Instability of unburnt gas for a scalar nonconvex combustion model

The ignition solutions for the scalar nonconvex Chapman-Jouguet (CJ) combustion model are studied as the ignited perturbation vanishes. We let the perturbation vanish in the result of the interactions of the combustion waves and noncombustion waves, thereby obtaining that the unburnt gas is unstable when the binding energy is larger than a critical value. Furthermore, in the vanishing process, the transitions between deflagration and detonation waves are observed.     

The ignition problem for a scalar nonconvex combustion model

The ignition problem for the scalar Chapman-Jouguet combustion model without convexity is considered. Under the pointwise and global entropy conditions, we constructively obtain the existence and uniqueness of the solution and show that the unburnt state is stable (unstable) when the binding energy is small (large), which is the desired property for a combustion model. The transitions between deflagration and detonation are shown, which do not appear in the convex case.     

THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR NONCONVEX COMBUSTION MODEL-THE PERTURBATION ON INITIAL BINDING ENERGY

In this article,we study the generalized Riemann problem for a scalar nonconvex Chapman-Jouguet combustion model in a neighborhood of the origin (t ＞ 0) on the (x,t) plane.We focus our attention to the...     

THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR COMBUSTION MODEL --THE PERTURBATION ON INITIAL BINDING ENERGY

In this paper, we study the generalized Riemann problem for a scalar Chapman-Jouguet combustion model in a neighborhood of the origin on upper half of the （x, t）plane. We focus our attention on the perturbation on initial binding energy. Under the entropy conditions, the solutions are obtained constructively. It shows that the perturbed Riemann solutions possess the structural stability except the case that the corresponding Riemann solutions contain CJDT, for which CJDT may transform into SDT after perturbation on initial binding energy in the neighborhood of the origin.     

Non-selfsimilar global solutions and their structure for the multi-dimensional combustion models

We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.     

UNIFORM FORMULA FOR THE RIEMANN SOLUTIONS OF A SCALAR COMBUSTION MODEL

In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional,while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed.     

Pointwise Green function bounds and stability of combustion waves

Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave solutions of an abstract viscous combustion model including both Majda's model and the full reacting compressible Navier-Stokes equations with artificial viscosity with general multi-species reaction and reaction-dependent equation of state, under the necessary conditions of strong spectral stability, i.e., stable point spectrum of the linearized operator about the wave, transversality of the profile as a connection in the traveling-wave ODE, and hyperbolic stability of the associated Chapman-Jouguet (square-wave) approximation. Notably, our results apply to combustion waves of any type: weak or strong, detonations or deflagrations, reducing the study of stability to verification of a readily numerically checkable Evans function condition. Together with spectral results of Lyng and Zumbrun, this gives immediately stability of small-amplitude strong detonations in the small heat-release (i.e., fluid-dynamical) limit, simplifying and greatly extending previous results obtained by energy methods by Liu-Ying and Tesei-Tan for Majda's model and the reactive Navier-Stokes equations, respectively.     

Simulation of quasi-dimensional combustion model for predicting diesel engine performance

In order to improve the precision of quasi-dimensional combustion model for predicting diesel engine performance and promote the real time operating performance of the simulation model, a new phase-divided spray mixing model is proposed and the quasi-dimensional combustion model of diesel engine working process is developed. The software MATLAB/Simulink is utilized to build the quasi-dimensional combustion model of diesel engine working process, and the performance for diesel engine is simulated. The simulation results agree with experimental data quite well. The comparisons between them show that the relative error of power and brake specific fuel consumption is less than 2.8% and the relative error of nitric oxide and soot emissions is less than 9.1%. By utilization of this simulation model with personal computer, the average computational time for one diesel engine working process is 36 s, which presents good real time operating performance of the model. At the same time, the influence of parameters in calculation of air entrainment on prediction precision of diesel engine’s simulation model is analyzed.     

Propagation effects of model-calculated probability values in Bayesian networks

Probabilistic causal interaction models have become quite popular among Bayesian-network engineers as elicitation of all probabilities required often proves the main bottleneck in building a real-world network with domain experts. The best-known interaction models are the noisy-OR model and its generalisations. These models in essence are parameterised conditional probability tables for which just a limited number of parameter probabilities are required. The models assume specific properties of intercausal interaction and cannot be applied uncritically. Given their clear engineering advantages however, they are subject to ill-considered use. This paper demonstrates that such ill-considered use can result in poorly calibrated output probabilities from a Bayesian network. By studying, in an analytical way, the propagation effects of noisy-OR calculated probability values, we identify conditions under which use of the model can be harmful for a network's performance. These conditions demonstrate that use of the noisy-OR model for mere pragmatic reasons is sometimes warranted, even when the model's underlying assumptions are not met in reality.     

具有饱和的Prey—Predator模型的长时间行为

本文研究了具有饱和的Ｐｒｅｙ－Ｐｒｅｄａｔｏｒ模的长时间为。     

The generalized Riemann problem for a scalar Chapman–Jouguet combustion model

The generalized Riemann problem for a scalar Chapman–Jouguet combustion model in a neighborhood of the origin (t > 0) on the (x, t) plane is studied. Under the entropy conditions, we obtain the solutions constructively. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a combustion wave CJDT into SDT in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution doesn’t contain combustion waves, which exhibits the instability for unburnt states. This work is supported by NSFC 10671120     

基于分类的资源公平分配决策方法

针对资源分配问题,本文提出了基于分类的决策方法以实现效率与公平的权衡。首先,研究了效率最优分配与完全均等分配过程,阐明了边际效用对分配结果的影响,指出个体间边际效用相差越小,两种分配的结果越接近。其次,构建0-1整数规划模型求解分类结果,目标是使类与类之间边际效用相差尽可能小。然后,按类对资源进行分配,类间采用完全均等分配,类中采用效率最优分配。通过选择分类数量可以实现不同程度的公平。最后,运用算例验证方法的有效性,说明分类数量对效率与公平的影响。     

基于模糊GM(1,1)模型的时间序列预测

提出了一种模糊GM(1,1)预测模型,即FGM(1,1)模型,该方法是在GM(1,1)模型中引入模糊成员函数,通过模糊成员函数对时间序列数据进行模糊化,达到数据优化选择,实现历史数据"重近轻远"的预测效果.仿真结果表明所提出的预测方法有效可靠,为提高预测精度提供了新的途径.     

蚁群算法在战损装备抢修任务指派中的应用研究

结合战时装备保障实际情况和战损装备抢修任务特点,分析了现有战损装备抢修任务指派模型的特点及不足.依据紧急程度对战损装备抢修任务进行分类,建立了不同紧急度对应的装备抢修任务指派模型,重点是利用蚁群算法对模型进行求解.最后通过某装备保障想定的实例进行了验证,结果表明该算法操作简单、切实有效,能有效实施战损装备应急抢修任务的指派,在装备保障智能决策系统中有较好的应用前景.     

SUR模型回归系数的估计

本文证明了一个关于SUR模型回归系数最小方差线性无偏估计(MVLUE)的充要条件,并利用此充要条件讨论了几类SUR模型回归系数的MVLUE估计及两步估计.在方法上避免了与分块矩阵求逆有关的运算,所得结论推广和完善了已有的一些结果.     

Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models

In a certain class of semelparous Leslie matrix models, either a positive equilibrium is stable and an invariant set on the boundary of the nonnegative cone is unstable or vice versa generically if the model dimension is two or three. This dynamic dichotomy is expected to be failed in the four-dimensional case. Our study focuses on a semelparous Leslie matrix model with specific nonlinearities and rigorously proves that the dynamic dichotomy does not hold in the four-dimensional case. This result is derived by showing that the four-dimensional semelparous Leslie matrix model can be uniformly persistent with respect to the boundary of the nonnegative cone even if there exists an unstable positive equilibrium. In such a situation, there are no missing age-classes but population oscillation occurs.     

Existence of Chapman-Jouguet detonation for a viscous combustion model

In [SIAM J. Appl. Math. 41 (1981) 70-93], Majda proposed a model for the interaction between chemical reactions and compressible fluid dynamics. This model is a low Mach number limit of the one-component reactive Navier-Stokes equations [SIAM J. Appl. Math. 43 (1983) 1086-1118] and was extended to the case where the diffusion coefficient is positive by Larrouturou [Nonlinear Anal. 77 (2001) 405-418]. In this paper, the existence of a one-dimensional Chapman-Jouguet detonation wave, or equivalently a heteroclinic orbit, for the extended model is proven. The proof is based on an application of topological arguments to a system of ordinary differential equations which is obtained from the partial differential equations describing the interaction.     

Einfluss eines Verbrennungsvorganges auf den Wärme- und Stoffaustausch in einer laminaren Grenzschicht

Summary The influence of combustion on heat and mass transfer is investigated on the following model. A mixture of an inert with a combustible gas (air) flows in steady, laminar flow over a flat plate. A mass flux of gaseous fuel away from the plate surface is produced by some means. Combustion is assumed to occur with very fast reaction rate so that the process is purely controlled by diffusion and the equilibrium is assumed as very close to complete combustion. It is studied under which conditions the combustion occurs at the surface or when the flame is displaced into the boundary layer. The influence of combustion on the heat transfer from a hot gas to the plate surface is calculated, for the condition that combustion occurs at the surface.      

Perturbed Riemann Problem for a Scalar Chapman-Jouguet Combustion Model

The author considers the perturbed Riemann problem for a scalar ChapmanJouguet combustion model which comes from Majda’s model with a modified, bump-type ignition function proposed in the results of Lyng and Zumbrun in 2004. Under the entropy conditions, the unique solution in a neighborhood of the origin on the(x, t) plane(t > 0) is obtained. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a strong detonation into a weak deflagration in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution does not contain combustion wave, which exhibits the instability for the unburnt state.     

关于两种DEA超效率模型的进一步探讨

对数据包络分析模型中的两种超效率模型——LJK模型和MAJ模型进行了分析和研究,通过变量替换,对原有模型进行了变形,在不变规模效益和非零输入条件下,分析了它们和AP模型之间的内在联系,得出并证明了若干重要性质,最后给了实例证明.