The eigenvalue problem of an infinite-dimensional Hamiltonian
operator appearing in the isotropic plane magnetoelectroelastic
solids is studied. First, all the eigenvalues and their
eigenfunctions in a rectangular domain are solved directly. Then the
completeness of the eigenfunction system is proved, which offers a
theoretic guarantee of the feasibility of variable separation method
based on a Hamiltonian system for isotropic plane
magnetoelectroelastic solids. Finally, the general solution for the
equation in the rectangular domain is obtained by using the
symplectic Fourier expansion method.

We study the evolutionary snowdrift game in a heterogeneous
Newman--Watts small-world network. The heterogeneity of the network
is controlled by the number of hubs. It is found that the moderate
heterogeneity of the network can promote the cooperation best.
Besides, we study how the hubs affect the evolution of cooperative
behaviours of the heterogeneous Newman--Watts small-world network.
Simulation results show that both the initial states of hubs and the
connections between hubs can play an important role. Our work gives
a further insight into the effect of hubs on the heterogeneous
networks.

This paper studies a conformal invariance and an integration of
first-order differential equations. It obtains the corresponding
infinitesimal generators of conformal invariance by using the
symmetry of the differential equations, and expresses the
differential equations by the equations of a Birkhoff system or a
generalized Birkhoff system. If the infinitesimal generators are
those of a Noether symmetry, the conserved quantity can be obtained
by using the Noether theory of the Birkhoff system or the
generalized Birkhoff system.

Starting from an improved mapping approach and a linear variable
separation approach, a new family of exact solutions (including
solitary wave solutions, periodic wave solutions and rational
function solutions) with arbitrary functions for a general
(2+1)-dimensional
Korteweg de Vries system (GKdV) is derived. According to the derived
solutions, we obtain some novel dromion-lattice solitons, complex wave excitations and
chaotic patterns for the GKdV system.

The performance of the so-called superconvergent quantum
perturbation theory (Wenhua Hai {\em et al} 2000 \emph{Phys. Rev.} A
{\bf 61} 052105) is investigated for the case of the ground-state
energy of the helium-like ions. The scaling transformation
$r\rightarrow r/Z$ applied to the Hamiltonian of a two-electron
atomic ion with a nuclear charge $Z$ (in atomic units). Using the
improved Rayleigh--Schr\"{o}dinger perturbation theory based on
the integral equation to helium-like ions in the ground states and
treating the electron correlations as perturbations, we have
performed a third-order perturbation calculation and obtained the
second-order corrected wavefunctions consisting of a few terms and
third-order energy corrections. We find that third-order and
higher-order energy corrections are improved with decreasing nuclear
charge. This result means that the former is quadratically
integrable and the latter is physically meaningful. The improved
quantum perturbation theory fits the higher-order perturbation case.
This work shows that it is a development on the quantum perturbation
problem of helium-like systems.

This paper obtains an entangled condition for isotropic-like states
by using an atomic map. It constructs a class of bound entangled
states from the entangled condition and shows that the partial
transposition of the state from the constructed bound entangled
class is an edge bound entangled state by using range criterion.

A new simplified formula is presented to characterize genuine
tripartite entanglement of $(2\otimes 2\otimes n)$-dimensional
quantum pure states. The formula turns out equivalent to that given
in (\wx{Quant. Inf. Comp.}{7}(7) 584 (2007)), hence it also shows
that the genuine tripartite entanglement can be described only on
the basis of the local $(2\otimes 2)$-dimensional reduced density
matrix. In particular, the two exactly solvable models of spin
system studied by Yang (\wx{Phys. Rev. {\rm A}}{71} 030302(R)
(2005)) are reconsidered by employing the formula. The results show
that a discontinuity in the first derivative of the formula or in
the formula itself of the ground state just corresponds to the
existence of quantum phase transition, which is obviously different
from the concurrence.

This paper investigates thermal entanglements of a two-qubit
Heisenberg $XY$ chain in the presence of the Dzyaloshinskii--Moriya
anisotropic antisymmetric interaction. By the concept of
concurrence, it is found that the effects of spin--orbit coupling on
the entanglement are different from those of spin--spin model. The
analytical expressions of concurrence are obtained for this model.

In this paper, Hawking radiation from the Kerr--Newman de Sitter black
hole is studied via gauge anomaly and gravitational anomaly. The
obtained results of Hawking radiation from the event horizon and the
cosmological horizon accord with those by other methods.

Using the related formula of dynamic black hole, we have calculated
the instantaneous radiation energy density of the slowly changing
dynamic Kerr--Newman black hole. It is found that the instantaneous
radiation energy density of a black hole is always proportional to
the quartic of the temperature of the event horizon in the same
direction. By using the Hamilton--Jacobin equation of scalar particles in
the curved spacetime, the spontaneous radiation of the slowly
changing dynamic Kerr--Newman black hole is studied. The energy
condition for the occurrence of the spontaneous radiation is
obtained.

A modified de Broglie--Bohm approach is generalized to the
Schwarzschild black hole. By using this method, the quantum
potential and the quantum trajectories of the black hole are
investigated. And we find that the linear combination of two
particular solutions of the black hole wavefunction is not physical
although each of them is physical, if we think that the quantum
gravity should reduce into its corresponding classical counterpart
in which the gravity vanishes. It seems to confirm the argument,
given by Alwis and MacIntire, that a possible resolution on the
quantum gravity is to give up the superposition principle.

This paper studies the mean first passage time (or exit time, or
escape time) over the non-fluctuating potential barrier for a system
driven only by a dichotomous noise. It finds that the dichotomous
noise can make the particles escape over the potential barrier, in
some circumstances; but in other circumstances, it can not. In the
case that the particles escape over the potential barrier, a
resonant activation phenomenon for the mean first passage time over
the potential barrier is obtained.

This paper introduces a new four-dimensional (4D) hyperchaotic
system, which has only two quadratic nonlinearity parameters but
with a complex topological structure. Some complicated dynamical
properties are then investigated in detail by using bifurcations,
Poincar\'{e} mapping, LE spectra. Furthermore, a simple fourth-order
electronic circuit is designed for hardware implementation of the 4D
hyperchaotic attractors. In particular, a remarkable
fractional-order circuit diagram is designed for physically
verifying the hyperchaotic attractors existing not only in the
integer-order system but also in the fractional-order system with an
order as low as 3.6.

With the polarization of quantum-dot cell and quantum phase serving
as state variables, this paper does both theoretical analysis and
simulation for the complex nonlinear dynamical behaviour of a
three-cell-coupled Quantum Cellular Neural Network (QCNN), including
equilibrium points, bifurcation and chaotic behaviour. Different
phenomena, such as quasi-periodic, chaotic and hyper-chaotic states
as well as bifurcations are revealed. The system's bifurcation and
chaotic behaviour under the influence of the different coupling
parameters are analysed. And it finds that the unbalanced cells
coupled QCNN is easy to cause chaotic oscillation and the system
response enters into chaotic state from quasi-periodic state by
quasi-period bifurcation; however, the balanced cells coupled QCNN
also can be chaotic when coupling parameters is in some region.
Additionally, both the unbalanced and balanced cells coupled QCNNs
can possess hyper-chaotic behaviour. It provides valuable
information about QCNNs for future application in high-parallel
signal processing and novel ultra-small chaotic generators.

This paper proposes a scheme of parameter perturbation to suppress
the stable rotating spiral wave, meandering spiral wave and
turbulence in the excitable media, which is described by the
modified Fitzhugh--Nagumo (MFHN) model. The controllable parameter in
the MFHN model is perturbed with a weak pulse and the pulse period
is decided by the rotating period of the spiral wave
approximatively. It is confirmed that the spiral wave and spiral
turbulence can be suppressed greatly. Drift and instability of
spiral wave can be observed in the numerical simulation tests before
the whole media become homogeneous finally.

Cellular Automaton (CA) based traffic flow models have been
extensively studied due to their effectiveness and simplicity in
recent years. This paper develops a discrete time Markov chain
(DTMC) analytical framework for a Nagel--Schreckenberg and
Fukui--Ishibashi combined CA model (W$^2$H traffic flow model) from
microscopic point of view to capture the macroscopic steady state
speed distributions. The inter-vehicle spacing Markov chain and the
steady state speed Markov chain are proved to be irreducible and
ergodic. The theoretical speed probability distributions depending
on the traffic density and stochastic delay probability are in good
accordance with numerical simulations. The derived fundamental
diagram of the average speed from theoretical speed distributions is
equivalent to the results in the previous work.

This paper reports that low-temperature heat capacities of
N-methylnorephedrine C$_{11}$H$_{17}$NO(s) have been measured by a
precision automated adiabatic calorimeter over the temperature range
from $T$=78\,K to $T$=400\,K. A solid to liquid phase transition of
the compound was found in the heat capacity curve in the temperature
range of $T$=342--364\,K. The peak temperature, molar enthalpy and
entropy of fusion of the substance were determined. The experimental
values of the molar heat capacities in the temperature regions of
$T$=78--342\,K and $T$=364--400\,K were fitted to two polynomial
equations of heat capacities with the reduced temperatures by least
squares method. The smoothed molar heat capacities and thermodynamic
functions of $N$-methylnorephedrine C$_{11}$H$_{17}$NO(s) relative
to the standard reference temperature 298.15\,K were calculated
based on the fitted polynomials and tabulated with an interval of
5\,K. The constant-volume energy of combustion of the compound at
$T$=298.15\,K was measured by means of an isoperibol precision
oxygen-bomb combustion calorimeter. The standard molar enthalpy of
combustion of the sample was calculated. The standard molar enthalpy
of formation of the compound was determined from the combustion
enthalpy and other auxiliary thermodynamic data through a Hess
thermochemical cycle.

The thermodynamic properties of the $\varepsilon $ phase of solid
oxygen are studied by using the analytic mean field approach (AMFP).
Analytic expressions for the Helmholtz free energy, internal energy
and equation of state of solid oxygen have been derived based on the
multi-exponential potential. The formulism for the case of
double-exponential (DE) model is applied to the $\varepsilon $ phase
of solid oxygen. Its four potential parameters are determined
through fitting the experimental compression data of the
$\varepsilon $ phase of solid oxygen. Numerical results of the
pressure dependence of the volume calculated by using the AMFP are
in good agreement with the original experimental data. This suggests
that the AMFP is a useful approach to study the thermodynamic
properties of the $\varepsilon $ phase of solid oxygen. Furthermore,
we predict the variation of the volume, lattice parameters and
intermolecular distances with pressure, and some thermodynamic
quantities versus volume, at several higher temperatures.

In this paper, an evolutionary model of bus transport network in
B-space is developed. It includes the effect of the overlapping
ratio of new route on network performance and overcomes the
disadvantage, i.e. lack of economic consideration, in the
evolutionary bus transport network model in P-space proposed by Chen
{\it et al} (2007). The degree distribution functions are derived by
using the mean-field method and the master equation method,
separately. The relationship between the new stop ratio of a route,
$\lambda $, and the error in exponential of degree distribution
function from the mean-field method is developed as
${\Delta}$Slope$=\lambda/(1 - \lambda ) + \ln (1 - \lambda)$.
Finally, the bus transport networks of Hangzhou and Nanjing are
simulated by using this model, and the results show that some
characteristic index values of the simulated networks are closer to
the empirical data than those from Chen's model.

It is a very complex and time-consuming process to simulate the
nuclear reactor neutron spectrum from the reactor core to the export
channel by applying a Monte Carlo program. This paper presents a new
method to calculate the neutron spectrum by using the convolution
technique which considers the channel transportation as a linear
system and the transportation scattering as the response function.
It also applies Monte Carlo Neutron and Photon Transport Code (MCNP)
to simulate the response function numerically. With the application
of convolution technique to calculate the spectrum distribution from
the core to the channel, the process is then much more convenient only with
the simple numerical integral numeration. This saves computer time
and reduces some trouble in re-writing of the MCNP program.

This paper investigates the absorptive reduction and the width
narrowing of electromagnetically induced transparency (EIT) in a
thin vapour film of $\Lambda $-type atoms confined between two
dielectric walls whose thickness is comparable with the wavelength
of the probe field. The absorptive lines of the weak probe field
exhibit strong reductions and very narrow EIT dips, which mainly
results from the velocity slow-down effects and transient behaviour
of atoms in a confined system. It is also shown that the lines are
modified by the strength of the coupling field and the ratio of $L /
\lambda$, with $L$ the film thickness and $\lambda $ the wavelength
of the probe field. A simple robust recipe for EIT in a thin medium
is achievable in experiment.

The non-dissociative charge-transfer processes in collisions between
O$^{3 + }$ and H$_{2}$ are investigated by using the
quantum-mechanical molecular-orbital coupled-channel (QMOCC) method.
The adiabatic potentials and radial coupling matrix elements
utilized in the QMOCC calculations are obtained with the
spin-coupled valence-bond approach. Electronic and vibrational
state-selective differential cross sections are presented for
projectile energies of 0.1, 1.0 and 10.0\,eV/u in the H$_{2}$
orientation angles of 45$^\circ$ and 89$^{\circ}$. The electronic
and the vibrational state-selective differential cross sections show
similar behaviours: they decrease as the scattering angle increases,
and beyond a specific angle the oscillating structures appear.
Moreover, it is also found that the vibrational state-selective
differential cross sections are strongly orientation-dependent,
which provides a possibility to determine the orientations of
molecule H$_{2}$ by identifying the vibrational state-selective
differential scattering processes.

A normalized two-dimensional band-limited Weierstrass fractal
function is used for modelling the dielectric rough surface. An
analytic solution of the scattered field is derived based on the
Kirchhoff approximation. The variance of scattering intensity is
presented to study the fractal characteristics through theoretical
analysis and numerical calculations. The important conclusion is
obtained that the diffracted envelope slopes of scattering pattern
can be approximated as a slope of linear equation. This conclusion
will be applicable for solving the inverse problem of reconstructing
rough surface and remote sensing.

Considering a two-level atom interacting with the competing two-mode
field, this paper investigates the entanglement between the
two-level atom and the two-mode field by using the quantum reduced
entropy, and that between the two-mode field by using the quantum
relative entropy of entanglement. It shows that the two kinds of
entanglement are dependent on the relative coupling strength of
atom-field and the atomic distribution, and exhibit the periodical
evolution. The maximal atom--field entanglement state can be prepared
via the appropriate selection of system parameters and interaction
time.

In this paper a scheme is proposed for the purification of entangled
states for two atoms trapped in two distant cavities via cavity
decay. In the scheme, the atoms have no probability of being
populated in the excited state and thus the atomic spontaneous
emission is suppressed. This scheme is valid no matter when the
cavity decay rate is larger or smaller than the effective
atom-cavity coupling strength. The fidelity of the final state is
not affected by the imperfection of the photodetectors.

The $q$-analogues of two-mode squeezed states are introduced by
virtue of deformation quantization methods and the technique of
integration within an ordered product (IWOP) of operators. Some new
completeness relations about these squeezed states composed of the
bra and ket which are not mutually Hermitian conjugates are
obtained. Furthermore, the antibunching effects of the two-mode
squeezed vacuum state $S_2' (r)\left| {00} \right\rangle $ are
investigated. It is found that, in different ranges of the squeezed
parameter $r$, both modes of the state exhibit the antibunching
effects and the two modes of the state are always nonclassical
correlation.

Fibre sensors exhibit a number of advantages over other sensors such
as high sensitivity, electric insulation, corrosion resistance,
interference rejection and so on. And laser self-mixing interference
can accurately detect the phase difference of feedback light. In
this paper, a novel laser self-mixing interference fibre sensor that
combines the advantages of fibre sensors with those of laser
self-mixing interference is presented. Experimental configurations
are set up to study the relationship between laser power output and
phase of laser feedback light when the fibre trembles or when the
fibre is stretched or pressed. The theoretical analysis of pressure
sensors based on laser self-mixing interference is indicated to
accord with the experimental results.

Using the equations of fluid mechanics with proper boundary
conditions and taking account of the gas properties, we can
numerically simulate the process of single bubble sonoluminescence,
in which electron--neutral atom bremsstrahlung, electron--ion
bremsstrahlung and recombination radiation, and the radiative
attachment of electrons to atoms and molecules contribute to the
light emission. The calculation can quantitatively or qualitatively
interpret the experimental results. We find that the accumulated
heat energy inside the compressed gas bubble is mostly consumed by
the chemical reaction, therefore, the maximum degree of ionization
inside Xe bubble in water is much lower than that in sulfuric acid,
of which the vapour pressure is very low. In addition, in sulfuric
acid much larger $p_{\rm a}$ and $R_{0}$ are allowed which makes the
bubbles in it much brighter than that in water.

This paper investigates the collision between two nonlinear waves
with arbitrary angle in two-dimensional nonlinear lattice. By using
the extended Poincar\'{e}--Lighthill--Kuo perturbation method, it
obtains two Korteweg--de Vries equations for nonlinear waves in both
the $\xi$ and $\eta$ directions, respectively, and derives the
analytical phase shifts after the collision of two nonlinear waves.
Finally, the solution of $u(v)$ up to $O(\epsilon^{3})$ order is
given.

This paper evaluates the interaction potential between a hydrogen
and an antihydrogen using the second-order perturbation theory
within the framework of the four-body system in a separable two-body
basis. It finds that the H--$\bar{\rm H}$ interaction potential
possesses the peculiar features of a shallow local minimum located
around interatomic separations of $r\sim 6$\,a.u. and a barrier
rising at $r\lesssim5 $\,a.u.

The transition energies, wavelengths and dipole oscillator strengths
of 1s$^{2}$2p-1s$^{2}n$d ($3 \le n \le 9$) for Cr$^{21 +}$ ion are
calculated. The fine structure splittings of 1s$^{2}n$d ($n \le 9$)
states for this ion are also calculated. In calculating energy, we
have estimated the higher-order relativistic contribution under a
hydrogenic approximation. The quantum defect of Rydberg series
1s$^{2}n$d is determined according to the quantum defect theory. The
results obtained in this paper excellently agree with the
experimental data available in the literature. Combining the quantum
defect theory with the discrete oscillator strengths, the discrete
oscillator strengths for the transitions from initial state
1s$^{2}$2p to highly excited 1s$^{2}n$d states ($n \ge 10$) and the
oscillator strength density corresponding to the bound--free
transitions are obtained.

A femtosecond laser pulse can be tailored to control the two-photon
transitions using the ultra-fast pulse-shaping technique. This paper
theoretically and experimentally demonstrates that two-photon
transitions in molecular system with broad absorption line can be
effectively controlled by square phase-modulation in frequency
domain, and the influence of all parameters characterizing the
square phase-modulation on two-photon transitions is systemically
investigated and discussed. The obtained results have potential
application in nonlinear spectroscopy and molecular physics.

This paper calculates the equilibrium structure and the potential
energy functions of the ground state ($X^2\Si ^{ + })$ and the low
lying excited electronic state ($A^2{\it \Pi}$) of CN radical are
calculated by using CASSCF method. The potential energy curves are
obtained by a least square fitting to the modified Murrell--Sorbie
function. On the basis of physical theory of potential energy
function, harmonic frequency ($\omega _{\rm e}$) and other
spectroscopic constants ($\omega _{\rm e}\chi _{\rm e}$, $\beta
_{\rm e}$ and $\alpha _{\rm e})$ are calculated by employing the
Rydberg--Klein--Rees method. The theoretical calculation results are
in excellent agreement with the experimental and other complicated
theoretical calculation data. In addition, the eigenvalues of
vibrational levels have been calculated by solving the radial
one-dimensional Schr\"{o}dinger equation of nuclear motion using the
algebraic method based on the analytical potential energy function.

Density functional theory (DFT) (B3P86) of Gaussian 03 has been used
to optimize the structure of the Cr$_{2}$ molecule, a transition
metal element molecule. The result shows that the ground state for
the Cr$_{2}$ molecule is a 13-multiple state, indicating that there
exists a spin polarization effect in the Cr$_{2}$ molecule.
Meanwhile, we have not found any spin pollution because the wave
function of the ground state does not mingle with wave functions of
higher-energy states. So the ground state for Cr$_{2}$ molecule
being a 13-multiple state is indicative of spin polarization effect
of the Cr$_{2}$ molecule among transition metal elements, that is,
there are 12 parallel spin electrons in the Cr$_{2}$ molecule. The
number of non-conjugated electrons is greatest. These electrons
occupy different spatial orbitals so that the energy of the Cr$_{2}$
molecule is minimized. It can be concluded that the effect of
parallel spin in the Cr$_{2}$ molecule is larger than the effect of
the conjugated molecule, which is obviously related to the effect of
electron d delocalization. In addition, the Murrell--Sorbie potential
functions with the parameters for the ground state and other states
of the Cr$_{2}$ molecule are derived. The dissociation energy {\it
D}e for the ground state of the Cr$_{2}$ molecule is 0.1034\,eV,
equilibrium bond length {\it R}e is 0.3396\,nm, and vibration
frequency $\omega_{\rm e}$ is 73.81\,cm$^{-1}$. Its force constants
$f_2$, $f_3$ and $f_4$ are 0.0835, $-$0.2831 and
0.3535\,aJ\,$\cdot$\,nm$^{- 4}$ respectively. The other
spectroscopic data for the ground state of the Cr$_{2}$ molecule
$\omega_{\rm e}\chi _{\rm e}$, $B_{\rm e}$ and $\alpha_{\rm e}$ are
1.2105, 0.0562 and 7.2938\,$\times10^{-4}$cm$^{-1}$ respectively.

The chaotic behaviours of the Rydberg hydrogen atom near a metal
surface are presented. A numerical comparison of Poincar\'{e}
surfaces of section with recurrence spectra for a few selected
scaled energies indicates the correspondence between classical
motion and quantum properties of an excited electron. Both results
demonstrate that the scaled energy dominates sensitively the
dynamical properties of system. There exists a critical scaled
energy $\varepsilon _{\rm c} $, for $\varepsilon < \varepsilon _{\rm
c} $, the system is near-integrable, and as the decrease of
$\varepsilon $ the spectrum is gradually rendered regular and finally
turns into a pure Coulomb field situation. On the contrary, if
$\varepsilon>\varepsilon_{\rm c}$, with the increase of
$\varepsilon$, the system tends to be non-integrable, the ergodic
motion in phase space presages that chaotic motion appears, and more
and more electrons are adsorbed on the metal surface, thus the
spectrum becomes gradually simple.

First-principle calculations are performed to study geometric and
electronic properties of both neutral and anionic In$_{4}M$ and
In$_{12}M$ ($M$ = C, Si, In) clusters. In$_{4}$C and In$_{4}$Si are
found to be tetrahedral molecules. The icosahedral structure is
found to be unfavourable for In$_{12}M$. The most stable structure
for In$_{12}$C is a distorted buckled biplanar structure while for
In$_{12}$Si it is of an In-cage with the Si located in the centre.
Charge effect on the structure of In$_{12}M$ is discussed. In$_{4}$C
has a significantly large binding energy and an energy gap between
the highest-occupied molecular-orbital level and the lowest
unoccupied molecular-orbital level, a low electron affinity, and a
high ionization potential, which are the characters of a magic
cluster, enriching the family of doped-group-IIIA metal clusters for
cluster-assembled materials.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Within the magnetohydrodynamics (MHD) frame, we analyse the effect
of viscosity on magneto-Rayleigh--Taylor (MRT) instability in a
Z-pinch configuration by using an exact method and an approximate
method separately. It is demonstrated that the plasma viscosity
indeed has a stabilization effect on the MRT mode in the whole
wavenumber region, and its influence increases with the perturbation
wavenumber increasing. After the characteristics and feasibility of
the approximate method have been investigated, we apply it to the
stability analysis of viscous plasma where a sheared axial flow
(SAF) is involved, and we attain an analytical dispersion relation.
It is suggested that the viscosity and the SAF are complemental with
each other, and a wide wavenumber range of perturbation is possible
to be restrained if the SAF and the viscosity are large enough.
Finally, we calculate the possible value of viscosity parameter
according to the current experimental conditions, and the results
show that since the value of viscosity is much less than the
threshold value, its mitigation effect is small enough to be
neglected. The role of the viscosity in the stabilization becomes
considerable only if special techniques are so developed that the
Z-pinch plasma viscosity can be increased greatly.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Titanium oxide films were prepared by annealing DC magnetron
sputtered titanium films in an oxygen ambient. X-ray diffraction
(XRD), Auger electron spectroscopy (AES) sputter profiling, MCs$^{ +
}$-mode secondary ion mass spectrometry (MCs$^{ + }$-SIMS) and
atomic force microscopy (AFM) were employed, respectively, for the
structural, compositional and morphological characterization of the
obtained films. For temperatures below 875\,K, titanium films could
not be fully oxidized within one hour. Above that temperature, the
completely oxidized films were found to be rutile in structure.
Detailed studies on the oxidation process at 925\,K were carried out
for the understanding of the underlying mechanism of titanium
dioxide (TiO$_{2})$ formation by thermal oxidation. It was
demonstrated that the formation of crystalline TiO$_{2}$ could be
divided into a short oxidation stage, followed by crystal forming
stage. Relevance of this recognition was further discussed.

Under certain growth conditions for systems with a film/substrate
lattice misfit, the deposited material is known to aggregate into
island-like shapes. We have obtained an analytical expression of the
total free energy, which consists of strain energy, surface energy
and interfacial energy of a coherent island/substrate system, and
the change of equilibrium aspect ratio versus the volume of the
island and the misfit of lattices in the system, which provides a
broad perspective on island behaviour. These then were used to study
the equilibrium shapes of the system. The results show that in order
to minimize the total free energy, a coherent island will have a
particular height-to-width aspect ratio, called equilibrium aspect
ratio, that is a function of the island volume and misfit. The
aspect ratio is increased with increasing island volume at a fixed
misfit, and with increasing misfit strain between the island and
substrate at a fixed island volume. Moreover, the effect of misfit
dislocation on the equilibrium shape of the island is also examined.
The results obtained are in good agreement with experiment of
observations and thus can serve as a basis for interpreting the
experiments.

Through introducing a generalized optimal speed function to consider
spatial position, slope grade and variable safe headway, the effect
of slope in a single-lane highway on the traffic flow is
investigated with the extended optimal speed model. The theoretical
analysis and simulation results show that the flux of the whole road
with the upgrade (or downgrade) increases linearly with density,
saturates at a critical density, then maintains this saturated value
in a certain density range and finally decreases with density. The
value of saturated flux is equal to the maximum flux of the upgrade
(or downgrade) without considering the slight influence of the
driver's sensitivity. And the fundamental diagrams also depend on
sensitivity, slope grade and slope length. The spatiotemporal
pattern gives the segregation of different traffic phases caused by
the rarefaction wave and the shock wave under a certain initial
vehicle number. A comparison between the upgrade and the downgrade
indicates that the value of saturated flux of the downgrade is
larger than that of the upgrade under the same condition. This
result is in accordance with the real traffic.

This paper reports that by using the hydrofluoric acid (HF) as the
acid catalyst, F doped nanoporous low-k SiO$_{2}$ thin films have
been prepared by means of sol-gel method. The characterization of
atomic force microscopy and Fourier transform infrared spectroscopy
demonstrates that the HF catalyzed films are more hydrophobic. The
N$_{2}$ adsorption/desorption experiments show that the suited
introduction of HF increases the porosity and decreases the pore
size distribution (about 10\,nm) in the films. The above results
indicate that the hydrofluoric acid is the more suitable acid
catalyst than the hydrochloric one for preparing nanoporous ultra
low-k SiO$_{2}$ thin films.

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

This paper studies the effect of a~charged~impurity together with or
without an external homogeneous~electric field~on a~quantum~ring
threaded by a magnetic field $B$ and containing two electrons.
The potential caused by the impurity has been plotted which is
helpful to the understanding of the electronic structures inside the
ring. The deep valley appearing in the potential curve is the source
of localization, which affects seriously the Aharonov--Bohm
oscillation (ABO) of the energy and persistent current. It also
causes the fluctuation of the total orbital angular momentum $L$ of
the pair of electrons. It is found that the appearance of the impurity
reduces the domain of the fractional ABO. During the increase
of $B$, the domain of the integral ABO may appear earlier when $B$
is even quite small. The transition from the localized states to
extended states has also been studied. Furthermore, it has deduced a
set of related formulae for a transformation, by which an impurity
with a charge $e_p$ placed at an arbitrary point ${\bm R}_p$ is
equivalent to an impurity with a revised charge $\tilde {e}_p$
placed at the $X$-axis with a revised radial distance $\tilde
{R}_p$. This transformation facilitates the calculation and
make the analysis of the physical result clearer.

Lubricant spreading on solid substrates has drawn considerable
attention not only for the microscopic wetting theory but also for
the dramatic application in head-disk interface of magnetic storage
drive systems. Molecular dynamic simulation based on a
coarse-grained bead-spring model has been used to study such a
spreading process. The spreading profiles indicate that the hydrogen
bonds among lubricant molecules and the hydrogen bonds between
lubricant molecules and polar atoms of solid substrates will
complicate the spreading process in a tremendous degree. The
hydrogen bonds among lubricant molecules will strengthen the
lubricant combination intensity, which may hinder most molecules
from flowing down to the substrates and diffusing along the
substrates. And the hydrogen bonds between lubricant molecules and
polar atoms of solid substrates will confine the lubricant molecules
around polar atoms, which may hinder the molecules from diffusing
along the substrates and cause precursor film to vanish.

Local density functional is investigated by using the full-potential
linearized augmented plane wave (FP-LAPW) method for ScN in the
hexagonal structure and the rocksalt structure and for hexagonal
structures linking a layered hexagonal phase with wurtzite structure
along a homogeneous strain transition path. It is found that the
wurtzite ScN is unstable and the layered hexagonal phase, labelled as
$h_{\rm o}$, in which atoms are approximately fivefold coordinated,
is metastable, and the rocksalt ScN is stable. The electronic
structure, the physical properties of the intermediate structures
and the energy band structure along the transition are presented. It
is found that the band gaps change from 4.0 to 1.0\,eV continuously
when $c/a$ value varies from 1.68 to 1.26. It is noticeable that the
study of ScN provides an opportunity to apply this kind of material
(in wurtzite[$h$]-derived phase).

In the framework of the effective mass theory, this paper calculates
the electron energy levels of an InAs/GaAs tyre-shape quantum ring
(TSQR) by using the plane wave basis. The results show that the electron
energy levels are sensitively dependent on the TSQR's section
thickness $d$, and insensitively dependent on TSQR's section inner
radius $R_1$ and TSQR's inner radius $R_2$. The model and results
provide useful information for the design and fabrication of
InAs/GaAs TSQRs.

Using the tight-binding model approximation, this paper investigates
theoretically spin-dependent quantum transport through an
Aharonov--Bohm (AB) interferometer. An external magnetic field is
applied to produce the spin-polarization and spin current. The AB
interferometer, acting as a spin splitter, separates the opposite
spin polarization current. By adjusting the energy and the direction
of the magnetic field, large spin-polarized current can be obtained.

Using first-principles calculations in the generalized gradient
approximation, the electronic properties of BAs and B$_{x}$Ga$_{1 -
x}$As alloys are studied. At the Brillouin-zone centre, the lowest
conduction band is the three-degenerate p-like $\Ga _{\rm 15c}$
state rather than s-like $\Ga_{\rm 1c}$ state, and the conduction
band minimum (CBM) is along the \textit{$\De$} line between the
$\Ga$ and $X$ points-at approximately 11/14(1,0,0)2$\pi /a$. With
boron content at 0{\%}--18.75{\%}, B$_{x}$Ga$_{1 - x}$As alloys have
a small (2.6\,eV) and relatively composition-independent band-gap
bowing parameter, the band-gap increases monotonically by
$\sim$18\,meV/B{\%} with increasing boron content. In addition, the
formation enthalpies of mixing for B$_{x}$Ga$_{1 - x}$As alloys with
boron content at 6.25{\%} and 12.5{\%} are calculated, and the large
formation enthalpies may explain the difficulty in alloying boron to
GaAs.

The dynamical process of charge injection from metal electrode to a
nondegenerate polymer in a metal/polythiophene (PT)/metal structure
has been investigated by using a nonadiabatic dynamic approach. It
is found that the injected charges form wave packets due to the
strong electron-lattice interaction in PT. We demonstrate that the
dynamical formation of the wave packet sensitively depends on the
strength of applied voltage, the electric field, and the contact
between PT and electrode. At a strength of the electric field more
than $3.0\times 10^{4}$\,V/cm, the carriers can be ejected from the
PT into the right electrode. At an electric field more than
$3.0\times 10^{5}$\,V/cm, the wave packet cannot form while it moves
rapidly to the right PT/metal interface. It is shown that the
ejected quantity of charge is noninteger.

Nanoscale Schottky barrier metal oxide semiconductor field-effect
transistors (MOSFETs) are explored by using quantum mechanism
effects for thin-body devices. The results suggest that for small
nonnegative Schottky barrier heights, even for zero barrier height,
the tunnelling current also plays a role in the total on-state
current. Owing to the thin body of device, quantum confinement
raises the electron energy levels in the silicon, and the tradeoff
takes place between the quantum confinement energy and Schottky
barrier lowering (SBL). It is concluded that the inclusion of the
quantum mechanism effect in this model, which considers an infinite
rectangular well with a first-order perturbation in the channel, can
lead to the good agreement with numerical result for thin silicon
film. The error increases with silicon thickness increasing.

Nb/Al--AlO$_x$/Nb tunnel junctions are often used in the studies of
macroscopic quantum phenomena and superconducting qubit applications
of the Josephson devices. In this work, we describe a convenient and
reliable process using electron beam lithography for the fabrication
of high-quality，submicron-sized Nb/Al--AlO$_x$/Nb Josephson
junctions. The technique follows the well-known selective Nb etching
process and produces high-quality junctions with $V_m$=100\,mV at
2.3 K for the typical critical current density of 2.2\,kA/cm$^2$,
which can be adjusted by controlling the oxygen pressure and
oxidation time during the formation of the tunnelling barrier. We
present the results of the temperature dependence of the sub-gap
current and in-plane magnetic-field dependence of the critical
current, and compare them with the theoretical predictions.

Effects of Nd-doping on the magnetic properties and magnetocaloric
effects (MCEs) of Nd$_{x}$La$_{1 - x}$Fe$_{11.5}$Al$_{1.5}$ have
been investigated. Substitution of Nd leads to a weakening of the
antiferromagnetic (AFM) coupling and an enhancement of the
ferromagnetic (FM) coupling. This in turn results in a complex
magnetic behaviour for Nd$_{0.2}$La$_{0.8}$Fe$_{11.5}$Al$_{1.5}$
characterized by the occurrence of two phase transitions at
$\sim$188\,K (PM--AFM) and $\sim $159\,K (AFM--FM). As a result, a
table-like MCE (9\,J/kg$\cdot$K) is found in a wide temperature
range (160--185\,K) for a field change of 0--5\,T around the
transition temperature, as evidenced by both the magnetic and
calorimetric measurements. Based on the analysis of low-temperature
heat capacity, it is found that the AFM--FM phase transition modifies
the electron density significantly, and the major contribution to
the entropy change comes from the electronic entropy change.

The exchange interaction between the electrons in the different
magnetic ions and the spin-fluctuation of the magnetic ions exist in
the paramagnetic media NdF$_{3}$. The exchange interaction between
the electrons in the different magnetic ions may be equivalent to an
effective field $H_{in}$ that is in direct proportion to the
magnetization $\bm M$. The spin-fluctuation of the magnetic ions
leads the coefficient of the effective field to vary with
temperature. The effective field is given as $\bm H_{\rm in} = -
(0.75 + 0.22{\rm T})\times 10^{^{ - 5}}\bm M$ in NdF$_{3}$. When the
secondary crystal field effect is taken into account, the magnetic
susceptibility and Verdet constant are calculated for NdF$_{3}$ by
means of the effective field $\bm H_{\rm in} $ and the applied field
$\bm H_e$. The calculated results are in agreement with the measured
ones.

This paper reports the fabrication of novel white organic
light-emitting device(WOLED) by using a high efficiency blue
fluorescent dye
$N$-(4-((E)-2-(6-((E)-4-(diphenylamino)styryl)naphthalen-2-yl)vinyl)phenyl)-$N$-phenylbenzenamine
($N$-BDAVBi) and a red phosphoresecent dye bis (1-(phenyl)
isoquinoline) iridium (III) acetylanetonate (Ir(piq)$_{2}$(acac)).
The configuration of the device was ITO/PVK:TPD/CBP: $N$-BDAVBi
/CBP/ BALq: Ir(piq)$_{2}$(acac)/BCP/Alq$_{3}$/LiF:AL. By adjusting
the proportion of the dopants ($N$-BDAVBi, Ir(piq)$_{2}$(acac)) in
the light-emitting layer, white light with Commission Internationale
de l'Eclairage (CIE) coordinates of (0.35, 0.35) and a maximum
luminance of 25350cd/m$^{2}$ were obtained at an applied voltage of
22V. The WOLED exhibits maximum external quantum and current
efficiency of 6.78{\%} and 12cd/A respectively. By placing an
undoped spacer CBP layer between the two light-emitting layers and
using BCP as hole blocking layer, the colour stabilization slightly
changed when the driving voltage increased from 6 to 22\,V.

Wurtzite CdS nanoribbons are prepared by using a simple thermal
evaporation method. Electron microscopy shows that the ribbons are
smooth in surface and uniform in size. Besides the intrinsic
emission, the photoluminescence spectrum of a CdS nanoribbon shows a
peak at about 580\,nm, which may arise from the defect- and the
trap- related transitions. The photoresponse of single CdS
nanoribbons is researched. When these nanoribbons are exposed to a
laser with a wavelength of 400\,nm, their conductivity is enhanced
greatly. The conductivity of CdS nanoribbons cannot be restored to a
value without any illumination even at 5 minutes after the
illumination. A model is proposed to explain this phenomenon, which
may be due to a slow photoresponse induced by the trap.