海南岛清澜-八门湾潟湖潮汐水动力的模拟研究

基于DELFT3D模型研究了清澜-八门湾潟湖的水位分布和潮汐波内部结构,以及由于人类开垦引起的海岸线变化(以1962年、1985年和2008年为例)对潟湖水动力特性的影响。结果表明,清澜-八门湾潟湖潮汐是由多种分潮耦合而成的复杂驻波,其中K_1,O_1,M_2,S_2和M_4分潮的影响最大。由湾外向湾内传输,由于湾内红树林和浅滩引起的底部损耗增加,M_2,S_2,K_1和O_1分潮幅值减弱;M_4分潮幅值增强,表现出明显的浅水增幅效应;M_2和S_2分潮相位在文教河和文昌江领域表现出明显的干湿效应。不同年代海岸线的研究表明,1985年和2008年间,人类复垦导致潟湖及其潮汐汊道附近的红树林和滩涂区域严重破坏,海岸线缩减,引发了水位降低、纳潮量减少和潟湖潮汐汊道底摩擦弱化,从而削弱了干湿、潮呛和浅水效应。后果提示持续的人类复垦活动将会引发清澜-八门湾潮汐水动力环境的进一步恶化,可能导致未来发生更大的自然灾害。     

The strain energy criterion of mixed-mode brittle fracture

In this paper, we proposed a new cr tenon or mixea-moae brittle fracture, i.e., the strain energy criterion, which can be stated as (K_Ⅰ/K_Ⅰc)² +(K_Ⅰ/K_Ⅰc)²+(K_Ⅱ/K_Ⅱc)²=1. This criterion is shown to be in good agreement with known experimental data.In this paper, an experimental criterion:(K_Ⅰ/K_Ⅰc)^m+(K_Ⅱ/K_Ⅱc)ⁿ=1, 1≤_n^m≤2.is also proposed.     

Fixed point theorem of nonexpansive mappings in convex metric spaces

Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:d(T_x,T_y)≤ad(x,t)+b{d(x,T_x)+d(y,T_y)}+c{d(x,T_x)+d(y,T_y)}for all x,y in K,where 0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1, then T has a unique fixed point in K.     

近源堆沉积土石体细观结构与抗剪强度指标关联分析

细观结构是认知土石体力学行为本质的关键科学问题。本文通过引入物理学和数学等方法,借助颗粒物质力学理论,从几何排列与接触力的空间分布来定量刻画水平固结与山前坡地堆积两种典型环境下土石体的细观结构特征,并建立其与抗剪强度指标的关联。研究表明,（1）两种环境的土石体在细观结构上存在较大差异。在几何排列上,水平固结环境下的土石体具有长程无序和短程有序的特点,坡地堆沉积环境下的土石体表现出了无序的无定形结构;在接触力与单位接触向量的空间分布上,两者较为相似,绝大多数接触力以小于均值接触力的形式存在,其概率密度曲线P（f）呈幂函数衰减;90%以上接触方位角集中在40°~160°和220°~340°范围内。（2）基于径向分布函数、接触力概率密度和单位接触向量分别定义细观结构的特征量K_a,K_s和K_o,发现三个特征量的增大对内摩擦角呈线性促进作用,对黏聚力呈非线性削弱作用。     

The analytical solution for Helmholtz boundary problem in non-horizontally stratified domains

There are N domains D_j(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces S_j,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:V²H⁽¹⁾+K_jH⁽¹⁾=0 (j=0,1,…,N-1)(H⁽⁰⁾-H⁽¹⁾)=δ(S) (δ(S):generalized function)(H¹-Hⁱ⁺¹)=0 (j=0,1,…,N-2)The analytical solution of the above problem is given in this paper.     

投影方向极值原理的滑裂面应力矢量极限平衡抗滑稳定计算理论

根据有限元成果的滑动面切向应力达到可用极限值的抗滑稳定极限平衡概念,建立投影方向极值原理单元滑面应力矢量极限平衡抗滑稳定计算理论模型,揭示不平衡虚拟耗散力、耗散能和极值条件方程的力学本质联系。根据投影极值方向平衡状态时的垂直方向还存在不平衡耗散力,提出复杂滑裂面极限平衡状态接近程度系数λ及矢量安全度系数K_λ评价抗滑稳定性能的最佳路径。通过边坡考题和坝基深层抗滑稳定算例的势能极值规律存在性和极值点的吻合度,证明了理论模型的合理可靠性。有限元应力矢量理论模型的建立及其安全度系数K_λ是极限平衡抗滑稳定计算理论发展的重要基础理论突破和全新理论研究成果。     

THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

In this paper, we show that Backlund transformation derived by Leibbrandt et al. for the Liouville’s equation in three spatial dimensions, ▽²a=expa, ▽²=-∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville’s equation in N spatial dimensions.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅲ)-BASIC THEORIES

By basic equations, two basic theories are presented: 1. Theory of stock’s value v^*(t)=v^*(0) exp (ar₂^*t);2. Theory of conservation of stock’s energy. Let stock’s energy Φbe defined as a quadratic function of stock’s price v and its derivative v, Φ=Av²+Bv+Cv²+Dv, under the constraint of basic equation, the problem was reduced to a problem of constrained optimization along optimal path. Using Lagrange multiplier and Euler equation of variation method, it can be proved that Φkeeps conservation for any v,v. The application of these equations and theories on judgement and analysis of tendency of stock market are given, and the judgement is checked to be correct by the recorded tendency of Shenzhen and Shanghai stock markets.     

On near-wall hot-wire measurements

A specially constructed hot-wire probe was used to obtain very near-wall velocity measurements in both a fully developed turbulent channel flow and flat plate boundary layer flow. The near-wall hot-wire probe, having been calibrated in a specially constructed laminar flow calibration rig, was used to measure the mean streamwise velocity profile, distributions of streamwise and spanwise intensities of turbulence and turbulence kinetic energy k in the viscous sublayer and beyond; these distributions compare very favorably with available DNS results obtained for channel flow. While low Reynolds number effects were clearly evident for the channel flow, these effects are much less distinct for the boundary layer flow. By assuming the dissipating range of eddy sizes to be statistically isotropic and the validity of Taylor's hypothesis, the dissipation rate ɛ _iso in the very near-wall viscous sublayer region and beyond was determined for both the channel and boundary layer flows. It was found that if the convective velocity U _c in Taylor's hypothesis was assumed to be equal to the mean velocity Uˉ at the point of measurement, the value of (ɛ⁺ _iso)₁ thus obtained agrees well with that of (ɛ ⁺)_DNS for y ⁺ ≥ 80 for channel flow; this suggests the validity of assuming U _c=Uˉ and local isotropy for large values of y ⁺. However, if U _c was assumed to be 10.6u _τ , the value of (ɛ⁺ _iso)₂ thus obtained was found to compare reasonably well with the distribution of (ɛ⁺ _iso)_DNS for y ⁺≤ 15. Received: 31 May 1999/Accepted: 20 December 1999     

Studying the stability of equilibrium solutions in a planar circular restricted four-body problem

The Newtonian circular restricted four-body problem is considered. We obtain nonlinear algebraic equations determining equilibrium solutions in the rotating frame and find six possible equilibrium configurations of the system. Studying the stability of equilibrium solutions, we prove that the radial equilibrium solutions are unstable, while the bisector equilibrium solutions are stable in Lyapunov’s sense if the mass parameter satisfies the conditions μ ∈ (0, μ₀, where μ₀ is a sufficiently small number, and μ ≠ μ_j, j = 1, 2, 3. We also prove that, for μ = μ₁ and μ = μ₃, the resonance conditions of the third order and the fourth order, respectively, are satisfied and, for these values of μ, the bisector equilibrium solutions are unstable and stable in Lyapunov’s sense, respectively. All symbolic and numerical calculations are done with the Mathematica computer algebra system. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 66–82, January–March, 2007.     

The analysis of orthotropic skew bridge slabs

Summary A method is presented for the direct stress analysis of orthotropic skew bridge slabs.The method of analysis employs the Principle of Least Work, in conjunction with the assumption that the stress resultants may be expressed as Fourier series in the chordwise co-ordinate, the coefficients being functions of the spanwise position only. A system of oblique co-ordinates is used to simplify the analysis.Nomenclature O(x, y) system of orthogonal co-ordinates - O(u, v) system of oblique co-ordinates - angle between axes Ou, Ov - , non-dimensional oblique co-ordinates - l oblique span of slab - L right span of slab - c transverse slab width - t slab thickness - r _i c/(2il) - M _x , M _y , M _xy bending and twisting moments per unit length - M _u , M _v , M _uv oblique bending and twisting moments - S _x , S _y shear forces per unit length - normal load intensity - p oblique normal load intensity - E _x , E _y E _xy , G _xy elastic moduli defining stress-strain relationships in orthotropic plates - A _ij strain energy coefficients - F _i , G _i bending moment functions - R _i , S _i twisting moment functions - C ₁, C ₂, C ₃ statical bending and twisting moment constants - D operator d/d - S _u , S _v oblique shear forces per unit length     

Aerodynamic characteristics of a two-dimensional supersonic biplane, covering its take-off to cruise conditions

Supersonic biplanes can possibly achieve low-boom and low-drag supersonic flights. In the present study, aerodynamic analysis and design of two-dimensional (2-D) biplanes were investigated with the help of computational fluid dynamics (CFD) tools. By utilizing an inverse-design method, a 2-D biplane configuration with lower wave drag than the single flat-plate airfoil at sufficient lift conditions (C _l > 0.14) was designed at its design Mach number (M _∞ = 1.7). In general, although, supersonic biplanes show superior aerodynamic characteristics at their design Mach numbers, unfortunately, they are characterized by poor performances under their off-design conditions. Flow choking occurs at high subsonic speeds, and continues to Mach numbers greater than the design Mach number in the acceleration stage due to flow hysteresis. Hinged slats and flaps were applied as high-lift devices to avoid the flow choking and concomitant hysteresis problems, and were also used as actual high-lift devices under take-off and landing conditions. As further improvement, morphing and Fowler motion were considered. Finally, a series of 2-D biplane configurations from take-off (and landing) to cruise conditions were studied by applying the slats and flaps, as well as morphing mechanisms, to our inversely designed biplane.      

The role of instrument compliance in normal force measurements of polymer melts

Schweizer et al. [J Rheol 48(6):1345–1363, 2004] showed nonlinear step shear rate data for a polystyrene melt (M _w=200 kg/mol, M _w/M _n=1.06, T=175°C). For different rheometers, cone angles, and sample sizes, the delayed normal force rise observed therein relative to a compliance-free reference N ₁ (from a thermodynamically consistent reptation model) is shown to depend on rheometer compliance characterized by the instrument stiffness K _A. K _A can be obtained from mapping N ₁ on the measured N _1,meas. or directly from mechanical contact measurement with a mismatch of 20–30%. The ranking of the stiffnesses found is K _A(RMS 800)>K _A(MCR 300)>K _A(ARES LR2). Once K _A is known, N _1,meas.-data can be corrected by solving the ill-posed Volterra equation involved in it. The correction shown for experiments with the 0.15-rad cone angle gives very good results. The characteristic decay time of the normal force after cessation of flow scales linearly with the axial response time t _a calculated from K _A, cone angle, and sample radius. The torque decay time is practically independent of t _a.Extended Version of a paper presented at the 2nd Annual European Rheology Conference in Grenoble, France, April 21–25, 2005.     

Soret effect and slow mass diffusion as a catalyst for overstability in Marangoni-Bénard flows

We study the onset of time dependent Marangoni-Bénard convection in binary mixtures subject to Soret effect by numerical computation of linear instability thresholds in infinite fluid layers and two-dimensional boxes. The calculations are done for positive Marangoni numbers (Ma > 0) and negative Marangoni Soret parameters S _M = –(D _S γ _c )/(Dγ _T ) where D _S and D are the Soret and mass diffusion coefficients, respectively, and γ _T , γ _c are the first derivatives of the surface tension with respect to temperature and concentration. Our purpose is to understand why for particular choices of Prandtl and Schmidt numbers, the increase of the stabilizing solutal contribution leads to a decrease of the critical temperature difference, a phenomenon already reported by Chen & Chen [5] and Skarda et al. [12] For various choices of Prandtl and Schmidt numbers we analyze the evolution of the critical Marangoni number Ma _c , critical wavenumber k _c and angular frequency ω _c with S _M and compute the corresponding eigenvectors. We next propose a physical mechanism which explains how the stabilizing solutal contribution acts as a catalyst for overstability. Finally, we extend our results to two dimensional boxes of small aspect ratio.     

Numerical study of non-uniqueness of the factors influencing relative permeability in heterogeneous porous media by lattice Boltzmann method

The effects of capillary number Ca and viscosity ratio M on non-uniqueness of the relative permeability (RP) – wetting saturation (S_w) relationships of steady-state immiscible two-phase flow in the heterogeneous porous media are studied by a developed lattice Boltzmann method (LBM). In this work, it is suggested that the non-uniqueness of capillary number Ca and viscosity ratio M influencing RP–S_w curves is due to the presence of the heterogeneity of porous media. For the different Ca and M, the RP–S_w curves in the homogenous and heterogeneous porous media with the same porosity are discussed in detail. It is found that (1) the pore-size distributions in porous media have significant effect on the RPs of both wetting phase (WP) and non-wetting phase (NWP); (2) the heterogeneity of porous media has negative effect on the increment of the RP of NWP caused by the large capillary number. The lubricating effect is strongly dependent on pore-size distributions in porous media; and (3) the large viscosity ratio increases the RP of NWP, while it has little effect on the RP of WP. The effect on the RP of NWP may be magnified by the heterogeneity of porous media.     

Effects of magnetic field,porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions T _t and T _θ , respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also, the effects of the stenosis shape m, the constant of permeability X, the Hartmann number H _α and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery. Further, the wall shear stress distribution increases with increasing T _t and γ while decreases with increasing T _θ , M, C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed) is smaller than those in a tethered tube.     

Out-of-plane deflections of metallic and composite pin-loaded coupons

The projection shadow moiré technique was employed to determine an out-of-plane contouring history of aluminum, [(+45/–45)]_3S , [(0/90₃,0] _S and [(0/90/+45/–45)]_2S fiberglass epoxy pin-loaded specimens experimentally. The contouring interval was limited to 0.0254 mm by experimental concerns. Qualification of the projection shadow moiré optical arrangement was initially accomplished by the out-of-plane contouring of a clamped, centrally loaded, circular aluminum plate. Experimental results indicate significant out-of-plane displacements in the bearing region of the coupon at load levels well below ultimate. Effects of material anisotropy could be seen in the fiber-oriented shape of the displacement contours. Comparisons with three-dimensional finite-element results indicate that experimental out-of-plane contours were significantly larger than their finite-element counterparts in the region above the pin for the [(+45/–45)]_3S , [(0/90)₃, 0] _S laminates. These deviations increased with increasing pin-load level. These variations could be attributed to linear-elastic through-thickness moduli assumptions as well as through-thickness finite-element mesh coarseness.     

Parameter estimation for a three‐dimensional numerical barotropic tidal model with adjoint method

The parameters of a three‐dimensional (3‐D) barotropic tidal model are estimated using the adjoint method. The mode splitting technique is employed in both forward and adjoint models. In the external mode, the alternating direction implicit method is used to discretize the two‐dimensional depth‐averaged equations and a semi‐implicit scheme is used for the 3‐D internal mode computations. In this model the bottom friction is expressed in terms of bottom velocity which is different from the previous works. Besides, the bottom friction coefficients (BFCs) are supposed to be spatially varying, i.e. the BFC at some grid points are selected as the independent BFC, while the BFC at the other grid points can be obtained through linear interpolation with these independent BFCs. On the basis of the simulation of M₂ tide in the Bohai and North Yellow Seas (BNYS), twin experiments are carried out to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of open boundary conditions (OBCs), the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The ‘observations’ are produced by the tidal model and recorded at the position of TOPEX/Poseidon altimeter data, tidal gauge data and current data. The experiments discuss the influence of initial guesses, model errors and data number. The inversion has obtained satisfactory results and the prescribed distributions have been successfully inverted. The results indicate that the inversion of BFC is more sensitive to data error than that of OBC and the vertical eddy viscosity profiles. Copyright © 2007 John Wiley & Sons, Ltd.     

Mapping the stiffness-temperature-moisture relationship of solid biomaterials at and around their glass transition

Mechanical changes in biomaterials at and around their glass transition are key factors in their functionality and/or stability. They are described in terms of a relationship betwen a relative stiffness R(T,M) defined as the ratio between a modulus or storage modulus at a temperature T, and moisture M, and its magnitude in the glassy state. The relationship, in turn, is expressed by the model R(T,M) = 1/[1+exp [{T-T _c,(M))/a(M)]} where T _c(M) is a critical temperature identifying the transition temperature range and a(M) a constant representing the relationship's slope. The proposed model correctly accounts for the downward concavity of the stiffness vs temperature relationship at the transition onset. Published data on biosolids indicate that T _c(M) can be described by a single exponential decay term, and so most probably also a(M). Incorporation of these terms into the model enables the creation of realistic three-dimensional maps of the relative stiffness-temperature-moisture relationship at and in the neighborhood of the glass transition region. In principle, the same method can also be used to describe the effect of plasticizers other than water if their influence on T _cand the steepness parameter can be formulated as an algebraic expression.     

Extensional flow of polymer solutions through porous media

The flow behaviour of various polymer solutions of non-hydrolyzed polyacrylamide, hydrolyzed polyacrylamide, polyox and Xanthan was investigated in a plexiglass column having a succession of enlargements and constrictions, and compared with the flow behaviour and mechanical degradation of a solution of non-hydrolyzed polyacrylamide in a packed column of non-consolidated sand. The flow behaviour of this solution was found to be very similar in both the sand pack and plexiglass pore.Apart from the Xanthan solution, all other polymer solutions showed a viscoelastic behaviour in the plexiglass pore. The onset of viscoelastic behaviour, which has previously been defined using the shear rate ( ), stretch rate ( _s ) and Ellis number (E ₁), could be more precisely evaluated using a modified stretch rate (S _G). The pressure losses across the plexiglass pore for different polymer solutions of the same type were found to follow a unique curve provided the suggested group (S _G) was used, a situation which was not achieved with the other rheological parameters.The multipass mechanical degradation of the non-hydrolized polyacrylamide was tested through the sand pack against the suggested group (S _G) and Maerker's group (M _a). It was found that the loss of the solution viscoelasticity due to multipass mechanical degradation was better represented usingS _G thanM _a. A cross-sectional area (cm²) - C ^* critical concentration of polymer (ppm) - d plexiglass pore enlargement diameter - D average sand grain diameter (cm) - e equivalent width for the plexiglass pore - E ₁ Ellis number (a Deborah number) - F _R resistance factor - F _Ri resistance factor at the first pass - h height of the flow path of the plexiglass pore - K power-law constant - K _h,K _w effective permeability to hydrocarbon and water, respectively (10^–8 cm²) - M _a Maerker's group for a given porosity (s^–1) - M _ai value ofM _a at the first pass - N _D Deborah number - n power-law index - Q flow rate (cm³/s) - R capillary radius (cm) - R _g radius of gyration - S _G suggested group of rheological parameters representing a modified maximum stretch rate (s^–1) - S _Gi value ofS _G at the first pass - T _R,t characteristic time for the fluid (s) - t _s residence time (s) - V ₀ superficial velocity (cm/s) - V mean velocity of flow through a porous medium (cm/s) - average axial velocity in the enlargement section of the plexiglass pore (cm/s) - V ₁,V ₂ maximum velocity at a plexiglass enlargement neck and centre - [] intrincis viscosity - viscosity (mPa s) - _r relative viscosity (ratio of the viscosity of the polymer solution to that of the solvent) - shear rate (s^–1) - _s stretch rate (s^–1) - characteristic time for the polymer solution (s)