关于凸体覆盖的Hadwiger猜想的两个等价形式

令K是一个内部(记作intK)包含原点o的凸体,bdK为其边界,m为覆盖K所需的intK的平移的最小个数.本文证明,存在正实数η和含于η(bdK)的m元点集C1使得C1+int K覆盖K;存在正实数η′、实数γ∈(0,1)和含于η′(bd K)的m元点集C2使得C2+γK覆盖K.基于这两个事实,本文得到关于凸体覆盖的Hadwiger猜想的两个等价形式.本文还引入一个可以替代宗传明提出的攻克Hadwiger猜想的数量方案中的γm(K)的新泛函.     

CH4/空气简化动力学机理数值验证

选择绕圆柱预混燃烧算例，验证CH₄/空气三种简化动力学机理（16s41r、15s19r和53s325r）.考虑均匀来流，忽略湍流和湍流与燃烧相互作用以及燃料扩散效应，假设层流有限反应速率，采用保自由流5阶WENO格式求解多组分Euler方程组，得到CH₄/空气预混燃烧流场温度等值线、沿驻点线压力和温度及其CH₄、CO和CO₂质量百分数分布.结果表明：三种简化动力学机理给出的流场均出现弓形激波和火焰面，弓形激波和火焰驻点距离及其形状、诱导区宽度和简化动力学机理相关.当圆柱直径增大，弓形激波和火焰向圆柱上游移动，对应的驻点距离均增大，诱导区宽度变短，点火延时变小，但火焰和弓形激波位置次序未变化.53s325r模型要比16s41r模型和15s19r模型精度要高，点火延时覆盖的压力和温度范围也较宽，所有简化机理均未完全反应，在较大圆柱直径下游达到化学平衡.     

Measure of segments which intersect a convex body from rotational formulae

Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R³. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.     

The Effects of CO2 Additional on Flame Characteristics in the CH4/N2/O2 Counterflow Diffusion Flame

The effects (chemical, thermal, transport, and radiative) of CO₂ added to the fuel side and oxidizer side on the flame temperature and the position of the flame front in a one-dimensional laminar counterflow diffusion flame of methane/N₂/O₂ were studied. Overall CO₂ resulted in a decrease in flame temperature whether on the fuel side or on the oxidizer side, with the negative effect being more obvious on the latter side. The prominent effects of CO₂ on the flame temperature were derived from its thermal properties on the fuel side and its radiative properties on the oxidizer side. The results also highlighted the differences in the four effects of CO₂ on the position of the flame front on different sides. In addition, an analysis of OH and H radicals and the heat release rate of the main reactions illustrated how CO₂ affects the flame temperature.     

Kirchhoff动力学比拟对弹性薄壳的推广

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应,在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法.在直法线假设下,在弹性中面上构筑空间正交轴系,此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度.沿两个...     

Effects of pressure rise rate on laminar flame speed under normal and engine-relevant conditions

Laminar flame speed (LFS) is one of the most important physicochemical properties of a combustible mixture. At normal and elevated temperatures and pressures, LFS can be measured using propagating spherical flames in a closed chamber. LFS is also used in certain turbulent premixed flame modelling for combustion in spark ignition engines. Inside the closed chamber or engine, transient pressure rise occurs during the premixed flame propagation. The effects of pressure rise rate (PRR) on LFS are examined numerically in this study. One-dimensional simulations are conducted for spherical flame propagation in a closed chamber. Detailed chemistry and transport are considered. Different values of PRR at the same temperature and pressure are achieved through changing the spherical chamber size. It is found that the effect of PRR on LFS is negligible under the normal and engine-relevant conditions considered in this study. This observation is then explained through the comparison between the unsteady and convection terms in the energy equation for a premixed flame.     

增强型喷射器对爆轰波DDT过程的影响

在激波、火焰及射流同时存在的流场中,组织燃烧转爆轰过程是脉冲爆震发动机实现点火、起爆的关键问题。设计一类喷射器,采用C_2H_2/O_2/Ar反应,数值验证了该喷射器能增强爆震室燃料燃烧转爆轰的可行性,并讨论了流场中热点的点火机制。结果显示:该装置在流场中可激发不稳定性,产生漩涡,加速能量、质量的交换。流场产生热点,促进火焰速度加快,追赶前导激波。喷射器位置影响前导激波的运动速度。在一定范围内,前导激波速度越大,碰撞产生的热点越容易激发燃烧转爆轰过程。     

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.