Partitioning large networks without breaking communities

The identification of cohesive communities is a key process in social network analysis. However, the algorithms that are effective for finding communities do not scale well to very large problems, as their time complexity is worse than linear in the number of edges in the graph. This is an important issue for those interested in applying social network analysis techniques to very large networks, such as networks of mobile phone subscribers. In this respect, the contributions of this paper are twofold. First, we demonstrate these scaling issues using a prominent community-finding algorithm as a case study. Then, we show that a two-stage process, whereby the network is first decomposed into manageable subnetworks using a multilevel graph partitioning procedure, is effective in finding communities in networks with more than 10⁶ nodes.     

Manufacturing applications of octrees

It is well understood that effective and comprehensive CAD representation methods are necessary for modelling all the design and manufacturing functions in an automated environment. Recent research work has concentrated on using Constructive Solid Geometry (CSG) methods and Boundary Representation (B-Rep) schemes for representing design and manufacturing functions. This paper presents several novel ideas on the application of octree and quadtree based representation schemes in several manufacturing areas such as robotic task planning, tolerance representation and inspection, feature-based design, and assembly modelling and verification. Suggestions on the application of extended octrees for modelling metal forming operations are also presented.     

Finite element solutions of the non-self-adjoint convective-dispersion equation

Finite element formulations based on the Galerkin and variational principles have been developed for the self-adjoint and non-self-adjoint problems represented respectively by the flow and convective-dispersion equations in the cylindrical polar system of co-ordinates. The formulation based on the variational principle is shown to be restricted to dispersion-dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.     

Three-dimensional laminar flow and heat transfer in a parallel array of microchannels etched on a substrate

Heat transfer and laminar fluid flow in an array of parallel microchannels etched on a silicon substrate with water as the circulating fluid was studied numerically. The fluid region consisted of a microchannel with a hydraulic diameter of 85.6 μm and aspect ratios ranging from 0.10 to 1.0. A constant heat flux of 90 W/cm² was applied to the y = H face of the computational domain, which simulates thermal energy generation from an integrated circuit. Generalized transport equations were discretized and solved in three dimensions for velocities, pressure, and temperature. The SIMPLE algorithm [S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980] was used to link pressure and velocity fields, and a thermally repeated boundary condition was applied in the lateral direction to model the repeating nature of the geometry. The numerical results for apparent friction coefficient and convective thermal resistance at the channel inlet and exit closely matched the experimental data in the literature for the case of 0.32 aspect ratio. Apparent friction coefficients were found to increase linearly with Reynolds number. Inlet and outlet thermal resistance values monotonically decreased with increasing Reynolds number and increased with aspect ratio.     

Graphical and computer-aided approaches to plan experiments

Design of experiments is a quality technology to achieve product excellence, that is to achieve high quality at low cost. It is a tool to optimize product and process designs, to accelerate the development cycle, to reduce development costs, to improve the transition of products from R & D to manufacturing and to troubleshoot manufacturing problems effectively. It has been successfully, but sporadically, used in the United States. More recently, it has been identified as a major technological reason for the success of Japan in producing high-quality products at low cost. In the United States, the need for increased competitiveness and the emphasis on quality improvement demands a widespread use of design of experiments by engineers, scientists and quality professionals. In the past, such widespread use has been hampered by a lack of proper training and a lack of availability of tools to easily implement design of experiments in industry. Three steps are essential, and are being taken, to change this situation dramatically. First, simple graphical methods, to design and analyse experiments, need to be developed, particularly when the necessary microcomputer resources are not available. Secondly, engineers, scientists and quality professionals must have access to microcomputer-based software for design and analysis of experiments.¹ Availability of such software would allow users to concentrate on the important scientific and engineering aspects of the problem by computerizing the necessary statistical expertise. Finally, since a majority of the current workforce is expected to be working in the year 2000, a massive training effort, based upon simple graphical methods and appropriate computer software, is necessary.² The purpose of this paper is to describe a methodology based upon a new graphical method called interaction graphs and other previously known techniques, to simplify the correct design of practically important fractional factorial experiments. The essential problem in designing a fractional factorial experiment is first stated. The interaction graph for a 16-trial fractional factorial design is given to illustrate how the graphical procedure can be easily used to design a two-level fractional factorial experiment. Other previously known techniques are described to easily modify the two-level fractional factorial designs to create mixed multi-level designs. Interaction graphs for other practically useful fractional factorial designs are provided. A computer package called CADE (computer aided design of experiments), which automatically generates the appropriate fractional factorial designs based upon user specifications of factors, levels and interactions and conducts complete analyses of the designed experiments is briefly described.¹ Finally, the graphical method is compared with other available methods for designing fractional factorial experiments.     

Simulation of the Viscous Sintering of Two Particles

The viscous sintering of two initially spherical particles is modeled as creeping flow in response to surface tension. The governing equations are solved using the finite-element method. The condensed results of this simulation, the center-to-center approach velocity, and the rate of change of contact area were presented earlier. Some details of the flow field during sintering and the evolution of the neck geometry in the early stages of sintering are presented here. Important numerical issues are detailed.     

Determination of compressive residual stress in a doubly-clamped microbeam according to its buckled shape

In this work, an analytical relationship is derived for a doubly-clamped microbeam when it buckles after release from the substrate. In terms of the relationship, compressive residual stress in the doubly-clamped microbeam can be determined according to its buckled shape, allowing one to find the compressive residual stress directly without much experimental effort. This relationship has been used to determine compressive residual stresses in four types of doubly-clamped SiO₂ microbeams. In addition, four methods have been applied to find the elongations of these SiO₂ microbeams, and the corresponding results are compared. Finally, the residual stresses in doubly-clamped SiO₂ microbeams predicted according to the derived relationship are compared with those found in SiO₂ microcantilevers, and the results have a good match.     

Micro-measurement using grating microscopy

In this paper, two quantitative methods to measure micro-deformation using grating microscopy are proposed, a grating diffraction method and a full-field grating phase-shift method. A compact optical transmitting microscope with white light source is reconstructed by developing a loading and recording system. For direct strain measurement, a grating diffraction method is presented. With the help of a Bertrand lens, the Fourier spectrum of the grating is formed on the CCD sensor plane with high image quality. Software for precise, fast and automatic determination of the diffraction spot centroids is developed. Local strains are thus measured with high resolution. For the deformation measurement, a phase-shifting grating microscope method with high sensitivity and spatial resolution is proposed. Phase-shifting is based on the slab refraction effect and is realized via a tilting compensator. The system possesses a high spatial resolution (1 μm), and a displacement precision of 0.1–0.03 μm. The combination of the grating diffraction method and the phase-shifting method in the same test provides simultaneous measurement of strain and displacement, thus demonstrating that the grating techniques are viable in the microscope environment.