Brief Description on Industrial Activities

** **

As a part of the special year devoted to the `*Application and
Numerical Solutions to Partial Differential Equations'*, we (along with R.S.
Anderssen from CMA and CSIRO, Canberra) had organised two miniconferences one
on Free and Moving and Diffusion Problems and the second one on Inverse
problems in Partial Differential Equations in the Centre for Mathematical
Analysis at the Australian National University, Canberra.

The primary aim was to stimulate strong interaction between
practioners (scientists, industrialists and engineers) with specific problems
arising in both these areas and mathematicians (pure, applied and computational)
working on the analysis and approximate solutions of such problems. In
addition, the Miniconferences aimed to foster the interest of younger
colleagues to research connected with these problems. A number of speakers not
only from Australia, but also from Germany, Russia, India, Italy, Hong Kong, UK
and USA were invited to participate. Each of these programs continued for two
months and the Miniconferences were organised.

As one of the organisers, I had opportunity
to interact with the scientists from various Australian Industries. With this
in back ground, I along with few of my colleagues at our Institute (IIT,
Bombay) started interacting with few industries in Bombay and also in Baroda.
What we gathered:` the technical language barriers have to be narrowed down'.
So we had for the first time organised a Workshop on ` Industrial Mathematics'
in Baroda from 6-9th July'93.

About 33 engineers and scientists
from major industries and scientific institutions like ONGC, ISRO, L&T,
GEB, IPCL, Jyoti Ltd. etc. participated in the Workshop. The unique features of
this workshop were the computer aided environment and the actual case
study-approach. From the responses we had received after the Workshop, we
understand that this is well taken up. One major objective behind these
activities is to look for job opportunities for our M. Sc. as well as Ph. D.
students.

To get acquainted with the language
of industries, we have locally started interacting with CAD Center and the
Chemical Engineering Dept. (ref. M.Sc Projects). As a part of this interaction,
we had a joint Ph. D. student with Professor Kannan Moudgalya. Further, we
(with M. C. Joshi, R. K. Mallik and Kannan M. Moudgalya) had organized three
Workshops on `Engineering Optimizations' in CAD Center, IITB (1994, 95, 96) for
Engineers and Scientists from Industries and Research & Development
Organizations. A package called `Optimize' was developed for this purpose with
the following distinct features: Case Study, User Defined Problems and
Analysis. Most of the Modules start with a Case Study, then Mathematical tools
are developed and finally, the case study is revisited. A module on constrained
Optimization was developed by us jointly with Prof. M. C. Joshi.

In 1995 summer, I had given 6 hours
lectures on Numerical Methods to Engineers and Research Scientists in Larson
and Toubro, Powai.

More recently, we have interacted
with Crompton & Greaves and Larson & Toubro on a mission mode project
on `Development of Tools for Analysis of Switchgear Mechanism' under Technology
Development Mission on Integrated Design and Competitive Manufacture in the
Mechanical Engg. DEPT. at IIT, B. As a part of the theoretical subgroup, our
role was to help the group to simulate numerically the resulting differential
algebraic equations.

As a co-coordinator of M. Sc. (ASI
programme) projects and Work Visits for two years in the past, I had occasions
to interact with CDAC (Pune), TRDDC (Pune); Jyoti Ltd., ORG, Patwa Kinarewala,
ABB from Baroda; ONGC (Mumbai); Mahindra & Mahindra, Hindustan Lever Ltd.
(Mumbai) etc. This is more for getting M. Sc. projects, making them aware of
our new programme and identifying appropriate persons for future interaction.

Development

We
wish to establish a long term partnership between industry and academia by

- Providing
viable mathematical framework to analyze and comprehend efficient and
novel methodologies in Technological process.
- Designing appropriate
mathematical software for industrial problems supplemented with courseware
and teachware.
- Establishing
computer aided instructional environment equipped with a software library
developed in-house.
- Developing
a Network of Industrial Mathematicians for collaborating with local
industrial units on a continuing basis.
- Creating an
FTP site for public domain numerical software packages to function as a
mirror site of similar centers in the world.

We have already received a massive project from Dept. Science and Technology to work on the few above mentioned programmes. Recently, we (with Professor Kannan Moudgalya) are working on the numerical simulation of particle size distribution in emulsion polymerization process, which is of great industrial importance. Some Indian industries like Hindustan Lever Ltd. and Pedelites have already shown some interest on this problem and we plan to involve them in future. More recently, we are also looking at the mathematical modeling, simulation as well as designing of Controllers for the Crystal Size Distributions in an Industrial Crystallizer.

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*Dynamic Model for Particle Size Distribution in Emulsion Polymerization Process. (with Kannan Moudgalya from Chemical Engineering Dept.*Emulsion polymerization is a process of great industrial importance, used for the manufacture of latexes for variety of applications such as latex paint, adhesive, coating, binder in paper and textile products and synthetic rubber etc. The mathematical model, developed by Professor Kannan and his group in chemical engg. department in IIT B gives rise to a coupled system of 24 ODE, an integro-differential equation and one first order hyperbolic integro-differential equation. Presently, we are working on the efficient numerical procedures and in future we plan to concentrate not only on the convergence analysis, but also on theoretical investigations like existential analysis and controllability of such systems.

#### Possible Outcomes

- Numerical simualator (longterm plan)
- Analysis of Numerical methods applied to such problems (in progress)
- Related Theoretical studies like existential analysis and controllability etc.

Related problems on Crystal Size Distributions in an Industrial Crystallizer are presently we are working on.

*Differential Algebraic Equations arising in Chemical Processes. (with Kannan Moudgalya and Jyoti Agrawal)*#### Work in progress:

- Automatic Index Detection for DAE ( imlemented a graph theoretic
algorithm and presently it is supplemented with DAE solvers like RADAU )

Unfortunately most of the DAE solvers requires the input of index (Roughly, index is the minimum number of differentiations needed to transform a DAE to an ODE system) from the user and this limits the use of such solvers. It is proposed to enhance these solvers by supplenting with an automatic index detection algorithm. - Detection and Integrationn across the discontinuties in a dynamic simulator.

- Automatic Index Detection for DAE ( imlemented a graph theoretic
algorithm and presently it is supplemented with DAE solvers like RADAU )
**Numerical Simulation of pricing of option derivatives.**#### Work in progress:

- Calculation of Volatility using the most recent algorithms.
- Finite difference methods for pricing the American Options