The Computational Science Colloquium Series 2000

Venues: All talks to be held at the Computational Science Seminal Room, Blk SOC1, #07-41, Faculty of Science

Please contact the co-ordinator for further details.

Schedule

Date Time Speaker Topic
11 December 2000 4:00pm Prof S. Narayanan
Dean of Academic Research
Indian Institute of Technology,
Madras, India
Numerical Analytical Methods for Non-linear Dynamical System Analysis
7 December 2000 4:00pm Prof. Jia Zhongxiao
Department of Applied Mathematics
Dalian University of Technology, P.R. China, and
Department of Mathematical Sciences
Tsinghua University, P. R. China
Implicitly Restarting the refined Arnoldi method and the refined harmonic Arnoldi method
23 November 2000 4:00pm Professor Bernd A Berg
Department of Physics
Florida State University, USA
MULTICANONICAL SIMULATIONS
16 November 2000 4:00pm Dr. Wenyu Sun
Department of Mathematics, University of Brasilia
Brasilia, DF, 70910-900, Brazil
and
Department of Computational Mathematics and Optimization
Nanjing Normal University, China
Conic Trust Region Method to Solve Optimization
19 October 2000 4:00pm Prof. Koji Ohkitani
Research Institute for Mathematica Sciences
Kyoto University, Kyoto 606-8502
Japan
Numerical study of singularity formation
in a class of Euler and Navier-Stokes flows
5 October 2000 4:00pm Prof. Daiqian Xie
School of Chemistry
Sichuan University, China
Photodissociation Dynamics of Methyl Iodide
20 September 2000 4:00pm Prof. Nhan Phan-Thien
Department of Mechanical Engineering
NUS
BEM Modelling of Stokes Flows Problems
14 September 2000 4:00pm Dr. Gunaretnam Rajagopal
TCM Group, Cavendish Laboratory
University of Cambridge, UK
Quantum Monte Carlo Simulations: From atoms to Solids
7 September 2000 4:00pm Prof. Maya Paczuski
Department of Mathematics
Imperial College, UK
A network model of competition in markets
29 August 2000 4:00pm Prof. Tuck Chuen Choy
School of Physics
University of Melbourne, Australia
Van der Waals interaction for the hydrogen molecule: An exact density functional approach
3 August 2000 4:00pm Prof. C. Jayaprakash
Department of Physics
Ohio State University, USA
Synchronization in Various Oscillator Systems
13 July 2000 4:00pm Dr Bao Weizhu
School of Mathematics
Georgia Institute of Technology, USA
The random projection method for hyperbolic conservation laws with stiff source terms
4 July 2000 4:00pm Dr Venkatraman Mohan
Assistant Director, Ibis Therapeutics
ISIS Pharmaceuticals, USA
Targeting RNA : Rational and Combinatorial Drug Design Approaches
13 June 2000 3:00pm Prof. Ping Sheng
Department of Physics
Hong Kong University of Science & Technology
Photonic Crystals Formation and Bandgaps from Metallo-Dielectric Microspheres
  6 June 2000 4:00pm Prof. Huang Wenzhang
Department of Mathematics
University of Alabama in Huntsville, USA
Time delayed differential equations and singular perturbation problem arising from application
29 May 2000 4:00pm Dr. Yeung Man-chung
Department of Mathematics
University of California
Applications of Multiple Lanczos Method: ML(k)BiCGSTAB and Transpose-free Matrix Pade
19 May 2000 4:00pm Prof. Jiang Yuan-Sheng
Department of Chemistry
Nanjing University, China
Valence Bond Calculations of Medium-sized Conjugated Molecules
27 April 2000 4:00pm Prof. Leslie V. Woodcock
Department of Computational Science
NUS
Mesoscale modelling: predicting new processes for materials made from powders
24 April 2000 4:00pm Prof. Hiroshi Sugiyama
Institute for Biomaterials and Bioengineering
Tokyo Medical and Dental University
Japan
Rational Design of Sequence-Specific DNA Alkylating Agents
20 April 2000 4:00pm Prof. K.L. Teo
Department of Applied Mathematics
The Hong Kong Polytechnic University
The Control Parametrization Enhancing Approach to Constrained Optimal Control Problems
13 April 2000 4:00pm Dr. Faming Liang
Department of Statistics and Applied Probability
NUS
Dynamic Weighting in Simulation and Optimization
22 Feb 2000 4:00pm Dr. Michael A. Collins
Research School of Chemistry
Australian National University
Molecular Potential Energy Surfaces For Chemical Dynamics
17 Feb 2000 4:00pm Prof. Chi-Wang Shu
Division of Applied Mathematics
Brown University
Providence, Rhode Island, USA
Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Problems
15 Feb 2000 4:00pm Prof. Huang Wenzhao
Department of Mathematical Finance
Beijing University, China
Empirical study of nonlinear Dynamical behaviour of stock market (in China)
3 Feb 2000 4:00pm Prof. J. G. Muga
Department of Physics
Bilbao University, Spain
Complex Potentials in Scattering Calculations
27 Jan 2000 4:00pm Prof. K.N.Seetharamu
School of Mechanical Engineering
University Science Malaysia
Malaysia
Finite Element Analysis in Engineering Applications
20 Jan 2000 4:00pm Dr Mette Machholm
Dept of Chemistry
Aarbus University
Atoms and Molecules in laser fields
6 Jan 2000 4:00pm J. N. Reddy
Oscar S. Wyatt Chair Professor
Dept of Mech. Engineering
Texas A&M University
The Penalty Function Method in the Numerical Simulations of Viscous Incompressible Fluids and Shear Deformable Plates


Abstracts

11th December 2000, Prof S. Narayanan
Numerical Analytical Methods for Non-linear Dynamical System Analysis
Mechanical systems can exhibit non-linear characteristics due to geometry, material properties or boundary conditions. Examples of non-linear systems include squeeze-film dampers in flexible rotor-bearing systems, interface friction in turbine blades as well as clearances in gear meshes and bearings. The traditional technique for the dynamic analysis of such systems has been direct numerical integration, which involves considerable computational effort. Further, a huge initial condition map has to be swept in order to capture the bifurcation in solution branches leading to non-linear system specific solutions such as sub-harmonic, quasi-periodic or chaotic responses. There is also a need to compute unstable solutions for the study of chaos as chaotic orbits are composed of several unstable periodic orbits. In addition, there is a need to understand the dynamic behavior of the mechanical system as a particular design parameter is changed. As the size of the problem increases, the computational cost increases exponentially. All of the problems mentioned above can be overcome by efficiently using parameter path following or continuation methods.

Parametric continuation, embedding or homotopy methods have long served as useful tools in mathematics. A number of papers exist in the l iterature with different applications of the continuation or homotopy procedures. In the latter half of the nineties investigations, related to the application of path following in non-linear dynamical systems, began to appear. These techniques, based either on shooting methods or the harmonic balance method, are primarily meant for periodically excited non-linear systems.

A review of the current state-of-the-art will be presented with regard to parametric continuation or path following methods for the analysis of non-linear dynamical systems. Various techniques available for path following as well as algorithms for step size variation will be discussed. The efficiency of these techniques, in identifying parameter regimes where sub-harmonic, quasi-periodic or chaotic solutions can exist, will be demonstrated. This will be done using three different examples, (a). Flutter of an airfoil section, (b). Duffing oscillator, and (c). Impact oscillator. Potential application of this technique to larger mechanical systems and some of the issues associated with this will also be addressed.

7th December 2000, Prof. Jia Zhongxiao
Implicitly Restarting the refined Arnoldi method and the refined harmonic Arnoldi method
Large scale matrix eigenproblems arise in a lot of applied sciences and engineering. We are frequently required to compute a small number of selected eigenvalues and/or associated eigenvectors. Efficient and reliable numerical solvers play a key role in scientific applications. The Arnoldi method and it harmonic version have been two major methods for solving the mentioned problem over the past two decades. However, it has been shown that although approximate eigenvalues may converge under some necessary conditions, approximate eigenvectors, on the other refined harmonic Arnoldi method, in which the approximate eigenvectors are obtained from a given projection subspace using a completely different approach. Then new methods have been shown to overcome the possible nonconvergence of their original counterparts. To make all the four methods succeed in practice, restart is necessary due to the limitation of storage and computational cost. Implicit restart proprosed by Sorensen has appeared to be a most successful restarting technique. Applying this technique to the four methods, we get corresponding implicitly restarted algorithms. The key for overall efficiency of algorithms is the suitable selection of certain shifts involved. In contrast to those so called exact shifts used in the original algorithms, we propose refined shifts for use within the implicitly restarted refined algorithms. Numerical experiments have been conducted on some real world problems using the four algorithms. They indicate that our refined algorithms ourperform the original counterparts considerably.

23rd November 2000, Professor Bernd A Berg
MULTICANONICAL SIMULATIONS
Multicanonical and related simulations consist of two parts. First, suitable weight factors for the problem at hand are identified and calculated. Second, (large scale) equilibrium Monte Carlo simulation with the final (fixed) weight factors are applied to the problem at hand. calculating the weights appears to be a stumbling block for newcomers to the method. The talk will discuss various approaches and present a computer animation for a robust, recursive algorithm. Subsequently, a few selected applications are summarized: (1) First order phase transitions. (2) Multi-overlap spin glass simulations. (3) Simulations of small proteins (peptides), including alpha helix formation of poly-alanine.

16th November 2000, Dr. Wenyu Sun
Conic Trust Region Method to Solve Optimization
Trust region methods for conic models to solve unconstrained and constrained optimization problems are proposed. We analyze the trust region approach for conic models and present necessary and sufficient conditions for the solution of the associated trust region subproblems. A corresponding numerical algorithm is developed and has been tested for 19 standard test functions in unconstrained optimization. The numerical results show that this kind of methods is superior to some advanced methods. We also prove that the proposed methods have global convergence and Q-superlinear convergence properties.

19th October 2000, Prof. Koji Ohkitani
Numerical study of singularity formation in a class of Euler and Navier-Stokes flows
We study numerically a class of stretched solutions of the three-dimensional Euler and Navier-Stokes equations identified by Gibbon, Fokas and Doering (1999). Pseudo-spectral computations of an Euler flow starting from a simple smooth initial condition suggests a breakdown in finite time. Moreover, this singularity apparently persists in the Navier-Stokes case. Independent evidence for the existence of a singularity is given by a Taylor series expansion in time. The mechanism underlying the formation of this singularity is the two-dimensionalization of the vorticity vector under strong compression; that is, the intensification of the azimuthal components associated with the diminishing of the axial component. It is suggested that the hollowing of the vortex accompanying this phenomenon may have some relevance to studies in vortex breakdown. 
This is a joint work with John D. Gibbon (Imperial College).

5th October 2000, Prof. Daiqian Xie
Photodissociation Dynamics of Methyl Iodide
We present three-dimensional quantum mechanical calculations on the photodissociation dynamics of CH3I and CD3I on new ab initio potential energy surfaces. The wave packet is propagated in the Chebyshev order domain. The absorption spectra, product rotational and vibrational distributions, I* quantum yield are calculated and compared with experiments. It is shown that the overall rotation has significant effects on the methyl rotational and vibrational distributions as well as the I* yield.

20th September 2000, Prof. Nhan Phan-Thien
BEM Modelling of Stokes Flows Problems
"Suspensions" is a generic term describing multiphase fluids, made up of particles and/or bubbles suspended in a fluid or a solid phase (the solvent or the matrix). They are found in a variety of natural and man-made materials: blood, paint, slurries, mineral concentrates, mine tailings, clay, cement, bitumen, bread dough, etc. The concept of suspension is of course only meaningful when there are two widely different length scales in the problem: l is a typical dimension of a suspended particle and L is a typical size of the apparatus. When these two length scales differ by several orders of magnitude, l << L, one speaks of a suspension rather than a collection of discrete individual particles suspended in a medium, which could be a solid or a fluid. When viewed at level l, one sees a great deal of fluctuations, and when viewed at level L, one sees a continuum of some effective properties. The term micromechanics refers to the detailed solutions at the micro level, and the process of averaging out the fluctuations at the microscale level to arrive at the description at the continuum level is termed homogenisation. The task of linking the micromechanics to the macro description (or finding the constitutive equation) of the material is the central problem in Mechanics. Some of the computational techniques for modelling suspensions will be discussed in this talk, together with the results obtained for them. They include the Completed Double Layer Boundary Method, the direct simulation techniques, and the Brownian Configuration Field methods. Some of these are ideal candidates for parallelisation in a distributed environment.

14th September 2000, Dr. Gunaretnam Rajagopal
Quantum Monte Carlo Simulations: From atoms to Solids
This seminar describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. The algorithms are intrinsically parallel and currently available high performance computers allow applications to large systems. With these tools one can study complicated problems such as the properties of solids and defects, while including electron correlation effects with high precision. A selection of applications to ground and excited states of atoms, molecules, clusters and solids will be discussed.

7th September 2000, Prof. Maya Paczuski
A network model of competition in markets
We present a simple model of agents competing in a market where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority, penalizing those in the majority. Agents that perform poorly change their strategy. The strategies in the market coevolve, and exhibit a "Red-Queen" effect where previously successful strategies eventually fail. The network self-organizes to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.
(Paczuski, Bassler, Corral. Phys. Rev. Lett. (2000).)

29th August 2000, Prof. Tuck Chuen Choy
Van der Waals interaction for the hydrogen molecule: An exact density functional approach
Van der Waals forces are universal to ALL atomic systems and for closed shell atoms, represent the only mechanism for molecular binding. While its general theory can be explained in terms of electrodynamics, a proper quantitative calculation is only available after the advent of quantum mechanics. Its formal theory was first constructed by Fritz London in 1931. In this talk I shall review the EXACT calculation of the van der Waals interaction for the hydrogen molecule, probably the first non-trivial manybody problem to be solved analytically in quantum chemistry. Unfortunately there were numerous errors and confusion of the theoretical methods used by the pioneers such as London, Pauling, Slater, Kirkwood and later Lowdin, Hirshfelder and others. The famous book of Pauling and Wilson stands to be corrected in detail on this topic as will be shown. The advancement of local density functional (LDA) theory due to Kohn and Sham has led to some unresolved difficulties in the treatment of van der Waals forces within LDA. Thus the exactly solvable hydrogen system provides an important test bed for density functional approaches. I shall demonstrate that there is a density functional theory for this system that is exact and thereby partially answering some early objections to the Hohenberg-Kohn density functional theory first raised by Elliott Lieb in the 80's.

3rd August 2000, Prof. C. Jayaprakash
Synchronization in Various Oscillator Systems
Experimental results on synchronous neural activity in the brain has generated theoretical work in understanding synchronization in networks of neural oscillators. I will (i) present results for the Integrate-and-Fire Oscillator system showing how it can be arranged to synchronize quickly and (ii) discuss relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving near-zero phase-lag synchrony. I will begin with a general introduction, present the models and results, and conclude with some open questions.

13th July 2000, Dr Bao Weizhu
The random projection method for hyperbolic conservation laws with stiff source terms
In this talk we present the random projection method for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows:

U_t + F(U)_x + G(U)_y = 1/e P(U)

In this problem, the chemical time scales may be orders of magnitude faster than the fluid dynamical time scales, making the problem numerically stiff. A classic spurious numerical phenomenon, the incorrect propagation speeds of discontinuities, occurs in underresolved numerical solutions. We introduce a random projection method for reaction term by replacing the ignition temperature with a uniformly distributed random variable. The statistical average of this method corrects the spurious shock speed, as will be proved with a scalar model problem and demonstrated by a wide range of numerical examples in inviscid denotation waves in both one and two space dimensions.

4th July 2000, Dr Venkatraman Mohan
Targeting RNA : Rational and Combinatorial Drug Design Approaches
Designing drugs that target RNA is a novel and attractive concept in sharp contrast to the traditional way of targeting proteins. The antisense concept of drug discovery is based on the inhibition of gene expression at the message level. Sequence-specific binding of oligonucleotides to an RNA targets is achieved by exploiting Watson-Crick base pairing rules. The first drug based on antisense technology for CMV was approved by FDA in 1998. An overview of the basic concepts and computational chemistry applications is this research area will be presented. The complex 3D folds of RNA represent specific targets for small molecule drug recognition. Structures of protein-RNA complexes based on X-ray as well as NMR techniques have been published recently. Given the 3D structure of target RNA, we have developed protocols to successfully identify best possible structures of ligand-receptor complex based on exhaustive onformational search of flexible ligands. An overview of the integrated drug discovery paradigm based on combinatorial chemistry approach and the role of computational chemistry will be discussed.

13th June 2000, Prof. Ping Sheng
Photonic Crystals Formation and Bandgaps from Metallo-Dielectric Microspheres
We have fabricated multiply-coated microspheres with diameters ranging from submicron to 50 microns.  The coated microspheres exhibit significant response to externally applied electric (E) and/or magnetic (H) fields. Under crossed E and H fields, a Martensitic transformation was observed when the H/E ratio exceeds a minimum value.  The structural transformation, from the body-centered-tetragonal arrangement of the coated microspheres under just the electric field, to the face-centered-cubic arrangement when a perpendicular magnetic field was applied, is quantitatively predicted by the minimization of combined electrostatic and magne tostatic free energy densities.

When assembled together, these mesocrystals formed by coated microspheres also have novel optical properties.  In particular, they form viable building blocks for photonic band gap materials.  We have shown by explicit calculations that any periodic structure built from the coated microspheres possesses photonic bandgap.  The calculations are based on the multiple scattering technique. We consider a generic system where the building blocks are touching metallo-dielectric spheres, where the metal dielectric is modelled by a large and negative constant.  We show in the figure below the frequency (marked by the squares) and the size (marked by the bars) of the photonic gaps for a variety of structures.  The angular frequency in the figure is scaled by the diameter of the spheres.  We found that an absolute photonic gap always emerges for such a system when the volume filling ratio of the metallic spheres exceeds a threshold, and the size of the gap increases monotonically as a function of the filling ratio.  A potentially distinct feature of the present system is that the photonic gap depends on the filling ratio and the short-range order rather than on symmetry and long-range order, as in the case of dielectric photonic crystals.

To verify the theoretical predictions, we have constructed photonic crystal slabs in the simple cubic and face-centered-cubic symmetries and measured the transmittance in the microwave regime along two distinct crystal orientations. Measured results are in good agreement with theory, demonstrating the existence of photonic bandgaps in the system formed by metallo-dielectric spheres.

6th June 2000, Prof. Huang Wenzhang
Time delayed differential equations and singular perturbation problem arising from application
In this talk we will give a derivation of delay-differential equations from some physical models (such as models of the transmission line in an electrical circuit and the optical transmission of a cavity filled with a nonlinear medium) where the time delayed feed back can be clearly identified. In addition we will use the singular perturbation method to study the existence and stability of an important type of solutions, the square wave periodic solution, when the delay-differential equations exhibit a multiple-time-scale phenomenon.

29th May 2000, Dr. Yeung Man-chung
Applications of Multiple Lanczos Method: ML(k)BiCGSTAB and Transpose-free Matrix Pade
A Lanczos procedure for multiple starting vectors was recently developed. It is a natural generalization of the classical one. This talk is about two applications of the multiple Lanczos procedure:

  1. a variant of the popular BiCGSTAB method for solving nonsymmetric linear systems, which we denote by ml(k)bicgstab.
  2. a Transpose-free matrix Pade method (TFMPVL) for the reduced-order modeling and simulation of large-scale, multi-input multi-output dynamical systems.
ML(k)BiCGSTAB is derived from the multiple Lanczos procedure using multiple starting left vectors and one starting right vector. Compared with the original BiCGSTAB method, our new method requires fewer matrix-vector products at each iteration step, on average requiring only 1 + 1/k matvec's per step. Theoretically, ML(k)BiCGSTAB can be viewed as a bridge connecting the Arnoldi-based FOM/GMRES methods and the Lanczos-based BiCGSTAB methods. Empirically, it also seems to be more stable and faster convergent.

Multi-input multi-output dynamical systems are usually characterized by transfer functions of the form H(s) = L'*F(s)*R, where F(s) is the inverse of the function matrix I - s*A. Matrix Pade method via multiple Lanczos procedure (MPVL) computes the partial sums of the Taylor expansion of H(s). TFMPVL is mathematically equivalent to MPVL, but avoids the use of the transpose of the system matrix A, and under certain circumstances will actually reduce the total number of matrix-vector products needed. The method is illustrated with some numerical examples.

19th May 2000, Prof. Jiang Yuan-Sheng
Valence Bond Calculations of Medium-sized Conjugated Molecules
An algorithm for coding the Slater determinants is proposed for CVB calculations. It extends the VB calculations up to benzenoids of 28 Pi-electrons having 40 million configurations. Results of 89 species are given which are used to rationalize the trend of aromaticity of benzenoid hydrocarbons.

27th April 2000, Prof. Leslie V. Woodcock
Mesoscale modelling: predicting new processes for materials made from powders
Many modern synthetic materials, e.g. ceramics, composites, pharmaceuticals, flame retardants, high temperature superconductors, cracking catalysts etc. are manufactured from binary powders that do not like to mix, yet where homogeneity is paramount.

The study of idealised powders and steady-state processes by mesoscale modelling, yields information about the conditions whereupon powders can behave like molecular liquids. When fluidised under certain conditions of external vibrations the particles obey the equipartition of energy. These conditions are predictable from mesoscale simulations.

This leads to a definition of "thermodynamic" properties of powders, as a function of granular "temperature" and granular "pressure" and consequently the prediction of conditions for mixing dissimilar powders homogeneously; some that are impossible to mix by any other means (on Earth) due to severe gravity induced size segregation effects.

The computations have resulted in the prediction and discovery of a phase behaviour of binary powders using accoustic vibrations which will be shown on a 5-min. video.

Novel steady-state processes for characterising the solidification process are being researched computationally. All ceramic and composite solid materials are non-equilibrium. They can only have uniquely defined and reproducible properties (like fluids) if they can be produced homogeneously and continuously and then characterised by process parameters, i.e. by rate constant that defines the continuous (steady-state) production process.

New, idealised, processes are being researched computationally to produce continuously and homogeneously dense states from dilute states by uniaxial compactions. The real batch processes to which the continuous process relates are sedimentation, filtration, slip casting or centrifugation. A program is also being developed for epitaxial deposition.

It is believed that the simulations will pave the way to the design of new continuous processes that will produce truly homogeneous and well-characterised advanced solid materials.

20th April 2000, Prof. Hiroshi Sugiyama
Rational Design of Sequence-Specific DNA Alkylating Agents
By the completion of the human genome project, many diseases including cancer, hereditary and viral diseases can be understood by the DNA sequence level. Control of the specific gene expression will provide ultimate gene therapy. Minor groove binding polyamides containing N-methylpyrrole and N-methylimidazole amino acids exhibit promising performance based on the recognition of nucleic acid sequences. Various types of sequence-specific DNA binding agents are developed and used for the regulation of gene expression. We synthesized novel type of polyamide-alkylator conjugates based on the reactivity of natural products. These synthetic compounds alkylated predetermined DNA sequences selectively, and also some of them possessed selective potency for certain cancer cell lines. In this presentation, we will focus on recent progress of minor groove binding polyamides that play important roles in the rational recognition of nucleic acid sequences. One of the future directions of rational design of molecular medicine in the post genome era is proposed.

20th April 2000, Prof. K.L. Teo
The Control Parametrization Enhancing Approach to Constrained Optimal Control Problems
In this talk, I shall begin with the review of the classical control parametrization approach to standard constrained optimal control problems. The control parametrization technique is then used in conjunction with the recently developed control enhancing transform to 2 unconventional optimal control problems: (i) optimal control problems in which certain time points are decision variables to be optimized; and (ii) optimal control problems in which the sizes and the locations of the state jumps are decision variables to be optimized.

13th April 2000, Dr. Faming Liang
Dynamic Weighting in Simulation and Optimization
Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, spin-glasses simulation, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

22nd February 2000, Dr. Michael A. Collins
Molecular Potential Energy Surfaces For Chemical Dynamics
The theoretical study of chemical reactions from fundamental principles has had to surmount two principal difficulties, the accurate quantum dynamics of the atomic nuclei on the molecular potential energy surface (PES), and the evaluation of the PES itself.

Ab initio quantum chemistry calculations can now provide accurate values of the potential energy at almost any given molecular geometry. This lecture will describe a method which automates the construction of multi-dimensional PES by interpolation of ab initio calculations. We show how a Bayesian analysis of the interpolation errors can be used to enhance the accuracy and "automated learning" character of the approach.

17th February 2000, Prof. Chi-Wang Shu
Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Problems
We will present the basic ideas and recent development in the construction, analysis, and application of high order WENO (Weighted Essentially Non-Oscillatory) finite difference and finite volume schemes for solving hyperbolic conservation laws. WENO schemes are high order accurate finite difference or finite volume schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically give more weights to the locally smoother stencils, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. WENO schemes have been quite successful in computational fluid dynamics and other applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. Numerical examples will be shown to illustrate the capabilities of the methods.

15th February 2000, Prof. Huang Wenzhao
Empirical study of nonlinear Dynamical behaviour of stock market (in China)
The crash of stock price during the Asian crisis shaked the premise of the classic economy theory. The magnitude of stock price falling and the depth and width of its influence showed its nonlinearity.

The structure of limit set and some properties of strange attractors for general dynamic system have been studied. We exploited the fractional dimension of the strange attractor, Lyapunov exponents and entropy of the stock market in Shanghai, Shenzeng, Hong Kong Market. These quantities provide useful information of the market from different points of views and strong evidences on the nonlinear dynamical bahaviour of the market.

3rd February 2000, Prof. J. G. Muga
Complex Potentials in Scattering Calculations
The talk begins with an introduction to the use of complex potentials in scattering calculations. Different functional forms are compared, with particular attention to the ones proposed recently in La Laguna, which use the interference between multiple collisions in composite complex potential barriers to enhance the absorption significantly. An example of application is discussed (collinear H+H_2).

27th January 2000, Prof. K.N.Seetharamu
Finite Element Analysis in Engineering Applications
A brief introduction to the nature of finite element method (FEM) is given. Application of FEM to the systems governed by differential equations are illustrated through industrial examples such as heat exchangers, gas turbine blade cooling, cooling of electronic packages etc.

20th January 2000, Dr Mette Machholm
Atoms and Molecules in laser fields
This talk consists of two parts: 1) Controlling photochemical reactions by laser induced nuclear wave packet dynamics; 2) Collisions between laser cooled alkaline earth atoms in a weak laser field.

The invention of femtosecond lasers has enabled experimental studies of how atoms in a molecule move during a chemical reaction, with the time scale of the atom's movements typically 10-100 fs. Probing the "transition state" (the intermediate structure of the molecule) became experimental reality and more than a theoretical concept. In parallel, theoretical concepts have been developed, where photochemical reactions are controlled providing selectivity in population of competing channels. The time-dependent models use the wave packet concept.

I will introduce the basic concepts of controlling photochemical reactions by lasers, and present a theoretical model for a control scheme. In this scheme the spatial distribution of photofragments is controlled by first forcing the dynamics of the nuclear wave packet in the ground state potential well, creating a "classical" oscillatory motion. Secondly, only molecules of a selected orientation are dissociated, when these molecules have their bond stretched.

Laser cooling of atoms is a very successful research field, which has lead to many spectacular results. The cooling of samples of atoms to micro Kelvin temperatures by lasers has many applications, e.g. increasing the precision of atomic clocks, or the construction of "atom lasers". It is also a precondition for the further cooling to create Bose-Einstein-Condensates.

I will introduce the basic principles of laser cooling, and trapping of laser cooled atoms. Collisions heat the sample of trapped atoms, and are the limiting processes for the number of atoms, which can be trapped, and the temperatures, which can be reached. During these collisions quasi-molecules, which can be 1000 =C5 large, are formed. Alkali-metal atoms have been widely studied experimentally and theoretically, recently also alkaline-earth atoms have been laser cooled. The latter have the advantage that only a few quasi-molecular states are present, where the alkali-metal atoms have hundreds of states due to hyperfine structure. I will present the first theoretical studies of collisions between laser cooled alkaline earth atoms.

6th January 2000, J. N. Reddy
The Penalty Function Method in the Numerical Simulations of Viscous Incompressible Fluids and Shear Deformable Plates
The penalty function method is an approximate method to reduce a constrained problem to an unconstrained problem. In contrast to the classical Lagrange multiplier method, the penalty function method does not introduce additional dependent unknowns - Lagrange multipliers. The application of the method to the treatment of the incompressibility constraint in the numerical simulation of viscous incompressible fluids by the finite element method will be discussed.

In addition, application of the method to the classical plate theory to obtain the first-order shear deformation plate heory will also be discussed.


Biodata

Prof S. Narayanan
Professor S. Naryanan (SN) is currently the Dean of Academic Research at the Indian Institute of Technology (IIT) Madras, India. He has made seminal contributions in engineering education, research and consultancy in the areas of vibration, acoustics with particular emphasis in Random Vibration. He has been engaged in teaching in the areas of mechanics, dynamics of machinery, vibration, random vibration, acoustics and noise control for 28 years both at IIT Madras, INDIA and IIT Kanpur, INDIA. His contributions are very well recognised both nationally and internationally. Oflate, he is working in the areas: chaos, nonlinear dynamical systems and smart structures. He has been consistently invited to present papers in a number of IUTAM symposia where participation is only by invitation. He has organized a number of courses and workshops and coauthored a book "Application of Random Vibration " with Prof. P.C. Nigam. He has published extensively both in journals and conferences. He has guided 12 Ph.D theses and 10 M.S theses.

He has been elected as the Fellow of the National Academy of Engineering, Fellow of the Aeronautical Society of India and the Fellow of the Acoustical Society of India.

Prof. Jia Zhongxiao
Jia Zhongxiao, Professor at Department of Applied Mathematics, Dalian University of Technology, China, Concurrent Professor at Department of Mathematical Sciences, Tsinghua University, China. His major research interests are numerical linear algebra, large scale matrix computations and scientifc computing. He was awarded the Leslie Fox Prize in Numerical Analysis in 1993 for his significant contributions to large scale unsymmetric matrix eigenproblems. He has given the invited presentations at important international conferences in various countries. In 1998, he organized and chaired an International Symposium on Large Scale Matrix Computations in Dalian, which attracted most internationally renowned experts in the field. He has given a general analysis for commonly used projection methods for solving eigenproblems and has shown possible nonconvergence of approximate eigenvectors. To correct this problem, he has proposed a class of refined projection methods, which have been accepted to be one of three classses of projection methods. He has given some elegant and computationally viable refined algorithms, which can often be much more efficient than their conventional counterparts. The celebrated G.W. Stewart's book "Matrix Algorithms: Vol.II, Eigensystems" and Van der Vorst's book "Computational Methods for Large Eigenvalue Problems" have cited and described many theoretical results and algorithms of Jia's works. Jia has got some other awards and honors, such as "ISI Classic Citation Award" and one of the fifty-seven outstanding young scientists (under 45) in China.

Professor Bernd A Berg
Prof Bernd Berg obtained his Diplom in Physics from Freie Universitaet Berlin in 1974, and PhD in 1977 in the same University. He got his Habilitation and Privatdozent for Physics from University of Hamburg in 1980. After few junior positions in Germany, he settled down in Florida State University since 1985. His research interests include theoretical high energy physics, lattice gauge theory, quantum field theory and quantum measurement, complex systems and statistical physics, Monte Carlo algorithms, statistical analysis of Monte Carlo and real data. He is very well-known for the multi-canonical Monte Carlo method.

Prof Bernd Berg is visiting NUS 22-24 November 2000, hosted A/Prof Wang Jian-Sheng.

Prof. Koji Ohkitani
Doctor of Science in Physics (Kyoto University, March 1989)
Postdoctoral fellowships of the Japan Society for the Promotion of Science for Japanese Junior Scientists. April 1, 1989-June 30, 1990
Research Associates
Research Institute for Mathematical Sciences, Kyoto University. July 1, 1990-March 31, 1994
Associate Professor
Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University. April 1, 1994-September 30, 1996
Associate Professor
Research Institute for Mathematical Sciences, Kyoto University. Octobetr 1996-.

Prof. Nhan Phan-Thien
Professor Nhan Phan-Thien was awarded the Edgeworth David Medal in 1982 (awarded by the Royal Society of New South Wales to a Scientist under 35) for distinguished research in Applied Mechanics. He was awarded the ASR Medal in 1997 by the Australian Society of Rheology, for distinguished contributions to Rheology. He won the prestigious Gordon Bell Award in the Price/Performance category at the Supercomputing Conference at San Jos, 1997, given by the IEEE Computing Division, for superior effort in practical parallel processing techniques. His research interest is in the general area of viscoelastic fluid mechanics, suspensions, and computational methods dealing with non-Newtonian fluid flows. He has written over 260 refereed journals papers, including two books by Elsevier and Oxford University Press, and is on the Editorial Board of 6 journals, including three computational journals. He was elected to the Australian Academy of Science in 1999.

Prof. Jiang Yuan-Sheng
Professor Jiang Yuan-Sheng is one of the leading theoretical chemists in China. He received his MSc degree from Jilin University with Professor Tang Ao-Qing, and is one the eight most influential students of Professor Tang. Professor Jiang is among the first batch scholars who were promoted to full professorship soon after the reform began. In 1991, he was elected as a member of Chinese Academy of Science for his outstanding working in theoretical chemistry. Professor Jiang received numerous awards, including the two most prestigious awards in China: 1st Class National Science Prize (1982, 1987), and one 1st Class Science and Technology Progress Awards (1999).

Prof. K.N.Seetharamu
Professor Seeetharamu received his B.E. from University of Mysore in 1960 and M.E. from Indian Institute of Science, Bangalore, India in 1962. He later obtained his Ph.D in the area of Heat Transfer from IIT, Madras, India. Professor Rohsenow, a world-renowned authority from MIT had commended his thesis as one of the BEST THESIS and mentioned, it was a pleasure to go through the thesis.

During his distinguished professional career spanning over 30 years at IIT, Madras, Prof. Seetharamu published more than two hundred research articles, including 75 journal papers and 140 national and international conference papers. He has co-authored one book on Finite Element Methods in Heat Transfer Analysis published by John Wiley in 1996. Prof.Seetharamu has so far guided 24 students for Ph.D and 15 for M.S. (by research) degrees. He has been a regular visiting Scientist at University college of Swansea, a pioneering institute in Finite Element Methods. He has been on the editorial boards of several journals and had been one of the chief editors for the International Journal for Engineering Analysis and Design. Prof.Seetharamu has handled several national and international sponsored research and consultancy projects on the modeling of various industrial applications.

Professor Seetharamu joined the School of Mechanical Engineering, University Science Malaysia by invitation and is actively engaged in the research area related to Electronic Packaging. The poster paper presented at the International Conference on Electronic Packaging held in December 1997 at San Diego, USA, was awarded the Best Paper Prize. The University of Science Malaysia awarded prize for the best research carried out during 1997. He is currently the Secretary of IMAPS, Malaysia Chapter.

Prof. J. G. Muga
Dr Muga got his PhD in Bilbao (Spain) in 1984. He did postdoctoral work with I. Prigogine (Brussels), R. D. Levine (Jerusalem) and R. Snider (Vancouver). In 1990 got a permanent position in the Physics Dept. of La Laguna University and has recently moved back to Bilbao as research full professor. His main current interest is in Foundations of Quantum Mechanics, in particular in the theoretical treatment of time. Ha has published 80 papers. The most recent may be found in quant-ph. A Phys. Rep. on the arrival time will appear soon.