Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight

This paper studies the Hankel determinants generated by a discontinuous Gaussian weight with one and two jumps. It is an extension in a previous study, in which they studied the discontinuous Gaussian weight with a single jump. By using the ladder operator approach, we obtain a series of difference and differential equations to describe the Hankel determinant for the single jump case. These equations include the Chazy II equation, continuous and discrete Painlevé IV. In addition, we consider the large n behavior of the corresponding orthogonal polynomials and prove that they satisfy the biconfluent Heun equation. We also consider the jump at the edge under a double scaling, from which a Painlevé XXXIV appeared. Furthermore, we study the Gaussian weight with two jumps and show that a quantity related to the Hankel determinant satisfies a two variables' generalization of the Jimbo‐Miwa‐Okamoto σ‐form of the Painlevé IV.     

A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes d_ε is equal to or much larger than the size of the holes ε. Such a diluted porous medium is interesting because it contains some cases where we have a non-negligible effect on the solution when(ε, d_ε) →(0, 0).Smaller distances were avoided for mathematical reasons and for these large distances, the geometry of the holes does not affect or rarely affect the asymptotic result. Very recently, it was shown for the 2D-Euler equations that a porous medium is non-negligible only for inter-holes distances much smaller than the sizes of the holes.For this result, the boundary regularity of holes plays a crucial role, and the permeability criterion depends on the geometry of the lateral boundary. In this paper, we relax slightly the regularity condition, allowing a corner, and we note that a line of irregular obstacles cannot slow down a perfect fluid in any regime such thatε ln d_ε→ 0.     

A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations

Science China Mathematics - For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied...     

低雷诺数俯仰振荡翼型等离子体流动控制

针对低雷诺数翼型气动性能差的特点, 通过介质阻挡放电(dielectric barrier discharge, DBD)等离子体激励控制的方法, 提高翼型低雷诺数下的气动特性,改善其流场结构. 采用二维准直接数值模拟方法求解非定常不可压Navier-Stokes方程,对具有俯仰运动的NACA0012翼型的低雷诺数流动展开数值模拟.同时将介质阻挡放电激励对流动的作用以彻体力源项的形式加入Navier-Stokes方程,通过数值模拟探究稳态DBD等离子体激励对俯仰振荡NACA0012翼型气动特性和流场特性的影响.为了进行流动控制, 分别在上下表面的前缘和后缘处安装DBD等离子体激励器,并提出四种激励器的开环控制策略,通过对比研究了这些控制策略在不同雷诺数、不同减缩频率以及激励位置下的控制效果.通过流场结构和动态压强分析了等离子体进行流场控制的机理. 结果表明,前缘DBD控制中控制策略B(负攻角时开启上表面激励器,正攻角时开启下表面激励器)效果最好,后缘DBD控制中控制策略C(逆时针旋转时开启上表面激励器,顺时针旋转时开启下表面激励器)效果最好,前缘DBD控制效果会随着减缩频率的增大而下降, 同时会导致阻力增大.而后缘DBD控制可以减小压差阻力, 优于前缘DBD控制,对于计算的所有减缩频率(5.01~11.82)都有较好的增升减阻效果.在不同雷诺数下, DBD控制的增升效果较为稳定, 而减阻效果随着雷诺数的降低而变差,这是由流体黏性效应增强导致的.      

The Effect of Surface Roughness on Immiscible Displacement Using Pore Scale Simulation

Transport in Porous Media - Pore scale immiscible displacement is crucial in oil industry. The surface roughness of throat is an important factor affecting water–oil interface movement. In...     

Invariant torus and its destruction for an oscillator with dry friction

Nonlinear Dynamics - Mechanical systems with dry friction are typical Filippov systems. Such class of systems have complicated dynamical behaviors due to the existence of sliding motion. In this...     

基于空间视角下产业协同集聚对区域创新的影响

选取2009-2018年中国30个省(市、自治区)的数据,运用区位商相对差异指数和熵权TOPSIS法分别测算其产业协同集聚度和区域创新水平,研究二三产业协同集聚对区域创新的影响.研究表明:产业集聚通过"知识技术、劳动力、物力"等外部规模经济增加创新产出;2009-2018年,两产业协同集聚水平由中西部向东部递减,区域创新水平东部明显高于中西部,空间溢出效应显著;两产业协同集聚对创新的影响呈现"倒U型"特征;最后基于计量结果提出相关建议.     

基于收益共享机制的干支线衔接运输联合定价模型

在班轮运输网络中,支线运输与干线运输具有互补性,干线承运人与支线承运人之间的合作能够为托运人提供更高的便利度和更完善的运输服务。本文在考虑可替代运输路径之间竞争关系的基础上,研究干支线衔接路径的定价问题,在运输链纵向一体化和分散化两种结构下,构建Bertrand博弈模型研究上下游承运人的均衡运价。同时,设计合理的收益共享机制,使承运人在分散结构的运输系统中仍能实现运输链的协调。     

Homogeneous Einstein-like metrics on symmetric spaces

In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M, which is not isometric to a compact Lie group and has rank greater than 1. Whenever there exists a closed proper subgroup G′ of G = Isom_0(M) acting transitively on M, we find all the G′-invariant A-metrics and B-metrics on M. More precisely, we prove that G′-invariant metrics on M must be A-metrics, and G′-invariant B-metrics on M are always Einstein.     

卷烟主流烟气中巴豆醛在线光谱分析方法研究

卷烟主流烟气是卷烟燃烧时被人体吸食到体内的主要气体,其减焦降害已成为全社会高度关注的问题。在各种卷烟主流烟气组分中,巴豆醛以其强烈的基因毒性,成为国家规定的卷烟中七种主要有害指标物之一。传统的巴豆醛分析方法大都采用高效液相色谱法等实验室分析方法,需繁琐的样品前处理过程,无法测量巴豆醛的实时浓度,难以准确评估巴豆醛对人体健康的影响。为了快速、准确地检测卷烟主流烟气中的巴豆醛组分,本研究搭建了一套可以直接与吸烟机耦合的傅里叶红外光谱分析系统（FTIR）,并创新性开发过采样数据驱动光谱分析方法（ODDSA）,从复杂、变动的卷烟主流烟气中准确提取巴豆醛的光谱组分信息。ODDSA方法从实验设计入手,采用随机设计的思路尽可能模拟实际卷烟样品的分布范围,以构建具备良好光谱数据结构的样品集。在此基础上,创新性地将高密度小波变换引入红外光谱数据的处理过程中,以时/频双域过采样的方式提升了光谱解析分辨率,进而降低了其他基质组分对巴豆醛光谱信息的干扰。最后,发展改良竞争自适应重加权采样方法,从多倍冗余的高密度小波系数中准确提取待测物质的最佳变量组合,由此构建高质量的巴豆醛光谱定量分析模型。为了验证ODDSA方法的有效性,实验中采集了15种典型市售卷烟品牌,每个品牌在线采集8支样品的主流烟气红外光谱,随后采用随机挑选的25个验证集样本对ODDSA方法进行验证。结果表明,检验集的线性拟合系数为0.971,相对均方根误差为5.5%,其预测精度能有效满足卷烟主流烟气中巴豆醛的在线分析需求,并可拓展到环境二手烟气中其他组分的在线监测,进而为吸烟与健康评估提供全新手段。