Simulation of shockwave propagation with a thermal lattice Boltzmann model

A two‐dimensional 19‐velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u⁴) rather than the usual O(u³) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher‐order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13‐velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 John Wiley & Sons, Ltd.     

Shock wave-induced vortex loops emanating from nozzles with singular corners

The focus of the current study is to examine experimentally the diffracted shock wave pattern and the consequent vortex loop formation, propagation, and decay from nozzles having singular corners. Non-intrusive qualitative and quantitative techniques: schlieren, shadowgraphy, and particle image velocimetry (PIV) are employed to analyze the induced flow-fields. Eye-shaped nozzles were used with the corner joints representing singularities. The length of the minor axes are a = 6 and 15 mm, with the major axis b = 30 mm for both cases. The experiments are performed for flow Reynolds numbers in the range 0.8 × 10⁵ and 4.6 × 10⁵. Air is used in both driver and driven sections of the shock tube.     

厦门沪救码头附近海底滑坡特征及机理

根据多种勘察手段的识别,查明厦门沪救码头附近海底地形等值线明显扭曲;码头南侧外块石与淤泥互为翻转;滑体后方淤泥可见到蜂窝状孔隙;北码头一带不连续分布有新近沉积的灰黄色淤泥且沿海岸;另外地震映像也出现绕射波相对严重等现象。本文结合地形、地层、海洋水动力条件等因素,对滑动机理进行综合分析;在不考虑海浪、地震作用下,对水下坡体采用极限平衡理论方法、后壁岸坡选择圆弧条分法进行不同的稳定性评价。研究得出:该海底滑坡形成是自然地质、人为活动和重力、海洋动力共同作用以及地层因素的综合结果。     

On the Role of Variable Latent Periods in Mathematical Models for Tuberculosis

The qualitative behaviors of a system of ordinary differential equations and a system of differential-integral equations, which model the dynamics of disease transmission for tuberculosis (TB), have been studied. It has been shown that the dynamics of both models are governed by a reproductive number. All solutions converge to the origin (the disease-free equilibrium) when this reproductive number is less than or equal to the critical value one. The disease-free equilibrium is unstable and there exists a unique positive (endemic) equilibrium if the reproductive number exceeds one. Moreover, the positive equilibrium is stable. Our results show that the qualitative behaviors predicted by the model with arbitrarily distributed latent stage are similar to those given by the TB model with an exponentially distributed period of latency.     

Validation of the thermal equilibrium assumption in the transient conjugated forced convection channel flow

 The validity of the local thermal equilibrium assumption in the transient conjugated forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insure the validity of the local thermal equilibrium assumption. It is found that three dimensionless parameters control the local thermal equilibrium assumption. These parameters are the Biot number Bi, the dimensionless channel length ξ_max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these three parameters on the channel thermalization time are investigated. Received on 9 August 2000     

Nets with Hexagonal Cell Structure

We establish a continuum theory of inextensible nets with hexagonal cell structure. Some qualitative properties of the equilibrium problem and possible singularities are discussed.      

On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

 The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L ¹ topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L ¹ to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term. (Accepted 25, October 2002) Published online March 14, 2003 Communicated by P.-L. Lions     

Global analysis of a Holling type II predator–prey model with a constant prey refuge

A global analysis of a Holling type II predator–prey model with a constant prey refuge is presented. Although this model has been much studied, the threshold condition for the global stability of the unique interior equilibrium and the uniqueness of its limit cycle have not been obtained to date, so far as we are aware. Here we provide a global qualitative analysis to determine the global dynamics of the model. In particular, a combination of the Bendixson–Dulac theorem and the Lyapunov function method was employed to judge the global stability of the equilibrium. The uniqueness theorem of a limit cycle for the Lineard system was used to show the existence and uniqueness of the limit cycle of the model. Further, the effects of prey refuges and parameter space on the threshold condition are discussed in the light of sensitivity analyses. Additional interesting topics based on the discontinuous (or Filippov) Gause predator–prey model are addressed in the discussion.     

Characterizing developing adverse pressure gradient flows subject to surface roughness

An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and X-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., T _∞, U _ref, and C _p) were maintained for smooth, k ⁺ = 0, and rough, k ⁺ = 41–60, surfaces with Reynolds number based on momentum thickness, 3,000 < Re _θ < 40,000. The experiment was carefully designed such that the x-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91–108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33–79, 1998a) scaling of the mean velocity deficit, U _∞δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.     

基于数量化理论的岩堆稳定性评价模型

影响岩堆稳定的定性因素难以在极限平衡、数值分析中全面反映和定量表述。数量化理论可通过定性指标定量化,充分考虑定性指标的影响。基于数量化理论,提出岩堆稳定性评价模型。根据岩堆组成物质及内部颗粒接触情况进行结构分类;基于主因素分析,采用岩石单轴饱和抗压强度（分为四级）、岩堆结构（分为四级）、地形坡度（分为三级）及地下水发育情况（分为二级）4个评价指标建立了岩堆稳定性评价模型。模型在云南水富-麻柳湾高速公路中的应用成果表明：影响岩堆稳定性的主要因素是岩堆结构、岩石强度和地下水。     

Validation of Thermal Equilibrium Assumption in Transient Forced Convection Flow in Porous Channel

The validity of the local thermal equilibrium assumption in the transient forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insures the validity of the local thermal equilibrium assumption. It is found that four dimensionless parameters control the local thermal equilibrium assumption. These parameters are the porosity , the volumetric Biot number Bi, the dimensionless channel length _max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these four parameters on the channel thermal equilibrium relaxation time are investigated.     

Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

The capillary pressure?Csaturation (P ^c?CS ^w) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P ^c?CS ^w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P ^c?CS ^w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as ??hysteresis??. A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389?C3904, 1993a) suggests that, by introducing a new state variable, called the specific interfacial area (a ^nw, defined as the ratio of fluid?Cfluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure?Csaturation relationship using a dynamic pore-network model. The simulation results imply that P ^c?CS ^w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure?Csaturation?Cinterfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P ^c?CS ^w?Ca ^nw relationship.     

A comprehensive experimental study of the rheological behaviour of HDPE.

Extensional properties of four high density polyethylenes with different molecular weights and molecular weight distributions are presented. The samples have already been well characterized in shear and non-isothermal extensional flow. The data were collected at 180 °C for elongational rates between 3 · 10^–1 and 10^–4s^–1. Some qualitative and quantitative generalizations of the results are given.     

An encapsulated dumbbell model for concentrated polymer solutions and melts II. Calculation of material functions and experimental comparisons

The consitutive equation derived in Part I [1] is used to compute steady-state and time-dependent material functions. A procedure is suggested for determining the four independent model parameters (λ_H, b, σ, β) from experimental data.Material functions have been calculated using parameters determined by experimental data for concentrated solutions of nearly monodisperse linear polymers. The theoretical curves for steady shear properties (η and Ψ₁) are in quantitative agreement with the data well into the range of nonlinear behavior. The calculated time-dependent properties (η*, η⁺, Ψ⁺, η^?) are in qualitative agreement with observed behavior. Theoretical curves for elongational viscosity are reasonable, but suitable experimental data are not available for comparison.     

On Large-Time Behavior of Solutions to the Compressible Navier-Stokes Equations in the Half Space in R 3

 The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R ³ under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L ² norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L ² norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in . Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space. (Accepted May 8, 2002) Published online October 18, 2002 Communicated by T.-P. LIU     

Model representations of the interaction between the solar wind and the supersonic interstellar medium flow. prediction and interpretation of experimental data

The planning and conducting of physical experiments requires the development of theoretical models capable either of predicting possible experimental data or explaining those already obtained. The processes taking place in the physical world can be understood only in terms of the close interaction between theory and experiment. Developing any quantitative or qualitative model of a physical phenomenon requires a mathematical apparatus, on the basis of which such models can be constructed. The branch of theoretical science using the methods of magnetohydrodynamics and hydroaeromechanics for studying space physics problems is usually called cosmic gasdynamics; it is mostly used in developing models of physical phenomena occurring under space conditions. In order to emphasize the importance of cosmic gasdynamics in the development of astrophysics and space research, we will present several examples of models constructed by aerodynamicists. These models not only played an important role in qualitative predictions but are still being developed due to the need for the quantitative interpretation of the experimental data. The solar corona was long thought to be a formation in a state of gravitational equilibrium (Chapman model). However, it turned out that the pressure at infinity obtained on the basis of this equilibrium solution is considerably greater than the estimated pressure in the interstellar gas surrounding the solar corona. In [1] it was concluded that in this case the solar corona gas must expand and a solution describing this expansion was obtained by invoking the steady-state hydrodynamics equations in the spherically-symmetric approximation. The solution of these equations led to the theoretical prediction of the solar wind, a radial flow of fully ionized hydrogen plasma issuing from the solar corona at a low subsonic velocity but already hypersonic at the Earth’s orbit. Subsonic-to-supersonic transition is ensured by solar gravitation which in this case plays the role of a convergent-divergent nozzle. Within a year, the theoretical prediction of the solar wind [1] was confirmed by its experimental detection [2] onboard the Soviet spacecraft Luna-2. It turned out that at the Earth’s orbit the mean velocity of the solar wind V _E ≈ 450 km·s^?1, the mean proton temperature T _E ≈ 6 · 10⁴ K (the electron temperature is somewhat higher), and the mean concentration of protons (and electrons) n _E ≈ 10 cm^?3. The first hydrodynamic model of the supersonic solar-wind flow past the Earth’s magnetosphere [3] was only qualitative, since it considered a flow past a plane magnetic dipole in the approximation of a thin layer between the bow shock and an “obstacle” embedded in the flow. However, it was constructed before the actual discovery of the solar wind and provided further important impetus to the development of models of the supersonic solar wind flow past planets with a detached shock. One more example is furnished by the gasdynamicmodel of the solar wind flow past cometary atmospheres, first suggested in In this work, a model of the interaction between the supersonic solar wind and the supersonic flow of the local, i.e., surrounding the Sun, interstellar medium is considered; it was first suggested in [6] in a much simplified formulation. This model has been actively developed in connection with the flights of the spacecraft Voyager 1 and 2, Ulysses, Hubble Space Telescope, SOHO, and others, exploring the outer regions of the solar system.     

THE FLOW-INDUCED VIBRATION OF A FLEXIBLE STRIP HANGING VERTICALLY IN A PARALLEL FLOW PART 1: TEMPORAL AEROELASTIC INSTABILITY

The effect of several parameters in a fluid–strip system are studied for linear/nonlinear models in detail. Such parameters are: the number of modes in the Galerkin discretization, the length of the strip, and the flow velocity. The present simulation clearly shows that when nonlinear forces are considered the response approaches a flutter-type limit cycle at supercritical flow speeds. The Reynolds number at which the strip begins to oscillate is about 10⁴–10⁵. With a further increase of the flow velocity the strip oscillates regularly. At higher flow velocities the oscillation becomes violent and irregular. The amplitude, frequency and drag coefficient at the limit cycle are presented as functions of the flow velocity for a given strip. The numerical predictions are in qualitative agreement with previous experimental data.     

非圆截面弹性细杆的平衡稳定性与分岔

本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题,在两端受力矩单儿作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性,文中对杆截面的对称性,以及杆的初始曲率和挠率对平衡状态性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的列态分岔现象。     

Preparation of modified MFI (ZSM-5 and silicalite-1) zeolites for potassium extraction from seawater

Modified nanosized MFI (ZSM-5 and silicalite-1) zeolites were successfully synthesized by a hydrothermal method using aluminum isopropoxide and tetraethylorthosilicate as the raw materials. The synthetic zeolites were characterized by X-ray diffraction, energy dispersion spectroscopy, and scanning electron microscopy. The ZSM-5 and silicalite-1 zeolites exhibited ellipse-like and cubic columns, respectively. The K⁺ ion-exchange equilibrium and ion-exchange capacity of the synthetic zeolites in seawater were investigated. The K⁺ ion-exchange of synthetic zeolites was rapid and reached an ion-exchange balance in approximately 20 min. The K⁺ ion-exchange capacity of ZSM-5 and silicalite-1 in seawater was 56.7 and 48.7 mg/g, respectively. The synthetic zeolites have high selectivity toward K⁺, and therefore, they can be used to selectively extract potassium from seawater.