General Background

Ultimately, I guess, I should say that what interests me most as a scientist is to gain an understanding of why things are the way they are.
Mostly, this has been a physics affair to me and I plan to continue that way since, in principle at least, Physicists have actually been able to answer some of the fundamental questions.
Nevertheless, for a full understanding of Nature from a human point of view, it is definitely important to also consider the philosophical side. Therefore, as a student, I spent many years reading the likes of Heidegger and Kant and eventually obtained a Master's degree in Philosophy even before I completed my 'real' major in Physics. I do hope to be able to spend some more time reading Metaphysics again in the future.

My main field of research is in Chaos, Nonlinear Dynamics and Complex Systems. I am especially interested in systems which display universal properties and can thus serve as prototypes for classes of natural phenomena. When time permits, I also like to study the fundamental aspects of Quantum Physics and its philosophical implications.

  Coupled Map Lattices

Coupled Map Lattices are fascinating since they are among the simplest high dimensional chaotic systems. They are discrete in both time and space but have a continuous variable. This allows them to be computationally efficient while maintaining an infinite state space. Coupled Map Lattices exhibit a fabulously rich spectrum of unexpected and fascinating behaviors that can serve as paradigms for complex phenomena in Nature.

Main Interest: Universality in Coupled Maps

Current Research Focus

  • Universality: I have discovered that many coupled map lattices display remarkably similar overall phenomenologies (see this recent paper). Most importantly, it turns out that a large group of lattices follows the same basic pattern sequence when increasing the nonlinearity from a small value.
    At the moment I am investigating two aspects as with regards to this. Firstly, I would like to know what exactly determines whether a coupled map follows the basic pattern sequence. Secondly, I would like to find an analytical proof for the similarity.

  • Scaling: In the same paper mentioned above, I also found that the wave-type solution of the pattern selection regime scales linearly with the coupling range. This linear scaling seems to be true for all the coupled maps that have this type of solution and I would like to find and analytical proof for this scaling behavior.

  • Higher Dimensions: Perhaps not so surprisingly, the rich phenomenology of the one dimensional coupled map lattice does not directly translate into a similar phenomenology in higher dimensions. In particular, to my knowledge, the beautiful longer-range wave-type solutions of the one dimensional case have not been observed in higher dimensions thus far. I am interested in seeing whether there are conditions under which regular solutions can be observed in higher dimensions

Coupled Map Simulator

This is a real time coupled map simulator which I wrote in X. Since it uses the Athena widget set that is a part of the standard X distribution, it compiles on most Unix systems. My current version is for Linux but in the past I used it on IBM, HP and Sun workstations.

The screenshot on the right shows the Frozen Pattern regime at higher coupling strengths. Overall, the band structure (i.e. the low and high areas in the figure) remain constant but the domain walls continuously move.

Click on the screenshot to see an enlarged picture
  Life as a Complex System

Life is certainly complicated and indeed often complex. However, is it a “complex system” in the Physicists’ sense? I believe so but I guess to certain degree that's still an open question.

Underlying the ideas of life as a complex system is the notion that complex systems have intrinsic properties that can lead to unexpected but robust and adaptable dynamics. This is rather different from the view that evolution is a random walk over adaptation space. Whether this notion eventually will prevail or not, the consideration of life as a complex system is in my view an excellent example of a concept where interdisciplinary research is an enriching experience.

Main Interest: Dynamics of simple cellular systems

Current Research Focus

  • Open Chaos: Probably the most important difference between coupled map lattices like the globally coupled logistic map and the open systems studied in the context of life as a complex system is the appearance and disappearance of elements. Or in other words the growth and death of cells.

  • Universality:I guess it is fair to say that universality plays an important role in all classes of dynamical systems (be it trough its absence or presence). Similarly, I am very interested in investigating what types of universal behavior can be found in open systems.

Coupled Cell Simulator

This is a real-time simulator for systems with growth and death which I wrote in Qt. This screen shot shows the dynamics of one of the regimes of Kaneko's model of (through a source term) globally coupled circle maps with growth and death.

Click on the screenshot to see an enlarged picture