Simple lattice Boltzmann model for traffic flows

A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

连续型联想细胞神经网络局部指数稳定性研究

由于细胞神经网络的潜在应用前景 ,它现已成为神经网络研究的新热点。首先给出连续型联想细胞神经网络的数学模型 ,得到了连续型细胞神经网络平衡点局部指数稳定的充要条件及平衡点指数吸引域的估计 ,研究表明对平衡点的指数吸引域的估计 ,只要计算平衡点处的导算子矩阵的对数范数即可。该研究对连续型联想细胞神经网络的设计和应用均有重要的作用。

水下滑翔机器人运动机理仿真与实验

对水下滑翔机器人SEA-WING的定常滑翔运动和空间定常螺旋回转运动进行机理分析,针对其特定水动力系数进行仿真,得出其运动机理特性。在此基础上,通过湖试实验数据对仿真结果进行验证,认为对于定常滑翔运动,以约36°航迹角滑行可得到最大水平速度;在相同航迹角航行情况下,水平方向速度随净浮力的增大而增大。对于定常回转运动,回转半径由载体的质量、俯仰角、水动力参数、横滚角确定。在质量和俯仰角保持不变条件下,横滚角对回转半径的影响较明显,系统的回转半径可以通过控制横滚角来实现的。

粘弹性介质中的地震波传播与波形反演研究

The real earth is far away from an ideal elastic ball. The movement of structures or fluid and scattering of thin-layer would inevitably affect seismic wave propagation, which is demonstrated mainly as energy nongeometrical attenuation. Today, most of theoretical researches and applications take the assumption that all media studied are fully elastic. Ignoring the viscoelastic property would, in some circumstances, lead to amplitude and phase distortion, which will indirectly affect extraction of traveltime and waveform we use in imaging and inversion. In order to investigate the response of seismic wave propagation and improve the imaging and inversion quality in complex media, we need not only consider into attenuation of the real media but also implement it by means of efficient numerical methods and imaging techniques. As for numerical modeling, most widely used methods, such as finite difference, finite element and pseudospectral algorithms, have difficulty in dealing with problem of simultaneously improving accuracy and efficiency in computation. To partially overcome this difficulty, this paper devises a matrix differentiator method and an optimal convolutional differentiator method based on staggered-grid Fourier pseudospectral differentiation, and a staggered-grid optimal Shannon singular kernel convolutional differentiator by function distribution theory, which then are used to study seismic wave propagation in viscoelastic media. Results through comparisons and accuracy analysis demonstrate that optimal convolutional differentiator methods can solve well the incompatibility between accuracy and efficiency, and are almost twice more accurate than the same-length finite difference. They can efficiently reduce dispersion and provide high-precision waveform data. On the basis of frequency-domain wavefield modeling, we discuss how to directly solve linear equations and point out that when compared to the time-domain methods, frequency-domain methods would be more convenient to handle the multi-source problem and be much easier to incorporate medium attenuation. We also prove the equivalence of the time- and frequency-domain methods by using numerical tests when assumptions with non-relaxation modulus and quality factor are made, and analyze the reason that causes waveform difference. In frequency-domain waveform inversion, experiments have been conducted with transmission, crosshole and reflection data. By using the relation between media scales and characteristic frequencies, we analyze the capacity of the frequency-domain sequential inversion method in anti-noising and dealing with non-uniqueness of nonlinear optimization. In crosshole experiments, we find the main sources of inversion error and figure out how incorrect quality factor would affect inverted results. When dealing with surface reflection data, several frequencies have been chosen with optimal frequency selection strategy, with which we use to carry out sequential and simultaneous inversions to verify how important low frequency data are to the inverted results and the functionality of simultaneous inversion in anti-noising. Finally, I come with some conclusions about the whole work I have done in this dissertation and discuss detailly the existing and would-be problems in it. I also point out the possible directions and theories we should go and deepen, which, to some extent, would provide a helpful reference to researchers who are interested in seismic wave propagation and imaging in complex media.

矾山杂岩体成因及其与磷（铁）矿的成矿关系

The Fanshan complex consists of layered potassic ultramafic-syenite intrusions. The Fanshan apatite (-magnetite) deposit occurs in the Fanshan complex, and is an important style of phosphorus deposit in China. The Fanshan complex consists of three (First- to Third-) Phases of intrusion, and then the dikes. The First-Phase Intrusive contains ten typical layered rocks: clinopyroxenite, biotite clinopyroxenite, coarse-grained biotite clinopyroxenite, pegmatitic orthoclase-biotite clinopyroxenite, variegated orthoclase clinopyroxenite, interstitial orthoclase clinopyroxenite, biotite rock, biotite-apatite rock, biotite rock and magnetite-apatite rock. This layered intrusive consists of nine rhythmic units. Each rhythmic unit essentially comprises a pair of layers: clinopyroxenite at the bottom and biotite clinopyroxenite at the top. The apatite (-magnetite) deposit is situated near the top of rhythmic Unit no. 6 of the First-Phase Intrusive. The Second-Phase Intrusive contains three typical rocks: coarse-grained orthoclase clinopyroxenite, . coarse-grained salite syenite and schorlomite-salite syenite. The Third-Phase Intrusive includes pseudo-trachytic salite syenite, porphyritic augite syenite, fine-grained orthoclase clinopyroxenite and fine-grained salite syenite. The origin of the Fanshan complex is always paid attention to it in China. Because most layered igneous intrusion in the world not only have important deposit in it, but also carry many useful information for studying the formation of the intrusion and the evolvement of magma. Two sketch maps were drawn through orebodies along no. 25 cross-cut on 425 mL and no. 1 cross-cut on 491 mL in the Fanshan mine. Through this mapping, a small-scaled rhythmic layering (called sub-rhythmic layering in the present study) was newly found at the top of the rhythmic Unit no. 6. The concept of sub-rhythmic layering is defined in this article. The sub-rhythmic layering is recognized throughout this apatite-rich part, except for magnetite-apatite rock. Presence of the layered magnetite-apatite rock is one of the characteristics of the Fanshan apatite (-magnetite) deposit. Thus, from this layer downwards six units of sub-rhythmic layering are recognized in the present study. Each unit consists of biotite clinopyroxenite (or biotite rock and biotite-apatite rock) layer at the bottom and apatite rock layer at the top. To study this feature in detail is an important work for understanding the origin of the Fanshan complex and apatite (-magnetite) deposit. The origin of the Fanshan complex and the relation of the formation of the apatite(-magnetite)deposit will be interpreted by the study of sub-rhythmic layering on the basis of previous research works. The magma formed the Fanshan complex was rich in K2O, early crystallized pyroxene, and after this phase more biotite crystallized, but no amphibole appeared. This indicated that the activity of H2O in the magma was low. Major element compositions of biotite and clinopyroxene (on thin sections) in the sub-rhythmic layering were analyzed using electron microprobe analyzer. The analytical results indicate Mg/(Mg+Fe*+Mn) atomic ratios (Fe*, total iron) of these two minerals rhythmically changed in sub-rhythmic layering. The trends of Mg/(Mg+Fe*+Mn) atomic ratio (Fe*, total iron) of biotite and clinopyroxene indicate that the magma evolved markedly from relatively magnesian bottom layer to less magnesian top layer in each sub-rhythmic unit. A general trend through the sub-rhythmic layering sequence is both minerals becoming relatively magnesian upwards. The formation temperatures for sub-rhythmic layering yield values between 600 and 800 ℃, were calculated using the ratio of Mg/(Mg+Fe+Mn) in the salite and biotite assemblage. The equilibrium pressures in the rhythmic layers calculated using the contents of Al in the salite were plotted in the section map, shown a concave curve. This indicates that the magma formed the First-Phase Intrusive crystallized by two vis-a-vis ways, from its bottom and top to its centre, and the magnetite-apatite rock was crytallized in the latest stage. The values of equilibrium pressures in the sub-rhythmic layering were 3.6-6.8(xlO8) Pa with calculated using the contents of Al in the salite. The characteristics of geochemistry in various intrusive rocks and the rocks or apatite of sub-rhythmic layers indicated that the Fanshan complex formed by the comagmatic crystallization. The contents of immiscible elements and REEs of apatite rock at the top of one sub-rhythmic unit are more than biotite clinopyroxenite at the bottom. The contents of immiscible elements and REEs of apatite of biotite clinopyroxenite at the bottom of one sub-rhythmic unit are higher than apatite rock at the top. The curves of rocks (or apatite) in the upper sub-rhythmic units are between two curves of the below sub-rhythmic unit in the primitive mantle-normalized trace element abundance spider diagram and the primitive mantle-normalized REE pattern. The trend for the contents of immiscible elements and REEs inclines to the same contents from the bottom to the top in sub-rhythmic layering. These characteristics of geochemistry of rocks or apatites from sub-rhythmic layering indicate that the latter sub-rhythmic unit was produced by the residual magma after crystallization of the previous sub-rhythmic unit. The characteristics of petrology, petrochemistry, geochemistry in the Fanshan complex and sub-rhythmic layers and the trends of Mg/(Mg+Fe+Mn) atomic ratio of biotite and clinopyroxene in sub-rhytmic layering rejected the hypotheses, such as magma immiscibility, ravitational settling and multiple and pulse supplement of magma. The hypothesis of differentiation by crystallization lacks of evidences of field and excludes by this study. On the base of the trends of formation temperatures and pressures, the characteristics of petrology, petrochemistry, geochemistry for the Fanshan complex and the characteristics of geochemistry for the rocks (or apatites), the trends of Mg/(Mg+Fe+Mn) atomic ratio of biotite and clinopyroxene in sub-rhytmic layering, and the data of oxygen, hydrogen, strontium and neodymium isotopes, this study suggests that the magma formed the Fanshan complex was formed by low degree partial melting of mantle at a low activity of H2O, and went through the differentiation at the depth of mantle, then multiply intruded and crystallized. The rhythmic layers of the First-Phase Intrusive formed by the magma fractional crystallized in two vis-a-vis ways, from the bottom and top to the centre in-situ fractional crystallization. The apatite (-magnetite) deposit of the Fanshan complex occurs in sub-rhythmic layering sequence. The the origin of the sub-rhythmic layering is substantially the origin of the Fanshan apatite (-magnetite) deposit. The magma formed the rhythmic layers of First-Phase Intrusive was rich in H2O, F and P at the later stage of its in-situ fractional crystallization. The Fanshan apatite (-magnetite) deposit was formed by this residual magma in-situ fractional crystallization. The magnetite-apatite rock was crystallized by two vis-a-vis ways at the latest stage in-situ fractional crystallization in the rhythmic layers. The result was light apatite layer below heavy the magnetite-apatite layer, formed an "inversion" phenomenon.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

Analysis of Instabilities in Non-Equilibrium Plasmas

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by 6rst-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in Plasma, the electron attachment rate coefficient and electron temperature) are described.

Equilibrium of isolated magnetostatic flux structure

Two-dimensional magnetostatic models of flux structure confined in stratified atmosphere are discussed in the present paper. The magnetic field in the flux structure is assumed to be force-free at the first step. Numerical solutions for this nonlinear free boundary problem are obtained by finite element method. Results show clearly the relation between the inside fields and outside pressure, especially the influence of atmospheric pressure distribution on the flux structure.

Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

Magnetostatic equilibrium of isolated magnetic-flux tube

In the present paper, an isolated axisymmetric flux tube is discussed for slender magnetic configuration. The magnetostatic model and the stratified atmospheric model are applied, respectively, to the regions inside and outside the flux tube. The problem is described mathematically by the nonlinear partial differential equations under the nonlinear boundary condition at the free boundary of flux tube. According to the approximation of a small expansive angle, the solutions of series expressions are obtained formally. The model of polytropic plasma is discussed in detail especially. The results show the distributions of thermodynamic quantities and magnetic field extending from the high β region to the low β region, and the flux tube may be either divergent or convergent according to the pressure difference outside and inside the flux tube.

Magnetohydrodynamic equilibrium of plasma ball lightning

Thin foil observations using transmission electron microscopy reveal that the density of dislocations within the band is extremely high and the tangled arrangement of dislocations tends to align along the length of the shear band. The grains in the band were also elongated along the shear band and clearly exhibited a crystallographic nature.

Non-axisymmetric magnetostatic equilibrium with strong twisted component of magnetic field

The perturbation theory is applied further to the discussion of the equilibrium properties of a sunspot-like magnetic field with a strong twisted component. The basic state reduces to the usual one discussed extensively for the axisymmetric magnetostatic equilibrium with twisted component of magnetic field, and the perturbed state is described by two coupled equations. As the magnetic force-line is twisted, there is a magnetic tension in the azimuthal direction. In this case, the perturbed total pressure is no longer independent of the azimuthal variable θ, and the magnetic field in the dark penumbal fibril may be either stronger or weaker relatively.

The magnetohydrostatic equilibrium of horizontal prominence of torus configuration

There are several examples of horizontal ringlike prominences in the observations of Ha monochromatic image of the sun. In the present paper the statie equilibrium of the plasma loop is discussed. The analytic solutions to magnetic field and density are obtained for the axisymmetrie case under the closed boundary condition. Results show the great influence of the gravity and different force-free factors on the configurations of magnetic surfaces and the distributions of thermodynamical quantities for the prominence.