Asymptotic spreading of KPP reactive fronts in incompressible space–time random flows

We study the asymptotic spreading of Kolmogorov–Petrovsky–Piskunov (KPP) fronts in space–time random incompressible flows in dimension d>1$d>1$. We prove that if the flow field is stationary, ergodic, and obeys a suitable moment condition, the large time front speeds (spreading rates) are deterministic in all directions for compactly supported initial data. The flow field can become unbounded at large times. The front speeds are characterized by the convex rate function governing large deviations of the associated diffusion in the random flow. Our proofs are based on the Harnack inequality, an application of the sub-additive ergodic theorem, and the construction of comparison functions. Using the variational principles for the front speed, we obtain general lower and upper bounds of front speeds in terms of flow statistics. The bounds show that front speed enhancement in incompressible flows can grow at most linearly in the root mean square amplitude of the flows, and may have much slower growth due to rapid temporal decorrelation of the flows.     

Anomalous invasion in a 2d model of chemotactic predation

It has been hypothesized that plankton predators sense the presence of their prey through detection of chemical signals exuded by the prey. This process is formulated using elements of existing models, tailored to correspond to the specific process under investigation. The motivation for the resulting model is discussed in detail. Numerical results are then presented. It is found that the front representing the advance of the predator into the prey is irregular in a novel way, and the reasons for this anomalous invasion are discussed. It is recognized that reaction-diffusion models, starting perhaps with Turing, can lead to what might have been thought of as anomalous patterns — yet the “flicker” front advance discovered here is indeed novel.     

Front dynamics in heterogeneous diffusive media

We herein consider two-component reaction-diffusion systems with a specific bistable and odd symmetric nonlinearity, which have the bifurcation structure of pitchfork type traveling front solutions with opposite velocities. We introduce a spatial heterogeneity, for example, a Heaviside-like abrupt change at the origin in the space, into diffusion coefficients. Numerically, the responses of traveling fronts via the heterogeneity can be classified into four types of behavior depending on the strength of the heterogeneity, which, in the present paper, is represented by the height of the jump: passage, stoppage, and two types of reflection. The goal of the present paper is to reduce the PDE dynamics to finite-dimensional ODE systems on a center manifold and show the mathematical mechanism for producing the four types of response in the PDE systems using finite-dimensional ODE systems. The reduced ODE systems include the terms (referred to as heterogeneous perturbations) originating from the interaction between traveling front solutions and the heterogeneity, which is very important for determining the dynamics of the ODE systems. In the present paper, we succeed in calculating these heterogeneous perturbations exactly and explicitly.     

高质量三维光子晶体的制备及其透射谱研究

设计了简易的压强可控自组装实验装置,制备了由直径为260 nm的聚苯乙烯(PS)胶体球组成的面心立方光子晶体.分析了压强的变化对光子禁带(PBG)深度及光子带隙边缘(PBE)坡度的影响,确定了合适的压强生长环境(P=5999.5 Pa).利用该实验装置,还进行了光子晶体的小批量制备,一次性制得了三块光子晶体,并从不同角度对每一块光子晶体的透射谱及不同光子晶体的透射谱进行了测量.同一光子晶体不同位置透射谱的重合、同一批次制备的不同光子晶体透射谱的一致性及光子禁带两侧的Fabry-Pérot振荡等均说明:该装置制备的光子晶体在大区域、大面积上是高度有序、均一和平整的;利用该实验装置进行光子晶体的小批量制备是可行的.     

Uniform convergence for the incompressible limit of a tumor growth model

We study a model introduced by Perthame and Vauchelet [19] that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We adopt the viscosity solution approach to establish an optimal uniform convergence result of the tumor density as well as the pressure in the incompressible limit. The system lacks standard maximum principle, and thus modification of the usual approach is necessary.     

On a Strongly Damped Wave Equation for the Flame Front

In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation （K-S）. However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics.     

一类广义Liénard型系统周期解的存在性和不存在性

讨论了一类广义Liénard型系统.x=p(y)k(x),.y=-f(x,y)p(y)q(y)-g(x)h(y)非零周期解的存在性和不存在性,给出了非零周期解的存在和不存在的一类充分条件.     

光纤法布里-珀罗腔传感器双波长解调法及波长优化设计

提出了光纤法布里珀罗(F-P)腔传感器的双通道双波长解调方法,并在此基础上建立了传感器的实验解调系统。理论分析与实验研究了双波长法解调光纤法布里珀罗腔传感器的基本原理,证明了双波长双通道解调法可以补偿传感器光网中和波长无关的变动引起的误差。根据已知的法布里珀罗腔传感器初始腔长和腔两端面反射率,从腔长变化的动态范围、线性、灵敏度等方面考虑,对工作波长以及线宽进行了优化设计。对双波长双通道解调系统进行了实验和数据分析,经最小二乘法拟合后的线性拟合度达到98.35%。实验结果表明:该方法可满足解调光纤法布里珀罗腔传感器在灵敏度、响应速度以及稳定度上的要求。     

Quasi-periodic solutions of a semilinear Liénard equation at resonance

We are concerned with the existence of quasi-periodic solutions for the following equation

Coupling of a simplified flow with a phenomenological fire spread modelCouplage d'un écoulement simplifié à un modèle phénoménologique de propagation des feux

Our long-range aim is to propose a forest fire simulator. To this end, we have developed a phenomenological model of fire spread. Then, we have improved it in order to take into account advective transfers thanks to a simplified flow. In this paper, we present in a synthetic way our modelling approach that can also be applied to other phenomenological models. Finally, we compare the model predictions to laboratory experiments. To cite this article: A. Simeoni et al., C. R. Mecanique 330 (2002) 783–790.