Qualitative Features of Periodic Solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space H ^N , N ≥ 0, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree.     

Re-weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

Nuclear quantum effects in finite temperature simulations of molecular clusters are determined by taking advantage of a recently developed method based on the Feynman Path Integral. The structural and thermodynamic properties, including the nuclear quantum effects are determined for three Stockmayer clusters. The ionic system contain a lithium ion solvated by six strong dipoles and 12 weaker ones. The presence of the ion in the mixed Stockmayer cluster drastically enhances the fluxional nature of the less polar components which occupy the second solvation layer, whereas the neutral counterpart has the effect of reducing it. The nuclear quantum effects are significant at room temperature and above for the solvated ionic system. These are attributable to two factors: (a) the lightness of the lithium ion and (b) the stiffness of the ion-dipole interactions. At 300 K, the difference between the fully converged quantum and the classical heat capacities is about 1.3 K_B for the ionic cluster. This difference is about 10 SDs obtained from 95% confidence estimates of the statistical fluctuations. Cubic convergence is confirmed for temperatures as low as 50 K by regression analysis. The nuclear quantum effects do not change the peak melting temperature of the cluster.     

Massive Radiation via Tunneling in a BTZ Black Hole

Hawking radiation can usefully be viewed as a semi-classical tunneling process that originates at the black hole horizon. Massive radiation from a BTZ black hole is investigated. The conservation of energy implies the effect of self-gravitation. Viewed as a tunneling process, the emission spectrum derivates from the pure thermal spectrum, but it is consistent with an underlying unitary theory. The result is the same as that of massless particles.     

Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass

We extend the validity of Brill’s axi-symmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.     

Fractional diffusion-wave problem in cylindrical coordinates

In this Letter, we present analytical and numerical solutions for an axis-symmetric diffusion-wave equation. For problem formulation, the fractional time derivative is described in the sense of Riemann-Liouville. The analytical solution of the problem is determined by using the method of separation of variables. Eigenfunctions whose linear combination constitute the closed form of the solution are obtained. For numerical computation, the fractional derivative is approximated using the Grünwald-Letnikov scheme. Simulation results are given for different values of order of fractional derivative. We indicate the effectiveness of numerical scheme by comparing the numerical and the analytical results for α=1 which represents the order of derivative.     

Moving least squares reconstruction for sharp interface immersed boundary methods

We propose a new approach for reconstructing velocity boundary conditions in sharp-inerface immersed boundary (IB) methods based on the moving least squares (MLS) interpolation method. The MLS is employed to not only reconstruct velocity boundary conditions but also to calculate the pressure and velocity gradients in the vicinity of the immersed body, which are required in fluid structure interaction problems to obtain the force exerted by the fluid on the structure. To extend the method to arbitrarily complex geometries with nonconvex shaped boundaries, the visibility method is combined with the MLS method. The performance of the proposed curvilinear IB MLS (CURVIB-MLS) is demonstrated by systematic grid-refinement studies for two- and three-dimensional tests and compared with the standard CURVIB method employing standard wall-normal interpolation for reconstructing boundary conditions. The test problems are flow in a lid-driven cavity with a sphere, uniform flow over a sphere, flow on a NACA0018 airfoil at incidence, and vortex-induced vibration of an elastically-mounted cylinder. We show that the CURVIB-MLS formulation yields a method that is easier to implement in complex geometries and exhibits higher accuracy and rate of convergence relative to the standard CURVIB method. The MLS approach is also shown to dramatically improve the accuracy of calculating the pressure and viscous forces imparted by the flow on the body and improve the overall accuracy of FSI simulations. Finally, the CURVIB-MLS approach is able to qualitatively capture on relatively coarse grids important features of complex separated flows that the standard CURVIB method is able to capture only on finer grids.     

High-order curvilinear mesh generation technique based on an improved radius basic function approach

A high-order curvilinear hybrid mesh generation technique is developed for high-order numerical method (eg, discontinuous Galerkin method) applications to improve the accuracy for problems with curve boundary. The grid generation technique is based on an improved radius basic function (RBF) approach by which the straight-edge mesh is converted into high-order curve mesh. Firstly, an initial straight-edge mesh is prepared by traditional grid generation software. Then, high-order interpolation points are inserted into the mesh entities such as edges, faces, and cells according to the final demand of mesh order. To preserve the original geometry, the inserted points on solid wall are then projected onto the CAD model using an open source tool “Open Cascade.” Finally, other inserted points in the field near the solid wall are moved to appropriate positions by the improved RBF approach to avoid tangled cells. If we use the original RBF approach, then the inserted points on the edge and face entities normal to the solid boundary in the region of boundary layer will move to improper positions. To overcome this problem, a weighting based on the local grid aspect ratio between normal direction and tangential direction is introduced into the baseline RBF approach. Three typical configurations are tested to validate the mesh generator. Meanwhile, a third-order solution of subsonic flow over an analytical 3D body of revolution in the second International Workshop on High-Order CFD Methods is supplied by a discontinuous Galerkin solver. These numerical tests demonstrate the potential capability of present technique for high-order simulations of complex geometries.     

Numerical Experiences with New Truncated Newton Methods in Large Scale Unconstrained Optimization

Recently, in [12] a very general class oftruncated Newton methods has been proposed for solving large scale unconstrained optimization problems. In this work we present the results of an extensive numericalexperience obtained by different algorithms which belong to the preceding class. This numerical study, besides investigating which arethe best algorithmic choices of the proposed approach, clarifies some significant points which underlies every truncated Newton based algorithm.     

星模拟器星点能量中心修正方法的研究

对星模光学系统中各种像差对几何中心位置的影响及像差对显示星点能量中心位置造成的偏差进行了分析与综合评估.分析结果表明,视场位置越大的星点产生的像点能量越不均匀,重心偏移越明显,系统中慧差和畸变对于星点能量中心影响较大.根据球面镜组成的共轴光学系统性质可知,能量中心的偏移发生在星点所在极半径方向上,因此提出了一种基于极坐标的星点位置修正方法,只需在星点所在方向对极半径进行修正.该方法简化了基于二维坐标轴分区修正的过程,减少了数据计算量.利用极坐标修正方法对星模拟器修正前后的单星位置误差进行了测试,实验结果表明极坐标修正过程较以往修正方法简单快捷,且修正结果更加准确.     

二维拉格朗日坐标系下气粒混合双向耦合对激波流场影响的计算

喷射颗粒与气体混合是内爆压缩领域的热点和难点. 针对喷射混合中的气粒双向耦合问题, 开展了理论建模、离散算法以及颗粒反馈对激波流场的影响研究. 建立了拉格朗日计算框架下的数学模型; 给出了耦合源项的离散算法; 开展了平面及汇聚构型条件下, 气粒双向耦合的数值模拟研究; 发现了颗粒反馈导致气体激波提速现象以及气区流场物理量分布形态的改变, 初步获得了量化分析结果. 本文建立的数学模型、计算方法和获得的新的物理认识, 为深入理解喷射混合现象、解决相关工程应用问题提供了重要理论支撑.