Previous Projects in Applied Mathematics

The following gives a description of various projects in applied mathematics I have been involved in during several internships as part of my studies at INSA:

• Cryogenic pulse tube modelling,
• Bacteria-bacteriophage modelling in the cheese industry,
• Developing numerical terrain models from raw satellite imagery,
• DNA modelling.

There are also descriptions of practical projects and reports I have been involved in during my studies at INSA:

• Linear programming,
• Partial differential equations using finite element methods,
• MP3 compression techniques,
• Non linear opitimisation, comparing some methods,
• Subband image compression,
• Solving numerically the heat equation in 2D,
• Numerical analysis project: Heterogeneous diffusion,
• Solving differential equations with splines.

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Cryogenic pulse tube

Céline Cattoën (INSA)

February-July 2003

Abstract: We develop a mathematical model for a cryogenic pulse tube which is based on the use of an approximate Stirling cycle. A complete set of governing equations (the equations of mass, momentum, and energy) are used to obtain a model of the behaviour of the working fluid (helium) in every component of the cryocooler. We present some computational results.The modelling problem is suprisingly difficult. Prior to the work reported here, there were no extant models for the entire system, but only limited attempts at modelling one or at most two parts.
Pdf file not available for download.

Supervisor: Dr. Graham Weir, Industrial Research Limited, Lower Hutt, New Zealand. Report written in English.

Bacteria-bacteriophage modelling in the cheese industry

Céline Cattoën (INSA)

November 2003

Abstract: This project consists of describing bacteria-bacteriaphage interaction, analysing some mathematical models, getting some useful experimental data to determine coefficients, and some modelling results of the bacteria-bacteriaphage behaviour.
Download pdf file.

Supervisors: Dr. Geoff Barnes, Dr. Tammy Smith, Massey University, Palmerston North, New Zealand. Report written in English.

Nettoyage de modèle numérique de terrain issu d'images satellites

(Developing numerical terrain models from raw satellite imagery)

Céline Cattoën, Ranveig Wallace, (INSA)

May 2003

Abstract: we develop various numerical methods for processing satellite images, erasing numerical mistakes, and developing numericalterrain models from the cleaned data.
Pdf file not available for download.

Supervisor: Renaud Fraisse (Renaud.Fraisse@astrium-space.com), Astrium, Toulouse, France. Report written in French.

DNA modelling

Celine Cattoen (INSA)

July-August 2002

Abstract: this project consists of modelling DNA molecules to observe twisting and how DNA molecules react to applied forces. From a force field model for the simulation of DNA, an approach of an energy function has been derived. Some results show that calculating only short-range energy is not as accurate a reproduction of the electrostatic interactions as the whole energy function would be.
Download pdf file.

Superviser: Professor Roger Smith, Department of Mathematical sciences, Loughborough University,UK. Report written in English.

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Compte-rendu de TP: Programmation lineaire

(Practical project on linear programming)

Céline Cattoën, Ranveig Wallace, (INSA)

May 2003

Abstract Solving different problems using linear programming.
Download pdf file.

Report written in French.

Compte-rendu de TP d'équations aux dérivées partielles, introduction a la méthode des élements finis

(Practical project: partial differential equations using finite element methods)

Céline Cattoën, Ranveig Wallace, (INSA)

February 2003

Abstract: Solving an elliptic problem numerically with a finite element method.
Download pdf file.

Report written in French.

Technique de compression MP3

(MP3 compression techniques)

Céline Cattoën, Nicolas Prestat, (INSA)

January 2003

Abstract: General principle using the Fourier transform, filters and encoding scheme.
Download pdf file.

Optimisation non linéaire

(Non linear opitimisation, comparing some methods)

Céline Cattoën, Ranveig Wallace, (INSA)

December 2002

Abstract: Numerically solving on the Rosenbrock function with various non linear optimisation methods.
Download pdf file.

Report written in French.

Compte-rendu de TP: Compression d'images par codage en sous-bandes

(Practical project: subband image compression)

Céline Cattoën, Eléonore Gravier, (INSA)

November 2002

Abstract: We realise a subband image compression with filter bank allowing perfect reconstruction (combinations of low-pass and high-pass filters).
Download pdf file.

Report written in French.

Compte-rendu de TP: Résolution numérique de l'équation de la chaleur en 2D

(Practical project: solving numerically the heat equation in 2D)

Céline Cattoën, Ranveig Wallace, (INSA)

November 2002

Abstract: this project consists of a theoritical and numerical analysis of a general heat equation (stationary, non-stationary, and general solution).
Download pdf file.

Report written in French.

Projet d'analyse numérique: Diffusion en milieu hétérogène

(Numerical analysis project: Heterogeneous diffusion)

Céline Cattoën, Bénédicte Lienhardt, (INSA)

June 2002

Abstract: this project consists of solving numerically a diffusion equation in a heterogeneous medium (discontinute diffusion coefficient) with a theta-scheme, and studying the convergence and stability conditions.
Download pdf file.

Report written in French.

Projet d'analyse numérique: Résolution d'equations differentielles a l'aide de splines

(Numerical analysis project: Solving differential equations with splines)

Céline Cattoën, Bénédicte Lienhardt, (INSA)

April 2002

Abstract: this project consists of solving numerically a set of differential equations using splines.
Download pdf file.

Report written in French.

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