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PhD Thesis: Spatial models and networks of living systems

PhD thesis front page

When studying the dynamics of living systems, insight can often be gained by deriving a mathematical model that can predict future behaviour of the system or help classify the system characteristics. However, in living cells, organisms, and especially groups of interacting individuals, a large number of different factors influence the time development of the system. This often makes it challenging to construct a mathematical model from which one can draw conclusions.

One traditional way of capturing the dynamics in a mathematical model is to formulate a set of coupled differential equations for the essential variables of the system. However, this approach disregards any spatial structure of the system, which may potentially change the behaviour drastically. An alternative approach is to construct a cellular automaton with nearest neighbour interactions, or even to model the system as a complex network with interactions defined by network topology.

The main part of the thesis is based on six different articles, which I have co-authored during my three year PhD at the Center for Models of Life. Apart from these, I have co-authored another six articles, which also relate to spatial models of living systems. These are included as appendixes, but not described in detail in the thesis.

The thesis can be downloaded here.

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Master’s thesis: Spreading, exploiting, and concealing information in complex systems and games

My master’s thesis consisted of three different projects: One about multiple diseases spreading on a lattice, one about a lowest unique bid auction game, and one about the reception game.

You can download the thesis here.

Disease cluster

Unique bid auction

Recption Game

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Bachelor’s project: Low energy trajectories to the moon

Bachelor's project front page

A new design strategy for finding low energy trajectories from Earth orbit to Moon orbit through the first Lagrange point has been developed. The found trajectories are very close to the theoretical minimum values of v necessary to go from Earth orbit to L1 and from L1 to Moon orbit. However, a large velocity change at L1 gives the most fuel effective trajectory a total vof 4369.5 m/s.

As part of the project, seven different one step integrators have been compared, with six of these being symplectic integrators. It was found that the integrator, which approximated the flow of the restricted three body system the fastest and most accurately, was the non-symplectic 4th order Runge-Kutta Method.

You can download the project here.

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Estimation and Measurement of AC Losses in Bi2Sr2Ca2Cu3O10+x Multifilament Tapes and One Layer Single Phase Cables

Meissner effect of a superconductor

Existing models for estimation of AC loss in multifilament superconducting tapes have been analysed and compared to experimental data. This examination strongly supports the Norris ellipse model and Gömöry-Gherardi model for concentric shells in preference to the Norris strip model or Däumling’s numeric model for rectangular superconductors.

AC loss of a 3.15 m test cable made from 31 multifilament tapes were measured and analysed based on 31 independent tapes and the monoblock model respectively. By also considering themagnetic field produced by the nearest neighbours, an expanded analytical model was developed, improving the estimation of AC losses to a deviation of less than 10 % from the measured.

Collaborator: Esben Tore Mølgaard.

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First year project: Syntese og undersøgelse af type II superledere

Superconductor levitating

Superconductor levitating

My first year project was conducted in collaboration with Esben Tore Mølgaard and Sonja Holm. We manufactured three different high-temperature superconductors and investigated their lattice structure, susceptibility, resistivity, and critical current. Also, we carried out the same experiments on a YBCO sample with reduced oxygen level.

You can download the project here and the appendices here.

The project is in danish