On front solutions of the saturation equation of two-phase flow in porous media

We investigate the existence of “front” solutions of the saturation equation of two-phase flow in porous media. By front solution we mean a monotonic solution connecting two different saturations. The Brooks–Corey and the van Genuchten models are used to describe the relative-permeability – and capillary pressure–saturation relationships. We show that two classes of front solutions exist: self-similar front solutions and travelling-wave front solutions. Self-similar front solutions exist only for horizontal displacements of fluids (without gravity). However, travelling-wave front solutions exist for both horizontal and vertical (including gravity) displacements. The stability of front solutions is confirmed numerically.     

重分数布朗运动的列维连续模

重分数布朗运动是布朗运动的一种推广，有较强的实用背景.该过程的增量既不是独立的，也不是平稳的. 本文研究了它的列维连续模.     

一类高次多项式系统极限环的存在性和唯一性

通过变换将一类高次多项式系统转化为广义Liénard系统,并利用广义Liénard系统的结果研究了其极限环存在性问题,推广了相关文献的结果.     

Experimental and computational visualization of the flow field in a thermoacoustic stackVisualisation expérimentale et numérique du champ de vitesse dans un réfrigérateur thermoacoustique

The oscillating flow field in a thermoacoustic stack is visualized experimentally using PIV measurements, and computationally using results of low-Mach-number simulations. The experiments and computations are performed under similar conditions. Results are obtained for two distinct configurations, involving thin and thick stack plates. In the first case, the flow field around the edge of the stack exhibits elongated vorticity layers, while in the latter it is dominated by the shedding and impingement of concentrated vortices. A close agreement between experimental and computational results is found, thus providing strong support for both approaches and further predictions. To cite this article: P. Blanc-Benon et al., C. R. Mecanique 331 (2003).     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

Convergence to a Single Wave in the Fisher-KPP Equation

The authors study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation,with an initial condition that is a compact perturbation of a step function.A well-known result of Bramson states that,in the reference frame moving as 2t-(3/2) log t+x∞,the solution of the equation converges as t-→ +o∞ to a translate of the traveling wave corresponding to the minimal speed c* =2.The constant x∞ depends on the initial condition u(0,x).The proof is elaborate,and based on probabilistic arguments.The purpose of this paper is to provide a simple proof based on PDE arguments.     

Méthode particulaire anisotropeAnisotropic particle method

A particle method has been used to simulate the vorticity transport in a two-dimensional flow of an incompressible inviscid fluid. In this method, not only the location and the circulation of the particle are used but also the moments of the internal vorticity. The transport equation for these moments has been derived from the vorticity transport equation. The method has been compared to the usual particle method as well as to Teng's elliptic vortex model. The test case is that of the evolution of two circular patches of vorticity already used by Teng. To cite this article: A. Beaudoin et al., C. R. Mecanique 330 (2002) 51–56     

Direct numerical simulations of two-layer viscosity-stratified flow

Two-dimensional simulations of flow instability at the interface of a two-layer, density-matched, viscosity-stratified Poiseuille flow are performed using a front-tracking/finite difference method. We present results for the small-amplitude (linear) growth rate of the instability at small to medium Reynolds number for varying thickness ratio n, viscosity ratio m, and wavenumber. We also present results for large-amplitude non-linear evolution of the interface for varying viscosity ratio and interfacial tension. For the linear case, the interfacial mode is neutrally stable for as predicted by analysis. The growth rate is proportional to Reynolds number for small Re, and increases with viscosity ratio. The growth rate also increases when the thickness of the more viscous layer is reduced. Strong non-linear behavior is observed for relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger that penetrates into the lower viscosity layer. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. Drop formation at the small Reynolds number considered in this study is precluded by the two-dimensional nature of the calculations.