Department of Mathematics,
Chalmers University of Technology,
and
Göteborg University

I supervise in
**ECMI Modelling week 2001, Klagenfurt, Aug. 31-Sept. 9**
I suggest the following topics:

**A pencil beam model for charged particles **

This is an interdisciplinary problem in particle/medical physics concerning electron and photon dose calculations of radiative transfer/radiation treatment.

The project is to model a forward-peaked scattering process in the
linear transport equation and study both asymptotic behavior
and numerical approximations for the such obtained beam particles.

A front line application is, e.g. in radiation therapy where the
objective is twofold: (i) To maximize the deposit of electron dose
(energy) inside seek cells (ii) To minimize the deposit of energy
in surrounding healthy tissue. In this way one has an optimization
(max-min) problem with many challenging and interesting aspects.
A more detailed **abstract** can be found in the following file:

abstract (ps-file) ,
abstract (pdf-file) .

Implementations are easily done writing **MatLab** codes. However,
knowledge in the following programing/software may be very much useful:

Mathematica, Fortran, PDE tool-box, and
if possible **DSMC (Direct Simulated Monte-Carlo)**.

**Here are some relevant literature:**

M. Asadzadeh,

Streamline diffusion methods for the Fermi and
Fokker-Planck equations,

* Transport Theory and Statistical Physics*, (1997), 319--340.

M. Asadzadeh,

Characteristic Methods for Fokker-Planck and Fermi Pencil Beam
Equations,

* Proceedings of 21th International Symposium on Rarefied Gas
Dynamics,
ed. by R. Brun et al *, Vol II, 205--212, Marseille 1998.

M. Asadzadeh,

A posteriori error estimates for the Fokker-Planck and Fermi
pencil beam equations,

* Math. Models and Methods in Appl. Sci.*,
10(2000), 737--769.

C. Borgers and E. W. Larsen,

The trasversely integrated scalar flux for a norrowly focused particle
beam,

*SIAM J. Appl. Math. * 55(1955), 1--22.

C. Borgers and E. W. Larsen,

On the accuracy of the Fokker-Planck and Fermi pencil beam equations
for charged particle transport,

*Med. Phys. * 23 (1996), nr. 10, 1749--1759.

C. Borgers and E. W. Larsen,

Asymptotic derivation of the Fermi pencil beam approximation,

*Nucl. Sci. Eng. * 123(1996), 343--357

D. Jette

Electron Beam Dose Calculations,
Radiation therapy physics,

* ed by A. Smith, Springer* (1995), 95--121

D. Jette,

Electron dose calculation using multiple-scattering theory.
A. Guassian multiple-scattering theory.

*Med. Phys. * 15 (1988), 123--137.

J. Lang,

Adaptive Multilevel Solution of Nonlinear Parabolic PDE System,

*Lecture Notes in Computational Science and Engineering, Springer
*, 16 (2000).

E. W. Larsen,

The amplitude and radius of a radiation beam,

*Proceedings of the International Conference on Latest Developments
and Fundamental Advances in Radiative Transfer (Los Angeles, CA,
1996). Transport Theory Statist. Phys. *
26 (1997), no. 4-5, 533--554.

G. C. Pomraning,

The Fokker-Planck operator as an asymptotic limit,

* Math. Models and Methods in Appl. Sci.*,
2(1992), 21--36.

G. C. Pomraning and A. Prinja,

High-order multiple scattering theories for charged particle
transport,

*Med. Phys. * 23 (1996), nr. 10, 1761--1744.

Mohammad Asadzadeh <mohammad@math.chalmers.se> Last modified: Mon Sep 10 12:46:23 MET DST 2001