Influence of water mist on propagation and suppression of laminar premixed flame

The combustion of premixed gas mixtures containing micro droplets of water was studied using one-dimensional approximation. The dependencies of the burning velocity and flammability limits on the initial conditions and on the properties of liquid droplets were analyzed. Effects of droplet size and concentration of added liquid were studied. It was demonstrated that the droplets with smaller diameters are more effective in reducing the flame velocity. For droplets vaporizing in the reaction zone, the burning velocity is independent of droplet size, and it depends only on the concentration of added liquid. With further increase of the droplet diameter the droplets are passing through the reaction zone with completion of vaporization in the combustion products. It was demonstrated that for droplets above a certain size there are two stable stationary modes of flame propagation with transition of hysteresis type. The critical conditions of the transition are due to the appearance of the temperature maximum at the flame front and the temperature gradient with heat losses from the reaction zone to the products, as a result of droplet vaporization passing through the reaction zone. The critical conditions are similar to the critical conditions of the classical flammability limits of flame with the thermal mechanism of flame propagation. The maximum decrease in the burning velocity and decrease in the combustion temperature at the critical turning point corresponds to predictions of the classical theories of flammability limits of Zel'dovich and Spalding. The stability analysis of stationary modes of flame propagation in the presence of water mist showed the lack of oscillatory processes in the frames of the assumed model.     

温度压力对瓦斯爆炸危险性影响的实验研究

为了研究瓦斯的爆炸危险性,选取对其影响较大的初始温度和初始压力进行实验研究。运用特殊环境20 L爆炸特性测试系统,对不同初始温度(25~200 ℃)和初始压力(0.1~1.0 MPa)条件下瓦斯的爆炸极限、最大爆炸压力和点火延迟时间进行实验研究。结果表明:高温高压条件使瓦斯的爆炸上限升高、下限降低,爆炸极限范围扩大;随着初始温度升高,瓦斯爆炸的最大爆炸压力逐渐减小;初始温度越高,点火延迟时间越短。通过对实验结果的分析,运用安全原理知识和危险度定义,给出初步评估瓦斯爆炸危险性的方法。     

Quantum evolution speed and its limit in the driven double-well system

We investigate quantum evolution speed in the driven double-well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1-distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double-well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.     

微言要义之数列的上下极限

本文分别从语义,数学和教学三个方面讨论上下极限与极限概念之间的差别和联系,以求厘清差别,透彻理解上下极限概念的本质.     

Operations on convergent families of sets and functions

The lower limit of the images by a convex set-valued mapping of a family of convex sets is studied. Topological and metric results are given. Applications to variational convergence, in particular to epi-convergence of convex functions, are presented.     

Boundary behavior of monotone Sobolev functions on John domains in a metric space

This article deals with weighted boundary limits of monotone Sobolev functions on bounded s-John domains in a metric space.     

Rigorous Derivation and Analysis of Coupling of Kinetic Equations and Their Hydrodynamic Limits for a Simplified Boltzmann Model

In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.     

载流薄板中裂纹形成瞬间尖端附近的应力场

利用电磁场的热效应对带有裂纹的载流导体进行裂纹止裂,是为了达到延长其工作寿命,提高安全性、可靠性的一种行之有效的方法。本文在文献[1]的基础上,以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了载流无限大薄板在形成裂纹的瞬间,裂纹尖端附近电流密度、温度和应力的具体表达式。通过算例分析证实了：在给定参数的情况下,通入适当强度的电流时,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,同时伴有压应力的产生,从而可达到阻止裂纹扩展的目的。     

Approximation to Nonlinear Schrodinger Equation of the Complex Generalized Ginzburg-Landau Equation

In this paper, we prove that in the inviscid limit the solution of the generalized derivative Ginzburg-Landau equations converges to the solution of derivative nonlinear Schrödinger equation, we also give the convergence rates for the difference of the solution.     

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.