Past research projects
A parallel method for pseudo-arclength continuation
Collaborators: Dhavide Aruliah and Alex Dubitski.
Related publications: AVD, PAVD.
Key words: parallel computing, arclength continuation, scientific computing.
Abstract: We worked out a way to parallelize the inherently serial process of arclength continuation, following an elegant, recursive approach. This work resulted in a software package that can be applied to computationally intense continuation problems.
The saddle-node transcritical bifurcation
Collaborators: Ivanky Saputra, Reinout Quispel, Marvin Hoti
Related publications: SQV, SVQ, VH.
Key words: saddle-node-transcritical bifurcation, normal form theory, mathematical biology.
Abstract: This project grew out of Ivanky's PhD thesis and focuses on the interaction between saddle-node and transcritical bifurcations. The dynamics generated by this interaction are surprisingly rich, in fact they can be found in the unfolding of a degenerate Bogdanov-Takens point. The papers describe the unfolding of this singularity and its detection in a model of predator-prey-toxicant interaction.
1997-2002 Ph.D. at the mathematical institute of Utrecht university and the Royal Dutch Meteorological Institute, KNMI, supervised by Ferdinand Verhulst and Theo Opsteegh. The results are summarised in my thesis, "Time scale interaction in low-order climate models".
I used bifurcation and continuation techniques to analyse low-order models of the atmosphere and the ocean. This resulted in a mix of modeling, scaling, Galerkin truncation, bifurcation analysis, singular perturbations and a considerable amount of trouble to relate all that to "reality".
Another paper (KMV), not included in my thesis, is the result of joint work with Yuri Kuznetsov and Hil Meijer on a certain codimension two bifurcation.
ITFA, institute for theoretical physics of the university of Amsterdam. I specialized in statistical physics, writing my thesis on quasi-crystalline structure and random tiling models. The project was supervised by Bernard Nienhuis and Jan de Gier.
For a simple introduction to quasi crystals and random tiling models you might leaf through my thesis.