多级轴流透平气动特性计算方法研究

在多级轴流透平子午面中线上建立1.5维欧拉方程组,其中叶片作用力、流体的黏性作用、冷气的作用以源项的形式考虑到方程中,控制方程采用一步时间推进TVD-LW格式进行离散和求解.计算结果表明,该方法能够预测多级轴流透平的平均气动参数分布和气动性能,具有快速、灵活的特点,可以用于求解透平的特性曲线或进行气动优化.     

On complex singularities of the 2D Euler equation at short times

We present a study of complex singularities of a two-parameter family of solutions for the two-dimensional Euler equation with periodic boundary conditions and initial conditions in the short-time asymptotic régime. As has been shown numerically in Pauls et al. [W. Pauls, T. Matsumoto, U. Frisch, J. Bec, Nature of complex singularities for the 2D Euler equation, Physica D 219 (2006) 40-59], the type of the singularities depends on the angle ? between the modes p and q. Thus, the Fourier coefficients of the solutions decrease as with the exponent α depending on ?. Here we show for the two particular cases of ? going to zero and to π that the type of the singularities can be determined very accurately, being characterised by α=5/2 and α=3 respectively. In these two cases we are also able to determine the subdominant corrections. Furthermore, we find that the geometry of the singularities in these two cases is completely different, the singular manifold being located “over” different points in the real domain.     

Quantum Mayer Graphs for Coulomb Systems and the Analog of the Debye Potential

Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length ^–1 _D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way.     

毛细作用的变分法理论

以圆柱形毛细管内壁、毛细管内的液体和气体为研究对象.设毛细管液体的表面为旋转面,写出了系统的自由能(表面能及重力势能)的泛函.使自由能泛函取极值的欧拉方程就是关于附加压强的拉普拉斯公式.泛函取极值时在可动边界(毛细管内壁)上的边界条件就可导出关于接触角的杨氏方程.此二方程是自由能取极值的密不可分的两个必要条件.     

A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets in Bipartite Graphs

This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn’s information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the bipartite graph is regular on one side, but may be irregular on the other, the extended entropy-based proof technique yields the same bound as was conjectured by Kahn (2001) and proved by Sah et al. (2019).     

一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法

针对目前没有合适的方法从产生方来表征纠缠量子微波信号的质量好坏, 提出了一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法. 利用双模压缩真空态描述了纠缠量子微波的信号格式, 给出了光子数与压缩参量之间的函数关系, 以熵评估纠缠态信号所占比例, 分析了熵与压缩参量和光子数之间的关系. 仿真结果表明, 纠缠量子微波信号中的光子数是由压缩参量决定的, 它们之间呈指数平方的规律性变化; 熵随着压缩参量的增大而减小, 但是减小的趋势越来越平缓, 近似呈负指数关系, 熵的极限值约为65%. 研究结果表明, 通过选择合适的压缩参量可以提高纠缠微波信号生成质量以满足实际需要, 因此, 本研究对于生成双路径纠缠量子微波电路参数选择、提高系统可用性提供了方法和依据.     

The effect of shocks on second order sensitivities for the quasi-one-dimensional Euler equations

The effect of discontinuity in the state variables on optimization problems is investigated on the quasi-one-dimensional Euler equations in the discrete level. A pressure minimization problem and a pressure matching problem are considered. We find that the objective functional can be smooth in the continuous level and yet be non-smooth in the discrete level as a result of the shock crossing grid points. Higher resolution can exacerbate that effect making grid refinement counter productive for the purpose of computing the discrete sensitivities. First and second order sensitivities, as well as the adjoint solution, are computed exactly at the shock and its vicinity and are compared to the continuous solution. It is shown that in the discrete level the first order sensitivities contain a spike at the shock location that converges to a delta function with grid refinement, consistent with the continuous analysis. The numerical Hessian is computed and its consistency with the analytical Hessian is discussed for different flow conditions. It is demonstrated that consistency is not guaranteed for shocked flows. We also study the different terms composing the Hessian and propose some stable approximation to the continuous Hessian.     

Continuity of the Integrated Density of States on Random Length Metric Graphs

We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by compact subgraphs. A trace per unit volume formula holds, similarly as in the Euclidean case. Our setting includes periodic graphs. For a model where the edge lengths are random and vary independently in a smooth way we prove a Wegner estimate and related regularity results for the integrated density of states. These results are illustrated for an example based on the Kagome lattice. In the periodic case we characterise all compactly supported eigenfunctions and calculate the position and size of discontinuities of the integrated density of states.      

The Characteristic Equation of Corrugated Square Groove Waveguides

When the periodic spacing of corrugated wavesguides is much less than wavelength , the slot width dL, and the space harmonics are neglected, the characteristic equation of corrugated square groove waveguides is formulated based on Maxwell's equations and boundary conditions.     

广义特征坐标系计算膨胀波与激波优越性的数值验证

最近提出的以流体速度和声速的线性组合为速度而运动的广义特征坐标系,是-个更为-般的坐标系统,当参数取不同特殊值的时候,就可以得到其他经典的坐标系统.这种坐标系的最大特点是,它能跟随膨胀波(当然也可以跟随激波和接触间断)运动,从而在使用同-计算格式的前提下,使得膨胀波的计算精度更高.对膨胀波和激波进行数值试验,结果显示广义特征坐标系在计算膨胀波和激波时明显优于传统的坐标系.     

Comparative analysis of electric field influence on the quantum wells with different boundary conditions.

Analytical solutions of the Schrödinger equation for the one‐dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small , the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC‐dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two‐level approximation elementary explains the negative polarizations as a result of the field‐induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann‐Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero‐voltage position entropies are BC independent and for all states but the ground Neumann level (which has ) are equal to while the momentum entropies depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC‐dependent zero‐energy and zero‐polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.     

复杂换热网络MINLP中的非线性特性分析

针对复杂换热网络MINLP问题,本文应用多维函数渐变法探索和分析了连续变量和整型变量引起的网络性能非线性和非凸特性。研究表明,当系统规模增大时,不但连续变量的叠加效应将增加系统的非线性,整型变量将使得非线性特性更为严重。     

Global regularity of the 4D restricted Euler equations

We are concerned with the critical threshold phenomena in the restricted Euler (RE) equations. Using the spectral and trace dynamics we identify the critical thresholds for the 3D and 4D restricted Euler equations. It is well known that the 3D RE solutions blow up. Projected on the 3-sphere, the set of initial eigenvalues which give rise to bounded stable solutions is reduced to a single point, which confirms that the 3D RE blowup is generic. In contrast, we identify a surprisingly rich set of the initial spectrum on the 4-sphere which yields global smooth solutions; thus, 4D regularity is generic.     

The Boundary States of the q-Deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra Uq[sl(2|1)]. We give the bosonization of the boundary states.``     

Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.     

The Boundary States of the q-Deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U_q[\widehat{sl(2|1)}]. We give the bosonization of the boundary states.     

球面波的相奇异分布区域特征

从波动方程出发，在基尔霍夫边界条件下，根据积分的物理意义，简明地研究了发散和汇聚球面波的相奇异区域分布。结果表明，除了汇聚的球面波焦点区域存在相奇异现象外，焦点以外的区域及对发散的球面波同样存在相奇异现象。发散球面波的相奇异区位于入射空间，在相奇异区域的不同部分相奇异规律不同，源点是相奇异区里的一个特殊点。汇聚的球面波的相奇异区域存在于像空间，结构简单，焦点是相奇异区域里的一个特殊点。