Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Electromechanical control of vibration on a plate submitted to a non-ideal excitation

This paper deals with the enhancement of electromechanical control of vibration on a thin plate submitted to non-ideal excitation. Modelling of the systems displays the non-ideal source used as external excitation above the structure on a particular surface and control force acting at specific points under the structure. The electromechanical device is composed by a RL circuit with a saturated inductance and stings connected to the plate is used as connection between the structure and the controller. Routh–Hurwitz criteria are used to obtain the stability condition of the controlled system and some dynamics exploration leads us to the condition for which the amplitude of vibration is reduced in the mechanical structure.     

Optimal disturbances above and upstream of a flat plate with an elliptic-type leading edge

Adjoint-based iterative methods are employed to compute linear optimal disturbances in a spatially growing boundary layer around an elliptic leading edge. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. The optimisation problem is solved using power iterations combined with a matrix-free formulation, where the state is marched forward in time with a standard direct numerical simulation solver and backward with the adjoint solver until a chosen convergence criterion is fulfilled. We consider the global and, more relevant to receptivity studies, the upstream localised optimal initial condition leading to the largest possible energy amplification at time T. We find that the two-dimensional initial condition with the largest potential for growth is a Tollmien–Schlichting-like wave packet that includes the Orr mechanism and is located inside the boundary layer downstream of the leading edge. Three-dimensional optimal disturbances induce streaks by the lift-up mechanism. Requiring the optimal initial condition to be localised upstream of the plate enables us to better study the effects of the leading edge on the boundary layer receptivity mechanisms. Two-dimensional upstream disturbances are inefficient at triggering unstable eigenmodes, whereas three-dimensional disturbances induce streamwise streaks with significant growth.     

Partially Strong Transparency Conditions and a Singular Localization Method In Geometric Optics

This paper focuses on the stability analysis of WKB approximate solutions in geometric optics with the absence of strong transparency conditions under the terminology of Joly, Métivier and Rauch. We introduce a compatible condition and a singular localization method which allows us to prove the stability of WKB solutions over long time intervals. This compatible condition is weaker than the strong transparency condition. The singular localization method allows us to do delicate analysis near resonances. As an application, we show the long time approximation of Klein–Gordon equations by Schrödinger equations in the non-relativistic limit regime.     

游离水对点接触区润滑油成膜特性的影响

水污染作为润滑系统污染的常见形式,对润滑油本身以及机械系统都有巨大的危害.目前关于水分对点接触区润滑特性造成影响的直接观测研究还较少,更多的是通过磨损后的接触副状态来推测可能的破坏机理.因此开展水分存在条件下与润滑接触区油池的相互作用,以及对接触区润滑能力造成影响的研究,能够对探究水分造成的机械元件早期失效机理,开展水污染的防护工作起到理论指导作用.本文作者研究了不同润滑条件下游离水对点接触区成膜特性的影响,提出了游离水对接触区膜厚产生影响的无量纲判据,发现了游离水对点接触润滑油池及轨道的冲刷及乳化作用,是造成接触区膜厚下降及回流减弱的主要原因,直接证明了游离水可造成点接触结构的早期润滑失效.     

Comprehensive Seepage Simulation of Fluid Flow in Multi-scaled Shale Gas Reservoirs

Shale gas seepage behaviour is a multi-field/-scale problem and makes transient pressure analysis a very challenging task. Non-Darcy flow in nanopores is prominent due to the broken of continuity hypothesis. Slippage effect and Knudsen diffusion are two important seepage mechanisms in nanopores, while recent studies show surface diffusion is another important transporting mechanism on surface of nanopores. Porous kerogen system contains large amounts of dissolved gas, which should not be overlooked. In this study, a comprehensive mathematical model was established by pseudo-quadruple porosity medium conception, coupling the effects of slippage flow, Knudsen diffusion, surface diffusion, ad-/desorption and gas transferring from kerogen to nanopore system, while fluid flow in fractures/macropores is described by Darcy’s law. Transient pressure behaviours of a multiple fractured horizontal well in box-shaped shale gas reservoir were studied, with nine possible flow regimes divided and parameters sensitivity analysed. Adsorbed constant and dissolved constant were defined to reflect the amount of adsorbed gas and dissolved gas, respectively. Research shows that adsorbed gas and dissolved gas are two important gas storage forms, neither of which should be neglected. The study can not only help us understand fluid flow mechanisms in nanopores from microscopic perspective, but enable us to analyse production performance and determine key operational parameters from macroscopic perspective.     

Leaky Tap Behavior Described by a Simple Discrete Mapping

The complex variety of phenomena associated with the dynamical behavior of a dripping faucet is reproduced with a simple map deduced from a one-dimensional analog mass-on-spring simulation, which has a dependence on a reduced number of parameters. It is analyzed how the dynamics of the real tap depends on the flow rate and on the geometrical parameters of the tip. Experimental bifurcation diagrams and attractors illustrate the adherence of the mapping to the real dynamics. The enormous simplifications in reducing the actual physical system to a simple oscillator mapping allows to us to investigate more deeply the parameter space and to understand the most important dynamical mechanisms of the leaky tap.     

On the Existence of a Weak Solution of Viscous Incompressible Flow Past a Cascade of Profiles with an Arbitrarily Large Inflow

The paper deals with the analysis of a stationary viscous incompressible flow through a cascade of profiles representing a blade row of a turbine. The initial-boundary value problem for the Navier–Stokes system is formulated in a domain having the form of one spatial period of the cascade. In comparison to previous results, we solve the problem with an arbitrarily large inflow into the turbine. We formulate the “artificial” boundary condition on the outflow (the modification of the so called do-nothing condition) that enables us to prove the existence of a weak solution.     

On the direct interactions between heat transfer,mass transport and chemical processes within gradient elasticity

The behaviour of complex material systems often results from the combined effects of several multi-scale mechanisms and simultaneously occurring coupled physical processes. In this paper, we focus on such complex response of a class of geomaterials in which heat conduction, mass diffusion, chemical reactions and gradient-type elastic strain mechanisms interact. Our purpose is to develop within a formal thermodynamic framework a complete set of constitutive equations which account for most of the possible aforementioned direct couplings and the associated relevant size effects in a unified phenomenological way. For the sake of simplicity, the volume element is described at the macroscopic scale as a classical homogeneous continuous mixture of chemically active species. Based on theories of second-gradient elasticity endowed with the concepts of both nonlocality residual and constitutive insulation condition, a thermo-diffuso-chemo-elastic formulation is proposed in the restricted case of small perturbations. Coupling terms entering the relevant constitutive relations are discussed throughout the paper. Then, the model is applied to a simple one-dimensional situation, in which only the mechanical response is reported. The implementation of such modelling in a finite element code should enable us to address more specific problems, such as the stress solution phenomenon in hollow cylinders subjected to external loading.     

Generalized canonical transformation for second-order Birkhoffian systems on time scales

The theory of time scales, which unifies continuous and discrete analysis, provides a powerful mathematical tool for the study of complex dynamic systems. It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems. In this paper, the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied, which extends the canonical transformation theory of Hamilton canonical equations. First, the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second, based on this condition, six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given. Also, the relationships between new variables and old variables for each of these cases are derived. In the end, an example is given to show the application of the results.     

Subsonic axisymmetric wake in a viscous gas

The problem of the subsonic axisymmetric flow of a compressible viscous perfect gas in the wake behind a cylindrical body with a flat base section is considered under the condition that the stream parameters are given at infinity and at some distance x_w upstream of the base section. (Let us note that the possibility of the existence of an axisymmetric wake at moderate Reynolds numbers has been shown experimentally [1].) The problem is solved by the numerical build-up method in a cylindrical x, y coordinate system on the basis of the Navier-Stokes equations, by a method elucidated in [2, 3]. Equations obtained from the fundamental system by a passage to the limit while taking into account the symmetry conditions on the axis y=0 are used on the axis of symmetry.     

PROPER ORTHOGONAL DECOMPOSITION OF RANDOM WIND PRESSURE FIELD

This paper discusses the application of the Proper Orthogonal Decomposition (POD) technique to randomly fluctuating wind pressure fields acting on a building surface. POD is a method of detecting a new coordinate system which can most efficiently represent the original fluctuating phenomena. This method can identify the deterministic or systematic structure hidden in the random fluctuations and thus help us to understand the phenomena better. It also demonstrates that the coordinate system employed is the most efficient, and can greatly reduce the amount of data that needs to be stored to re-examine the phenomena. Precautions in its application to random fields with mean values and with a singular condition are also mentioned. Furthermore, this paper introduces an example of the method's application to the evaluation of properties and the prediction of responses to wind forces acting on high-rise buildings; the validity of the method is also verified.     

Complex system and influence of delayed decision on the stability of a triopoly price game model

A triopoly price game model has been established based on nonlinear and economics theories in this paper, and all 3 firms of triopoly market are supposed to make a price decision with bounded rationality. By discrete dynamical system theory and jury condition, we obtain the expression of Nash equilibrium point’s stable region. Then traditional two-dimensional and creative three-dimensional diagrams of the local stable region are given by numerical simulation, and both 2D and 3D diagrams showed us some law about the Nash equilibrium point’s stable region. First, the number of time-delay decision makers has no necessary relationship with system stability; Second, under the same number of time-delay decision makers, the delay parameter has a positive influence of system stability, i.e., the price making relying more on current period profits can lower the system risk of falling into chaos. These results have significant theoretical and practical value to the price making of firms in related markets.     

Poiseuille-Bénard流的出口边界条件及其谱元法计算

研究二维矩形管道中底部加热的不可压缩Ｐｏｉｓｅｕｉｌｌｅ－Ｂｅｎａｒｄ流的谱元法数值计算问题．讨论各种不同的出口边界条件的处理及其对谱元法数值模拟的影响．通过干扰区、干扰幅度和计算时间的比较,确定比较理想的出口边界条件．     

基于GIS的滑坡综合预测预报信息系统

由于滑坡的复杂性、随机性和不确定性,加之目前的滑坡灾害预测预报理论研究还存在局限性,大大增加了滑坡预报的难度。本文针对目前滑坡预测预报研究中的不足,提出了滑坡综合预测预报信息系统,并对该系统的结构、功能和内容等进行了详尽地设计和开发。滑坡综合预测预报信息系统以G IS为平台,利用智能决策支持系统的理论和方法将以监测资料为依据的滑坡定量预报与以专家经验知识为依据的滑坡定性预报有机结合起来,做到了各取所长,优势互补,实现了滑坡的综合预测预报,提高了滑坡的预报水平。运用该系统不仅可以判断滑坡体的变形破坏机制、目前的稳定性状况和破坏概率,而且可以对滑坡体的变形演化阶段以及滑动时间作出预测预报,从而给滑坡现场工程师的综合判断和决策提供了重要的参考和有关科学依据的实用化工具。     

Nucleation of cracks in a perforated heat-releasing material with temperature-dependent elastic properties

A mathematical model of crack nucleation in a perforated heat-releasing material attenuated by a biperiodic system of cooling cylindrical channels with a circular cross section is constructed. Solving the problem of equilibrium of an isotropic perforated heat-releasing material with temperature-dependent properties containing nucleating cracks is reduced to solving systems of algebraic and nonlinear singular integral equations with a Cauchy-type kernel. The forces in crack nucleation regions are found by using the solution of these equations. The condition of crack emergence is formulated with allowance for the criterion of ultimate stretching of bonds in the material.     

Analysis of the Cahn–Hilliard Equation with a Relaxation Boundary Condition Modeling the Contact Angle Dynamics

We analyze the Cahn–Hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary. An L ^∞ estimate is established which enables us to prove the global existence of the solution. We also study the sharp interface limit of the system. The dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations.     

Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L ^∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.     

Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws

The basic existence theory of Kato and Majda enables us to obtain local-in-time classical solutions to generally quasilinear hyperbolic systems in the framework of Sobolev spaces (in x) with higher regularity. However, it remains a challenging open problem whether classical solutions still preserve well-posedness in the case of critical regularity. This paper is concerned with partially dissipative hyperbolic system of balance laws. Under the entropy dissipative assumption, we establish the local well-posedness and blow-up criterion of classical solutions in the framework of Besov spaces with critical regularity with the aid of the standard iteration argument and Friedrichs’ regularization method. Then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin–Lerner spaces (mixed space-time Besov spaces). This fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well-posedness and stability by assuming at all times the Shizuta–Kawashima algebraic condition. As a direct application, the corresponding well-posedness and stability of classical solutions to the compressible Euler equations with damping are also obtained.     

A theoretical investigation on the wave forces on the multiple cylinders in shallow water

The diffraction problem of two kinds of shallow water wave, cnoidal wave and solita. wave, around a group of cylinders is discussed. A Bessel corrdinate transformation i. employed to uniform the coordinate system, and thus the boundary condition on each cylinder’s surface can be satisfied by determining the coefficients in the solution. Several examples are calculated for two kinds of incident wave and various arrangement of the cylinders, and the results are discussed and compared with the available experimental data.