A variable separation approach is proposed and extended to the
(1+1)-dimensional physics system. The variable separation solution of
(1+1)-dimensional Ito system is obtained. Some special types of solutions
such as non-propagating solitary wave solution, propagating solitary wave
solution and looped soliton solution are found by selecting the arbitrary
function appropriately.

This paper investigates the momentum-dependent symmetries for nonholonomic
nonconservative Hamilton canonical systems. The definition and determining
equations of the momentum-dependent symmetries are presented, based on the
invariance of differential equations under infinitesimal transformations
with respect to the generalized coordinates and generalized momentums. The
structure equation and the non-Noether conserved quantities of the systems
are obtained. The inverse issues associated with the momentum-dependent
symmetries are discussed. Finally, an example is discussed to further
illustrate the applications.

The description of modern differential geometry for time-dependent Chetaev
nonholonomic mechanical systems with unilateral constraints is studied. By
using the structure of exact contact manifold, the geometric framework of
time-dependent nonholonomic mechanical systems subject to unilateral
nonholonomic constraints and unilateral holonomic constraints respectively
is presented.

This paper focuses on studying the Lie symmetry and a conserved quantity of
a system of first-order differential equations. The determining equations of
the Lie symmetry for a system of first-order differential equations, from
which a kind of conserved quantity is deduced, are presented. And their
general conclusion is applied to a Hamilton system, a Birkhoff system and a
generalized Hamilton system. Two examples are given to illustrate
the application of the results.

Based on the classical Roe method, we develop an interface capture method
according to the general
equation of state, and extend the single-fluid Roe method to the
two-dimensional (2D) multi-fluid flows, as
well as construct the continuous Roe matrix for the whole flow field. The
interface capture equations and
fluid dynamic conservative equations are coupled together and solved by
using any high-resolution
schemes that usually suit for the single-fluid flows. Some numerical
examples are given to illustrate the
solution of 1D and 2D multi-fluid Riemann problems.

New exact solutions, expressed in terms of the Jacobi elliptic functions, to
the nonlinear Klein--Gordon equation are obtained by using a modified mapping
method. The solutions include the conditions for equation's parameters and
travelling wave transformation parameters. Some figures for a specific kind
of solution are also presented.

By use of the Hartree approximation and the method of multiple scales, we
investigate quantum solitons and intrinsic localized modes in a
one-dimensional antiferromagnetic chain. It is shown that there exist
solitons of two different quantum frequency bands: i.e., magnetic optical
solitons and acoustic solitons. At the boundary of the Brillouin zone, these
solitons become quantum intrinsic localized modes: their quantum
eigenfrequencies are below the bottom of the harmonic optical frequency band
and above the top of the harmonic acoustic frequency band.

Using the mapping approach via a Riccati equation, a series of variable separation
excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW)
equation are derived. In addition to the usual localized coherent soliton excitations like
dromions, rings, peakons and compactions, etc, some new types of excitations
that possess fractal behaviour are obtained by introducing appropriate
lower-dimensional localized patterns and Jacobian elliptic functions.

A new model of a quantum refrigeration cycle composed of two adiabatic and
two isomagnetic field processes is established. The working substance in the
cycle consists of many non-interacting spin-1/2 systems. The performance of
the cycle is investigated, based on the quantum master equation and
semi-group approach. The general expressions of several important
performance parameters, such as the coefficient of performance, cooling
rate, and power input, are given. It is found that the coefficient of
performance of this cycle is in the closest analogy to that of the classical
Carnot cycle. Furthermore, at high temperatures the optimal relations of the
cooling rate and the maximum cooling rate are analysed in detail. Some
performance characteristic curves of the cycle are plotted, such as the
cooling rate versus the maximum ratio between high and low ``temperatures''
of the working substances, the maximum cooling rate versus the ratio between
high and low ``magnetic fields'' and the ``temperature'' ratio between high
and low reservoirs. The obtained results are further generalized and
discussed, so that they may be directly applied to describing the performance
of the quantum refrigerator using spin-$J$ systems as the working substance.
Finally, the optimum characteristics of the quantum Carnot and Ericsson
refrigeration cycles are derived by analogy.

It has recently been established that quantum strategies have great
advantage over classical ones in quantum games. However, quantum
states are easily affected by the quantum noise resulting in
decoherence. In this paper, we investigate the effect of quantum
noise on the restricted quantum game in which one player is
restricted in classical strategic space, another in quantum
strategic space and only the quantum player is affected by the
quantum noise. Our results show that in the maximally entangled
state, no Nash equilibria exist in the range of
$0

The so-called extended hyperbolic complex (EHC) function method
is used to study further the stationary axisymmetric Einstein--Maxwell theory with
$p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural
Riemann--Hilbert (RH) transformations are constructed and are then shown to give
an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is
verified to have the structure of semidirect product of Kac--Moody group
$\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal
forms of these
two RH transformations are calculated and found to give exactly the same
infinitesimal transformations as in previous author's paper
by a different scheme. This demonstrates that the results
obtained in the present paper provide some exponentiations of all the infinitesimal
symmetry transformations obtained before.

The massless scalar quasinormal modes (QNMs) of a stationary axisymmetric
Einstein--Maxwell dilaton--axion (EMDA) black hole are calculated
numerically using the continued fraction method first proposed by
Leaver. The fundamental quasinormal frequencies
(slowly damped QNMs) are obtained and the peculiar
behaviours of them are studied. It is shown that these frequencies depend on
the dilaton parameter $D$, the rotational parameter $a$,
the multiple moment $l$ and the azimuthal number $m$,
and have the same values
with other authors at the Schwarzschild and Kerr limit.

This paper proposes a new, simple and yet applicable output feedback
synchronization theorem for a large class of chaotic systems. We take a
linear combination of drive system state variables as a scale-driving
signal. It is proved that synchronization between the drive and the response
systems can be obtained via a simple linear output error feedback control.
The linear feedback gain is a function of a free parameter. The approach is
illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic
oscillators.

This paper deals with the robust fuzzy control for chaotic systems in the
presence of parametric uncertainties. An uncertain Takagi--Sugeno fuzzy model
for a Lorenz chaotic system is first constructed. Then a robust fuzzy state
feedback control scheme ensures the control for stable operations under
bounded parametric uncertainties. For a chaotic system with known
uncertainty bounds, a robust fuzzy regulator is designed by choosing the
control parameters satisfying the linear matrix inequality. To verify the
validity and effectiveness of the proposed controller design method, an
analysis technique is suggested and applied to the control of an uncertain
Lorenz chaotic system.

A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic
synchronization (LSISAAS) method is proposed to asymptotically synchronize
Duffing system with unknown parameters which also are considered as system
states. The LSISASS strategy depends on the only information, i.e. one state of
the master system. According to the LSIST, the LSISASS method can
asymptotically synchronize fully the states of the master system and the unknown
system parameters as well. Simulation results also validate that the LSISAAS
approach can obtain asymptotic synchronization.

Considering the properties of slow change and quasi-periodicity of
magnetocardiography (MCG) signal, we use an integrated technique of adaptive
and low-pass filtering in dealing with two-channel MCG data measured by high
$T_{\rm c}$ SQUIDs. The adaptive filter in the time domain is based on a noise feedback
normalized least-mean-square (NLMS) algorithm, and the low-pass filter with
a cutoff at 100Hz in the frequency domain characterized by Gaussian functions is
combined with a notch at the power line frequency. In this way, both
relevant and irrelevant noises in original MCG data are largely eliminated.
The method may also be useful for other slowly varying quasi-periodical
signals.

A new method, while takes into account the contribution of direct neutron
decay of analogue resonances to the isomeric ratio resulting from (p,n)
reaction, is used to analyse the published experimental data for the
reaction $^{104}$Ru(p,n)$^{104}$Rh and also estimate a minimum probability
of direct decay.

For more than 20 years nuclear physicists have used the GEANT code to
simulate particle-matter interaction. In most recent version, GEANT4 is a
toolkit for simulating the passage of particles though matter, which
contains a complete range of functionality including tracking, geometry,
physics models, and hits. In this article, an attempt to use GEANT4 to model
a double-gap resistive plate chamber (RPC) with its improved efficiency is
presented. The efficiencies of the double-gap RPC have been evaluated as a
function of gamma energy range 0.005--1000MeV. A comparison to available
previous simulation
package GEANT3 data is also performed.

We investigate the diffraction characteristics of an incident Gaussian
beam cut
by a straight edge bounding a semi-infinite opaque plane using Kirchhoff
scalar wave theory in the Fresnel limit, and propose a new and simple mirror
scheme to reflect atoms by using the intensity gradient induced by a
blue-detuned semi-Gaussian laser beam. The optical potential of the
diffracted light of the knife-cut semi-Gaussian beam for
$^{85}$Rb atom and its spontaneous emission probability are calculated and
compared with the performance of the evanescent-wave mirror. Our study shows
that the optical potential of the diffracted light of the semi-Gaussian beam
is far higher than that of the evanescent light wave, and the maximum normal
velocity of the incident atoms can be far greater than that of the
evanescent light wave under the same parameters, so the blue-detuned
semi-Gaussian beam, as a novel atomic mirror, can be used to efficiently
reflect cold atoms with a normal velocity of greater than 1 m/s. However,
the intensity gradient (force) of the diffracted light of the
semi-Gaussian-beam is much smaller than that of the evanescent light wave, so
its spontaneous emission probability is greater than that from the
evanescent-wave when the normal velocity of incident atoms is greater.

Surface-enhanced resonance Raman scattering (SERRS) of
Rhodamine 6G (R6G) adsorbed on colloidal silver clusters has been studied.
Based on the great enhancement of the Raman signal and the quench of the
fluorescence, the SERRS spectra of R6G were recorded for the samples of dye
colloidal solution with different concentrations. Spectral inhomogeneity
behaviours from single molecules in the dried sample films were observed with
complementary evidences, such as spectral polarization, spectral diffusion,
intensity fluctuation of vibrational lines and even ``breathing'' of the
molecules. Sequential spectra observed from a liquid sample with an average of
0.3 dye molecules in the probed volume exhibited the expected Poisson
distribution for actually measuring 0, 1 or 2 molecules. Difference between
the SERRS spectra of R6G excited by linearly and circularly polarized light
were experimentally measured.

The potential for nonlinear conversion between two laser
pulses in a three-level V-type medium with assistance of an auxiliary
microwave resonant radiation is studied. The results show that
microwave driven field can lead to the parametric generation of a new
laser pulse with high conversion efficiency when a weak pump
laser pulse is applied.

With a coupling laser locked to caesium 6S$_{1 / 2}$ $F_{\rm
g}$=4--6P$_{3 / 2}$
$F_{\rm e}$=5 cycling transition and a co-propagating probe laser
scanned across
6S$_{1 / 2}$ $F_{\rm g}$=4--6P$_{3 / 2}$ $F_{\rm e}$=3, 4 and 5 transitions, a novel scheme
for sub-Doppler spectra in Doppler-broadened V-type three-level system is
demonstrated by detecting the transmission of the coupling laser through a
caesium vapour cell. The Autler--Townes doublet in the sub-Doppler spectra of the
coupling laser is clearly observed. The effects of coupling laser intensity
on the splitting and linewidth of the Autler--Townes doublet are experimentally
investigated and the results agree well with theoretical predictions. Taking
the multiple hyperfine levels of caesium atom into account, a brief analysis
is presented.

Based on the polynomial interpolation, a new finite difference (FD)
method in solving the full-vectorial guided-modes for step-index optical
waveguides is
proposed. The discontinuities of the normal components of the electric
field across abrupt dielectric interfaces are considered in the absence of
the limitations of scalar and semivectorial approximation, and the present
FD scheme can be applied to both uniform and non-uniform mesh grids. The
modal propagation constants and field distributions for buried rectangular
waveguides and optical rib waveguides are presented. The hybrid nature of
the vectorial modes is demonstrated and the singular behaviours of the minor
field components in the corners are observed. Moreover, solutions are in good
agreement with those published early, which tests the validity of the
present approach.

In this study, the Reynolds-averaged Navier--Stokes (RANS) method is
employed to simulate the flow within and
over an intersection model with three kinds of \textit{k--$\varepsilon $}
turbulence closure schemes,
namely, standard model, renormalization group (RNG) model and realizable
\textit{k--$\varepsilon $} model. The comparison
between the simulated and observed flow fields shows that the RANS simulation
with all the three turbulence models cannot completely and accurately reproduce
the observed flow field in all details. A detailed comparison between the
predicted profiles of wind velocities and the measured data shows that the
realizable \textit{k--$\varepsilon $} model is the best one among the three turbulence closure models
in general. However, the extent to which the improvement is achieved by
the realizable
\textit{k--$\varepsilon $} model is still not enough to completely and
accurately describe the turbulent flow in a relatively complex
environment.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

By using a standard multiple scale method, a Davey--Stewartson (DS) equation
has been derived and also applied to a multi-dimensional analytical
investigation on the interaction of an ultra-intense laser pulse with a cold
unmagnetized transparent electron-ion plasma. The regions of instability are
found by considering the modulation instability of a plane wave solution of
the DS equation. The DS equation is just of the Davey--Stewartson 1 (DS1) type
and admits a dromion solution, i.e. a two-dimensional (2D) dromion soliton
decaying exponentially in all spatial directions. A 2D relativistic
electromagnetic dromion-like soliton (2D REDLS) is derived for a vector
potential.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

We develop a microscopic theory of the nematic phase with consideration of the effect of the collective excitation on properties of nematic liquid crystals. The model is based on the Heisenberg's exchange model of the ferromagnetic materials. Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystals. Using the lattice model and the Holstein--Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameter and reduced temperature can be gotten. It is in good agreement with the experimental results in the low temperature region, the accordance is better than that of
the molecular field theory and the computer simulation. In high temperature region close to the transition point, by considering the effect of the higher-order terms in the Hamiltonian, theoretical prediction is in better agreement with the experiment. That indicates the many-body effect is important to nematic liquid crystals.

Spontaneous rupture of some polymer films upon heating is
commonplace. The very criterion for this instability is the system free
energy possessing a negative curvature. Within the framework of full
frequency-dependent theory of dispersion forces, we have derived the excess
free energy of a typical system---polystyrene film deposited on the silicon
substrate. The excess free energy, wavelengths and growth rates are
calculate and a comparison is made between the accurate results and the
approximate results. It is found that the stability of the film can be tuned
by the variation of the thickness of the coating and the retardation effects
can be significant sometimes.

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

A two-dimensional (2D) full band self-consistent ensemble Monte Carlo (MC)
method for solving the quantum Boltzmann equation, including collision
broadening and quantum potential corrections, is developed to extend the MC
method to the study of nano-scale semiconductor devices with obvious quantum
mechanical (QM) effects. The quantum effects both in real space and momentum
space in nano-scale semiconductor devices can be simulated. The effective
mobility in the inversion layer of n and p channel MOSFET is simulated and
compared with experimental data to verify this method. With this method 50nm
ultra thin body silicon on insulator MOSFET are simulated. Results indicate
that this method can be used to simulate the 2D QM effects in semiconductor
devices including tunnelling effect.

Under an external uniform electric field, the dielectric response of graded
cylindrical composites having generalized dielectric profile inclusions is
investigated. The generalized dielectric profile of graded cylindrical
inclusion is expressed in the form, $\varepsilon _i (r)=c(b+
r)^k\e^{\beta r}$ where $r$ is the radial variable of the cylindrical
inclusions and
$c$, $b$, $k$ and $\beta $ are parameters. The local potential solution of
generalized dielectric profile graded composites is derived by means of the
power series method and the effective dielectric response is predicted in
the dilute limit. Moreover, from the result of generalized profile, the
analytical solutions of local potentials and the effective responses of
graded composites having three cases of dielectric profiles, i.e., the
exponential profile $\varepsilon_\i (r)=c\e^{\beta r}$, the general power
law profile $\varepsilon_\i (r)=c(b+r)^k$ and the profile $\varepsilon_\i
(r)=cr^k\e^{\beta r}$, are sorted out, respectively. In the dilute limit,
our exact results are used to test the validity of differential effective
dipole approximation (DEDA) for estimating the effective response of graded
cylindrical composites, and it is shown that the DEDA is in excellent
agreement with the exact result.

Based on a tight-binding disordered model describing a single electron band,
we establish a direct current (dc) electronic hopping transport conductance
model of one-dimensional diagonal disordered systems, and also derive a dc
conductance formula. By calculating the dc conductivity, the relationships
between electric field and conductivity and between temperature and
conductivity are analysed, and the role played by the degree
of disorder in electronic
transport is studied. The results indicate the conductivity of systems
decreasing with the increase of the degree of disorder, characteristics of
negative differential dependence of resistance on temperature at low
temperatures in diagonal disordered systems, and the conductivity of systems
decreasing with the increase of electric field, featuring the non-Ohm's law
conductivity.

N and P-channel groove-gate MOSFETs based on a self-aligned CMOS process
have been fabricated and characterized. For the devices with channel length
of 140nm, the measured drain induced barrier lowering (DIBL) was 66mV/V for
n-MOSFETs and 82mV/V for p-MOSFETs. The substrate current of a groove-gate
n-MOSFET was 150 times less than that of a conventional planar n-MOSFET.
These results demonstrate that groove-gate MOSFETs have excellent
capabilities in suppressing short-channel effects. It is worth emphasizing
that our groove-gate MOSFET devices are fabricated by using a simple process
flow, with the potential of fabricating devices in the sub-100nm range.

High-quality oxide semiconductor ZnO thin films were prepared on
single-crystal sapphire and LaAlO$_{3}$ substrates by pulsed laser
deposition (PLD) in the mixture gas of hydrogen and argon. Low resistivity
n-type ZnO thin films with smoother surface were achieved by
deposition at 600$^\circ$C in 1Pa of the mixture gas. In addition,
ferromagnetism was observed
in Co-doped ZnO thin films and rectification $I-V$ curves were found in
p-GaN/n-ZnO and p-CdTe/n-ZnO heterostructure junctions. The
results indicated
that using mixture gas of hydrogen and argon in PLD technique was a flexible
method for depositing high-quality n-type oxide semiconductor films,
especially for the multilayer thin film devices.

In this paper, an exciton trapped by a Gaussian confining potential quantum
dot has been investigated. Calculations are made by using the method of
numerical diagonalization of Hamiltonian in the effective-mass
approximation. The dependences of binding energies of the ground state and
the first excited state on the size of the confining potential and the
strength of the magnetic field are analysed explicitly.

Novel oxyfluoride glasses are developed with the composition of 30SiO_{2},-15Al_{2},O_{3},-28PbF_{2},-22CdF_{2},-0.1TmF_{3},-xYbF_{3},-(4.9-x) AlF_{3},(x=0, 0.5, 1.0, 1.5, 2.0) in mol fraction. Furthermore, the upconversion luminescence characteristics under a 970nm excitation are investigated. Intense blue, red and near infrared luminescences peaked at 453nm, 476nm, 647nm and 789nm, which correspond to
the transitions of Tm_{3},: ^{1},D_{2}, \to ^{3}F_{4},,
^{1}G_{4} \to ^{3}H_{6}, ^{1}G_{4} \to ^{3}F_{4}, and ^{3}H_{4} \to ^{3}H_{6}, respectively, are observed. Due to the sensitization of Yb^{3+} ions, all the upconversion luminescence intensities are enhanced considerably with Yb^{3+} concentration increasing. The upconversion mechanisms are discussed based on the energy matching rule and quadratic dependence on excitation power. The results indicate that the dominant mechanism is the excited state absorption for those upconversion emissions.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

The melting curve of MgSiO_{3} perovskite is simulated using molecular
dynamics simulations method at high pressure. It is shown that the simulated
equation of state of MgSiO_{3} perovskite is very successful in
reproducing accurately the experimental data. The pressure dependence of the
simulated melting temperature of MgSiO_{3} perovskite reproduces the
stability of the orthorhombic perovskite phase up to high pressure of
130GPa at ambient temperature, consistent with the theoretical data of
the other
calculations. It is shown that its transformation to the cubic phase
and melting at high pressure and high temperature are in agreement
with recent experiments.

Along the geodesic we calculate the interference phase of the mass neutrinos
propagating in the radial direction in Robertson--Walker space--time. Since
our universe is expanding, the phase factor Ph is increasing under the
condition of the same proper physical distance l. Different values of
curvature parameter k in Robertson--Walker metric represent different
cosmological models, correspondingly, we obtain the different interference
phases.

The interesting phenomenon of frame dragging which is associated with the
rotation of the source in the field of Kerr family is discussed, and
the angular velocity of an uncharged test particle is obtained
with a straightforward mathematical method.

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining field-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.

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