Structural response of different Lewis number premixed flames interacting with a toroidal vortex

Simultaneous measurements of temperature, CH* and OH* chemiluminescent species are carried out to explore the impact of stretch rate and curvature on the structure of premixed flames. The configuration of an initially flat premixed flame interacting with a toroidal vortex is selected for the present study and reasons for this choice are discussed. Lewis number effects are assessed by comparing methane and propane flames. It is emphasized that the flame structure experiences very strong variations. In particular, the flame is shrunk (broadened) in the initial (final) period of the interaction with the vortex where strain rate (curvature) contribution of the stretch rate is predominant. By further analysing independently the thickness of the preheat and reaction zones, it is shown that for propane flames, not only the former but also the latter is significantly altered in zones where the flame curvature is negative. Changes in the reaction zone properties are further emphasized using CH* and OH* radicals. It is demonstrated that higher thermal diffusivity plays a significant role around curved regions, in which the enhanced diffusion of heat leads to a strong increase of CH* compared to OH* intensity. As an overall conclusion, this study suggests that it would be interesting to reassess the internal flame structure at lower and moderate Karlovitz numbers since changes might appear for a moderate vortex intensity with typical size much larger than the flame thickness.     

Influence of root resistivity on plant water uptake mechanism,Part II: analytical solutions for low/moderate soil-root conductivity ratio

A one-dimensional approximate analytical model, which preserves the main features of soil-crop-atmospheric hydrodynamics, has been suggested for plant roots of low soil-root conductivity ratio (SRCR). The proposed approach involves physically based concepts, such as mass balance equation, Darcy’s law, and related water uptake and plant transpiration functions. Two main assumptions have been made to derive the analytical solution: (1) gravitational flow is adopted and (2) the uniform soil moisture distribution within the root water activity zone is supposed. The mass balance equation in its integral form is solved by the method of characteristics. This leads to the two functional equations for soil pressure head and root potential, which can be solved simultaneously by using common software. The model has been further verified against the numerical one. The model represents a reasonable compromise between the complicated mechanism of unsaturated water flow with root water uptake (RWU) and still insufficient knowledge of the soil-plant-atmospheric continuum. It is able to account for temporal fluctuations in root activity zone and provides a relatively simple algorithm for investigation of RWU-mechanism. Besides the theoretical and applicative importance, this flow model yields water and velocity distributions within soil profile, and, thereby, constitutes a preliminary step toward solution of contaminant transport problems in vadose zone. Deceased     

Influence of root resistivity on plant water uptake mechanism,part I: numerical solution

The issue of water flow through the root zone of field crops represents a complex problem requiring knowledge of a large spectrum of phenomena from various disciplines. Although many investigations have been devoted to gain better understanding of water dynamics in the root zone, the problem is still insufficiently understood. The main objective of the presented work was to analyze the importance of root water resistivity in the plant water extraction process. The problem was solved numerically for a wide range of the soil–root conductivity ratio (SRCR). Two different types of root water uptake (RWU) mechanisms were obtained. The first one is related to low root resistivity or low SRCR, and, thus, exhibits a so-called “moving uptake front” (MUF) effect observed previously in several experimental studies. The second one is inherent in large values of root resistivity or high values of SRCR (larger than 10⁴), and is strongly dependent on the root density distribution. Deceased.     

Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects

In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay

Two-phase boundary dynamics near a moving contact line over a solid

Consideration is given to the nonlinear problem on a shape of boundary between two viscous liquids, of which one displaces the other one from a solid surface, the Reynolds number being rather low. An asymptotic theory of wetting dynamics is developed that is of the second order with respect to small capillary numbers and valid for any ratio of viscosity coefficients of the media. A formula describing the dynamic contact angle (i.e. the inclination angle of the tangent to the interface) as a function of a distance to the solid is derived. Limitations on the angles for which the second-order theory is valid are shown. If the phase 2 viscosity is zero, the asymptotic second-order theory is valid for angles below 128.7°. A theory applicability domain depends on the ratio of viscosity coefficients. The applicability domain is not limited if the viscosity coefficients differ by a factor of less than four.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

关于指数率Logistic方程在无限柱体内的波前解的存在性

与一维空间中研究连接两个常数的波前解的存在性不同的是,本文建立了在多维无限长的柱体内连接两个曲面的单调行波解的存在性.相应的模型是一种具有指数率的Logistic方程.所用的方法是一种改进了的单调性方法.本文的研究结果对自然界中波的实际传播行为给出了有益的启示.     

Travelling wave fronts in a vector disease model with delay

In this paper, we study the diffusive vector disease model with delay. This problem with strong biological background has attracted much research attention. We focus on the existence of traveling wave fronts, and find that there is a moving zone for the transition from the disease-free state to the infective state. To complete the theoretical analysis, we employ the mathematical tools including the monotone iteration technique as well as the upper and lower solution method.     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.     

Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure

We consider nonlinear parabolic systems of the form ut=−∇V(u)+u_xx$u_t=-\mathrm{\nabla }V(u)+u_{xx}$, where u∈Rn$u\in {\mathbb{R}}^n$, n?1$n?1$, x∈R$x\in \mathbb{R}$, and the potential V   is coercive at infinity. For such systems, we prove a result of global convergence toward bistable fronts which states that invasion of a stable homogeneous equilibrium (a local minimum of the potential) necessarily occurs via a traveling front connecting to another (lower) equilibrium. This provides, for instance, a generalization of the global convergence result obtained by Fife and McLeod [P. Fife, J.B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335–361] in the case n=1$n=1$. The proof is based purely on energy methods, it does not make use of comparison principles, which do not hold any more when n>1$n>1$.