A NON-OSCILLATORY NO-FREE-PARAMETER FINITE ELEMENT AND ITS APPLICATIONS IN CDF

A non-oscillatory no-free-parameter finite element method (NNFEM) is presented based on the consideration of wave propagation characteristic in different characteristic directions across a strong discontinuity through flux vector splitting in order to satisfy the increasing entropy condition. The algorithm is analysed in detail for the one-dimensional (1D) Euler equation and then extended to the 2D, axisymmetric and 3D Euler and Navier–Stokes equations. Its applications in various cases—in viscid oblique shock wave reflection, flow over a forward step, axisymmetric free jet flow, supersonic flows over 2D and 3D rectangular cavities—are given. These computational results show that the present NNFEM is efficient in practice and stable in operations and is especially capable of giving good resolution in simulating complicated separated and vortical flows interacting with shock waves. © 1997 by John Wiley & Sons, Ltd.     

超高层建筑受大型高速飞行物撞击所致非连续性坍塌模拟与研究

为了解大型高速飞行物撞击超高层建筑后,建筑物塌落过程及其特征,使用基于颗粒流的PFC3D作为平台对坍塌过程进行模拟。所构建的超高层建筑为核心筒-框架结构,飞行物由较大的三个颗粒组成,其撞击速度为720km/h,撞击高度为建筑侧面250m和100m。研究了撞击物进入层间运动的特征,及在两种高度撞击后的坍塌过程。模拟结果表明,飞行物非直接撞击核心筒时建筑不会发生整体破坏,核心筒的受撞破坏是建筑坍塌破坏的关键。建筑高处受撞击后坍塌可分为两个阶段,其现象和原因各不相同。指出了建筑高处和低处受撞坍塌过程的三点不同。最后分析了撞击塌落后的地面影响范围及特征。     

一种守恒型间断跟踪法用于处理一维Euler方程组中的若干问题

1引言间断跟踪法(front-tracking)是数值求解双曲型守恒型方程(组)的一种重要的数值方法,其主要特点是把间断作为移动的内边界来处理,光滑区域中的数值解用计算光滑解有效的数值方法来求解,而间断的移动和间断两侧的数值解的修正要满足Rankine-Hugoniot条件．我们称这样的跟踪法为传统的间断跟踪法(见[3],[14])．本文的第二作者多年来研究设计了一种基于解的守恒性质的间断跟踪法(见[11],[12]),其最主要的特点是以解的守恒性作为跟踪的机制,而不是象传统的间断跟踪法那样利用     

Propagation and Evolution of Wave Fronts in Two-Phase Porous Media

An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.     

A Toss without a Coin: Information,Discontinuity, and Mathematics in Quantum Theory

The article argues that—at least in certain interpretations, such as the one assumed in this article under the heading of “reality without realism”—the quantum-theoretical situation appears as follows: While—in terms of probabilistic predictions—connected to and connecting the information obtained in quantum phenomena, the mathematics of quantum theory (QM or QFT), which is continuous, does not represent and is discontinuous with both the emergence of quantum phenomena and the physics of these phenomena, phenomena that are physically discontinuous with each other as well. These phenomena, and thus this information, are described by classical physics. All actually available information (in the mathematical sense of information theory) is classical: it is composed of units, such as bits, that are—or are contained in—entities described by classical physics. On the other hand, classical physics cannot predict this information when it is created, as manifested in measuring instruments, in quantum experiments, while quantum theory can. In this epistemological sense, this information is quantum. The article designates the discontinuity between quantum theory and the emergence of quantum phenomena the “Heisenberg discontinuity”, because it was introduced by W. Heisenberg along with QM, and the discontinuity between QM or QFT and the classical physics of quantum phenomena, the “Bohr discontinuity”, because it was introduced as part of Bohr’s interpretation of quantum phenomena and QM, under the assumption of Heisenberg discontinuity. Combining both discontinuities precludes QM or QFT from being connected to either physical reality, that ultimately responsible for quantum phenomena or that of these phenomena themselves, other than by means of probabilistic predictions concerning the information, classical in character, contained in quantum phenomena. The nature of quantum information is, in this view, defined by this situation. A major implication, discussed in the Conclusion, is the existence and arguably the necessity of two—classical and quantum—or with relativity, three and possibly more essentially different theories in fundamental physics.     

应变局部化分析的嵌入强间断多尺度有限元法

固体材料的应变局部化行为是导致结构破坏失效的重要因素之一,开展相关数值模拟分析对于结构安全性评估具有重要意义.然而由于材料的非均质和多尺度特性,采用传统数值方法进行求解时通常需要从最小特征尺度离散求解的结构,这将大幅度增加计算规模和成本.针对这一问题,本文提出了一种基于嵌入强间断模型的多尺度有限元方法.该方法从粗细两个尺度离散求解模型,首先在细尺度单元上引入嵌入强间断模型来描述单元间断特性,所附加的跳跃位移自由度则通过凝聚技术进行消除,从而保持细尺度单元刚度阵维度不变.其次,提出了一种增强多节点粗单元技术,其可根据局部化带与粗单元边界相交情况自适应动态地增加粗节点,新构造的增强数值基函数可以捕捉细尺度间断特性,完成物理信息从细单元到粗单元的准确传递以及宏观响应的快速分析;再次,在细尺度解的计算中,将细尺度解分解为降尺度解与单胞局部摄动解,从而消除弹塑性分析时单胞内部的不平衡力.最后,通过两个典型算例分析,并与完全采用细单元的嵌入有限元结果进行对比,验证了所提出算法的正确性与有效性.     

NETWORK CHARACTERIZATION OF STEP DISCONTINUITY WITH GENERALIZED CONSERVATION OF COMPLEX POWER TECHNIQUE AND ITS APPLICATION TO ANALYZING PERIODIC DIELECTRIC WAVEGUIDES

The propagation of electromagnetic waves along open periodic, dielectric waveguides is formulated in the case that surface wave is guided and propagates normally to the corrugation. Our approximate analysis with the propagation characteristics is to consider a corresponding bounded waveguide problem in which perfect electric or magnetic walls are introduced, and the periodic corrugation is regarded as consisting of step discontinuities connected by a length of uniform slab waveguide. By properly taking into account of both surface modes and only a few non-surface-modes, a novel network approach is proposed for characterizing step discontinuity based on the generalized conservation of complex power technique (GCCPT). Employing solution selection rule (SSR), we can readily derive propagation characteristics in the Bragg interaction region. A number of numerical results are shown to demonstrate the usefulness of our approach.     

The dependence on and continuity of the energy and other molecular properties with respect to the number of electrons

It was recently shown that the size consistency of the energy implies that, for any system with a rational number of electrons, the energy is given by the weighted average of the two systems with the nearest integer numbers of electrons. Specifically, E[N+P/Q] = (1−P/Q)E[N] + (P/Q)E[N+1]. This paper extends that analysis, showing that the same result holds for irrational numbers of electrons. This proves that the energy is a continuous function of the number of electrons, and justifies differentiation with respect to electron number, providing a rigorous justification or the density-functional theoretic approaches to chemical concepts like the electronegativity and the Fukui function. Similar results hold for properties other than the energy. Specific emphasis is placed on molecular response properties associated with the density-functional theory of chemical reactivity.     

Coupled Quasisolutions of Volterra Intergral Equations with Discontinuons Terms in Banach Spaces

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Lipschitz continuity theorems for free discontinuity problem in several variables

In this paper, following the method in [S. Solimini, Simplified excision techniques for free discontinuity problems in several variables, J. Funct. Anal. 151 (1997) 1-34], we prove a regularity of the function in minimizer for free discontinuity problem. Namely, we prove that the function is globally Lipschitz continuous out of a small neighborhood of the singular set.