Division of Mechanics offers Master Theses in a wide range of topics, e.g., biomechancis, mechanics, optimization, surfance mechanics etc. The interested student is encouraged to contact our Director-of-Studies Peter Schmidt (email@example.com) for more information.
Available Master Theses:
1) Implementation of a numerical method for solving
optimization problems with matrix inequality constraints
Optimization problems with matrix inequality constraints occur frequently in
control theory and structural optimization. The goal of this project is
to implement and test a numerical method for solving such problem. The
project is suitable for students with strong background in programming
and mathematics, especially optimization theory.
For more information click here.
2) Parameter identification in models of cardiac electrophysiology
Computer simulations have proved to be very useful as tools for research
on biological systems and may also come to play important roles in medical
diagnosis. The simulations are often based on mathematical models
comprising nonlinear differential equations, which given suitable input
data in the form of detailed measurements of geometry and material parameters
are able to represent with good accuracy the behavior of the real-world
system under study. Advances in medical imaging technologies have made
acquisition of detailed geometrical data relatively straightforward, but
in many situations, material parameters are unfortunately not available
for direct measurements and one therefore has to resort to indirect methods;
i.e., parameter identification or estimation.
If you are interested, please contact Carl-Johan Thore.
This thesis project concerns parameter identification in systems of non-linear
reaction-diffusion equations based on the so-called FitzHugh-Nagumo model. These
models have been devised to capture important qualitative aspects of cardiac electrophysiology
while at the same time being relatively simple. In this project you will implement one of these
models and try to identify parameters in it using limited data, such as measurements of the
"electric potential" on the boundary of the modelled system. In general, this
type of problems
lack unique solutions and methods for alleviating this issue should therefore be tested.
The project is suitable for students at the M- or Y-programmes, or with similar background.
Experience of the following is desirable:
* Applied numerical optimization. This could for instance mean
optimal control or
* Numerical methods for solving PDEs, such as, e.g., finite elements or finite differences.
* Programming in Matlab and/or C/C++
The description can also be found in pdf-format here.
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Last updated: 2015-10-09