Covering a set of points in a plane using two parallel rectangles

In this paper we consider the problem of finding two parallel rectangles in arbitrary orientation for covering a given set of n points in a plane, such that the area of the larger rectangle is minimized. We propose an algorithm that solves the problem in O(n³) time using O(n²) space. Without altering the complexity, our approach can be used to solve another optimization problem namely, minimize the sum of the areas of two arbitrarily oriented parallel rectangles covering a given set of points in a plane.     

Electrophoresis of a finite rod along the axis of a long cylindrical microchannel filled with Carreau fluids

The boundary effect on the electrophoretic behavior of a particle in a non-Newtonian fluid is studied by considering the electrophoresis of a finite rod along the axis of a cylindrical microchannel filled with shear-thinning Carreau fluids, which include both Newtonian and power-law fluids as special cases. Under the conditions of low surface potential and weak applied electric field, the influences of the radius of the microchannel, the aspect ratio of the rod, the thickness of double layer, and the nature of the Carreau fluid on the mobility of the rod are investigated. We show that due to the shear-thinning effect, the mobility of the rod in the present case can be significantly larger than that in the corresponding Newtonian case; the former is more sensitive to the variation in the thickness of double layer than the latter, and the difference between the two increases with decreasing thickness of double layer. The shear-thinning effect is important under the following conditions: the double layer is thin, the boundary effect is important, and/or the aspect ratio is large. We show that increasing the aspect ratio can either raise or lessen its mobility, which is not found previously, and can play an important role in electrophoresis measurement.     

粒子模拟中一种非结构化通用并行通信模式的研究和范型实现

中国科学院过程工程研究所多相反应实验室,建立了一个通用粒子模拟平台并已开始应用。目前类似的并行模拟系统采用的Shift并行通信模式往往有一些问题,需要一种新的通信模式来弥补它的不足。本文设计具有良好通用性的非结构化通信模式All2All,用来完成通用粒子方法模拟平台中计算节点问的通信。本文的算例证明这种通信模式可解决在粒子并行模拟Shift通信模式所不能处理的,具有复杂拓扑关系的相邻节点间的数据通信问题。本文设计的All2All通信模式方法只需稍加修改,就可以方便地应用于其它领域的并行计算系统。     

Reflection and transmission of plane waves at an interface between two fluids

The propagation, reflection, and transmission of a plane wave through a column of two fluids with a material discontinuity is studied by three methods: a mixed finite element formulation with both pressure and velocity at a point taken as independent variables, and a scaled and an un-scaled acoustic pressure formulation in which only the pressure at a point is taken as an independent variable. It is found that when mass densities of two fluids are close to each other, the un-scaled acoustic pressure formulation gives reasonable results. However, when the speeds of sound in two fluids are close to each other but their mass densities are quite different, and for cases where the first fluid has high impedance relative to that of the second fluid, a mixed or scaled pressure formulation is necessary. Without the mixed or scaled pressure formulation, the continuity conditions at the interface between two fluids are not well satisfied for the un-scaled pressure formulation. The consideration of viscosity of the two fluids and using a dispersion correction method in the time integration scheme in the mixed formulation slightly improves results.     

A noninverting algorithm for path tracking of two cooperating robot arms and its parallel implementation

This paper presents an algorithm for path tracking of two robot arms with end-effectors gripping a common inertial load. The path is generated as a sequence of elementary motions. The most important feature of the present algorithm is that it avoids singularities, because there is no need of using the inverse kinematics. Direction and proximity criteria are introduced. Holonomic constraints are formulated for the position and orientation of the two end-effectors.The application of parallel processing methods to path tracking according to the previous algorithm is presented. The algorithm is implemented in the Alliant FX/80 parallel machine.     

Dynamic stiffness matrix of an axisymmetric shell and response to harmonic distributed loads

This paper describes a procedure for taking into account distributed loads in the dynamic stiffness matrix formulation, also known as the continuous element method. In that formulation, concentrated or linearly distributed loads are taken into account by considering the necessary number of elements in such a way that these loads are applied on element boundaries. As for distributed loads such as pressure and surface forces, they were not provided for in the formulation. The validation is achieved by comparison of accuracy and computational time of harmonic response calculations performed by the continuous element model and a finite element model.     

On conjugation of solutions to two integrable problems: Rolling of pointed body in the plane

In this paper, the problem of motion of heavy rigid body in the rough plane is studied. The surface of body is such that the axis of rotation has two “points,” where the plane tangent to the surface is not specified. The motion is described by two systems of equations; each of them is true for its side of the phase space. One of them is a system of equations that describes rolling of body in the plane without slippage (the body is tangent to the plane by its convex part); the second, is a system of equations that describes motion of body with the fixed point for the Lagrange case (the body is basing on the plane by the point). Questions of existence of global first integrals and potential of the cited one-dimensional system are studied.     

Development of programming language Espace and its application to parallel and distributed evolutionary computation

This article proposes a programming language called “Espace” for parallel and distributed computation. In general, it is difficult to code a distributed, parallel program due to multi-threading, message passing, managing clients, and so on. Espace involves a few simple syntax rules added to Java. Developers do not need to know how to write a parallel, distributed program source code in detail. This work applies Espace to parallelize an evolutionary computation program, and shows that the Espace compiler allows the conversion of an evolutionary computation program written in Java into a distributed, parallel system by adding a few words to the program.     

An improved stereologic method for three-dimensional estimation of particle size distribution from observations in two dimensions and its application

Single enzyme-altered hepatocytes; altered hepatic foci (AHF); and nodular lesions have been implicated, respectively in the processes of initiation, promotion, and progression in rodent hepatocarcinogenesis. Qualitative and quantitative analyses of such lesions have been utilized both to identify and to determine the potency of initiating, promoting, and progressor agents in rodent liver. Of a number of possible parameters determined in the study of such lesions, estimation of the number of foci or nodules in the liver is very important. The method of Saltykov has been used for estimating the number of AHF in rat liver. However, in practice, the Saltykov calculation has at least two weak points: (a) the size class range is limited to 12, which in many instances is too narrow to cover the range of AHF data obtained; and (b) under some conditions, the Saltykov equation generates negative values in several size classes, an obvious impossibility in the real world. In order to overcome these limitations in the Saltykov calculations, a study of the particle size distribution in a wide-range, polydispersed sphere system was performed. A stereologic method, termed the 25F Association method, was developed from this study. This method offers 25 association factors that are derived from the frequency of different-sized transections obtained from transecting a spherical particle, thus expanding the size class range to be analyzed up to 25, which is sufficiently wide to encompass all rat AHF found in most cases. This method exhibits greater flexibility, which allows adjustments to be made within the calculation process when NA((k,k)), the net number of transections from the same size spheres, was found to be a negative value, which is not possible in real situations. The reliability of the 25F Association method was tested thoroughly by computer simulation in both monodispersed and polydispersed sphere systems. The test results were compared with the original Saltykov method. We found that the 25F Association method yielded a better estimate of the total number of spheres in the three-dimensional tissue sample as well as the detailed size distribution information. Although the 25F Association method was derived from the study of a polydispersed sphere system, it can be used for continuous size distribution sphere systems. Application of this method to the estimation of parameters of preneoplastic foci in rodent liver is presented as an example of its utility. An application software program, 3D_estimation.exe, which uses the 25F Association method to estimate the number of AHF in rodent liver, has been developed and is now available at the website of this laboratory.     

A contribution to the calculation of the contact stress distribution between two elastic bodies of revolution with non-elliptical contact area

A numerical method is presented for calculating the contact area and the normal stress distribution between two elastic bodies of revolution with parallel axes. For the discretization of the Fredhom integral equation the contact area is divided into strips perpendicular to the axes of revolution. The stress distribution in each strip is assumed to be semi-elliptical in the strip direction and constant in the other direction. The contact area is calculated iteratively by satisfying the contact condition and the stress condition. In addition for a given total normal force an additional iteration is required to improve the value obtained for the rigid-body approach. The contact area and the stress distribution between two ellipsoids are compared with Hertzian solutions. To investigate the non-Hertzian contact problem a number of cases of wheel-rail contact are considered.     

Robust stability of an interval plant with respect to a convexregion in the complex plane

The determination of robust stability of interval polynomials with respect to an arbitrary closed convex contour in the left-half complex plane is considered. It is shown that the problem can be solved by checking only the root locations of a subset of the exposed edges of the family. The number of exposed edges to be checked depends on the damping margin defined by the contour and the degree of interval polynomials, but does not depend on the exact shape of the contour. A simple, easy-to-apply, graphical approach determines the subset of the exposed edges. An example illustrates the merit of the approach     

The use of the plane frames program as an aid to learning in structural analysis

Structural Analysis is the main theoretical and mathematically based topic studied within the subject area of Structural Engineering and often represents something of a hurdle to the student. The lecturer must ensure not only that the students are numerically competent and able to solve problems, but also that they understand the basic behaviour of the structures they analyse. There is evidence, from tests carried out on Civil Engineering graduates, that an overemphasis on numerically based worked examples does not necessarily lead to a qualitative understanding of structural behaviour. Nevertheless, the student must be competent to analyse a structure and obtain a correct solution. The paper describes the use of the standard ICL ‘Plane Frames’ program to accomplish both the qualitative and quantitative understanding of structures.In what appears at first to be a deceptively simple application, the student uses the computer program to generate the solution to a type of problem for which he chooses the structural dimensions and loads. This provides the solution which he must match with his hand calculation. Because each problem is unique to the student he is encouraged to gain assistance from his peers and this debate and the reworking of the problem to obtain the correct solution appears to contribute to the general understanding of the structural principles involved. In addition, the computer is used to generate data upon which the numerical solution is based. In this way, the particular method is emphasised.     

Corpus tools for parallel corpora of theatre plays: an introduction to TAligner and ACM-theatre

Software tools are of vital importance in corpus-based research, but they can also lead to restrictions on the type of supported corpora and the range of analyses that can be performed. For example, corpus analysis tools, as general purpose software, do not include specific features to process corpora of theatre plays. This situation is even worse for parallel corpora of theatrical texts, in that there is currently a lack of software that allows for both the alignment and analysis of parallel corpora here. In this contribution, we will first outline the peculiarities of theatre texts and suggest three software features to address them: annotation of the structural units of plays, alignment at the utterance level, and concordances and statistics using the annotated units. Second, we will present the specific functionalities of TAligner and ACM to build and analyse parallel corpora of play texts, showing how new avenues of research are opening up with the development of these tools.

     

On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall’s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index.     

Analysis of an adaptive algorithm to find the two nearest neighbors

Given a setS ofN distinct elements in random order and a pivotx ∈S, we study the problem of simultaneously finding the left and the right neighbors ofx, i.e.,L=max{u|u<x} andR=min{v|v>x}. We analyze an adaptive algorithm that solves this problem by scanning the setS while maintaining current values for the neighborsL andR. Each new element inspected is compared first against the neighbor in the most populous side, then (if necessary) against the neighbor in the other side, and finally (if necessary), against the pivot. This algorithm may require 3N comparisons in the worst case, but it performs well on the average. If the pivot has rankαN, where α is fixed and <1/2, the algorithm does (1+α)N+Θ(logN) comparisons on the average, with a variance of 3 lnN+Θ(1). However, in the case where the pivot is the median, the average becomes 3/2;N+Θ(√N), while the variance grows to (1/2−π/8)N+Θ(logN). We also prove that, in the αN case, the limit distribution is Gaussian. This work has been supported in part by Grant FONDECYT(Chile) 1950622 and 1981029. Online publication October 6, 2000.     

The merging of two gaseous bubbles with an application to underwater explosions

A numerical study of two gaseous bubbles merging into a single coalesced bubble as in underwater explosions is investigated in this paper. This explosive phenomenon is modeled using a boundary integral method. Two configurations, which are in-phase and out-of-phase explosions, are simulated and compared with available experimental results. The thickness of the liquid film between the two bubbles determines our coalescence criterion. Bubble shapes and periods of oscillation are predicted well, compared to those of the experiments.