**WORKSHOP ON INDUSTRIAL
MATHEMATICS**

**February 29, 2004**** – ****March 2, 2004**

**BOOK of ABSTRACT**

**INVITED TALKS**

**Industrial Mathematics Work in
Recent Years**

** **

Noel G. Barton

**Abstract **

The speaker was Director of the (Australian)
Mathematics-in-Industry Study Group from 1985 to 1993. In the mid 1990s,
he was also the Manager of 35 applied mathematicians in CSIRO,

The period since the mid 1980s saw steady growth of industrial mathematics initiatives and an increase in skill in targeting our work for best advantage of the discipline and our sponsors. It also involved new challenges for mathematics, particularly how to maintain the mathematical sciences as a core discipline in the face of two significant trends – the growing “mathematisation” of other disciplines and the emphasis on science funding from an end-user perspective.

This story will be told with as much liveliness, flair and realism as the speaker can assemble. It will have an Australian flavour but international relevance. Examples (successes, failures,…) will be given.

Noel Barton

**Abstract **

We describe recent progress on two computational tools under development in CSIRO Mathematical and Information Sciences. Both these tools are designed to be applicable for simulations and engineering design purposes. The first tool is Fastflo, a finite element solver for systems of Partial Differential Equations (PDEs). This package is especially suited for multiphysics problems in which there is a strong coupling between different physical mechanisms. Moreover, it is common that the domain changes with time, and the evolution must be computed as part of the problem. A good example, although there are many others, is fluid-structure interaction. The second tool is a Discrete Element Method (DEM) package for simulation of flowing granular material. In this method, the motion of all particles in the granular material is described using a specified model for particle-particle and particle-boundary impacts. This gives a system of ordinary differential equations that can be marched forward in time. We will show typical recent results such as for ploughshare mixers and grinding mills. Finally, we will discuss how we have made the DEM technology available over the internet in the particular case of autogenous (AG) and semi-autogenous grinding (SAG) mills.

**Rate
independent variational**

**and**

**Quasivariational**** inequalities in elastoplasticity**

Martin Brokate

**Abstract **

Variational formulations are commonly used for problems in mechanics, for mathematical analysis as well as for numerical approximations (e.g., finite elements). Elastoplastic constitutive laws possess the property of rate independence, and the variational inequality constitutes the proper mathematical setting which encompasses the interplay of elastic and plastic deformation. The admissible stresses form a closed convex subset of the stress space. In most cases of practical importance, the set of admissible stresses is not fixed, but depends on the loading history. In some cases, this varying set can be transformed to a fixed set, but if this is not possible, the more general and more difficult setting of a quasivariational inequality has to be considered. We present in particular some new results concerning existence and uniqueness of such a quasivariational inequality.

**Problem
of Biomechanics arising in Connection with Maxillofacial Surgery**

** **

Martin Brokate

**Abstract **

This talk presents results obtained in cooperation between medical scientists and mathematicians. In computer-aided surgery planning, questions arise whose current and future solution involves many different subfields of computer science and mathematics. We concentrate on problems connected with the surgery of the human mandible. In particular, numerical simulations of load-deformation situations are presented and questions of modeling are discussed.

**Factoring
integers, Producing primes and the RSA cryptosystem**

** **

**Abstract **

This will be an introductory talk. After having outlined some of the highlights of the “history of integer factorisation”, we will explain how to use the hardness of factoring integers to design the RSA public key cryptosystem.

The implementation of such a cryptosystem is the
motivation for primality testing. We will
review classical

**Finite fields, Permutation Polynomials.**

**Computational
aspects with**

**applications**** to public key cryptography**

** **

**Abstract **

We will start from finite fields, their construction and their interpolation properties. This will lead to permutation polynomials. First we will review a few basic properties and examples. Next, we will explain a possible use of permutation polynomials in cryptography. This will require recalling the classical Diffie Hellmann key exchange protocol. Finally we will propose the standard enumeration problems for permutation polynomials and some results about them.

**Computational
Aspects of percutaneous Drug Absorption**

** **

E.H. Twizell*

**Abstract **

The topical application of a finite dose of drug (ointment) is common practice. Simple models treat the absorption process as a linear diffusion problem but more advanced models, such as the dual absorption model which will be considered in the talk, treat the absorption as a non-linear diffusion process. A linear repeated-dose model will be presented and simultaneous metabolism will also be discussed. Finite-difference methods will be used to obtain concentration profiles.

*In collaboration with A.A. Al Ali, A.B. Gumel and K. Kubota

Computational Modelling of Wave Propagation

**in**** a Chemical System with Coupling**

E.H. Twizell*

**Abstract **

The chemical system investigated, which incorporates autocatalysis with decay, is modelled by a system of coupled reaction-diffusion equations in which the reaction terms are non-linear.

The system of PDEs is solved by an implicit finite-difference scheme which requires the use of only linear solvers at each time step and which is capable of implementation on a multiple-processor architecture.

Numerical simulations confirm the formation of travelling waves and the stability of the scheme.

*In collaboration with **K.M. Furati,
M. Al-Mannai, Z.A. ****Çınar**

**CONTRIBUTED TALKS**

**Direct Inversion of Measured
Hydraulic and Electric**

**Transport Properties into a
Geometrical Rock Model**

**Gabor****
Korvin**

** **

**Earth
Sciences Department**

**King Fahd University of Petroleum & Minerals **

**Abstract **

The prediction of the interior structure of sedimentary rocks from measured bulk physical data is an inverse problem with a huge number of unknowns, which can be solved only approximately using the Least Mean Squares Error, the Maximum Entropy or the Tikhonov Regularization methods. However, as has been shown by the success of the Cole-Cole model of the Induced Potential in rocks, or the Thomeer model of Mercury Injection, there are cases when an equivalent rock model with a few degrees of freedom can very well describe the behavior of a complex geologic system.

In this research we have shown that:

(a) The theory of Nabil Akbar (1994) provides an equivalent rock model which is able to reproduce the measured hydraulic and electric transport properties,

(b) The model has only three parameters (average radius
*r*, average distance between nearest pores *d*, average throat
radius d)

(c) These three parameters can be directly determined
from the measured porosity f, hydraulic
permeability *k *and cementation exponent *m. *of the rock, using
simple* *analytic expressions.

The derivation of these formulae is based on effective medium theory (Yonezawa & Cohen, 1983) and on Perez-Rozales' (1982) non-standard theory of electric conduction in rocks.

Examples will be presented for the direct inversion of carbonate rock measurements. The mathematically derived rock model will be shown to well agree with the structure seen in thin sections under the microscope.

** **

**Hassen**** A. Muttlak **

**Department of
Mathematical Sciences **

**King Fahd University of Petroleum & Minerals **

** **

**Abstract **

Different quality control charts for the sample mean are developed using ranked set sampling (RSS) and median ranked set sampling (MRSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS and MRSS are shown to have smaller average run length (ARL) than the classical chart especially if the process starts to get out of control. The MRSS is compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the ARL if the process starts to get out of control. Real data are collected using the SRS, RSS and MRSS. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. It turns out that the newly developed charts are more efficient in estimating the population mean and the process is more stable. Through this study we are assuming that the underlying distribution is normal. A check of the normality for our data set indicated that the normality assumption is reasonable.

** **

**Defect detection on umpainted car body**

**M. T. Mustafa**

**Department of
Mathematical Sciences **

**King Fahd University of Petroleum & Minerals **

** **

**Abstract **

The talk presents results of an industrial project from automobile industry. The purpose is to develop a fast defect detection method which is accurate enough in detection of defects as well as is well-suited for online inspection process.

During the manufacturing process, car bodies can have small defects, for
instance *ripples or bumps.* Such defects being very small in depth are
not visible until cars are painted. However, it is expensive to repair the
defects at this stage. A model is developed to detect *ripples or bumps *on
__unpainted car body__ by analyzing the scanned images, of unpainted car
body, using smoothing splines .

** **

** **

**Numerical Simulation in Reservoir Engineering: **

**An Overview**

**A. S. Harouaka
and H. Menouar**

**CPM/Research Institute
**

**King Fahd University of Petroleum & Minerals **

** **

**Abstract **

Reservoir simulation has been recently defined as the art, science and engineering of the modeling of flow in petroleum reservoirs by solving relevant equations using modern computers.

Specifically, we seek the solution to a system of highly nonlinear partial differential equations (PDE), describing a single or multiphase fluid flow in one two or three dimensions. The procedure most commonly used and accepted is to approximate the PDE by finite difference.

The discretisation process leads to a matrix A whose entries are mainly zeros. This matrix can be extremely large for reservoir engineering problems of a practical size. The solution technique needed to solve the matrix A is by far the most important part of any reservoir simulator and for large simulation problems, iterative solutions techniques have been preferred to direct ones.

The main objectives of this discussion are: 1) Present a brief description of a reservoir simulator; 2) show the different models currently being used and 3) describe how reservoir simulators are considered the primary tools for reservoir management.

** **

**An
Inverse Problem in the Presence**

**of****
a mixed Boundary**

** **

**F.D. Zaman
**

** **

**Department of
Mathematical Sciences **

**King Fahd University of Petroleum & Minerals **

**and**

**Khalid**** Masood**

**Hafr**** ****Al-Baten**** ****Community
College**

** **

**Abstract**

The inverse problems involving parameter identification have attracted considerable attention during recent years. The problem has been studies by various authors in seismic and acoustic context. These studies focus on the physical boundary of the medium satisfying one kind of boundary condition. We consider a model in which identification of an inhomogeinity is sought in the presence of mixed boundary conditions: the boundary consisting of two parts with different impedance coefficients. The Wiener-Hopf method provides with the solution of the mixed boundary value problem (direct scattering problem), while the inverse problem of the determination of inhomogeneity is reduced to the Fredholm integral equation of the first kind. The procedure can be applied to recover acoustic speed variation in an ocean due to a pollutant with non-homogeneous seabed seabed or in the atmosphere in the presence of mixed conditions at the ground.

**Optimal control of
deteriorating production **

**inventory**** systems under various settings**

**L. Tadj M. Bounkhel
Y. Benhadid R. Hedjar**

**King**** ****Saud**** ****University**

**Abstract**

We present in this paper various models to control
the production rate of dynamic production inventory systems with deteriorating
items. Among the models discussed are the model with inventory and production
targets, the model with stock-dependent demand, the continuous review and
periodic review models, and the predictive control model. We also propose some
open problems.