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Proceedings of the Infernofionol Conference on ScienMfic & Engineering Computation [IC-SEC] 2002 3 P
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Editors
H. R Lee K. Kumar ?! 8*
Imperial College Press — -
Proceedings of tlie International Conference on ScienfipcftEngineering Computation [IC-SEC] 3002
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Proceedings of Ihe International Conference on Scientific & Engineering Computation [IC-SEC] EDOB
Recent Rdvanc cienc Co 00 I 3 - 5 December 2002
Raffles City Convention Centre, Singapore
Editors
H. R Lee & K. Kumar (Institute of High Performance Computing, Singapore)
Co-Organisers:
1
IMUS
Institute of High Performance Computing
National University of Singapore
In Cooperation With:
CDGC The 5uporcomputing People
siHJTL
^AM
Imperial College Press
Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte: Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202,1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.
RECENT ADVANCES IN COMPUTATIONAL SCIENCE AND ENGINEERING Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC) 2002 Copyright © 2002 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN
1-86094-345-4 (pbk)
Printed by Fulsland Offset Printing (S) Pte Ltd, Singapore
INTERNATIONAL CONFERENCE ON SCIENTIFIC & ENGINEERING COMPUTATION (IC-SEC) 2002 Recent Advances in Computational Science & Engineering The inaugural IC-SEC 2002 is jointly organised by the Institute of High Performance Computing (IHPC), the Faculty of Engineering and Faculty of Science, and Institute for Mathematical Sciences of the National University of Singapore (NUS). The conference is also organised in cooperation with the Australian and New Zealand Industrial and Applied Mathematics (ANIZAM), Centre for Development of Advanced Computing (CDAC), Society for Industrial and Applied Mathematics (SIAM), and Theoretical and the Applied Mechanics Society - Singapore (SingTAM). IC-SEC 2002 aims to create a forum for engineers and scientists who are involved in the use of high performance computers, advanced numerical strategies, computational methods and simulation in various scientific and engineering disciplines. The conference offers participants a platform to present and discuss latest trends and findings or simply to learn about the state-of-the-art in their particular field(s) of interest. The conference also hopes to provide a forum for the interdisciplinary blending of computational efforts in various diversified areas of sciences such as biology, chemistry, physics and materials and all branches of engineering. The technical committee has therefore devised a broad range of topics and application areas surrounding the theme of this conference, all of which involves modelling and simulation work using high performance computers. Conference Topics and Application Areas MEMS Modelling & Simulation Computational Acoustics Computational Fluid Dynamics Computational Solid and Structural Mechanics Computational Electromagnetics Computational Electronics Computational Chemistry Computational Materials Science Computational Nano-Science Defence Modelling & Simulation Grid Computing & Applications Scientific Visualisation Fast Algorithms Parallel & Distributed Computing V
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Conference Committee Conference Chair Lam Khin Yong, Institute of High Performance Computing / National University of Singapore, Singapore Conference Co-Chairs Barbara Lee Keyfitz, University of Houston, USA Lee Seng Luan, National University of Singapore, Singapore Nhan Phan-Thien, National University of Singapore, Singapore International Scientific Advisory Members Francine D. Berman, University of California, San Diego, USA Rajkumar Buyya, Distributed Systems Engineering Lab, University of Melbourne, Australia Louis Chen, National University of Singapore, Singapore Chew Weng Cho, University of Illinois, Urbana-Champaign, USA Carolina Cruz-Neira, Iowa State University, USA David Ferry, Arizona State University, USA Gao Beng Qing, Beijing Institute of Technology, China Tony Hey, University of Southampton, UK Marc Ingber, University of New Mexico, USA Christian Joachim, Centre National De La Recherche Scientifique, France Carl Kesselman, Information Sciences Institute, The University of South California, USA Sangtae Kim, Lily Research Laboratories, USA S. Kitipomchai, City University of Hong Kong, Hong Kong, China Leo W M Lau, Chinese University of Hong Kong, Hong Kong, China Liu Wing Kam, Northwestern University, USA Mark S Lundstrom, Purdue University, USA Max G Q Lu, University of Queensland, Australia Kwan-Liu Ma, University of California, Davis, USA Shaker A Meguid, University of Toronto, Canada Eugenio Onate, International Centre for Numerical Methods in Engineering, Spain D R J Owen, University of Swansea, UK Maurice Petyt, Institute of Sound and Vibration Research, UK Ken Powell, University of Michigan, USA Sharad Purohit, Centre for Development of Advanced Computing, India J N Reddy, Texas A & M University, USA Dennis Salahub, Steacie Institute for Molecular Sciences, Canada William R. Schowalter, University of Illinois, Chicago, USA Satoshi Sekiguchi, National Institute of Advanced Industrial Science and Technology, Japan VII
VIM
Shi JiaoYing, Zhejiang University, China Young S. Shin, U.S. Naval Postgraduate School, USA Ian Sloan, University of New South Wales, Australia Charles Steele, Stanford University, USA Gilbert Strang, Massachusetts Institute of Technology, USA Jan K Sykulski, University of Southampton, UK Tong Liyong, The University of Sydney, Australia Gretar Tryggvason, Worcester Polytechnic Institute, USA Putchong Uthayopas, Kasetsart University, Thailand Vijay Varadan, Pennsylvania State University, USA Wang Bo Ping, The University of Texas at Arlington, USA Weinan E, Princeton University, USA Tomas Wierzbicki, Massachusetts Institute of Technology, USA Yao Zhenhan, Tsinghua University, China
CONTENTS
Plenary Multiscale Modeling and Computation of Incompressible Flow T.Y.Hou Splitting Methods for Incompressible Viscous Flow Problems with Free and Moving Boundaries E.J. Dean, R. Glowinski, L.H. Juarez and T.W. Pan
3
7
Contributed Papers COMPUTATIONAL CHEMISTRY Computational Chemistry 1 Cation-7r Interactions in Ag(l)-Substitued Alkylbenzenes Complexes: A Theoretical Study Y.P. Wong, KM. Ng and C.W. Tsang
15
Light Propagation in Biological Tissue Using Monte Carlo Simulation A. Aggarwal
19
Predicting Materials Properties Using First Principles Electronic Structure Calculation Y.P. Feng, A.T.L. Lim and J.C. Zheng
23
Correlation of the Distribution of Essential/Trace Elements in Human Hair for Lung Cancer Diagnosis P.L. Mao, H.L.K. Kueh, W.K.A. Ng, Y.T. Wang and P. Wu
28
Dynamic Simulation of an Anaerobic Digestion Process Using Orthogonal Collocation on Finite Elements Method T. T. Lee and P. Wu
32
IX
X
Computational Chemistry 2 Total Algebraic System Identification for Homogeneous Catalyzed Syntheses of Fine Chemicals (Alkenes to Aldehydes) E. Widjaja, C.Z. Li and M. Garland
36
Numerical Solution of Bound-Constrained Nonlinear Systems in Chemical Engineering S. Bellavia, M. Macconi and B. Morini
41
Phonon Dispersion, Structure Stability, Surface Relaxation and Surface Energy for Metals Ni, Cu and Pd J. Cai and J.S. Wang
45
On the Development of Weighted Two-Band Target Entropy Minimization for the Reconstruction of Pure Component Mass Spectra H.J. Zhang, M. Garland, Y.Z. Zeng and P. Wu Computer Aided Additives Study for Steel Hot Dip Galvanizing H.M. Jin, H.L. Liu and P. Wu
49
54
Computational Chemistry 3 Cation-7i Interactions in Ag(l)-Substituted Naphthalene Complexes: an Ab initio Molecular Orbital Study H.M. Lee and C.W. Tsang
58
Band-Target Entropy Minimization (BTEM) - A Novel Approach for Pattern Recognition in Chemical Spectrocopy E. Widjaja and M. Garland
62
Development of a Web-Based Statistical Process Control Analysis and Reporting System for Tablet Processing Plants T.T. Lee, Y.L Li, P. Wu, M.K. Chin, T. Lim and LK. See
67
Monte Carlo Simulation of Surface Segregation in Ni-Co Nanoparticles R. Jayaganthan and G.M. Chow
71
First Principles Studies of the Dissociation of Protonated Alanine (H+-ALA) Complex S. Abirami, C. Wong, N.L Ma, C.W. Tsang and N.K. Goh
76
XI
Molecules and Structures for Molecular Electronic Nanodevices P. Bai, S.W. Yang, P. Wu andE.P. Li
80
COMPUTATIONAL FLUID DYNAMICS Computational Heat Transfer CFD Analysis of Film Cooling of a Cyclindrical Leading Edge with Compound Angle Injection B.S. Chufal and A.R. Srikrihnan
84
Flow Analysis in Port and Cylinder of a Spark Ignition Engine with Oblique Valve M.J. Luo, G.H. Chen and Y.H. Ma
88
Analysis of Chemical Reactions in Argon Thermal Plasma Flow Using the Eddy Dissipation Concept K. Sundaravadivelu, H.W. Ng, S.C.M. Yu, J.C. Chaiand Y.C. Lam
93
Numerical Simulation of 2-D Reacting Flow in Nozzle of Liquid Rocket Motor H.F. Qiang, Y.C. Yang and X L Xia
97
Simulations of the Onset of Convection in a Non-Newtonian Liquid Under Fixed Surface Temperature Boundary Condition K.C. Ting, K.K. Tan and S.Y.T. Choong
102
Computer Visualisation of Fluid Circulation in Annuli of Heated Rotating Cylinders of Low Prandtl Number Fluids Z.D. Xu, Y.L. Huo and T.S. Lee
108
Finite Element Analysis of Hollow Brick Drying in Forced and Mixed Convection Environment H.N. Suresh, J.R. Kumar, P.A.A. Narayana and K.N. Seetharamu
112
Computational Fluid Dynamics 1 High Accuracy Simulation of Multi-Medium Flow C.W. Wang, T.G. Liu and B.C. Khoo
118
XII
The Modified Ghost Fluid Method T.G. Liu, K.C. Hung and B.C. Khoo
122
Gauss Quadrature vs. Analytic Integration for Finite-Element CFD Codes MM. El-Awad, M.J.N. Boyce and F. Tarlochan
126
A Projection Method for Solving Incompressible Viscous Flows on Domains with Moving Boundaries H. Pan, LS. Pan, D. Xu and T.Y. Ng
130
Multi-Physics Simulations of Vortex-Induced Cylinder Vibrations S. Y. Lee and M. Lee
134
Computational Fluid Dynamics 2 Characteristics of Airflow in a Prototype of a Hard Disk Drive X.G. Xu, N.M. Sudharsan, K. Kumar, T.H. Yip, M.A. Suriadi and E.H. Ong
139
Linearized Navier-Stokes Equations and its Applications in Unsteady Airfoil Flows R.J. Cao
143
Cost-Effective Formulation of a Finite-Element Model for Atmospheric Dispersion of Dense Gases M.M. El-Awad
147
Spatial Simulation of 2D Tollmien-Schlichting Wave over Volume Based Viscoelastic Layer Z. Wang, K.S. Yeo and B.C. Khoo
151
Numerical Study of Passive Displacement Ventilation H.J. Poh, J. Lou and K. Kumar
155
Computational Fluid Dynamics Simulation of the Dispersion of Airborne Contaminants in a Work Environment S.M. Salim and G. Xu
159
Numerial Simulation of Low Reynolds Number Channel Flow Over Dimpled Surface Z. Wang, K.S. Yeo, H Lim and B.C. Khoo
163
Computational Fluid Dynamics 3 CFD Modelling of Particle Transport and Biological Reactions in a Mixed Wastewater Treatment Vessel M. Brannock, T. Howes, M. Johns, B.D. Clercq andJ. Keller
167
A Computer Analysis of Turbulent Flow of Acid in the Pickling of Steel Strips B.C. Khoo, D. Xu, W.Y.D. Yuen and W.K. Soh
171
Finite Element Analysis of Non Linear Fluid Structure Interaction in Hydrodynamics Using Mixed Lagrangian-Eulerian Method N.M. Sudharsan, K. Murali and K. Kumar
176
Numerical Study of Fluid Flow through Multiple Bell-Shaped Constrictions in a Tube W. Liao, G.C. Li and T.S. Lee
180
A Mixing Interface Treatment for Numerical Simulation of Tip Clearance Flow of a Small Axial Flow Fan R.J. Cao
184
CFD Simulation of Precipitation Process C.N. Lim
188
Computational Fluid Dynamics 4 Effect of Rotor's Aspect Ratio on Entropy Generation in a Rotor-Casing Assembly B. Abu-Hijleh, J. Y. Tu and A. Subic Lattice Boltzman Method on Nonuniform Mesh M. Cheng and K.C. Hung Numerical Study of the Effects of Check Valve Closure Flow Conditions on Pressure Surges in Complex Fluid Systems with Air Entrainment T.S. Lee Numerical Simulation of Czochralski Crystal Growth by Fixed Grid Technique M.A. Suriadi, D. Xu and B.C. Khoo
192
196
200
204
XIV
A Pre/Post Processor for Finite Element Modelling for Coal Mining Applications S.G. Chen, S. Craig, H. Guo and D.P. Adhikary
209
Evaluation of Turbulence Models for Hydrofoil Turbulent Boundary Layer Flow at High Reynolds Numbers N. Mulvany, J. Y. Tu, L Chen and B. Anderson
213
Mesh Adaptation for Time-Accurate Viscous Compressible Fluid Flow O. Hassan, K.A. Sorensen, K. Morgan and N.P. Weatherill
217
A Numerical Study on Bubble Structure Interaction in Underwater Explosions K.C. Hung, C. Wang, E. Klaseboer, C.W. Wang and B.C. Khoo
223
COMPUTATIONAL ELECTROMAGNETICS AND ELECTRONICS Computational Electronics Delay Computation of Large Interconnect Network Y. CaoandE.C. Tan Modeling of On-Chip Buses for Placement Optimization in Integrated Circuits O. Peyran
227
231
Simulation of Nano-Scale Single-Electron Devices and Circuits P. Bai, E.P. Li and R.M. Patrikar
235
Surface Roughness Modeling R.M. Patrikar and K. Ramanathan
239
A Novel Scheme for Simulating Quantum Effects in Hydrodynamics Model E.P. Liu, E.P. li, P. BaiandR.Q. Han
243
A CAD Tool to Study Thermal Distribution for Block Level Placement in Embedded Systems R.M. Patrikar, K. Muraii and E.P. Li
247
XV
Computational Electromagnetics Applications 1 Comparative to FDTD, PSTD and MRTD Methods in Studies for Planar Stratified Media MS. Tong, Q.S. Cao, K.K. Tamma and Y.L Lu FDTD Analysis Effective of Printed Dipole Antenna M. Tangjitjesada, N. Anatrasirichai and T. Wakabayashi Radiation and Signal Integrity Analysis in Imperfectly Differential Transmission Lines with Full-Wave FDTD Method W.L. Yuan and E.P. Li
251
255
259
Radiated Emission Prediction in Electronics Circuit System Level J. Gao, S.B. Wee and E.P. Li
263
Web-Based Electromagnetic Simulation Y. Fan, Y.L Li, E.P. Li and S.K. Chin
267
Parallelized FDTD Method for Analysis of Signal Integrity in High-Speed Electronic Circuits H.F. Jin, E.P. Li, W.L. Yuan and LW. Li
271
Computational Electromagnetics Applications 2 Generic Approach to Overcome the Low-Frequency Breakdown in Electromagnetic Computations by Moment Methods A.J. Lapovok, N.L. Sudov and O.V. Grimalski
275
Crosstalk Simulation of High Speed Interconnects by an Efficient Finite Difference Method Y. Xiao, E.P. Lee and K.H. Lee
279
Transient Simulation of High Speed Interconnects using Coupled Model Order Reduction and FDTD-Macromodeling Technique E.X. Liu, E.P. Li, X. Ying, LW. Li and K.H. Lee
283
Zigzag Slot Antenna with CPW Feed N. Anantrasirichai, A. Lorphichian, J. Nakasuwan and T. Wakabayashi
287
Analysis Electromagnetic Field of Slot Antenna N. Anantrasirichai, S. Puntheeranurak, C. Jamjank and T. Wakabayashi
291
XVI
Computational Electromagnetics Applications 3 Load Characteristics Analysis of a 100kVA Synchronous Generator with High Temperature Superconducting Field Winding using Finite Element Modelling K.S. Ship, J.K. Sykulski and K.F. Goddard
295
Stochastic Modeling and Characterization of Electrical Trees in Composite Insulation Structure using Fractal Concepts R. Sarathi, C.R. Anilkumar and R. Jayaganthan
299
Application of Robust Design Techniques to Electromagnetic Devices Design Optimization X.K. Gao, J.T. Li, Z. Xie and Z.J. Liu
304
Numerical Simulation of Nonlinear Behavior of Electromagnetic Pulses Inside Dielectrics with Nonlinear Susceptibilities M.T.M. Ho and T.H. Huang
308
The Noise-Robust Variable Step-Size Algorithm for Lattice Form Adaptive MR Notch Filter C. Benjangkaprasert, S. Teerasakworakun and K. Janchitrapongvej A New Constant Modulus Algorithm for Adaptive Equalizer P. Tupchai, C. Benjangkaprasert and O. Sangaroon
316
320
Computing Engineering in Communication The Variable Step Size Blind Adaptive Decorrelating Detector PIC in DS/CDMA System S. Benchapornkullanij, C. Benjangkaprasert and M. Lertwatechakul Performance Evaluation of Finite-Length MMSE-DFE in Wideband Mimo Channel P. Changsuwan, M. Chamchoy, S. Promwong and P. Tangtisanon The Efficiency of WI-FI (IEEE 802.11B) in Presence of Bluetooth System Indoor Propagation T. Subson, P. Supanakoon, P. Rawiwan, M. Chamchoy, S. Promwong and P. Tangtisanon
324
328
332
XVII
A Study of Self-Similar Pseudorandom Teletraffic Generators for Simulation J.S.R. Lee, H.W. Park and H.D.J. Jeong The Delay-Bounded Source Model S. Ruttanawit, M. Lertwatechakul and P. Sooraksa Invertible Integer FFT and DCT Applied on Lossless Image Compression Y.S. Van, CM. Wang, G.D. Su and Q.Y. Shi
336
340
344
Fast and Parallel Electromagnetics Computation 1 Solution of Scattering by Homogeneous Dielectric Bodies using Parallel P-FFT Algorithm W.B. Ewe, Y.J. Wang, L.W. Li and E.P. Li The Common Component Architecture (CCA) Applied to Sequential and Parallel Computational Electromagnetic Applications D.S. Katz, E. R. Tisdale and CD. Norton
348
353
A Fast Algorithm for Three-Dimensional Electrostatic Analysis: Fast Fourier Transform on Multipole (FFTM) E.T. Ong, H.P. Lee, K.H. Lee and KM. Lim
357
An Alternative Implementation of Interpolation in Multilevel Fast Multipole Method (MLFMM) C.P. Lim, Y.J. Zhang, F. Wu and E.P. Li
361
Fast Matrix Algorithms for Hierarchically Semi-Separable Representations S. Chandrasekaran, T. Pals and M. Gu
365
Parallel Fast Multipole Method for Large-Scale Computation of Electromagnetic Scattering Y.J. Zhang, F. Wu, C.P.E. Lim and E.P. Li
369
Fast and Parallel Electromagnetics Computation 2 Two Classes of Preconditioning Techniques for Electromagnetic Wave Scattering Problems J. Zhang, J.H. Lee and C.C. Lu
373
XVIII
Arbitrary Order Edge Element Methods for 2D EM Scattering K. Morgan, P.D. Ledger, O. Hassan, N.P. Weatherill and J. Peraire Parallelization of Pre-Corrected FFT in Scattering Field Computation Y.J. Wang, L.W. Li and E.P. Li Finite Element Analysis of Photonic Crystal Fibres R. Yang and Y.L. Lu Parallelization of Fast Multipole Method using MPI on IBM High Performance Computers F. Wu, Y.J. Zhang, C.P.E. Lim and E.P. Li Parallel Unstructured Meshes Approach for the Simulation of Electromagnetic Scattering O. Hassan, J. Jones, B. Larwood, K. Morgan and N.P. Weatherill
377
381
385
389
393
COMPUTATIONAL MECHANICS Virtual Design Development of Parting Line Generation Tools for a 3D CAD Injection Mould System W.M. Chan and S.L. Lieow
398
Simulation of Temperature and Stress Field in Deposition Process for RPST by Homogenization Method G.L Wang, Z.H Xu and HO. Zhang
402
Geometric Model and Numerical Simulation for the Laying Process of Wire Rope G.L. Wang, J.F. Sun and H.O. Zhang
407
Agent-Based Composable Simulation for Virtual Prototyping W. Xiang, S.C. Fok and G. Thimm Knowledge-Based Rapid Virtual Engineering System for Product and Tooling Design R.D. Jiang, T.W. Lim and B.T. Choek
413
417
XIX
Virtual Aesthetic Design: Architecture and Some Results W.S. Li, S.H. Xu, G. Zhao and Y.L. Ke Numerical Simulation and Experiment on Prediction for Retention Force H.Z. Dong, T.W. Lim and B.H. Low
421
425
Couple Field Analysis and Nanostructured Material Failure Probability of Wire Bonding Packages F. Wang, Y. Y. Wang and C. Lu
429
Shape Control of Smart Composite Plate Structures Based on Actuator Shape Optimisation Q. Nguyen and L. Y. Tong
434
Numerical Investigation of Micro-Scale Sheet Metal Bending using Laser Beam Scanning Z.Q. Zhang, G.R. Liu andXM. Tan
438
Three-Dimensional Finite Element Study of the Elastic Fields in Quantum Dot Structures Q.X. Pei and C. Lu
443
Directional Dependence of Surface Morphological Evolution of Heteroepitaxial Films P. Liu, Y. W. Zhang and C. Lu
447
Forming of Nanostructured Materials: Numerical Analysis in Equal Channel Angular Extrusion (ECAE) of Magnesium, Aluminium and Titanium Alloys B.H. HuandJ.V. Kreij
454
CAD Mechanical Design 1 The Development of Standard Part Database for Progressive Die Design Z.H. Wang
459
The Application of Sensitivity Analysis to Modifying Car Body Configuration X.R. Zhang and M. Zhu
463
XX
The Simulation of the 7t-Type Constraint Bending Process H.Z. Xu
468
Optimising the Dimensions of Cylindrical Ultrasonic Motor Q.G. Yang and S.P. Lim
472
Design and Analysis of a High-Efficiency MR Valve W.H. Li, H. Du and N.Q. Guo
476
Computer Design and Visualization on New Loop Worm Transmission Q.S. Luoand B.L. Han
480
CAD Mechanical Design 2 A Computer-Aided Optimisation Approach for the Design of Cooling Channels and Selection of Process Parameters in Plastic Injection Moulding L.Y. Zhai, Y.C. Lam, K. Taiand S.C. Fok Wavelets-Based Multiresolution Representation and Manipulation of Closed B-Spline Curve G. Zhao, S.H. Xu, W.S. LiandX.X. Zhu A Piping Modeling and Calculation System H.X. Gao
485
490
494
Optimization of Injection Molded Part Based on the CAE Simulation V. LiandC.R. Pan
498
Evaluating Plane-Strain Forging of Magnesium Alloy AZ31 using Finite Element Analysis S.C.V. Lim, M.S. Yong and CM. Choy
502
Numerical Structural Analysis 1 Comparative Structural Evaluation of Protective Helmets using the Finite Element Method A. Subic, M. Takla and C. Mitrovic
506
XXI
Buckling Analysis of Composite Spherical Panels with Random Material Properties B.N. Singh, N.G.R. lyenagarand D. Yadav
510
Numerical Analysis of Adhesively Bonded Cylindrically Curved Lap Joints C. Y. Qian and L Y. Tong
514
Numerical Analysis of the Effect of Interphase on the Deformation of Particle-Reinforced Composites W.X. Zhang, P.P. Yang and T.J. Wang
518
Numerical Finite Deformation Analysis on Solid Propellant Grain using Finite Element Method Y.C. Yang, H.F. Qiang, G.M. Xu and H.S. Zhao
522
Investigation on the Counter-Intuitive Phenomenon of ElasticPlastic Beams Y.M. Liu, G.W. Ma and Q.M. Li
527
Numerical Structural Analysis 2 Computational Material Testing of Pre-Damaged Metals using Damage Mechanics Models Y. Toi and S. Hirose
531
Study of the Influence of the Suspension Parameters on Suspension Kinematics Characteristic D. Hua, Z.M. TaoandX.C. Gao
535
Computational Study of Vapor Pressure Assisted Crack Growth at Polymer/Ceramic Interfaces C.W. Chong, T.F. Guo and L. Cheng
539
Distortion Prediction using Finite Element Method Y.C. Tse, P. Liu, Y.Y. Wang, C. Lu, G.R. Liu and K.P. Quek
543
Interface Pressure Distribution in Automotive Drum Brake A. Tom a, M. Takla and A. Subic
548
A New High Precision Direct Integration Scheme for Nonlinear Rotor-Seal System J. Hua, Z.S. Liu, Q.Y. Xu and S. Swaddiwudhipong
552
XXII
Numerical Structural Analysis 3 Delamination Identification using Piezoelectric Fiber Reinforced Composite Sensors P. Tan and L. Y. Tong
557
A Simple Model for Predication of Crack Spacing in Concrete Pavements G. Chen and G. Baker
561
Hellinger-Riessner Mixed Formulation for the Nonlinear Frame Element with Lateral Deformable Supports S. Limkatanyu
565
Energy Approach to Numerical Modelling of Crack Spacing in Reinforced Concrete G. Chen and G. Baker
569
Effect of Bolt Connections on Dynamic Response of Cylindrical Shell Structures Q.H. Cheng, S. Zhang and Y.Y. Wang
573
Simulation of Ductile Fracture in Tubular Joints Through a Void Nucleation Model X.D. Qian, Y.S. Choo and J.Y.R. Liew
577
Stress Intensity Factors for Doubler-Plate Reinforced Tubular Joint Subjected to Axial Load R. Jiang and Y.S. Choo
583
Computational Dynamics Vibrational Analysis of Poroelastic Bar T.Z. Chen, Z. Zong and K.C. Hung
587
Finite Element Failure Modelling of Corrugated Panel Subjected to Dynamic Blast Loading J.W. Boh, LA. Louca and Y.S. Choo
591
Simulation of Acoustic Radiation and Scattering using Boundary Element Method Z.Y. Yan, K.C. Hung and H. Zheng
595
XXIII
Numerical Characterization of RC Plate Response and Fragmentation Under Blast Loading K.Xu, Y. Lu and H.S. Lim
599
Dynamic Analysis of Brick-Concrete Structure by using Wilson-6 Method DM. Hou, Y.B. Wang, M. Yin andX.Y. Ma
604
A New Computational Mathematical Model of Hydraulic Damper Y.B. Wang and DM. Hou
608
Broadband Echoes from Underwater Targets H. Lew and B. Nguyen
613
High Performance Computing and Numerical Methods 1 Competing Risks for Reliability Analysis Using Cox's Model F.AM. Elfaki, I. Daud, N.A. Ibrahim, M.Y. Abdullah and I. Lukman
618
Parallel Multibody Dynamics using the Message Passing Interface B. Fox, F.J. Welna, D.J. Lilja and L.S. Jennings
622
Some Computation Aspects in Model-Order Reduction of Flexible Structures R. Saragih
626
Meshless Analysis of the Obstacle Problem for Timoshenko Beams Based on a Locking-Free Formulation J.R. Xiao, F. Wang and Q.H. Cheng
632
Efficient Parallel Algorithm for Large-Scale Molecular Dynamics Simulation in Microscale Thermophysics B. Wang, J.W. Shu, WM. Zheng and J. Z. Wang
637
Improving the Cell Mapping Method and Determining Domains of Attraction of a Nonlinear Structural System Q. Ding, Z.S. Liu and J.J. Li
642
XXIV
High Performance Computing and Numerical Methods 2 High Rate Dynamic Response of Structure using SPH Method Z. S. Liu, S. Swaddiwudhipong and C. G. Koh
646
The Generalized Differential Quadrature Rule T.Y. Wu, Y.Y. Wang and G.R. Liu
651
Recovery Based Submodeling Finite Element Analysis H. Gu and Z. Zong
655
A Hierarchical Approach to Surface Partition of Polygonal Meshes J. Shen and D. Yoon
659
A Combined Meshfree Method and Molecular Dynamics in the Multiscale Length Simulation Q.X. Wang, T.Y. Ng, K.Y. Lam, H. Li and X.J. Fan
663
COMPUTATIONAL SCIENCE Computational Science 1 Self-Similar Problems in Multidimensional Conservation Laws S. Canic, B.L. Keyfitz and E.H. Kim
667
Variance Reduction of Monte Carlo Methods for Option Pricing under Stochastic Volitility Models X.Q. Liu and Y.Y. Wong
671
A Superlinearly Convergent Algorithm for Large Scale Multistage Stochastic Nonlinear Programming F.W. Meng, R. Tan and G.Y. Zhao
675
Computation of Network Delay with Prioritised Traffic Involving the Multi-Priority Dual Queue A. Bedford and P. Zeephongeskul
679
Simulation Solutions of Networks with Prioritised Traffic Involving the Multi-Priority Dual Queue A. Bedford and P. Zeephongeskul
683
XXV
Inverse of a Certain Band Toeplitz Matrix K.J. Lim
687
Computational Science 2 Time-Splitting Sine-Spectral Approximation for the Nonlinear Schrbdinger Equations W.Z. Bao Calculating Global Minimizers of a Nonconvex Energy Potential D. Gao and P. Lin
692 696
A QR-Type Method for Computing the SVD of a General Matrix Product/Quotient D.L. Chu
700
Newton's Method for Non-Differentiable Equations: Convergence and Applications D.F. Sun
705
Numerical Solution of Blow-Up Problems Using MeshDependent Variable Temporal Steps K.W. Liang, P. Lin and R.C.E. Tan
709
Nonlinear Boundary Layers of the Boltzmann Equation S. Ukai, T. Yang and S.H. Yu
713
Computational Science 3 A New Algorithm for Division of Polynomials L.H. Fan Ginzburg-Landau System and Superconductivity Near Critical Temperature X.B. Pan Geodesic Approximations of 2D Hydrodynamics W. Lawton Multi-Phase Flow Models and Methods for Lava Lamps and Life Sciences J. Shuo
717
722 726
730
XXVI
A Reynolds-Uniform Numerical Method for Prandtl's Boundary Layer Problem for Flow Past a Plate with Mass Transfer J.S. Butler, J.J.H. Miller and G.I. Shishkin
733
GRID COMPUTING Grid Computing and Related Issues Constructing an Ogsa-Based Grid Computing Platform W. Jie, T.Y. Zang, Z. Lei, W.T. Cai, S.J. Turner and LZ. Wang
738
An Ogsa-Based Directory Service Z. Lei, T. Y. Zang and W. Jie
742
Grid Resource Management Information Services for Scientific Computing H.N. Lim, D.P. Spooner, S.A. Jarvis, G.R. Nudd, LZ. Wang and W. Jie An Open Producer and Consumer Management System for Grid Environment 7". Y. Zang, Z. Lei and W. Jie
746
750
Replica Selection Framework for Bio-Grid Computing LZ. Wang, W.T. Cai, B. Schmidt, B.S. Lee and W. Jie
754
A Grid Testbed Supporting MPI Applications W. Jie, Z. Lei, T.Y. Zang and L.Z. Wang
758
Running MPI Application in the Hierarchical Grid Environment L.Z. Wang, W. Jie and W. Xue
762
Clustering Systems and Applications Cluster-Based Parallel Simulation for Large-Scale Power System Dynamics J.F. Yan, W. Xue, J.W. Shu, X.F. Wang and W. Jie
766
Hardware Impact on Communication Performance of Beowulf Linux Cluster Y. Tang, Y.Q. Zhang and Y.C. Lee
773
XXVII
D-GRIDMST: Clustering Large Distributed Spatial Databases J. Zhang and Y. Cao
777
Massively Parallel Sequence Analysis with Hidden Markov Models B. Schmidt and H. Schroder
781
Tabu Search and Simulated Annealing on the Scheduling of Pipelined Multiprocessor Tasks M.F. Ercan and Y.F. Fung
785
Distributed Systems and Applications TME - A Distributed Resource Handling Tool T. Imamura, Y. Hasegawa, N. Yamagishi and H. Takemiya
789
Protecting Integrity in a Distributed Computing Platform T.T. TayandY.Y. Chu
793
An Integrated Distributed Computing Platform on a Decentralized Architecture T.T. TayandY.Y. Chu Grid Based Problem Solving Environment for Scientists E. Sindhu, U. Periathampy and M. Kantharaj Management of EJB Applications using Java Management Extensions J.K. Park, J.B. Kim and D.J. Sohn
798
803
807
HIGH END COMPUTATIONS Data Mining On Applications of Data Mining to Human Resources Data V. Kamalesh and V. Kuralmani Linguistic Rule Extraction by GA Combining DDR and RBF Neural Networks X.J. FuandL.P. Wang
814
818
XXVIII
Web-Based Configuration and Control of HLA-Based Distributed Simulations N. Julka, D. Chen, B.P. Gan, S.J. Turner and W.T. Cai Competing Risks with Censored Data: A Simulation Study /. Lukman, N.A. Ibrahim, F. Maarof, I. Daud and M.N. Hassan Combining Support Vector Machine (SVR) with Genetic Algorithm (GA) to Optimize the Initial Positions of Agents in the Land Combat Simulation L.J. Cao, K.S. Chua, W.K. Chong, H.P. Lee and L Qian Acquisition of Background Coefficient X.Y. Qi, C. Lu andZ.G. Liu
822 826
830
834
Visualization A Framework for a Real-Time Distributed Rendering Environment H.B. ZhuandK.Y.T. Chan
838
Immersive Visualisation of Nano-lndentation Simulation of Cu S.H. Xu, J. Li, C.H. Li and F. Chan
846
Distributed Processing and Visualisation of MEG Data S. Date, S. Shinji, M.M. Yuko, S. Jie, B.S. Lee, W.T Cai and L.Z. Wang
850
A Fast Algorithm of Level Set Method for 3D Prostate Surface Detection F. Shao, K. V. Ling and W.S. Ng
855
A Pathological Diagnosis System for Brain White Matter Lesions S.H. Han and F. Li
859
Using Streaming SIMD Extension on High Level Image Processing M.F. Ercan and Y.F. Fung
867
An Approach for Optimization of Imaging Parameters for Ground Surface Inspection using Machine Vision V. Sivasankaran, A. Jothilingam, B. Rajmohan and G.S. Kandasami
871
XXIX
MICRO-ELECTRO-MECHANICAL SYSTEMS Model Development and Behavior Simulation of pH-StimulusResponsive Hydrogels H. Li, T.Y.NgandY.KYew
875
Fringe-Field and Ground Plane Effects for Electrostatic MEMS Simulations A. Ongkodjojo and F.E.H. Tay
879
A Coupled Multi-Field Formulation for Stimuli-Responsive Hydrogel Subject to Electric Field Z. Yuan, H. Li, T. Y. Ng and J. Chen
884
Numerical Simulation of Electromechanical Behavior for MEMS Optical Switch F. Wang, C. Lu and Z.S. Liu
888
Design and Modelling High-Efficiency Accelerometers AT. Ng, W.H. Li, H. Du andN.Q. Guo A Finite Element Analysis for Piezoelectric Smart Plates Including Peel Stresses Q. T Luo and L Y. Tong
893
897
MESHING A Study on Three-Dimensional Mesh Generation for Coal Mining Modeling S.G. Chen, S. Craig, D.P. Adhikary and H. Guo
901
Linear and Torsion Spring Analogies for Dynamic Unstructured Meshes in Fluid Structure Interaction Problems - A Comparative Study R. Ajaykumar, N.M. Sudharsan, K. Murali, K. Kumar and B.C. Khoo
905
Solving Biot's Consolidated Model using Sparse Matrix Technology Y.L Li and K. H.Lee
909
XXX
3-D Multi-Block Orthogonal Grid Generated by Laplace Equation with Sliding Boundary Condition Z.K. Zhang
913
Meshing Human Brain with Hexahedral Meshes from Images Slices using Mesh Mapping Method Y.L. LiandK.H. Lee
917
Plenary
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Multiscale Modeling and Computation of Incompressible Flow T h o m a s Y. Hou*
A b s t r a c t . Many problems of fundamental and practical importance contain multiple scale solutions. Direct numerical simulations of these multiscale problems are extremely difficult due to the range of length scales in the underlying physical problems. Here, we introduce a dynamic multiscale method for computing nonlinear partial differential equations with multiscale solutions. The main idea is to construct semi-analytic multiscale solutions local in time, and use them to approximate the multiscale solution for large times. Such approach overcomes the common difficulty associated with the memory effect and the non-uniqueness in deriving the global averaged equations for incompressible flows with multiscale solutions. It provides an effective multiscale numerical method for computing incompressible flow with multiscale solutions.
1
Introduction
Many problems of fundamental and practical importance have multiple scale solutions. Composite materials, porous media, and turbulent transport in high Reynolds number flows are examples of this type. The direct numerical solution of multiple scale problems is difficult due to the wide range of scales in the solution. It is almost impossible to resolve all the small scale features by direct numerical simulations due to the limited capacity in computing power. On the other hand, from an engineering perspective, it is often sufficient to predict the macroscopic properties of the multiscale systems, such as the effective conductivity, elastic moduli, permeability, and eddy diffusivity. Therefore, it is desirable to develop a method that captures the small scale effect on the large scales, but does not require resolving all the small scale features. In recent years, we have introduced a multiscale finite element method (MsFEM) for solving partial differential equations with multiscale solutions [5, 6, 4, 3]. The central goal of this approach is to obtain the large scale solutions accurately and efficiently without resolving the small scale details. The main idea is to construct finite element base functions which capture the small scale information within each element. The small scale information is then brought to the large scales through the coupling of the global stiffness matrix. Thus, the effect of small scales on the large scales is correctly captured. In our method, the base functions are constructed from the leading order homogeneous elliptic equation in each element. As a consequence, the base functions are adapted to the local microstructure of the differential operator. In the case of two-scale periodic structures, we have proved that the multiscale method indeed converges to the correct solution independent of the small scale in the homogenization limit [6]. We remark that the idea of using base functions governed by the differential equations has been used in the finite element community, see e.g. [1, 8, 2]. "Applied Mathematics, 217-50, Caltech, Pasadena, CA 91125, USA. Email:
[email protected]. Research was in part supported by a grant DMS-0073916 from the National Science Foundation.
3
4 2
Multiscale F i n i t e E l e m e n t M e t h o d
In this section, we briefly describe the multiscale finite element method for elliptic problems with highly oscillating coefficients: Leu := - V • ( a ( - ) V u ) = /
in fi, u = 0 on T = DQ,
(1)
where a(x) = (a,ij(x/e)) is a symmetric positive definite matrix. The main idea of MsFEM is to construct finite element base functions which capture the small scale information within each element. This is accomplished by requiring that the base functions satisfy the leading order homogeneous differential equation within each coarse grid element: Le<j>€ = 0,
x
eK,
with some appropriate boundary condition for cff in the boundary of the local element K. The choice of boundary conditions in defining the multiscale bases will play a crucial role in approximating the multiscale solution. Intuitively, the boundary condition for the multiscale base function should reflect the multiscale oscillation of the solution u across the boundary of the coarse grid element. The simplest choice of the boundary condition for the base function is a linear boundary condition. Using homogenization theory, we can show that the multiscale finite element method gives a convergence result uniform in e as e tends to zero. This is the main feature of this multiscale finite element method over the traditional finite element method. T h e o r e m 2.1 Let u 6 H2(ft) be the solution of (1) and «/, be the finite element solution obtained from the space spanned by the multiscale bases, 0 £ . Then we have \\u - uh\\Hi < C(h + e)\\f\\Li +c(^y'2\\u0\\H2, where «o £ H2(Q) n W 1,0 °(fi) is the solution of the homogenized 2.1
(2)
equation.
Over-Sampling
As we can see from the above theorem, the multiscale FEM indeed gives correct homogenized result as e tends to zero. This is in contrast with the traditional FEM which does not give the correct homogenized result as e —* 0. The error would grow like 0(h2/e ) . On the other hand, we also observe that when h ~ e, the multiscale method attains large error in both H1 and L2 norms. This is what we call the resonance effect between the grid scale (h) and the small scale (e) of the problem. Motivated by our convergence analysis, we propose an over-sampling method to overcome the difficulty due to scale resonance [5]. The idea is quite simple and easy to implement. Since the boundary layer in the first order corrector is thin, O(e), we can sample in a domain with size larger than h + t and use only the interior sampled information to construct the bases; here, h is the mesh size and e is the small scale in the solution. By doing this, we can reduce the influence of the boundary layer in the larger sample domain on the base functions significantly. As a consequence, we obtain an improved rate of convergence.
5 2.2
F I N E SCALE RECOVERY
To solve transport problems in the subsurface formations, as in oil reservoir simulations, one needs to compute the velocity field from the elliptic equation for pressure, i.e v = —a e Vp, here p is pressure. For MsFEM, the fine scale velocity can be easily recovered from the multiscale base functions, noting that they provide interpolations from the coarse grid to the fine grid. To test the accuracy of the recovered velocity and effect of small-scale velocity on the transport problem, we have performed two sets of computations. In the first computation, we reconstruct the fine scale velocity field (1024 by 1024 grid) from a coarse grid (64 by 64 grid) pressure computation, and use the reconstructed fine scale velocity field to transport the saturation in the two-phase flow. In the second computation, we compute both the pressure and the saturation using a fine grid (1024 by 1024). To demonstrate that we can recover the fine grid velocity field from the coarse grid pressure calculation, we compare the velocity fields obtained by the two approaches. The agreement is excellent. The recovered velocity field captures very well the layer structure in the fine grid velocity field. Moreover, we observe that the agreement in the saturations obtained by the two approaches is striking. 3
M u l t i s c a l e M o d e l i n g of I n c o m p r e s s i b l e F l o w
In order to obtain a coarse grid model for two-phase flow, we need to derive a homogenized equation for the saturation equation which is hyperbolic. This is a very difficult problem due to the nonlocal memory effect [10]. The difficulty encountered here is similar in spirit to that in obtaining a large scale averaged equation for the incompressible Euler or Navier Stokes equations. One of the earliest attempts in deriving the homogenized equation for the incompressible Euler equation was made by McLaughlin, Papanicolaou and Pironneau in [9]. More specifically, they considered the following initial value problem:
ut + (u- V)u = -Vp, with V-u = 0 and highly oscillatory initial data u(x,0) = U{x) + W{x,x/e). They then constructed multiscale expansions for both the velocity field and the pressure. In doing so, they made an important assumption that the microstructure is convected by the mean flow. Under this assumption, they constructed a multiscale expansion for the velocity field as follows: u £ (x,t) =u(x,t)
+ w(
v
' ,-,x,t)
+ eu1{
v
,-,x,t)
+0(e2).
The pressure field p £ is expanded similarly. From this ansatz, one can show that 6 is convected by the mean velocity: 8t + u-V8 = 0, 8(x,0)=x. It is a very challenging problems to develop a systematic approach to study the large scale solution in three dimensional Euler and Navier-Stokes equations. The work of McLaughlin, Papanicolaou and Pironneau provided some insightful understanding how small scales interact with large scale and how to deal with the closure problem. However, the problem is still not completely resolved since the cell problem obtained this way does not have a unique solution. Additional constraints need to be enforced in order to derive a large scale averaged equation. With additional assumptions, they managed to derive a variant of the k — e model in turbulence modeling. Recently, together with Dr. Danping Yang [7], we have studied convection of microstructure of the 3-D incompressible Euler equations using a new approach. We found that the small scales
6 are convected by the full velocity field, i.e. it is more appropriate t o expand the velocity field as follows: ul{x,t) =u(x,t)+w(
v
,-,x,t)
+eiti(
,-,x,t)
+0(e2).
where 9t£ + u £ - V « £ = 0 ,
ee{x,0)=x.
Thus, the oscillatory part of 9e could have order one contribution t o the mean velocity of the incompressible Euler equation. By using a = 9e as a new variable, we can reformulate the Euler equation in (a, t) and perform multiscale expansion for the stream function and the flow map in terms of a/e. This change of variables amounts t o using a Lagrangian formulation of the Euler equation. Using this reformulation, we can derive both the homogenized equation and the periodic cell problem. The resulting problem is well-posed provided that we project certain resonance modes in the velocity field. We have also generalized this multiscale analysis to initial velocity field that has many or even continuous spectrum of scales. Similar analysis can be carried out for the two-phase flow with highly oscillating or random permeability field. References [1] I. Babuska, G. Caloz, and E. Osborn, Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients, SIAM J. Numer. Anal., 31 (1994), 945-981. [2] F . Brezzi, L. P. Franca, T. J. R. Hughes and A. Russo, b = J g, Comput. Methods in Appl. Mech. and Engrg., 145 (1997), 329-339. [3] Z. Chen and T. Y. Hou, A Mixed Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients, Math. Comput., published electronically on June 28, 2002. [4] Y. R. Efendiev, T. Y. Hou, and X. H. Wu, Convergence of A Nonconforming Element Method, SIAM J. Numer. Anal., 37 (2000), 888-910.
Multiscale
Finite
[5] T. Y. Hou and X. H. Wu, A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, J. Comput. Phys., 134 (1997), 169-189. [6] T . Y. Hou, X. H. Wu, and Z. Cai, Convergence of a Multiscale Finite Element Method for Elliptic Problems With Rapidly Oscillating Coefficients, Math. Comput., 68 (1999), 913-943. [7] T. Y. Hou and D.-P. Yang, Multiscale Analysis for Three-Dimensional Equations, in preparation, 2002.
Incompressible
Euler
[8] T. J. R. Hughes, Multiscale Phenomena: Green's Functions, the Dirichlet-to-Neumann Formulation, Subgrid Scale Models, Bubbles and the Origins of Stabilized Methods, Comput. Methods Appl. Mech Engrg., 127 (1995), 387-401. [9] D. W. McLaughlin, G. C. Papanicolaou, and O. Pironneau, Convection of Microstructure Related Problems, SIAM J. Applied Math, 45 (1985), 780-797.
and
[10] L. Tartar, Nonlocal Effects Induced by Homogenization, in P D E and Calculus of Variations, ed by F . Culumbini, et al, Birkhauser, Boston, 925-938, 1989.
Splitting Methods for Incompressible Viscous Flow Problems with Free and Moving Boundaries
E. J. Dean*, R. Glowinski*, L. H. Juarez*, T.W. Pan* *Department of Mathematics, University of Houston, Houston, Tx 77204-3008 t Departamento de Matematicas, Universidad Autonoma Metropolitana-I, Mexico, D. F., CP 09340 Email:
[email protected],
[email protected],
[email protected],
[email protected] The main goal of this presentation is to discuss an (almost) unified approach for the computational treatment of incompressible viscous flow problems with free or moving boundaries. The methodology to address the solution to these problems relies on the following ingredients (several of them fairly classical): (i) Time discretization by operator-splitting. (ii) Space approximation by finite element methods to take advantage of variational formulations of the existing above problems. (iii) In the case of flow with moving rigid boundaries, volume distributed Lagrange multiplier based fictitious domain methods to solve the flow equations on a fixed space region. This approach has proved efficient for the simulation of particulate flow with many particle3s (> 102, typically). (iv) Wave-like equation treatment of the advection. (v) H1 or L2-projection methods for the treatment of the incompressibility. We shall validate the above methodology through the solution of test problems in two and three-dimensions these problems include: the settling and interaction of spherical and ellipsoidal rigid bodies in Newtonian, Visco-Elastic, and Visco-Plastic fluids (see attached pictures) and the simulation of an incompressible viscous flow with surface tension on the free boundary.
7
8
?z!st8mmMam&s&!>
silfHBlSgSt iiiiffliHBg
1
0
Figure 1: Settling of a Rigid Ellipsoid in an Newtonian Incompressible Viscous fluid.
9
Figure 2: Settling of a Rigid Ellipsoid in an Incompressible Oldroyd-B Visco-Elastic Fluid.
10
-
L t=12.14
Figure 3: Settling and interaction of Two Rigid Ellipsoid in a Newtonian Incompressible Viscous fluid.
11
IDul
1.8
1.6
1.4
1.2
0
0.2
0.4
0.6
0.8
1
F i g u r e 4: Settling of rigid disks in an incompressible Bingham Visco-Plastic Fluid.
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Contributed Papers
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CATION-7C INTERACTIONS IN AG(I)-SUBSTITUED ALKYLBENZENES COMPLEXES: A THEORETICAL STUDY
;
Y. P. WONG, K. M. NG, AND C. W. TSANG* Department of Applied Biology & Chemical Technology, Hong Kong Polytechnic University E-mail:
[email protected] (*contactperson)
Introduction The binding of Ag (I) cation to alkylbenzenes (RBz) is chosen as model systems to investigate the alkyl substituent effects in cation-7i interactions, which have been postulated to be a new type of interaction forces important in biological recognition, nano-electronics and the design of therapeutic drugs.1
Experimental High-energy (4.7 keV, He as collision gas) and low-energy (15-45eV, Ar as collision gas) collision-induced dissociations (CID) of electrospray ionization (ESI) generated [RBz,Ag-RBz2]+ heterodimers (where RBz! and RBZ2 are alkylbenzenes) were measured with a Finnigan-MAT 95S B-E tandem mass spectrometer with B/E linked scans, and a Micromass Quattro II triple quadrupole mass spectrometer, respectively.
Theoretical Methodology Standard ab initio molecular orbital calculations were carried out by using the Gaussian 98 package on SGI Indigo2/Octane workstations at the approximate CCSD(T)/(HW(f), 631G(d)) level of theory using the additivity relation as below. CCSD(T)/(HW(f), 6-31G(d)) s CCSD(T)/STO-3G(d) + [MP2/(HW(f), 631G(d)) - MP2/STO-3G(d)]
Results and Discussion The relative Ag (I) ion binding energies (affinities) of 15 alkylbenzenes were measured by the standard mass spectrometric kinetic method2 based on the competitive dissociation of the [RBzi-Ag-RBz2]+ heterodimers to their respective monomer complexes under high-
15
16 Alkylbanzanas
In { fct*0-R*«i]* / A [ A B - R B « 2 ] * )
Bwizen*
0.00 0.97 1 0.06
Ethyl benzene
1.63 * 0.07 (0.31)
m-Xylerm
1.94 i 0.10
n-Propytbenzene
216 ' 0 . 1 0
I-Propyttwnzene
(0.04)
| V :-
2.20 * 0.11
n-Butytbsnztfrw
2.51 t 0 . l l
i-Butyl b o n z e no
2.59 i 0.12 2.68 - 0.13
s-Butyibenzsn* (0.02) t-Butylbenzene
—*"
1,3,5-Triroethylbenzene
2.70 10.15 2.87*0.15 3.11 +0.15
n-PerrtytmfiZBfW 0.50
Figure 1
1,2,4,5-Tatram«thy(banzsn»
3.61 tO. 15
Pantamethylbanzene
4.34 ±0.15
H«xamethyl benzene
4.88 - 0 16
Experimentally measured /n(k|Ag-RBZl]+ / kiAg-RB^]*) values for He-CID of Ag* bound heterodimers of alkylbenzenes. The /n(k|Ag.RBz1]+ / k[Ag-RBz2]+) values are taken to be equal to /n([Ag-RBzi]+ / [AgRBz2]+) ion intensity ratio values. The data presented under the heading /w(k[Ag.RBz]+ / k[Ag-Benzoie]+) are average ± standard derivation of cumulative values expressed relative to benzene. The values in parenthesis are the arithmetic difference of measured values having a common reference alkylbenzene.
Table 1 Experimental measured and theoretical calculated absolute Ag+ affinities of alkylbenzenes at OK. Alkylbenzenes
Theoretical Affinities^
Experimental Affinities
(kJ mol" )
(kJ mol"1)
Benzene
156.7
157.7
Toluene
168.8
169.4
Ethylbenzene
172.9
177.4
m-Xylene
181.2
181.2
n-Propylbenzene
—
183.8
i-Propylbenzene
—
184.3
n-Butylbenzene
—
188.1
i-Butylbenzene
—
189.0
s-Butylbenzene
—
190.1
t-Butylbenzene
1
190.4
17
1,3,5-Trimethylbenzene
193.4
192.4
—
195.3
200.6
201.4
Pentamethylbenzene
—
210.2
Hexamethylbenzene
209.4
216.8
n-Pentylbenzene 1,2,4,5-Tetramethylbenzene
a
Calculated at the CCSD(T)/(HW(f), 6-31G(d)) level. b Obtained from their relative Ag (I) affinities measured
from the high-energy CID.
Table 2 Experimental Ag+ afffinities at OK (kJmol"1) of acetone and acetonitrile. This worka AH [ A g-L n ]+
A(AS)app
RA Kinetics
Threshold-CID
Acetone
148.6+1.8(3.4)
0.6 + 0.8(1.5)
160±19 b
—
Acetonitrile
162.8 ±1.0 (1.9)
6.7 + 0.7(1.3)
—
162c
L„
a
Literature values
Weighted results with experimental uncertainties given as + S.D. (90% confidence interval). " Ref [4]. c Ref
[5].
Acknowledgement The award of a Hong Kong Polytechnic University research studentship and graduate scholarship to YPW and the funding support of the Research Grant Council of Hong Kong (Area of Excellence Project No. P-10/2001 and CERG Project No. 5190/00P) are gratefully acknowledged.
18 energy He-CID conditions. The experimental measured ion intensity ratio values, /n([AgRBz]]+ / [Ag-RBz2]+), are summarized in a relative Ag (I) ion affinity ladder diagram shown in Figure 1. Theoretically calculated values for benzene, toluene, ethylbenzene, mxylene, 1,3,5-trimethylbenzene, 1,2,4,5-tetramethylbenzene, pentamethylbenzene were calculated with an estimated uncertainty of ±15 kJ mol"1.3 Based on these theoretical calculated values, the experimental absolute affinities of the 15 alkylbenzenes (in kJ/mol) were established from their relative affinity ladder values and summarized in Table 1. These experimental absolute values were further validated by using them as reference values in extended kinetic method2, measurement of Ag (I) ion affinities of acetone (148.9 kJ mol"1) and acetonitrile (162.8 kJ mol"1), which were in good agreement with that obtained by radiative association kinetic analysis (160 + 19 kJmol" ) and the thresholdCID method (162 kJ mol"1)5, respectively. Our results show that the Ag(I) ion affinities of alkylbenzenes increase significantly with the number of methyl substitutions, the chain length of n-alkyl substituents, and the extent of branching in alkyl substituents.
The results are attributed to the positive
inductive effect and polarizability effect of the alkyl substituents, leading to enhanced ion-quadrupole and ion-induced dipole interaction between the Ag(I) ion and the aromatic ring.
Conclusions The absolute Ag (I) ion affinities of 15 alkylbenzenes were successfully established based on the theoretical calculated affinities. The alkyl substituents have been found to have a pronounced effect on Ag(I) ion affinities of alkylbenzenes.
References 1. 2. 3. 4.
Ma, J.C.; Dongherty, D.A. Chem. Rev. 1997, 97, 1303. Cooks, R.G.; Wong, P.S.H. Ace. Chem. Res., 1998, 31, 379. Ma, N. L. Chem. Phy. Lett., 1998, 297,230. Ho, Y. P.; Yang, Y. C ; Klippenstein, S. J.; Dunbar, R. C. J. Phy. Chem. A, 1997, 101, 3338. 5. Shoeib, T.; EI Aribi, H.; Siu, K. W. M.; Hopkinson, A. C. J. Phys. Chem. A 2001, 705,710.
Light Propagation in Biological tissue using Monte Carlo Simulation Aslmam
Aggarwal
Lecturer, Department of Electrical and instrumentation Engineering Sant Longowal Institute ofEngineering and Technology. Longowal. Sangrur, Punjab. INDIA Email:
[email protected] Non-invasive diagnosis is medicine has shown considerable attention in recent years. Several methods are already available for imaging the biological tissue like X-ray computerized tomography, magnetic resonance imaging and ultrasound imaging etc. But each has its own disadvantages. Optical tomography is one of the emerging methods in the field of medical imaging which is non-invasive in nature. The only problem that occurs in using light for imaging the tissue is that it is highly scattered inside tissue, so the propagation of light in tissue is not confined to straight lines as the case with X-ray tomography. So the need arises to understand the behavior of propagation of li^it in tissue. There are several methods for light interaction with tissue These methods can be divided into two categories viz. deterministic methods and stochastic methods. Deterministic methods involve the solution of radiative transfer equation (RTE) which is complex integrodifferential equation and is difficult to solve. Stochastic methods model the RTE through dealing individual interaction. The individual interactions are modeled explicitly by deriving probability density functions in random walk and Markov random field models. Monte Carlo method is stochastic method which is simple technique for simulation of light through tissue, m the Monte Carlo methods individual history of photons is simulated as they undergo scattering and absorption events in the biological tissue. This is continued until the photon is either absorbed or is emitted from the boundary of the tissue. The data obtained from the Monte Carlo simulation is the number of photons detected at different times which is known AS temporal point spreadfunction^TPSF). This TPSF is used by nonlinear optimization techniques to get the reconstruction of image.
1. Introduction Monte Carlo techniques1 are used to study the evolution and study state behavior of phenomenon, which are essentially stochastic in nature. Simulation of propagation of NIR light through tissue using Monte Carlo method is a conceptually simple technique. Photon packets are launched from the source and as this traverse through the medium, if the packet hits the position which is appointed as a detection point, photon packet is logged into a result matrix. Eventually, when a large number of photons have been detected, the average path length traversed can be obtained from the distribution of actual path lengths traversed, obtained from the detected photons. In practice, however a number of difficulties arise, all of which have their origin in the computationally time consuming nature of Monte Carlo method. Since we are only interested in photons that actually hit the detector, a lot of computation done is waste. The faction of photons that contribute depend on the optical properties2 of the simulated medium and the geometry, the distance between the source and the detector, but under very favorable conditions this fraction is no more than 1:100 which means that the total number of photon paths that have to be calculated is typically several millions for good results. As the distance of detector increases, the number of detected photon packets decreases rapidly. At some distance it is no longer useful to perform calculations, because the statistics become very poor and uncorrelated. Computation can be decreased by taking advantages of symmetries. In case of cylindrical geometry, if the homogeneity is taken co-axial with the background (in 2-D, concentric circles), at each angle, same data can be used. The finite size of detector has also to be considered. The simplest way of implementing detection is to assign detector status to a certain pixel, and thus making the detector size equal to the pixel size. It is tempting to make detector size large, in order to obtain a higher faction of detected photons. In reality, detector will be determined by the diameter of optical fiber used. 2. Monte Carlo Method Light beam is considered to consist of many packets of photons that behave like particles subject to scattering and absorption3 in tissue. The path of each packet is traced until it escapes from the medium, and a large number of packets are launched so that the statistical averages (such as mean, variance, autocorrelation) etc. are consistent, goingfromone estimate to other, and are meaningful. 2.1 Photon Initialization Monte Carlo begins by launching a photon packet into the tissue. The size of this packet is called weight (W) of the photon. Its initial weight is set to unity. The photon s initial direction is chosen downwards into the tissue. The coordinates of the photon are identical for all photons. At each step, some portion of the packet of photons would be absorbed and so the weight reduces after every step.
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2.2 Generating Step size The simplest Monte Cario method propagates each photon with fixed incremental step sizes. The fixed step size As must be small relative to the average mean path length of a photon in the tissue. The mean free path length is the reciprocal of the total attenuation coefficient4. (2.2.1) As — = ft
H.+H,
Where /J,,M, a n d / i a als ^c t o t a l attenuation, the absorption and the scattering coefficients respectively. If the step size is too small the photon will rarely interact with tissue and the Monte Carlo method will be inefficient, conversely if the step size is too large, the distance traveled by a photon is a poor approximation to that of an actual photon traveling through tissue. A much more efficient method chooses a different step size for each photon step. The probability density function5 for the step size follows Beer's law 6(i.e. it is more likely for a photon to travel a short distance than a long distance and the probability that the step size is As is proportional to ^n,^3 ). A function of random number § uniformly distributed between zero and one which yields a random variable' with this distribution is:
A,
.
(2- 2 - 2 )
_>!fe) M,
The stepsize As found using equation (2.2) represents the distance that a photon will travel before interacting (through absorption or scattering) with the tissue.
2.3 Changing Photon Direction When the photon interacts with the tissue, it gets scattered to a new direction, in addition to weight loss owing to absorption. The new direction in 3-D is defined by two angles, one an azimuthal and the other longitudinal. Following Mie theory8 a normalized phase function9 describes the probability for these azimuthal and longitudinal angles for a photon when it is scattered Scattering in time is characterized by the so-called Henyey Greenstein phase function10, which gives the azimuthal angle as: OOS0
1 2g
1+X+r
l-g
(2.3.1)
l-g+2g£]
Where g is called anisotropic factor" and for tissue its value is taken nearly equal to 0.9. If scattering is isotropic12 (g — 0 ) , the following equation for azimuthal angle is used cosO
2f-l
(2.3.2)
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I
»• -
—
•
-
\»»«
-
/
g-0
/
~~^- —
;
2.4 Moving the Photon The moving photon is uniquely described by three Cartesian coordinates for spatial position and the three direction cosines for direction of travel. For a photon located at (x,y,z) traveling a distance in the direction specified by the direction cosines14, the new coordinates are given by: y
=
x
+
M*-&3
y
=
y
+
ti,Ja
z'
=
z
+
/*,-AJ
( 2 -4.1)
In 2-D Monte Carlo method, for cylindrical geometry, the photon is traced in 2-D plane. So location is specified by (x,_y) and for moving the photon from location (xi, J ] ) to(x2,.V2)> ^ ^ size and angle of scattering is generated. The new location is given by: xi y2
= =
n + ^cosff y, + ,scos0
(2.4.2)
2.5 Photon Absorption After each propagation step, the photon packet is split into two parts, a fraction is absorbed and the rest is scattered. The fraction of the packet that is absorbed is: fraction
absorbed=^S. ft
^a_ fa+fs
=
x
^s fa + fs
x_a
(2-5.1)
Where a is called albedo constant Consequently, a new photon weight W is given by , which represents the traction of the packet that is scattered in this step. An absorption event requires both the location and the amount of light absorbed be recorded. For example, the appropriate element of the absorption matrix is incremented by (l-a)W .The number of bins in the absorption matrix is determined by spatial resolution required. Increasing the number of entries increases the spatial resolution, but also increases the computation. 2.6 Photon Termination The weight of photon packet will never reach zero and propagating a photon with very little weights yields no useful information. But if we discard all the photons when their weight drops below a specified
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minimum (e.g. 0.001), violates energy conservatioa The Roulette technique gives such photons (of weight W) one chance in m ( eg 10) of surviving with a weight mW or else its weight is reduced to zero. So the photon is terminated in an unbiased fashion without sacrificing energy conservation and without continuing propagation until its weight has reduced to zero. 3. Simulation Result As a result of simulation, following temporal point spread function is obtained The TPSF is obtained for all the source and detector positions and for all the orientations which is used by non-linear optimization techniques for reconstruction of image
t20B
|
BOP
000
400 -
Sw
»•
«o
«
sw
so*
too
References: [1] Malvin Kalos and Paula A- Whftlock. Monte Carlo Methods Volume 1: The Basics. Wiley, New York,
1986.
[2] W. F. Cheong, S. A. PrahL, and A. J. Welch, "A Review of the Optical Properties of Biological Tissues," IEEE J. Quantum Electronics, 26,2166-2185 (1990) [3] Simon R Arridge and Jeremy C Hebden, Optical imaging in medicine: II. Modelling and reconstruction, Phys. Med. Biol. 42 (1997)841-853. [4] K.R. Czerwmski, M. FoDcert, W. Thilly and E. Gostjeva, Towards a Scientific Basis for Estimatmg Expected Health Effects from Low Radiation Exposures Nuclear Engineering Department, MIT Center for Environmental Heafth Sciences, MTT [5] B P Flannery, SA Teukolsky and WT Vetterling, Numerical redpies in C, Cambridge University Press. [6]. F Alberto Graubaum and Jorge P Zubelli, Difiuse Tomography: Compu&ional aspects of the isotropic case, Inverse Problems (1992), 421-423. [7]. S A Prahl, M Keijzer, S L Jacques, A J Welch, A Monte Carlo method of light propagation in tissue, SPIE Institute series, Vol. IS 5 (1989). [8]. S R Arridge, M Cope, D T Delpy, The theoretical basis for the determination of optical path lengths in tissue: Temporal and frequency analysis, Physics in Medicine and Biology, 1992, Vol. 37, No.7,1531-1560 [9]. R. A. Forester and T. N. K. Godfrey, "MCNP—a general Monte Carlo code for neutron and photon transport,"m Methods and Applications in Neutronics, Photonics and Statistical, pp. 33-47, New York: Springer-Verlag, 1983. [10]. Y Yamada, light Tissue interaction and optical imaging in Biomedicme, Annual House, Inc, 1995.
Review of Heat transfer, Vol. 6, Begell
[11]. Stephen T Flock, Michael S Patterson, Monte Carlo modeling of light propagation in highly scattering tissue-I: Model predictions and comparison with diffusion theory, IEEE Transactions on Biomedical Engineering, Vol 36, No. 12, December 1989. [12]. M. Mrwa and Y. Ueda, "Development of time-cesolved spectroscopy system for quantitative noninvasive tissue measurement," in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, B. Chance and R.R. Alfano, eds., Proc. SPIE, voL 2389, pp. 142-149,1995.
PREDICTING MATERIALS PROPERTIES USING FIRST PRINCIPLES ELECTRONIC STRUCTURE CALCULATION
Y. P. FENG, A. T.-L. LIM, AND J. C. ZHENG Department of Physics, National University of Singapore 2 Science Drive 3, Singapore 11754.2 E-mail:
[email protected] Ab initio electronic structure theory has achieved a considerable level of reliability concerning predictions of structures and properties of materials. It provides understanding of matter at the atomic and electronic scale with an unprecedented level of detail and accuracy. The state-of-the-art ab initio electronic structure calculation methods based on the density functional theory and local density approximation is reviewed briefly and their applications in solids is illustrated using C3P4 as an example. Motivated by the success of first principles method in predicting properties of C3N4 and related materials, we use the density functional theory and pseudopotential method to explore the possibility of forming C3P4 crystal and to investigate its properties. Our calculations predict that the structure of C3P4 is quite different from that of similar material such as C3N4 and the pseudocubic structure is extremely stable compared to other possible structures. Our calculation also indicates that C3P4 can be possibly metallic or a narrow gap semiconductor.
1
Introduction
It has been almost a century since quantum mechanics was developed. This revolutionary theory is the foundation of modern physics and is indispensable to the understanding of atoms, molecules, atomic nuclei, and aggregates of these. Although quantum mechanics could in principle allow us to solve for any system but direct application of quantum mechanics to real materials was difficult because analytic solutions of the Schrodinger equation were only possible for a few simple systems such as a square potential well, a harmonic oscillator and the hydrogen atom. This was summarized by Dirac in his famous statement, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact application of these laws leads to equations much too complicated to be soluble. In the next half century following the establishment of quantum physics, various approximation methods were developed. However, direct solutions of the Schrodinger equation for real materials were impossible. It was not until the mid 1960s before an important break-through was finally made by Hohenberg and Kohn 1 and Kohn and Sham 2 who developed the density functional theory (DFT). Hohenberg and Kohn proved that the total energy, including exchange and correlation, of an electron gas (even in the presence of a static external potential) is a unique functional of the electron density. The minimum value of the total-energy functional is the ground-state energy of the system, and the density that yields this minimum value is the exact single-particle ground-state density. Kohn and Sham then showed that it is possible to replace the many-electron problem by an exactly
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equivalent set of self-consistent one-electron equations. An very important effect of a many-electron system is the exchange and correlation, and it is extremely difficult to calculate the correlation energy of a complex system. D F T provided some hope of a simple method for describing the effects of exchange and correlation in an electron gas. However, direct applications of D F T to real materials were still limited until the 1980s due to the demanding requirement on computational resources in order to solve the Schrodinger equation self-consistently for a given system. In the 1980s, it was the emergence of efficient algorithms and advances in computing power that finally made the direct applications of electronic structure calculation to real materials feasible. Noticeable algorithmic improvements included the molecular dynamics method by Car and Perrinello 3 , and direct minimization of the Kohn-Sham energy functional proposed by Payne et al.4. First principles calculation using DFT and particularly the local density approximation have proved to be a reliable and computationally tractable tool in materials science. It is now possible to simulate systems containing 100 or more atoms in a unit cell. The main advantage of the first principles method is that it requires no experimental parameters. Therefore, it is very powerful in predicting properties of new materials and is ideal for study of new materials. 2
D e n s i t y Functional T h e o r y
For a non-relativistic many-electron system, the Kohn-Sham total-energy functional for a set of doubly occupied electronic states ipi can be written as E[{^i}]
= 2^2
J in
+y /
V2Ad3f+
- ^
^^]
