Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics

A computational fluid dynamics (CFD) tool for performing turbulent combustion simulations that require finite-rate chemistry is developed and tested by modelling a series of bluff-body stabilized flames that exhibit different levels of finite-rate chemistry effects ranging from near equilibrium to near global extinction. The new modelling tool is based on the multi-environment probability density function (MEPDF) methodology and combines the following: the direct quadrature method of moments (DQMOM); the interaction-by-exchange-with-the-mean (IEM) mixing model; and realistic combustion chemistry. Using DQMOM, the MEPDF model can be derived from the transport PDF equation by depicting the joint composition PDF as a weighted summation of a finite number of multi-dimensional Dirac delta functions in the composition space. The MEPDF method with multiple reactive scalars retains the unique property of the joint PDF method of treating chemical reactions exactly. However, unlike the joint PDF methods that typically must resort to particle-based Monte-Carlo solution schemes, the MEPDF equations (i.e. the transport equations of the weighted delta-peaks) can be solved by traditional Eulerian grid-based techniques. In the current study, a pseudo time-splitting scheme is adopted to solve the MEPDF equations; the reaction source terms are computed with a highly efficient and accurate in-situ adaptive tabulation (ISAT) algorithm. A 19-species reduced mechanism based on quasi-steady state assumptions is used in the simulations of the bluff-body flames. The modelling results are compared with the experimental data, including mixing, temperature, major species and important minor species such as CO and NO. Compared with simulations using a Monte-Carlo joint PDF method, the new approach shows comparable accuracy.     

ON MORPHOLOGY AND MULTIPLE MELTING IN POLYPROPYLENE

A series of polypropylenes, including two modern high crystallinity materials (HCPP) were subjected to a stepwise crystallization procedure as a guide to their properties. The results were complicated by the development of double melting endotherms at the highest crystallization temperature. Both HCPP, when grown at the temperature of 145°C, give a double melting peak, but the proportions of the two peaks varied according to the density of nucleation. By partially melting a specimen between the two peaks, it was possible to assign the higher peak to radial dominant lamellae and the lower peak to mostly tangential subsidiary lamellae filling the space in between. Uniformly cross-hatched lamellae at the center of spherulites melt along with the lower melting population in the outer regions of the spherulites. Even if differences in crystallization temperature are eliminated, the properties of nucleated as opposed to nonnucleated PP may therefore be influenced by differences between the center and periphery of spherulites, with “central” properties much more in evidence in nucleated material. The development of these double endotherms is related to morphological constraint, rather than molecular fractionation. Their form is strongly influenced by cross-hatching, but the phenomenon is still found at 160°C where cross-hatching does not form.     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

ＦＩＸＥＤＰＯＩＮＴＳＡＮＤＣＯＵＰＬＥＤＦＩＸＥＤＰＯＩＮＴＳＦＯＲＩＮＣＲＥＡＳＩＮＧＯＰＥＲＡＴＯＲＳＷＩＴＨＡＰＰＬＩＣＭＩＯＮＳＴＯＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺＨＡＮＧＳＨＩＳＨＥＮＧＡＮＤＨＵ...     

OSCILLATION OF A FORCED SECOND ORDER NONLINEAR EQUATION

ＯＳＣＩＬＬＡＴＩＯＮ ＯＦ Ａ ＦＯＲＣＥＤ ＳＥＣＯＮＤ ＯＲＤＥＲ ＮＯＮＬＩＮＥＡＲ ＥＱＵＡＴＩＯＮ ￥ＫＯＮＧＱＩＮＧＫＡＩ；ＺＨＡＮＧＢＩＮＧＧＥＮＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｇｉｖｅｓｓｅｖｅｒａｌｃｒｉｔｅｒｉａｏｎｔｈｅｏ...     

前馈PMD补偿实验中从偏振度椭球获得差分群时延的研究

运用偏振度(DOP)椭球法从实验的有限样点数据中获得了差分群时延和偏振主态方向,这为前馈补偿实验提供了最关键的技术因素.在实验中获得了偏振主态方向和DGD,而且当DGD较小时,从实验所获得的DGD值与理论模拟的变化趋势基本一致.结果表明当DGD较小时,可以用偏振度椭球法从实验上得到正确的DGD和偏振主态方向.     

机载成像光谱仪CCD制冷系统设计与实现

为减小紫外成像光谱仪中CCD暗电流噪声,提高系统信噪比,需要对CCD进行制冷.为此采用模拟比例-积分-微分电路设计了CCD制冷电路,利用Zregler-Nicholas经验整定方法确定比例-积分-微分参量,以实现降温速率不大于5℃/min、温度稳定度为±0.05℃,满足最大制冷温差.将该制冷系统应用于机载成像光谱仪进行了测试,结果表明:环境温度变化不会影响制冷效果,在达到制冷目标温度-20℃后,CCD探测器暗背景下光谱维噪声平均灰度响应值为1 072,暗背景信号非均匀性下降到0.5%,满足光谱数据反演要求.     

On the regulator problem for linear degenerate control systems

In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.This work was performed under the auspices of the National Research Council of Italy, Gruppo Nazionale per l'Analisi Funzionale e le Sue Applicazioni, Rome, Italy.     

Time-delay effects on dynamics of a two-actor conflict model

We present a study of time-delay effects on a two-actor conflict model based on nonlinear differential equations. The state of each actor depends on its own state in isolation, its previous state, its inertia to change, the positive or negative feedback and a time delay in the state of the other actor. We use both theoretical and numerical approaches to characterize the evolution of the system for several values of time delays. We find that, under particular conditions, a time delay leads to the appearance of oscillations in the states of the actors. Besides, phase portraits for the trajectories are presented to illustrate the evolution of the system for different time delays. Finally, we discuss our results in the context of social conflict models.     

Differential operators and immersions of a Riemann surface into a Grassmannian

We consider equivariant holomorphic immersions of a universal cover of a compact Riemann surface X into a Grassmannian satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to that takes the natural action of the Galois group on to the action of the Galois group on defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism.