
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 wavetype 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 longerrange wavetype 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
realtime 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







