better
treatment of the problem.

Equilibrium parameters of ozone, such as equilibrium geometry
structure parameters, force constants and dissociation energy are
presented by CBS-Q
{\it ab initio} calculations. The calculated equilibrium geometry structure
parameters and energy are in agreement with the corresponding
experimental values. The potential energy function of ozone with a
C$_{\rm 2v}$ symmetry in the ground state is described by the
simplified Sorbie--Murrell many-body expansion potential function
according to the ozone molecule symmetry. The contour of bond
stretching vibration potential of an O$_{3}$ in the ground state,
with a bond angle ($\theta )$ fixed, and the contour of O$_{3}$
potential for O rotating around O$_{1}$--O ($R_{1})$, with O$_{1}$--O
bond length taken as the one at equilibrium, are plotted. Moreover,
the potentials are analysed.

The possibility of cooling a system from liquid helium temperature,
4.2~K, using a tunnel junction refrigerator is analysed. Calculations
show that the device can be used over a wide temperature range from
4~K down to well below 1~mK with necessary cooling power. However,
several serious difficulties must be overcome before the method can
be used in low temperature laboratories.

We report the formation and local electronic
structure of Ge clusters on the Si(111)-7$\times $7 surface
studied by using variable temperature scanning tunnelling microscopy
(VT-STM) and low-temperature scanning tunnelling spectroscopy (STS).
Atom-resolved STM images reveal that the Ge atoms are prone to
forming clusters with 1.0~nm in diameter for coverage up to 0.12~ML.
Such Ge clusters preferentially nucleate at the centre of the
faulted-half unit cells, leading to the `dark sites'
of Si centre adatoms from the surrounding three unfaulted-half
unit cells in filled-state images.
Bias-dependent STM images show the charge transfer
from the neighbouring Si adatoms to Ge clusters.
Low-temperature STS of the Ge clusters reveals
that there is a band gap on the Ge cluster and the large voltage
threshold is about 0.9~V.

In this paper electron capture on iron group nuclei in crusts of
neutron stars in a strong magnetic field is investigated. The
results show that the magnetic fields have only a slight effect on
electron capture rates in a range of 10$^{8}-10^{13}$G on surfaces of
most neutron stars, whereas for some magnetars the magnetic fields
range from 10$^{13}$ to 10$^{18}$~G. The electron capture rates of
most iron group nuclei are greatly decreased, reduced by even four
orders of magnitude due to the strong magnetic field.

Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light
clusters have been studied in detail for 25 MeV/nucleon $^{86}$Kr
+ $^{124}$Sn at large impact parameters by using a quantum
molecular dynamics model with different potential parameters. Four
sets of parameters including soft or hard equation of state (EOS)
with or without symmetry energy term are used. Both
number-of-nucleon ($A$) scaling of the elliptic flow versus
transverse momentum ($p_{\rm t}$) and the scaling of $v_4/A^{2}$ versus
$(p_{\rm t}/A)^2$ have been demonstrated for the light clusters in all
above calculation conditions. It is also found that the ratio of
$v_4/{v_2}^2$ maintains a constant of 1/2 which is independent of
$p_{\rm t}$ for all the light fragments. Comparisons among different
combinations of the EOS and the symmetry potential term show that
the above scaling behaviours are sound and independent of the
details of potential, while the strengths of flows are sensitive
to the EOS and the symmetry potential term.

Intermittency and fractal behaviour have been studied of
emission spectra of target associated fragments from
$^{84}$Kr--AgBr interactions at 1.7\,A GeV in emission angle
space and azimuthal angle space separately. The intermittent
behaviour is observed in the two spaces separately. From the
intermittency exponent, the anomalous fractal dimension $d_{q}$
is calculated and the variation of $d_{q}$ with the order $q$ is
investigated. It is found that the anomalous dimensions are
found to increase with the order of moments $q$, thereby
indicating the relation of multifractality to production
mechanism of target associated fragments.

The intermittency effect has been studied for an interaction of
3.7 A GeV $^{16}$O with emulsion using the distributions of both
the pseudorapidity intervals and the azimuthal angle intervals
of the shower particles emitted in a central rapidity region.
The scaled factorial moments, reduced scaled factorial moments
and multifractal moments as functions of the bin size in
pseudorapidity and in azimuthal angle have been calculated and
have revealed the presence of an intermittent behaviour which
may be due to the random cascading property of the reaction. The
anomalous fractal dimension has been found to increase with the
increase of rank of the moment.

Based on the vectorial structure of electromagnetic beam and the
method of stationary phase, the analytical structure of Hermite
Gaussian beam in far field is presented. The structural energy flux
distributions are also investigated in the far field. The structural
pictures of some Hermite Gaussian beams are depicted in the far
field. As the structure of Hermite Gaussian beam is dominated by the
transverse mode numbers and the initial transverse Gaussian half
width, it is more complex than that of Gaussian beam. The ratios of
the structural energy fluxes to the whole energy flux are independent
of the transverse mode numbers and the initial transverse Gaussian
half width.
The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\

The self-consistent differential equations, which describe a
laminar-flow equilibrium state in a magnetically focused intense relativistic
electron beam propagating inside a conducting waveguide, are presented. The
canonical angular momentum, $p_{\theta }$, defined under the conditions at the
source, uniquely determines the possible solutions of these equations. By
numerically solving these equations, the space-charge limited current and
the externally applied magnetic field are obtained in a solid beam
and a hollow beam in two cases of $p_{\theta }=0$ (magnetically shielded source)
and $p_{\theta }=$~const. (immersed source) separately. It is shown that the hollow beam
is more beneficial to the propagation of the intense relativistic beam
through a drift tube than the solid beam.

An exact, general solution for laser beams propagating in
longitudinally inhomogeneous plasmas is obtained in the form of
the diffraction integral. The Gaussian beam and the Hermite--Gaussian
beam are taken for example. In the case of an increasing plasma
density along the propagation distance, natural diffraction of the
Gaussian beam is retarded. This retardance has a less effect on the
central part of the Hermite--Gaussian beam while a considerable rise
of the power in bucket (PIB) occurs in the surrounding part of the
beam.

This paper reports that the nonlinear refractive index of
a novel organic optical storage film doped azo-diphenylamine polymer is
measured by using the $Z$-scan technique. The nonlinear refractive index up to
$3.7\times 10 ^{ - 6 }$~cm$^{2}$/W induced by thermo-optical effect is
obtained. It indicates that the sample has excellent optical nonlinear
properties. The physical mechanism of the great nonlinear optical effect is
analysed and the optical conjugate characteristic is also discussed with
degenerate four-wave-mixing. The phase conjugate wave diffracted from the
formative refractive index grating in the sample is acquired and its
equivalent reflectivity reaches about 22{\%}. On this basis, the reflective
wave phase-conjugated mirror system was designed, and the image aberration
experienced in propagation in the storage experiment is corrected by using
the system.

Two interacting light filaments with different initial phases
propagating in air are investigated numerically by using a ray
tracing method. The evolution of the rays of a filament is governed
by a potential field. During propagation, the two potential wells of
the two filaments can merge into one or repel each other, depending
on the initial phase difference between the two filaments. The study
provides a simple description of the interacting filaments.

A method of designing a photonic crystal grating slow-wave circuit in which
the cylinders of the 2D photonic crystals dot on a cross-sectional plane is
established by calculating the band structures of the 2D photonic crystals,
and the eigenfrequency of the equivalent waveguide grating. For calculating
the band structures, the eigenvalue equations of the photonic crystals in
the system of photonic crystal grating slow-wave circuit are derived in a
special polarization mode. Two examples are taken to show the method. The
design result is validated by the scattering parameters of the same circuit.
The result indicates that there exists no photonic band gap if the metal
gratings do not extend into the photonic crystals; the design of the circuit
without the metal gratings extending into the photonic crystals is less
flexible than that with the metal gratings extending into the photonic
crystals.

This article studies the feasibility of noninvasive temperature estimation
by detecting echo-strain including thermal expansion in therapeutic
ultrasound treatment. This technique evaluates distributions of echo-strain
and temperature inside the tissue by detecting echo signals pre- and
post-heating, in combination with the temperature dependence of sound speed
and thermal expansion. In the computer simulation and experimental study,
echo signals pre- and post-heating are acquired and then the temperature
elevation is evaluated by correlation analysis. Results demonstrate that
this technique can effectively extend the measured temperature range up to
75$^{\circ}$C with an accuracy of $\pm $2$\,^{\circ}$C.

The comparison between single-point energy scanning (SPES) and geometry
optimization (OPT) in determining the equilibrium geometry of the
$a^{3}\Sigma ^{ + }_{\rm u}$ state for $^{7}$Li$_{2}$ is made at numerous
basis sets such as 6-311++G(2df), cc-PVTZ, 6-311++G(2df,p), 6-311G(3df,3pd),
6-311++G(2df,2pd), D95(3df,3pd), 6-311++G, DGDZVP, 6-311++G(3df,2pd),
6-311G(2df,2pd), D95V++, CEP-121G, 6-311++G(d,p), 6-311++G(2df,pd) and
6-311++G(3df,3pd) in full active space using a symmetry-adapted-cluster/
symmetry-adapted-cluster configuration-interaction (SAC/SAC-CI) method
presented in Gaussian03 program package. The difference of the equilibrium
geometries obtained by SPES and by OPT is reported. Analyses show that the
results obtained by SPES are more reasonable than those obtained by OPT. We
have calculated the complete potential energy curves at these sets over a
wide internuclear distance range from about 3.0$a_{0}$ to 37.0$a_{0}$, and the
conclusion is that the basis set cc-PVTZ is the most suitable one. With the
potential obtained at cc-PVTZ, the spectroscopic data
($T_{\rm e}$, $D_{\rm e}$,
$D_{0}$, $\omega _{\rm e },\omega _{\rm e}\chi _{\rm e}$,
$\alpha _{\rm e}$ and $B_{\rm e})$ are computed and they are
1.006 eV, 338.71~cm$^{ - 1}$, 307.12 cm$^{ - 1}$, 64.88 cm$^{ - 1}$, 3.41
cm$^{ - 1}$, 0.0187 cm$^{ - 1}$ and 0.279 cm$^{ - 1}$, respectively, which
are in good agreement with recent measurements. The total 11 vibrational
states are found at $J$=0. Their corresponding vibrational levels and classical
turning points are computed and compared with available RKR data, and good
agreement is found. One inertial rotation constant ($B_{\upsilon })$ and six
centrifugal distortion constants ($D_{\upsilon }$ $H_{\upsilon }$,
$L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are
calculated. The scattering length is calculated to be --27.138$a_{0}$, which
is in good accord with the experimental data.

CROSS DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

This paper reports that pure hexagonal aluminium nitride microtubes
and nanowires growing along the [0001] direction have been
successfully synthesized by directly reacting AlCl$_{3}$ with
NaN$_{3}$ at low temperature (450\du) under condition of non-solvent
system. The grey--white powder of reacting product was characterized
by high-resolution transmission electron microscope (HRTEM), which
shows that the powder is long straight-wire morphology with outer
diameter from 40\,nm to 300\,nm and length up to several micrometres.
The results of both electron diffraction (ED) and x-ray diffraction
(XRD) indicate that the AlN microtubes have a pure hexagonal
monocrystal tubular structure with the combination of the curled AlN
nanobelts. Room-temperature photoluminescence spectrum of the
synthesized sample showed an emission peak, which is closely related
to the small size of the microtubes.

Based on the aircraft observations in the summer of 2003, we have studied
the aerodynamic size distributions of airborne particles at altitudes
ranging from 400~m to 2800~m over the central and southern areas of Jiangsu
province located in Yangtse River Delta of China. The sizes of airborne particles are
measured to be in a range of 0.47--30~$\mu $m with 57 channels, and
their number concentrations, surface area concentrations
and mass concentrations are also measured.
The results show that the concentrations of airborne particles are very low
above an altitude of 2000~m and the size distributions present a specific
multi-peak mode by using insufficient samples. Below 1000~m, however, the
concentrations of particles increase obviously, and their size distribution
is similar to that at the ground level. The study also indicates that the
concentrations, size distributions and median diameters of airborne
particles above and below the boundary layer are very different, displaying
different pollution features. Meanwhile, the results also show that the
pollution level of airborne particles has a descending tendency with
altitude increasing.

Lie symmetry algebra of linear nonconservative dynamical systems is
studied in this paper. By using 1--1 mapping, the Lie point and Lie
contact symmetry algebras are obtained from two independent
solutions of the one-dimensional linear equations of motion.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The influence of air pressure on mechanical effect of laser plasma
shock wave in a vacuum chamber produced by a Nd:YAG laser has been
studied. The laser pulses with pulse width of 10ns and pulse energy
of about 320mJ at 1.06$\mu $m wavelength is focused on the aluminium
target mounted on a ballistic pendulum, and the air pressure in the
chamber changes from
$2.8\times 10^{3}$ to 1.01$\times $10$^{5 }$Pa. The experimental results
show that the impulse coupling coefficient changes as the air
pressure and the distance of the target from focus change. The
mechanical effects of the plasma shock wave on the target are
analysed at different distances from focus and the air pressure.

In this article, four kinds of optical emission spectroscopic
methods of determining electron temperature are used to
investigate the relationship between electron temperature and
pressure in the cylindrical plasmas of dc glow discharges at low
pressures in laboratory by measuring the relative intensities of
ArI lines at various pressures. These methods are developed
respectively on the basis of the Fermi--Dirac model, corona
model, and two kinds of electron collision cross section models
according to the kinetic analysis. Their theoretical bases and
the conditions to which they are applicable are reviewed, and
their calculation results and fitting errors are compared with
each other. The investigation has indicated that the electron
temperatures obtained by the four methods become consistent with
each other when the pressure increases in the low pressure argon
plasmas.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

This paper reports that the Ge nanocrystals embedded in SiO$_{2}$
matrix are grown on Si(100) and quartz--glass substrates, and the
formation mechanism is systematically studied by using fluorescence
x-ray absorption fine structure (XAFS). It is found that the
formation of Ge nanocrystals strongly depends on the properties of
substrate materials. In the as-prepared samples with Ge molar content
of 60{\%}, Ge atoms exist in amorphous Ge (about 36{\%}) and GeO$_{2
}$ (about 24{\%}) phases. At the annealing temperature of 1073 K, on
the quartz--glass substrate Ge nanocrystals are generated from
crystallization of amorphous Ge, rather than from the direct
decomposition of GeO$_{2}$ in the as-deposited sample. However, on
the Si(100) substrate, the Ge nanocrystals are generated partly from
crystallization of amorphous Ge, and partly from GeO$_{2}$ phases
through the permutation reaction with Si substrate. Quantitative
analysis reveals that about 10{\%} of GeO$_{2}$ in the as-prepared
sample are permuted with Si wafer to form Ge nanocrystals.

A new technique, namely low pressure sputtering, has been developed
to fabricate Zn nanoparticles, with a subsequent oxidation to
synthesize ZnO nanoparticles in the ambient atmosphere at
500$\,^{\circ}$C. The synthesized ZnO nanoparticle has a size of
6--8~nm with a preferred orientation of $c$-axis. The produced ZnO
nanoparticles have a good UV photoluminescence (PL) emission energy
of 3.349 eV with a significant enhancement of donor--acceptor pair
emission located at 3.305 eV which implies a number of donor and
acceptor bounded excitons existing in the synthesized ZnO nano
particles. The near band edge PL emission of the fabricated ZnO is
dominated by the bounded excitons at 10~K.

Radiation effects of the floating gate read-only-memory (FG ROM) and
the static random access memory (SRAM) have been evaluated using the
14~MeV neutron and 31.9MeV proton beams and Co-60 $\gamma $-rays. The
neutron fluence, when the first error occurs in the FG ROMs, is at
least 5 orders of magnitude higher than that in the SRAMs, and the
proton fluence, 4 orders of magnitude higher. The total dose
threshold for Co-60 $\gamma $-ray irradiation is about 10$^{4}$~rad
(Si) for both memories. The difference and similarity are attributed
to the structure of the memory cells and the mechanism of radiation
effects. It is concluded that the FG ROMs are more reliable as
semiconductor memories for storing data than the SRAMs, when they are
used in the satellites or space crafts exposed to high energy
particle radiation.

In this paper we study the thermodynamic properties of
Y$_{3}$Al$_{5}$O$_{12}$ (YAG) by using molecular dynamic method combined with two-
and three-body potentials. The dependences of melting process, elastic constant and
diffusion coefficient on temperature of crystal YAG are simulated
and compared with the experimental results. Our results show that anion O
has the biggest self-diffusivity and cation Y has the
smallest self-diffusivity in a
crystal YAG. The calculated diffusion activation energies of ions O, Al and Y
are 282.55, 439.46, 469.71kJ/mol, respectively. Comparing with experimental
creep activation energy of YAG confirms that cation Y can restrict the
diffusional creep rate of crystal YAG.

GaN layers with different polarities have been prepared by radio-frequency
molecular beam epitaxy (RF-MBE) and characterized by Raman
scattering. Polarity control are realized by controlling
Al/N flux ratio during high temperature AlN buffer growth. The Raman results
illustrate that the N-polarity GaN films have frequency shifts at $A_{1}$(LO)
mode because of their high carrier density; the forbidden $A_{1}$(TO) mode
occurs for mixed-polarity GaN films due to the destroyed translation
symmetry by inversion domain boundaries (IDBS); Raman spectra for
Ga-polarity GaN films show that they have neither frequency shifts mode nor forbidden
mode. These results indicate that Ga-polarity GaN films have a better
quality, and they are in good agreement with the results obtained from the
room temperature Hall mobility. The
best values of Ga-polarity GaN films are 1042 cm$^{2}$/Vs with a carrier
density of 1.0$\times $10$^{17}$~cm$^{ - 3}$.

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

The effect of In doping on the electronic structure and optical
properties of SrTiO$_{3}$ is investigated by the
first-principles calculation of plane wave ultra-soft
pseudo-potential based on the density function theory (DFT). The
calculated results reveal that due to the hole doping, the Fermi
level shifts into valence bands (VBs) for
SrTi$_{1-x}$In$_{x}$O$_{3 }$ with $x=0.125$ and the system
exhibits p-type degenerate semiconductor features. It is
suggested according to the density of states (DOS) of
SrTi$_{0.875}$In$_{0.125}$O$_{3}$ that the band structure of
p-type SrTiO$_{3}$ can be described by a rigid band model. At
the same time, the DOS shifts towards high energies and the
optical band gap is broadened. The wide band gap, small
transition probability and weak absorption due to the low
partial density of states (PDOS) of impurity in the Fermi level
result in the optical transparency of the film. The optical
transmittance of In doped SrTiO$_{3}$ is higher than 85{\%} in a
visible region, and the transmittance improves greatly. And the
cut-off wavelength shifts into a blue-light region with the
increase of In doping concentration.

The growth of diamond-like carbon (DLC) films is studied using molecular
dynamics simulations. The effect of impact angle on film structure is
carefully studied, which shows that the transverse migration of the
incident atoms is the main channel of film relaxation. A
transverse-migration-induced film relaxation model is presented to
elucidate the process of film relaxation which advances the original
model of subplantation. The process of DLC film growth on a rough
surface is also investigated, as well as the evolution of
microstructure and surface morphology of the film. A
preferential-to-homogeneous growth mode and a smoothing of the film
are observed, which are due to the transverse migration of the
incident atoms.

Metal--insulator--metal (MIM) capacitors with atomic-layer-deposited
Al$_{2}$O$_{3}$ dielectric and reactively sputtered TaN electrodes in
application to radio frequency integrated circuits have been
characterized electrically. The capacitors exhibit a high density of
about 6.05\,fF/$\mu $m$^{2}$, a small leakage current of $4.8\times
10^{-8}$\,A/cm$^{2}$ at 3\,V, a high breakdown electric field of
8.61\,MV/cm as well as acceptable voltage coefficients of capacitance
(VCCs) of 795\,ppm/V$^{2}$ and 268\,ppm/V at 1\,MHz. The observed
properties should be attributed to high-quality Al$_{2}$O$_{3}$ film
and chemically stable TaN electrodes. Further, a logarithmically
linear relationship between quadratic VCC and frequency is observed
due to the change of relaxation time with carrier mobility in the
dielectric. The conduction mechanism in the high field ranges is
dominated by the Poole--Frenkel emission, and the leakage current in
the low field ranges is likely to be associated with trap-assisted
tunnelling. Meanwhile, the Al$_{2}$O$_{3}$ dielectric presents charge
trapping under low voltage stresses, and defect generation under high
voltage stresses, and it has a hard-breakdown performance.

The kinetic energy of ions in dielectric barrier discharge plasmas
are analysed theoretically using the model of binary collisions
between ions and gas molecules. Langevin equation for ions in other
gases, Blanc law for ions in mixed gases, and the two-temperature
model for ions at higher reduced field are used to determine the ion
mobility. The kinetic energies of ions in CH$_{4}$\,+\,Ar(He)
dielectric barrier discharge plasma at a fixed total gas pressure and
various Ar (He) concentrations are calculated. It is found that with
increasing Ar (He) concentration in CH$_{4}$\,+\,Ar (He) from 20{\%}
to 83{\%}, the CH$_{4}^{ + }$ kinetic energy increases from 69.6
(43.9) to 92.1 (128.5)\,eV, while the Ar$^{ + }$ (He$^{ + })$ kinetic
energy decreases from 97 (145.2) to 78.8 (75.5)\,eV. The increase of
CH$_{4}^{ + }$ kinetic energy is responsible for the increase of
hardness of diamond-like carbon films deposited by CH$_{4}$\,+\,Ar
(He) dielectric barrier discharge without bias voltage over
substrates.

Steady forcing can induce the amplitude death in chaotic systems, which
generally exists in coupled dynamic systems. Using the Lorenz system as a
typical example, this paper investigates the dynamic behaviours of the
chaotic system with steady forcing numerically, and finds that amplitude
death can occur as the strength of the steady forcing goes beyond a critical
constant.

In this paper, we investigate the quintessence models with an
oscillating equation of state (EOS) and its potentials. From the
constructed potentials, which have an EOS of
$\omega_{\phi}=\omega_0+\omega_1\sin z$, we find that they are all
the oscillating functions of the field $\phi$, and the oscillating
amplitudes decrease (or increase) with $\phi$. From the evolutive
equation of the field $\phi$, we find that this is caused by the
expansion of the universe. This also makes it very difficult to
build a model whose EOS oscillates forever. However one can build a
model with EOS oscillating for a certain period of time. Then we
discuss three quintessence models, which are the combinations of the
invert power law functions and the oscillating functions of the
field $\phi$. We find that they all follow the oscillating EOS.