In this paper, an optimal filter for a stochastic linear system with previous stage noise correlation is designed. Based on this result, together with the decomposition techniques of the stochastic singular linear system, the design of an optimal filter for a stochastic singular linear system is given.

The stability of the shapes of the growing crystal face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. Effects of the interface kinetics and anisotropy of crystallization and dissolution on the stability are also studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are of suitably shaped curves with their upper parts inclined backward properly no matter whether the interface kinetics and the anisotropy are taken into account or not. The stable shapes of the growing crystal faces and dissolution faces are calculated for various cases. The interface kinetics will make the inclination degree of stable crystal growth face reduce and that of stable dissolution face reduce slightly. The anisotropy of crystallization and dissolution may make the inclination degree of stable-growing crystal face smaller or larger, and that of the stable dissolution face varies very slightly.

In this paper, we have numerically solved the multi-fluid problems using an operator-split two-step high-resolution Godunov PPM (parabolic piecewise method) for the flow in complex geometries. By using the front capturing method, the PPM integrator captures the interface in the solution process. The basic multi-fluid integrator is coupled to a Cartesian grid algorithm where a VOF (volume of fluid) representation of the fluid interface is also used. As an application of this method, we test the 2D interfacial advection example and simulate an experimental hypervelocity launcher model from Sandia National Laboratories. The computational design of the hypervelocity launcher is also given in the paper.

Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.

Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate pattern-forming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

In this paper, we present a scheme to prepare a set of the multi-atom entangled states by the cavity quantum electrodynamics (QED) technology. The multi-atom entangled states have some particular entanglement properties. For example, the remaining reduced density matrices ρ_{ij} still retain entanglement or disentanglement when any N-2 atoms of the N atoms are traced out, which can be chosen freely according to our need, and the relative entanglement strength of any pair of atoms (measured by the concurrence) can be arbitrarily adjusted. In addition, they may be completely symmetric under the exchange of any two atoms, and perform certain quantum information tasks, such as telecloning, teleportation, secret sharing and so on.

We examine the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime. We derive the conditions on which the energy density can be negative. We then show that the energy density satisfies two quantum inequalities in the ultrarelativistic limit.

In light of the interference experiment of Bose－Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose－Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas－Fermi model.

Chessboard-like substrates are introduced in this paper, in order to study the diffusion-limited aggregation (DLA) and the motion of poly-atoms on heterogeneous surfaces. The effect of morphology of such substrates upon the cluster aggregation is investigated using the Monte Carlo simulation. It is found that the growth process and the cluster morphology are governed by the energetic topography of the substrates. Our simulation also indicate that the island density and the fractal dimension of the clusters depend strongly on the substrate topography and the activation energy.

Positive Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially. In this paper, we propose the modified version of the support vector machines (SVM) to deal with this problem. Based on recurrent least squares support vector machines (RLS-SVM), we introduce a weighted term to the cost function to compensate the prediction errors resulting from the positive global Lyapunov exponents. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to the Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.

Density functional method (DFT) (B3p86) of Gaussian98 has been used to optimize the structure of the Tc_2 molecule. The result shows that the ground state for Tc_2 molecule is an 11-multiple state and its electronic configuration is {}^{11}Σ_g^-, which shows the spin polarization effect of Tc_2 molecule of a transition metal element for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher energy states. So, that the ground state for Tc_2 molecule is an 11-multiple state is indicative of the spin polarization effect of Tc_2 molecule of a transition metal element: that is, there exist 10 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Tc_2 molecule is minimized. It can be concluded that the effect of parallel spin of the Tc_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 {}^{11}Σ_g^- and other states of Tc_2 molecule are derived. Dissociation energy D_e for the ground state of T_{c2} molecule is 2.266eV, equilibrium bond length R_e is 0.2841nm, vibration frequency ω_e is 178.52cm^{-1}. Its force constants f_2, f_3, and f_4 are 0.9200aJ·nm^{-2}, --3.5700aJ·nm^{-3}, 11.2748aJ·nm^{-4} respectively. The other spectroscopic data for the ground state of Tc_2 molecule ω_eχ_e, B_e, α_e are 0.5523cm^{-1}, 0.0426cm^{-1}, 1.6331×10^{-4}cm^{-1} respectively.

It is found that the two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders, and the degree of higher-order squeezing is greater than that of the second-order. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in two-mode squeezed states are presented for the first time. The product of higher-order noise moments is related to even order number N and the squeeze factor r.

A detailed study of the spectrum of partially coherent beams diffracted at an astigmatic aperture lens is performed. Considerable attention is paid to the effect of astigmatism on spectral switches of polychromatic Gaussian Schell-model beams. It is shown that the spectral switch can also take place in the vicinity of intensity minimum in a geometrical focal plane for the astigmatic case, but the astigmatism of the lens and the spatial correlation of the beam affect the critical position u_c, spectral minimum S_{min}, and transition height Δ of spectral switches.

The univalent calcium and strontium ions have been confirmed as ideal lasing substances both for self-terminating laser and recombination laser by theoretically analysing their energy level structures and lasing mechanisms. With the optimization of the excitation circuit and the improvement of the laser cavity as well as the laser discharge tube, the alternate laser oscillations of the two laser mechanisms were successfully realized by longitudinal pulsed discharge in mixture vapours of helium and univalent ions of calcium or strontium, respectively. The dependences of laser performance on working parameters, together with the characteristics of the photoelectric pulse waveforms were elementally studied and analysed.

We investigate the modulation instability of quasi-plane-wave optical beams in biased photorefractive－photovoltaic crystals by globally treating the space-charge field. The modulation instability growth rate is obtained, which depends on the external bias field, on the bulk photovoltaic effect, and on the ratio of the optical beam's intensity to that of the dark irradiance. Our analysis indicates that this modulation instability growth rate is identical to the modulation instability growth rate studied previously in biased photorefractive－nonphotovoltaic crystals when the bulk photovoltaic effect is negligible for shorted circuits, and predicts the modulation instability growth rate in open- and closed-circuit photorefractive－photovoltaic crystals when the external bias field is absent.

We present two numerical approaches to calculate the geometrical birefringence from two-dimensional refractive-index profile in single-mode fibres. One is the improved perturbation model theory, the other is based on the general solution of noncircular uniform optical waveguide in an arbitrary coordinate system. Using these methods, we can obtain not only the magnitude of geometrical birefringence, but also the orientation of birefringent axes. We report the calculation results of geometrical birefringence in a real single-mode fibre.

A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wave in Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rate agree with theoretical results very well.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The temporal intermittency of the fluctuation-driven particle transport fluxes is analysed by using data obtained from Langmuir probe array in the edge of the Sino-United Spherical Tokamak (SUNIST). The conditional statistics analysis indicates that the intermittent structures have a characteristic time width of about 30μs, which is the typical fluctuation time scaling. It is also found that the transport fluxes have a multifractal character over the fluctuation time scales, and exhibit a long-time-range correlation character with self-similar parameter H>0.5 in the plasma confinement time scales. Furthermore, the analyses show that the level of the intermittency and the long-range correlation of the fluxes vary with increasing plasma density. These observations are consistent with the prediction of the avalanche-like model.

Dependence of the bootstrap current fraction of spherical torus plasma on the aspect ratio and the triangular deformation is studied by using a simple equilibrium model, the Solov'ev-type equilibrium. Two bootstrap current models are used: one is the single-ion collisionless regime model, the other is the recently developed arbitrary collisional regime model. It is found that besides the well known favourable effect of the small aspect ratio on the enhancement of the bootstrap current fraction, the triangularity is beneficial for raising the total bootstrap current though it does not change its fraction much.

Basic shock phenomena are presented in a composite pinch, a hybrid of the Z-pinch. The successive transfer of current within the plasma structure is demonstrated by our calculations. Properties of the shock wave are described. The current distribution between the two shells after the outer shell hitting the inner shell is also discussed.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The thermal conductivity of GaAs/AlAs superlattices limited by the three-phonon Umklapp process and boundary scattering has been studied theoretically based on the model of lattice dynamics with force constant matrix. It was found that the Umklapp relaxation rate approximates BTω^2/n with a fitting parameter B. The thermal conductivity increases with the increase of temperature at low temperatures, and would show a peak behaviour at about 60K before falling off at high temperatures. In addition, the thermal conductivity increases with the increase of period thickness of the superlattices.

A simulation of the growth of an obliquely deposited thin film in a three-dimensional lattice was made using kinetic Monte Carlo method. Cu growth in three dimensions on a (001) substrate with high deposition rates has been simulated in this model. We mainly investigated the variation of three-dimensional morphology and microstructure of films with incidence angle of sputtered flux. The relation of roughness and densities of films with incidence angle was also investigated. The simulation results show that the surface roughness increases and the relative density of thin film decreases with increasing incidence angle, respectively; the columnar structures were separated by void regions for large incidence angle and high deposition rate. The simulation results are in good agreement with experimental results. However, the orientation angle of columns is not completely consistent with the classical tangent rule.

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

This paper presents the results of the self-consistent calculations on the electronic structure of anatase phase of TiO_2. The calculations were performed using the full potential-linearized augmented plane wave method (FP-LAPW) in the framework of the density functional theory (DFT) with the generalized gradient approximation (GGA). The fully optimized structure, obtained by minimizing the total energy and atomic forces, is in good agreement with experiment. We also calculated the band structure and the density of states. In particular, the calculated band structure prefers an indirect transition between valence and conduction bands of anatase TiO_2, which may be helpful for clarifying the ambiguity in other theoretical works.

We have studied the band structure and optical properties of 4H-SiC by using a full potential linearized augmented plane waves (FPLAPW) method. The density of states (DOS) and band structure are presented. The imaginary part of the dielectric function has been obtained directly from the band structure calculation. With band gap correction, the real part of the dielectric function has been derived from the imaginary part by the Kramers－Kronig (KK) dispersion relationship. The values of reflectivity for normal incidence as a function of photon energy have also been calculated. We found the theoretical results are in good agreement with the experimental data.

The specific heat and resistance of CeCu_{6-x}M_x (M=Ni,Zn) have been studied in the concentration range where they still retain the orthorhombic structure. The coefficient c of -ln T term in resistance R=R_0+bT-cln T, as well as the γ, have been found to vary in opposite directions with increasing x for Ni and Zn substitutions. The physical mechanism is discussed.

Within the framework of effective mass approximation, the ground state of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles is solved by using the stochastic variational method, in which the finite band offset and the heavy (light) hole exciton states are considered. The calculated 1s_e－1s_h transition energies for the chosen CdS/HgS/CdS QDQW samples are in good agreement with the experimental measurements. Moreover, some previous theoretical results are improved.

The quantum confined Stark effect (QCSE) of the self-assembled InAs/GaAs quantum dots has been investigated theoretically. The ground-state transition energies for quantum dots in the shape of a cube, pyramid or "truncated pyramid" are calculated and analysed. We use a method based on the Green function technique for calculating the strain in quantum dots and an efficient plane-wave envelope-function technique to determine the ground-state electronic structure of them with different shapes. The symmetry of quantum dots is broken by the effect of strain. So the properties of carriers show different behaviours from the traditional quantum device. Based on these results, we also calculate permanent built-in dipole moments and compare them with recent experimental data. Our results demonstrate that the measured Stark effect in self-assembled InAs/GaAs quantum dot structures can be explained by including linear grading.

A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.

2.0nmCo/tnmRu_{1-x}Pd_x multilayers with x=0, 0.05, 0.08, 0.24, 0.39 and 0.48 were prepared by magnetron sputtering. The spacer layer thickness of both Ru (before doping Pd) and RuPd (after doping Pd) varies from 0.2nm to 1.6nm. Two effects have been investigated: (1) the dependence of the interlayer coupling on the thickness of Ru_{1-x}Pd_x as a function of x and (2) the dependence of the interlayer coupling on Pd doping density, x, as a function of thickness of Ru_{1-x}Pd_x. Our results indicate that the interlayer coupling is strongly dependent on the doping density and the spacer layer thickness. The saturation field H_s increases when very low concentration of Pd doped in the Ru layers and a suitable spacer thickness are adopted.

Magnetic properties and crystal symmetry of electrochemical material LiFePO_{4} have been investigated by M?ssbauer spectroscopy and magnetization measurement. Magnetization reveals the antiferromagnetic nature of LiFePO_{4}. Temperature dependence of inverse susceptibility and that of hyperfine field confirm that there is an antiferromagnetic-paramagnetic transition at about 50K.

A tellurite fibre of TeO_{2}－ZnO－La_{2}O_{3}－Li_{2}O glass codoped with 20000 ppm ytterbium and 5000 ppm erbium was fabricated by the suction casting and rod-in-tube technologies. The absorption spectrum of Er^{3+}/Yb^{3+} -codoped bulk glass has been measured. From the Judd－Ofelt intensity parameters, the spontaneous emission probability and radiative lifetime τ_{rad} of Er^{3+}:{}^{4}I_{13/2}→{}^{4}I_{15/2} transition for the bulk glass have been calculated. The emission fluorescence spectra and lifetimes around 1.5μm, and subsequent upconversion fluorescence in the range of 500－700nm were measured in fibres and compared with those in bulk glass. The changes in amplified spontaneous emission with fibre length and pumping power was also measured. It was found that the emission spectrum from erbium in fibres is almost twice as broad as the corresponding spectrum in bulk glass when pumped at 980nm.

The Raman shifts of nanocrystalline GaSb excited by an Ar^{+} ion laser at wavelengths 514.5, 496.5, 488.0, 476.5, and 457.9nm are studied by an SPEX-1403 laser Raman spectrometer respectively, and they are explained by phonon confinement, tensile stress, resonant Raman scattering and quantum size effects. The Stokes and anti-Stokes Raman spectra of GaSb nanocrystals strongly support the Raman feature of GaSb nanocrystals. The calculated optical spectra compare well with experimental data on Raman scattering GaSb nanocrystals.

A model is built to study chemical processes in atmospheric plasmas at low altitude (high pressure) and at high altitude (low pressure). The plasma lifetime and the temporal evolution of the main charged species are presented. The electron number density does not strictly obey the exponential damping law in a long period. The heavy charged species are dominant at low altitude in comparison with the light species at high altitude. Some species of small amount in natural air play an important role in the processes.

For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.

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