The approximate direct reduction method is applied to the perturbed mKdV
equation with weak fourth order dispersion and weak dissipation. The
similarity reduction solutions of different orders conform to formal
coherence, accounting for infinite series reduction solutions to the
original equation and general formulas of similarity reduction
equations. Painlevé II type equations, hyperbolic secant and
Jacobi elliptic function solutions are obtained for zero-order
similarity reduction equations. Higher order similarity reduction
equations are linear variable coefficient ordinary differential
equations.

This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.

This paper consider a class of perturbed mechanism for the western
boundary undercurrents in the Pacific. The model of generalized
governing equations is studied. Using the perturbation method, it
constructs the asymptotic solution of the model. And the accuracy of
asymptotic solution is proved by the theory of differential
inequalities. Thus the uniformly valid asymptotic expansions of the
solution are obtained.

This paper studies a generalized nonlinear evolution equation. Using
the homotopic mapping method, it constructs a corresponding homotopic
mapping transform. Selecting a suitable initial approximation and
using homotopic mapping, it obtains an approximate solution with an
arbitrary degree of accuracy for the solitary wave. From the
approximate solution obtained by using the homotopic mapping method, it
possesses a good accuracy.

In this paper, we apply a simple walk mechanism to the study of the
traffic of many indistinguishable particles in complex networks. The
network with particles stands for a particle system, and every
vertex in the network stands for a quantum state with the
corresponding energy determined by the vertex degree. Although the
particles are indistinguishable, the quantum states can be
distinguished. When the many indistinguishable particles walk
randomly in the system for a long enough time and the system reaches
dynamic equilibrium, we find that under different restrictive conditions
the particle distributions satisfy different forms, including the
Bose--Einstein distribution, the Fermi--Dirac distribution and the
non-Fermi distribution (as we temporarily call it). As for the
Bose--Einstein distribution, we find that only if the particle density is
larger than zero, with increasing particle density, do more and more
particles condense in the lowest energy level. While the particle
density is very low, the particle distribution transforms from the
quantum statistical form to the classically statistical form, i.e.,
transforms from the Bose distribution or the Fermi distribution to
the Boltzmann distribution. The numerical results fit well with the
analytical predictions.

In this paper, we study the dynamical behaviour of an epidemic on
complex networks with population mobility. In our model, the number
of people on each node is unrestricted as the nodes of the network
are considered as cities, communities, and so on. Because people can
travel between different cities, we study the effect of a population's
mobility on the epidemic spreading. In view of the population's
mobility, we suppose that the susceptible individual can be infected
by an infected individual in the same city or other connected
cities. Simulations are presented to verify our analysis.

The purpose of this paper is to provide a new method called the
Lagrange--Noether method for solving second-order differential
equations. The method is, firstly, to write the second-order
differential equations completely or partially in the form of
Lagrange equations, and secondly, to obtain the integrals of the
equations by using the Noether theory of the Lagrange system. An
example is given to illustrate the application of the result.

It is shown in this paper that the upper triangular strip matrix of
Lie algebra can be used to construct a new integrable coupling
system of soliton equation hierarchy. A direct application to the
Ablowitz--Kaup--Newell-- Segur(AKNS) spectral problem leads to a
novel multi-component soliton equation hierarchy of an integrable
coupling system with sixteen-potential functions. It is indicated
that the study of integrable couplings when using the upper triangular
strip matrix of Lie algebra is an efficient and straightforward
method.

The generalized nonlinear Schr?dinger equation (NLSE), which
governs the dynamics of dispersion-managed (DM) solitons, is
considered. A novel transformation is constructed such that the DM
fibre system equation with optical loss (gain) is transformed to the
standard NLSE under a restricted condition. Abundant new soliton
and periodic wave solutions are obtained by using the transformation
and the solutions of standard NLSE. Further, we discuss
their main properties and the interaction scenario between two
neighbouring solitons by using direct computer simulation.

This paper finds the approximate analytical scattering state
solutions of the arbitrary l-wave Schr?dinger equation for the
generalized Hulthén potential by taking an improved new
approximate scheme for the centrifugal term. The normalized
analytical radial wave functions of the l-wave Schr?dinger
equation for the generalized Hulthén potential are presented and
the corresponding calculation formula of phase shifts is derived.
Some useful figures are plotted to show the improved accuracy of the
obtained results and two special cases for the standard Hulthén
potential and Woods--Saxon potential are also studied briefly.

The Fock--Darwin system is studied in noncommutative quantum mechanics.
We not only obtain its energy eigenvalues and eigenstates in
noncommutative phase space, but also give an electron orbit description
as well as the general expressions of the magnetization and the
susceptibility in a noncommutative situation. Further, we discuss two
particular cases of temperature and present some interesting results
different from those obtained from usual quantum mechanics such as
the susceptibility dependent on a magnetic field at high
temperatures, the occurrence of the magnetization in a zero magnetic
field and zero temperature limit, and so on.

We theoretically explore the possibility of realizing controllable
thermal entanglement of effective spins in a four-qubit anisotropic
Heisenberg XXZ coupling spin-star system constructed by coupled
microcavities. We analyse the dependence of thermal entanglement in
this system on temperature, inhomogeneity of the magnetic field, and
anisotropy, which can be readily tuned via the external laser
fields. The peculiar characteristic and the full controllability of
the thermal entanglement are demonstrated to be useful for quantum
information processing.

Using the method of the Jordan--Wigner transformation for solving
different spin--spin correlation functions, we have investigated the
generation of next-nearest-neighbouring entanglement in a
one-dimensional quantum Ising spin chain with the Gaussian
distribution impurities of exchange couplings and external magnetic
fields taken into account. The maximal value of entanglement
between the next-nearest-neighbouring qubits in the transverse Ising
model was analysed in detail by varying the effectively controlled
parameters such as interchange coupling, magnetic field and the
system impurity. For such systems, where both exchange couplings and
external magnetic field disorder appear, we show that it is possible
to achieve next-nearest-neighbouring entanglement better than the
previously discussed pure Ising spin chain case. We also show that
the Gaussian distribution impurity can induce
next-nearest-neighbouring entanglement, which can be used as a means
to characterize quantum phase transition.

This paper studies initial-boundary value problems for a class
of nonlinear thermoelastic plate equations. Under some certain
initial data and boundary conditions, it obtains an existence and
uniqueness theorem of global weak solutions of the nonlinear
thermoelstic plate equations, by means of the Galerkin method.
Moreover, it also proves the existence of strong and
classical solutions.

This paper presents a very simple method to derive the explicit
transformations of the optimal economical 1 to M phase-covariant
cloning. The fidelity of clones reaches the theoretic bound
[D'Ariano G M and Macchiavello C 2003 Phys. Rev. A 67
042306]. The derived transformations cover the previous
contributions [Delgado Y, Lamata L et al, 2007 Phys. Rev.
Lett.98 150502] in which M must be odd.

This paper proposes a scheme to generate a new χ-type four-atom
entangled state for the first time by using linear optics elements,
four one-sided cavities (one three-level atom) and a conventional
photon detector. The linear optical elements and conventional photon
detector are simple and accessible in experiments, which makes the
scheme more feasible with current technology. In addition, the
state |χ^{00}_{3214} with probability 1 can be generated
as long as there is no photon loss.

This paper presents a scheme for faithfully distributing a pure
entanglement between two parties over an arbitrary collective-noise
channel with linear optics. The transmission is assisted by an
additional qubit against collective noise. The receiver can take
advantage of the time discrimination and the measurement results of
the assistant qubit to reconstruct a pure entanglement with the
sender. Although the scheme succeeds probabilistically, the resource
used to get a pure entanglement state is finite, and so is easier to
establish entanglement in practice than quantum entanglement
purification.

The generalization of tomographic maps to hyperplanes is considered.
We find that the Radon transform of the Wigner operator in
multi-dimensional phase space leads to a normally ordered operator
in binomial distribution---a mixed-state density operator.
Reconstruction of the Wigner operator is also feasible. The normally
ordered form and the Weyl ordered form of the Wigner operator are
used in our derivation. The operator quantum tomography theory is
expressed in terms of some operator identities, with the merit
of revealing the essence of the theory in a simple and concise way.

Based on the analytical expression of relativistic free energy for a
weakly interacting Fermi gas in a weak magnetic field, by using the
method of quantum statistics, the stability conditions of the system
at both high and low temperatures are given, and the effects of
magnetic field and interparticle interactions on the stability of
the system are analysed. It is shown that at high temperatures, the
stability conditions of the system are completely the same, no
matter whether it is the ultrarelativistic case or nonrelativistic
case. At extremely low temperatures, the mechanical stability
conditions of the system show a similar rule through a comparison
between the ultrarelativistic case and nonrelativistic case. At the
same time, thermal stability of a relativistic Bose gas in a weak
magnetic field is discussed, and the influence of the effect of
relativity on the thermal stability of the system is investigated.

In this paper, the viscous continuum traffic flow model for a single
lane is extended to the traffic flow for two-lane freeways. The
proposed model is a higher-order continuum model considering the
coupling and lane changing effects of the vehicles on two adjacent
lanes. It results from integrating the Taylor series expansion of
the viscous continuum traffic flow model proposed by Ge (2006 Physica
A 371 667) into the multi-lane model presented by
Daganzo (1997 Transpn. Res. B 31 83). Our proposed
model may be used to describe non-anisotropic behaviour because of
lane changing in multi-lane traffic. A linear stability analysis
is given and the neutral stability condition is obtained. Also,
issues related to lane changing, shock waves and rarefaction waves,
local clustering and phase transition are investigated through a
simulation experiment. The simulation results show that the proposed
model is capable of explaining some particular traffic phenomena
commonly observable in real world traffic flow.

This paper presents a family of soliton solutions of the
one-dimensional nonlinear Schr?dinger equation which describes
the dynamics of the dark solitons in Bose--Einstein condensates with
an arbitrary x-dependent external potential. The obtained results
show that the external potential has an important effect on the dark
soliton dynamical characteristics of the condensates. The amplitude,
width, and velocity of the output soliton are relative to the source
position of the external potential. The smaller the amplitude of the
soliton is, the narrower its width is, and the slower the soliton
propagates. The collision of two dark solitons is nearly
elastic.

In this paper, the global impulsive exponential synchronization
problem of a class of chaotic delayed neural networks (DNNs) with
stochastic perturbation is studied. Based on the Lyapunov stability
theory, stochastic analysis approach and an efficient impulsive
delay differential inequality, some new exponential synchronization
criteria expressed in the form of the linear matrix inequality (LMI) are
derived. The designed impulsive controller not only can globally
exponentially stabilize the error dynamics in mean square, but also
can control the exponential synchronization rate. Furthermore, to
estimate the stable region of the synchronization error dynamics, a
novel optimization control algorithm is proposed, which can deal
with the minimum problem with two nonlinear terms coexisting in LMIs
effectively. Simulation results finally demonstrate the
effectiveness of the proposed method.

In this paper, an improved impulsive lag synchronization scheme for
different chaotic systems with parametric uncertainties is proposed.
Based on the new definition of synchronization with error bound and
a novel impulsive control scheme (the so-called dual-stage impulsive
control), some new and less conservative sufficient conditions are
established to guarantee that the error dynamics can converge to a
predetermined level, which is more reasonable and rigorous than the
existing results. In particular, some simpler and more convenient
conditions are derived by taking the same impulsive distances and
control gains. Finally, some numerical simulations for the Lorenz system
and the Chen system are given to demonstrate the effectiveness and
feasibility of the proposed method.

A control approach where the fuzzy logic methodology is combined
with impulsive control is developed for controlling some time-delay
chaotic systems in this paper. We first introduce impulses into each
subsystem with delay of the Takagi--Sugeno (TS) fuzzy IF--THEN rules and
then present a unified TS impulsive fuzzy model with delay for chaos
control. Based on the new model, a simple and unified set of
conditions for controlling chaotic systems is derived by the
Lyapunov--Razumikhin method, and a design procedure for estimating
bounds on control matrices is also given. Several numerical examples
are presented to illustrate the effectiveness of this method.

In this paper, the synchronization and the parameter identification
of the chaotic Pikovsky--Rabinovich (PR) circuits are investigated.
The linear error of the second corresponding variables is used to
change the driven chaotic PR circuit, and the complete
synchronization of the two identical chaotic PR circuits is realized
with feedback intensity k increasing to a certain threshold. The
Lyapunov exponents of the chaotic PR circuits are calculated by
using different feedback intensities and our results are confirmed.
The case where the two chaotic PR circuits are not identical is also
investigated. A general positive Lyapunov function V, which
consists of all the errors of the corresponding variables and
parameters and changeable gain coefficient, is constructed by using
the Lyapunov stability theory to study the parameter identification
and complete synchronization of two non-identical chaotic circuits.
The controllers and the parameter observers could be obtained
analytically only by simplifying the criterion dV/dt<0
(differential coefficient of Lyapunov function V with respect to
time is negative). It is confirmed that the two non-identical
chaotic PR circuits could still reach complete synchronization and
all the unknown parameters in the drive system are estimated exactly
within a short transient period.

Based on the fluid flow time-delayed model proposed by Misra
et al in internet congestion control, one
modified time-delayed model is presented, where the influence of the
communication delay on the router queue length is investigated in
detail. The main advantage of the new model is that its stability
domain is larger even without an extra controller. By linear
stability analysis and numerical simulation, the effectiveness and
feasibility of the novel model in internet congestion control are
verified.

A neighbour-based coordination scheme is proposed for a multi-agent
system with multiple leaders. Under assumptions of the connectivity
of the interconnection topology and a simple first-order dynamics
model for each mobile agent, the results show that all the agents
will flock to the polytope region formed by the leaders.

The shortcomings of traditional methods to find the shortest path
are revealed, and a strategy of finding the self-organizing shortest
path based on thermal flux diffusion on complex networks is
presented. In our method, the shortest paths between the source node
and the other nodes are found to be self-organized by comparing node
temperatures. The computation complexity of the method scales
linearly with the number of edges on underlying networks. The
effects of the method on several networks, including a regular
network proposed by Ravasz and Barabási which is called the RB
network, a real network, a random network proposed by Ravasz and
Barabási which is called the ER network and a scale-free network, are
also demonstrated. Analytic and simulation results show that the
method has a higher accuracy and lower computational complexity than
the conventional methods.

In view of differential geometry, the state space of thermodynamic
parameters is investigated. Here the geometrical structures of the
denormalized thermodynamic manifold are considered. The relation of
their geometrical metrics is obtained. Moreover an example is used
to illustrate our conclusions.

This paper develops a modified Tait equation of state (EOS) for
trans-decahydronaphthalene with four parameters A, B, V_{0} and
P_{0} being treated as linear functions of temperature. The
coefficients contained in these functions are determined through
fitting the experimental compression data in the literature between 293~K
and 446~K and at pressures from 10 to 200~MPa. Expressions for
the thermal expansivity, isothermal compressibility and
thermodynamic quantities are deduced and the numerical results are
analytically derived. The numerical results show that the precision
of the modified Tait EOS developed in this paper is superior to the
EOS in the literature.

In this article, we calculate the contribution from the
nonfactorizable soft hadronic matrix element to the decay
B^{0}\rightarrow χ_{cl}π^{0} with the light-cone quantum
chromo-dynamic (QCD) sum rules. The numerical results show that its
contribution is rather large and should not be neglected. The total
amplitudes lead to a branching fraction which is in agreement with
the experimental data marginally.

The α preformation factor and penetration probability
have been analyzed for even--even nuclei of Po, Rn, Ra using
experimental released energies and α decay half-lives in the
frame of the double folding model. It is shown that N=126 is a neutron
magic number from α preformation and shell effects play
an important role in α preformation. The closer the
nucleon number is to the magic number, the more difficult α
formation in the parent nucleus is. The preformation factor can
supply information on the nuclear structure and the penetration
probability mainly determines α decay half-life.

This paper shows the calculations of radioactivity and afterheat
in the components of the China Spallation Neutron Source (CSNS) target
station, with the Monte Carlo codes LAHET, MCNP4C and the multigroup
code CINDER'90. These calculations provide essential data for the
detailed design and maintenance of the CSNS target station.

The multi-configuration Dirac--Fock (MCDF) method is implemented to
study doubly excited 2s2p ^{1,3}P_{1} resonances of the helium atom
and the interference between photoionization and photoexcitation
autoionization processes. In order to reproduce the total
photoionization sprectra, the excited energies from the ground
1s^{2} \^{1}S_{0} state to the doubly excited 2s2p ^{1,3}P_{1} states and the relevant Auger decay rates and widths are
calculated in detail. Furthermore, the interference profile
determined by the so-called Fano parameters q and ρ ^{2} is
also reproduced. Good agreement is found between the present results
and other available theoretical and experimental results. This
indeed shows a promising way to investigate the Fano resonances in
photoionization of atoms within the MCDF scheme, although there are
some discrepancies in the present calculations of the 2s2p
^{3}P_{1} state.

Natural radiative lifetimes of five higher-lying odd-parity levels
5p7s ^{3}P_{1}^{o}, 5p5d ^{1}P_{1}^{o}, 5p6d
^{3}F_{2}^{o}, ^{3}D_{1}^{o} and ^{3}F_{3}^{o} in
neutral tin are measured by the time-resolved laser-induced
fluorescence (TR-LIF) technique and the atomic beam method. All
these lifetimes are not longer than 100 ns and they are found to be
shorter than the lifetimes of even-parity levels in the same energy
region. The results reported in this paper provide important
transition parameters for highly-excited atomic Sn, which may be useful
for theoretically calculating excited heavy atoms.

There can be found some notable discrepancies with regard to the
resonance structures when R-matrix calculations from the
Opacity Project and other sources are compared with recent absolute
experimental measurements of Bizau et al [Astron.
Astrophts.439 387 (2005)] for B-like ions N^{2+},
O^{3+} and F^{4+}. We performed close-coupling calculations
based on the R-matrix formalism for the photoionizations of
ions mentioned above both for the ground states and first excited
states in the near threshold regions. The present results are
compared with experimental ones given by Bizau et al and
earlier theoretical ones. Excellent agreement is obtained between
our theoretical results and the experimental photoionization cross
sections. The present calculations show a significant improvement
over the previous theoretical results.

This paper studies a miniature low power consumption laser-pumped atom
vapour cell clock scheme. Pumping ^{87}Rb with a vertical cavity
surface emitting laser diode pump and locking the laser frequency on
a Doppler-broadened spectral line, it records a 5× 10^{-11}τ^{-1/2} (τ <500~s) frequency stability with a
table-top system in a primary experiment. The study reveals that the
evaluated scheme is at the level of 2.7 watts power consumption,
90~cm^{3} volume and 10^{-12}τ ^{-1/2} short-term
frequency stability.

This paper investigates the dynamical instability and adiabatic
evolution of the atom--homonuclear--trimer dark state of a condensate
system in a stimulated Raman adiabatic passage aided by Feshbach
resonance. It obtains analytically the regions for the appearance of
dynamical instability caused by the interparticle interactions.
Moreover, the adiabatic property of the dark state is also studied
in terms of a newly defined adiabatic fidelity. It shows that the
nonlinear collisions have a negative effect on the adiabaticity of
the dark state and hence reduce the conversion efficiency.

This paper studies the molecular rotational excitation and
field-free spatial alignment in a nonresonant intense laser field
numerically and analytically by using the time-dependent Schr?dinger
equation. The broad rotational wave packets excited by the
femtosecond pulse are defined in conjugate angle space, and
their coefficients are obtained by solving a set of coupled linear
equations. Both single molecule orientation angles and an ensemble
of O_{2} and CO molecule angular distributions are calculated in
detail. The numerical results show that, for single molecule highest
occupied molecular orbital (HOMO) symmetry σ tends to have a
molecular orientation along the laser polarization direction and
the permanent dipole moment diminishes the mean of the orientation angles; for
an ensemble of molecules, angular distributions provide more complex
and additional information at times where there are no revivals in
the single molecule plot. In particular, at the revival peak
instant, with the increase of temperature of the molecular ensemble, the
anisotropic angular distributions with respect to the laser polarization
direction of the π _{g} orbital gradually transform to the
symmetrical distributions regarding the laser polarization vector and
for two HOMO configurations angular distributions of all directions
are confined within a smaller angle when the temperature of the molecular
ensemble is higher.

The potential energy curve of the CD(X^{2}П ) radical is obtained using the coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z. The potential energy curve is fitted to the Murrell--Sorbie function, which is used to determine the spectroscopic parameters. The obtained D_{0}, D_{e}, R_{e}, ω_{e}, ω_{e}χ _{e}, α_{e} and B_{e} values are 3.4971~eV, 3.6261~eV, 0.11197~nm,
2097.661~cm^{-1}, 34.6963~cm^{-1}, 0.2083~cm^{-1} and 7.7962~cm^{-1}, respectively, which conform almost perfectly to the available measurements. With the potential obtained at the UCCSD(T)/aug-cc-pV5Z level of theory, a total of 24 vibrational states have been predicted for the first time when J = 0 by solving the radial Schr?dinger equation of nuclear motion. The complete vibrational levels, the classical turning points, the inertial rotation constants and centrifugal distortion constants are reproduced from the CD(X^{2}П) potential when J = 0, and are in excellent agreement with the available measurements. The total and the various partial-wave cross sections are calculated for the elastic collisions between the ground-state C and D atoms at energies from 1.0× 10^{-11} to 1.0× 10^{-4}a.u. when the two atoms approach each other along the CD(X^{2}П) potential energy curve. Only one shape resonance is found in the total elastic cross sections, and the resonant energy is 8.36× 10^{-6}~a.u. The results show that the shape of the total elastic cross section is mainly dominated by the s partial wave at very low temperatures. Because of the weak shape resonances coming from higher partial waves, most of them are passed into oblivion by the strong total elastic cross sections.

The one-colour resonant two-photon ionization (R2PI) spectrum of the 1-fluoronaphthalene (1FN) dimer has been studied in the wavelength range of 304 to 322~nm by using a supersonic molecular beam and time-of-flight mass spectrometry. Compared with the original band 0_{0}^{0} (at 313.8~nm) of the S_{1} ≤ftarrow S_{0} transition of the 1FN monomer, a red-shifted band was observed in the 1FN dimer spectrum at about 315~nm with a relatively large linewidth, nearly 2~nm. Based on the consideration of inductive effect and ab initio calculations, this red-shifted band is assigned to the first electronic excited transition of the 1FN dimer. A possible geometric structure of the 1FN dimer is also obtained with calculations that the two 1FN molecules are combined through two hydrogen bonds which are formed between the hydrogen atom of a molecule and the fluorine atom of a neighbouring molecule. A time-dependent calculation was also carried out and the results are consistent with the experimental data.

A high-energy electron beam generator is used to generate a plasma
in atmosphere. Based on a Monte Carlo toolkit named GEANT4, a model
including complete physics processes is established to simulate the
passage of the electron beam in air. Based on the model, the
characteristics of the electron beam air plasma are calculated. The
energy distribution of beam electrons (BEs) indicates that
high-energy electrons almost reside in the centre region of the
beam, but low-energy electrons always live in the fringe area. The
energy deposition is calculated in two cases, i.e., with and without
secondary electrons (SEs). Analysis indicates that the energy
deposition of SEs accounts for a large part of the total energy
deposition. The results of the energy spectrum show that the electrons
in the inlet layer of the low-pressure chamber (LPC) are monoenergetic,
but the energy spectrum of the electrons in the outlet layer is not
pure. The SEs are largely generated at the outlet of the LPC.
Moreover, both the energy distribution of BEs and the magnitude of
the density of SEs are closely related to the pressure of LPC. Thus,
a conclusion is drawn that a low magnitude of LPC pressure is
helpful for reducing the energy loss in the LPC and also useful for
greatly increasing the secondary electron density in dense air.

The possibility of an electron beam exciting surface plasmons in
conducting metal is discussed in this paper. A planar
perfect-structure with subwavelength holes is proposed. The
phenomenon that mimicking
surface plasmon waves can be excited and amplified by an electron
beam is proved theoretically and numerically. The mechanism of transmission through a subwavelength hole
array is exploited to enhance the interaction between the electron beam
and the mimicking surface plasmons.

Taking partially coherent cosh--Gaussian (ChG) beams as an example
of more general partially coherent beams, we have studied the
spectral degree of coherence of partially coherent ChG beams in the
far field. It is shown that, unlike Gaussian Schell-model (GSM)
beams, in the strict sense there do not exist two partially coherent
ChG beams which can generate far fields with the same spectral
degree of coherence. However, under certain conditions it is
possible to find two partially coherent ChG beams with the same
spectral degree of coherence in the far field.

This paper presents a scheme for realizing the frequency
up-conversion between two collective atomic modes. In the scheme two
atomic samples are coupled to a cavity mode. Under the large
detuning condition, the two collective atomic modes are coupled via
the virtual excitation of the cavity mode and the effective
Hamiltonian corresponds to the frequency up-conversion. In the
scheme the cavity mode is only virtually excited and thus the
process is insensitive to cavity decay.

We propose and implement a quasi-discrete Hankel transform algorithm
based on Dini series expansion (DQDHT) in this paper. By making use
of the property that the zero-order Bessel function derivative
J' _{0}(0)=0, the DQDHT can be used to calculate the values
on the symmetry axis directly. In addition, except for the truncated
treatment of the input function, no other approximation is made,
thus the DQDHT satisfies the discrete Parseval theorem for energy
conservation, implying that it has a high numerical accuracy.
Further, we have performed several numerical tests. The test results
show that the DQDHT has a very high numerical accuracy and keeps
energy conservation even after thousands of times of repeating
the transform either in a spatial domain or in a frequency domain.
Finally, as an example, we have applied the DQDHT to the nonlinear
propagation of a Gaussian beam through a Kerr medium system with
cylindrical symmetry. The calculated results are found to be in
excellent agreement with those based on the conventional 2D-FFT
algorithm, while the simulation based on the proposed DQDHT takes
much less computing time.

A 2× 2 electro-optic switch is experimentally demonstrated
using the optical structure of a Mach--Zehnder interferometer (MZI) based
on a submicron rib waveguide and the electrical structure of a PIN diode on
silicon-on-insulator (SOI). The switch behaviour is achieved through
the plasma dispersion effect of silicon. The device has a modulation arm
of 1~mm in length and cross-section of 400~nm× 340~nm. The
measurement results show that the switch has a V_{π}L_{π}
figure of merit of 0.145~V\cdot cm and the extinction ratios of two
output ports and cross talk are 40~dB, 28~dB and -28~dB,
respectively. A 3~dB modulation bandwidth of 90~MHz and a switch
time of 6.8~ns for the rise edge and 2.7~ns for the fall edge are also
demonstrated.

The influence of applied electric fields on the absorption
coefficient and subband distances in asymmetrical AlN/GaN coupled
double quantum wells (CDQWs) has been investigated by solving
Schr?dinger and Poisson equations self-consistently. It is found
that the absorption coefficient of the intersubband transition
(ISBT) between the ground state and the third excited state (1_{odd}-2_{even}) can be equal to zero when the electric fields
are applied in asymmetrical AlN/GaN CDQWs, which is related to
applied electric fields induced symmetry recovery of these states.
Meanwhile, the energy distances between 1_{odd}-2_{even}
and 1_{even}-2_{even} subbands have different
relationships from each other with the increase of applied electric
fields due to the different polarization-induced potential drops
between the left and the right wells. The results indicate that an
electrical-optical modulator operated within the opto-communication
wavelength range can be realized in spite of the strong
polarization-induced electric fields in asymmetrical AlN/GaN CDQWs.

Based on an equivalent medium approach, this paper presents a
model describing the nonlinear propagation of acoustic waves in
a viscoelastic medium containing cylindrical micropores. The
influences of pores' nonlinear oscillations on sound
attenuation, sound dispersion and an equivalent acoustic nonlinearity
parameter are discussed. The calculated results show that the
attenuation increases with an increasing volume fraction of
micropores. The peak of sound velocity and attenuation occurs at the
resonant frequency of the micropores while the peak of the
equivalent acoustic nonlinearity parameter occurs at the half of the
resonant frequency of the micropores. Furthermore, multiple
scattering has been taken into account, which leads to a
modification to the effective wave number in the equivalent medium
approach. We find that these linear and nonlinear acoustic
parameters need to be corrected when the volume fraction of
micropores is larger than 0.1%.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The surface dynamics of supercooled liquid-glycerol is studied by
scanning the thickness of the glycerol film with single photon
detection. Measurements are performed at room temperature well above
the glycerol's glass transition temperature. It is shown that the
surface dynamics of the glycerol film is very sensitive to the
temperature. The linear relationship between the thickness of the
film and the viscosity predicted by the Vogel--Fulcher--Tammann--Hesse
(VFTH) law is also presented experimentally.

Highly uniformed barium-strontium titanate nanotube arrays were
fabricated using a porous anodic aluminum oxide template from a
barium-strontium titanate sol--gel solution. Electron microscope
results showed that nanotubes with uniform length and diameter were
obtained. The diameters and lengths of these nanotubes were
dependent on the pore diameter and the thickness of the applied
anodic aluminum oxide template. High resolution transmission
electron microscopy and the selected-area electron diffraction
pattern investigations demonstrated the perovskite structure and the
polycrystalline of the fabricated barium-strontium titanate
nanotubes. The characterization of the electrical and dielectric
properties had also been made. Compared to thin film material, the
intrinsic leakage current density is almost the same. Besides, at
30~℃, the dielectric constant and dielectric loss of the
fabricated nanotube is 80 and 0.027 at 1~MHz respectively.

Investigations of alloying Re and Ru in the [110](001) dislocation
core of the Ni/Ni_{3}Al interface were conducted within the framework of density functional theory. The energetic calculations show
that both elements can stabilize the [110](001) dislocation core. In
the dislocation core region, Re and Ru prefer to substitute for
Ni on the site in the γ -phase. Re is easier to segregate into
the dislocation core region as compared with Ru; it especially
prefers to substitute for Ni on the γ -(Ni)1 site.

This paper studies the elastic and electronic structure properties
of two new low-energy structures of PdN_{2} and PtN_{2} by
first-principles calculations. It finds that tetragonal and
monoclinic structures are more stable than a pyrite one.
The always positive eigenvalues of the elastic constant matrix
confirm that both the tetragonal and monoclinic structures are
elastically stable. The origin of the low bulk modulus of the two
structures is discussed. The results of the calculated density
of states show that both of the two low-energy structures are
metallic.

We investigate the interactions of lattice phonons with Frenkel
exciton, which has a small radius in a two-dimensional discrete
molecular lattice, by the virtue of the quasi-discreteness
approximation and the method of multiple-scale, and obtain that the
self-trapping can also appear in the two-dimensional discrete molecular
lattice with harmonic and nonlinear potential. The excitons' effect
on the molecular lattice does not distort it but only
causes it to localize which enables it to react again through phonon
coupling to trap the energy and prevent its dispersion.

The equilibrated grain boundary groove shapes of solid
solution Ag_{2}Al in equilibrium with an Al--Cu--Ag liquid were observed from
a quenched sample with a radial heat flow apparatus. The
Gibbs--Thomson coefficient, solid--liquid interfacial energy and
grain boundary energy of the solid solution Ag_{2}Al have been
determined from the observed grain boundary groove shapes. The
thermal conductivity of the solid phase and the thermal conductivity
ratio of the liquid phase to solid phase for Ag_{2}Al--28.3
at the %CuAl_{2} alloy at the melting temperature have also been
measured with a radial heat flow apparatus and Bridgman type growth
apparatus, separately.

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

We have investigated the exchange bias and training effect in the
ferromagnetic/antiferromagnetic (FM/AF) heterostructures using a
unified Monte Carlo dynamical approach. The magnetization of the
uncompensated AF layer is still open after the first field cycling
is finished. Our simulated results show obvious shift of hysteresis
loops (exchange bias) and cycling dependence of exchange bias
(training effect) when the temperature is below 45~K. The exchange
bias field decreases with decreasing cooling rate or increasing
temperature and the number of the field cycling. Essentially, these
two effects can be explained on the basis of the microscopical
coexistence of both reversible and irreversible moment reversals of
the AF domains. Our simulations are useful to understand the real
magnetization dynamics of such magnetic heterostructures.

The grain boundaries (GBs) have a strong effect on the electric
properties of ZnO thin film transistors (TFTs). A novel grain
boundary model was developed to analyse the effect. The model was
characterized with different angles between the orientation of the
grain boundary and the channel direction. The potential barriers
formed by the grain boundaries increase with the increase of the grain
boundary angle, so the degradation of the transistor characteristics
increases. When a grain boundary is close to the drain edge, the
potential barrier height reduces, so the electric properties were
improved.

Based on the nanostructured surface model that the (platinum,
Pt) nanocones grow out symmetrically from a plane substrate, the
local electric field near the conical nanoparticle surface is
computed and discussed. On the basis of these results, the adsorbed
CO molecules are modelled as dipoles, and three kinds of
interactions, i.e. interactions between dipoles and local electric
field, between dipoles and dipoles, as well as between dipoles and
nanostructured substrate, are taken into account. The
spatial configuration of CO molecules adsorbed on the nanocone
surface is then given by Monte-Carlo simulation. Our results show that
the CO molecules adsorbed on the nanocone surface cause local
agglomeration under the action of an external electric field, and
this agglomeration becomes more compact with decreasing conical
angle, which results in a stronger interaction among molecules.
These results serve as a basis for explaining abnormal phenomena
such as the abnormal infrared effect (AIRE), which was found when CO
molecules were adsorbed on the nanostructured transition-metal
surface.

This paper studies the dynamics of intra-acceptor hole relaxation in
Be δ -doped GaAs/AlAs multiple quantum wells (MQW) with
doping at the centre by time-resolved pump-probe spectroscopy using
a picosecond free electron laser for infrared experiments. Low
temperature far-infrared absorption measurements clearly show three
principal absorption lines due to transitions of the Be acceptor from
the ground state to the first three odd-parity excited states
respectively. The pump-probe experiments are performed at different
temperatures and different pump pulse wavelengths. The hole
relaxation time from 2p excited state to 1s ground state in MQW is
found to be much shorter than that in bulk GaAs, and shown to be
independent of temperature but strongly dependent on wavelength. The
zone-folded acoustic phonon emission and slower decay of the
wavefunctions of impurity states are suggested to account for the
reduction of the 2p excited state lifetime in MQW. The wavelength
dependence of the 2p lifetime is attributed to the diffusion of the
Be atom δ -layer in quantum wells.

Using the measured capacitance--voltage curves and the photocurrent
spectrum obtained from the Ni Schottky contact on a strained
Al_0.3Ga_0.7N/GaN heterostructure, the value of the relative
permittivity of the AlGaN barrier layer was analysed and calculated
by self-consistently solving Schr?dinger's and Poisson's
equations. It is shown that the calculated values of the relative
permittivity are different from those formerly reported, and reverse
biasing the Ni Schottky contact has an influence on the value of the
relative permittivity. As the reverse bias increases from 0 V to
--3~V, the value of the relative permittivity decreases from 7.184
to 7.093.

This paper reports that Cr_{2}O_{3} hollow nanospheres (HNs)
were synthesized via a hydrothermal approach and characterized by
scanning electron microscopy, x-ray powder diffraction, transmission
electron microscopy (TEM), selective area electron diffraction and
high resolution TEM, respectively. In addition, the room-temperature
(RT) gas sensing properties of Cr_{2}O_{3} HNs and conventional
powders (CPs) were investigated by means of the surface photovoltage
technique. The experimental data demonstrate that the RT gas sensor
of the as-fabricated HNs reaches below 5~ppm whereas that of the CPs
is about 40~ppm, which results from there being much more adsorbed and desorbed
oxygen in HNs than in CPs at RT. The as-prepared Cr_{2}O_{3} HNs
could have potential applications as RT nanosensors.

The properties of top-contact organic thin-film transistors
(TC-OTFTs) using ultra-thin 2, 9-dimethyl-4, 7-diphenyl-1,
10-phenanthroline (BCP) as a hole-blocking interlayer have been
improved significantly and a BCP interlayer was inserted into the
middle of the pentacene active layer. This paper obtains a fire-new
transport mode of an OTFT device with double-conductible channels. The
accumulation and transfer of the hole carriers are limited by the
BCP interlayer in the vertical region of the channel. A huge
amount of carriers is located not only at the interface
between pentacene and the gate insulator, but also at the two interfaces
of pentacene/BCP interlayer and pentacene/gate insulator,
respectively. The results suggest that the BCP interlayer may be
useful to adjust the hole accumulation and transfer, and can
increase the hole mobility and output current of OTFTs. The TC-OTFTs
with a BCP interlayer at V_{DS}=-20~V showed excellent hole
mobility μ_{FE} and threshold voltage V_{TH} of
0.58~cm^{2}/(V\cdots) and --4.6~V, respectively.

In this paper, a new structure of a 4H-SiC bipolar junction transistor
(BJT) with a buried layer (BL) in the base is presented. The current gain
shows an approximately 100% increase compared with that of the
conventional structure. This is attributed to the creation of a built-in
electric field for the minority carriers to transport in the base
which is explained based on 2D device simulations. The optimized
design of the buried layer region is also considered by numeric
simulations.

The present work investigates the effect of europium substitution on
the (Bi, Pb)-2212 system in the concentration range 0.5 ≤ x ≤
1.0. Phase analysis and lattice parameter calculations on the
powder diffraction data and the elemental analysis of EDX show that
the Eu atoms are successfully substituted into the (Bi, Pb)-2212
system. Resistivity measurements (64--300~K) reveal that the
system exhibits superconductivity at x ≤ 0.5 and
semiconductivity at x > 0.5. With the complete suppression of
superconductivity which is known to be a quasi-two dimensional
phenomenon in these materials, a metal to insulator transition takes
place at x=0.6 and the predominant conduction mechanism is found
to be variable range hopping between localized states, resulting
in macroscopic semiconducting behaviour. The results of electrical
and structural properties of the doped (Bi, Pb)-2212 compounds
suggest that the decrease of charge carrier concentration and the
induced structural disorder are the more effective and dominant
mechanisms in the origin of the metal to insulator transition and
suppression of superconductivity due to Eu substitution at its
Sr site.

We present a study on n-type ternary InGaN layers grown by
atmospheric pressure metalorganic vapour phase epitaxy (MOVPE) on
GaN template/(0001) sapphire substrate. An investigation of the
different growth conditions on n-type In_{x}Ga_1-xN
(x=0.06-0.135) alloys was done for a series of five samples.
The structural, electrical and optical properties were characterized by
high resolution x-ray diffraction (HRXRD), Hall effect and
photoluminescence (PL). Experimental results showed that
different growth conditions, namely substrate rotation (SR) and
change of total H_{2} flow (THF), strongly affect the properties
of InGaN layers. This case can be clearly observed from the analytical
results. When the SR speed decreased, the HRXRD scan peak of the
samples shifted along a higher angle. Therefore, increasing
the SR speed changed important structural properties of InGaN alloys
such as peak broadening, values of strain, lattice parameters
and defects including tilt, twist and dislocation density. From PL
results it is observed that the growth conditions can be changed to
control the emission wavelength and it is possible to shift the
emission wavelength towards the green. Hall effect measurement has
shown that the resistivity of the samples changes dramatically when
THF changes.

The optical properties of hexagonal boron nitride (h-BN) thin films
were studied in this paper. The films were characterized by Fourier
transform infrared spectroscopy, UV--visible transmittance and
reflection spectra. h-BN thin films with a wide optical band gap
E_{g} (5.86~eV for the as-deposited film and 5.97~eV for the
annealed film) approaching h-BN single crystal were successfully
prepared by radio frequency (RF) bias magnetron sputtering and
post-deposition annealing at 970~K. The optical absorption behaviour
of h-BN films accords with the typical optical absorption
characteristics of amorphous materials when fitting is made by the
Urbach tail model. The annealed film shows satisfactory structure
stability. However, high temperature still has a significant
effect on the optical absorption properties, refractive index n,
and optical conductivity σ of h-BN thin films. The
blue-shift of the optical absorption edge and the increase of E_{g} probably result from stress relaxation in the film under high temperatures. In addition, it is found that the refractive index
clearly exhibits different trends in the visible and ultraviolet regions.
Previous calculational results of optical conductivity of h-BN
films are confirmed in our experimental results.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

A new method is proposed to transform the time series gained from a
dynamic system to a symbolic series which extracts both overall
and local information of the time series. Based on the
transformation, two measures are defined to characterize the
complexity of the symbolic series. The measures reflect the
sensitive dependence of chaotic systems on initial conditions and
the randomness of a time series, and thus can distinguish periodic
or completely random series from chaotic time series even though the
lengths of the time series are not long. Finally, the logistic map
and the two-parameter Henón map are studied and the results are
satisfactory.

In this paper, the network equation for the slow neutron capture
process (s-process) of heavy element nucleosynthesis is
investigated. Dividing the s-process network reaction chains into
two standard forms and using the technique of matrix decomposition,
a group of analytical solutions for the network equation are
obtained. With the analytical solutions, a calculation for heavy
element abundance of the solar system is carried out and the results are
in good agreement with the astrophysical measurements.

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