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Hello, welcome to my homepage! |
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My diploma thesis in physics dealt with the
theoretical description of self-generated high-frequency current
oscillations in semiconductor multilayer structures. When an
electric field is applied parallel to the layers of such structures
one can observe a small interval with negative slope in the
current-voltage characteristic, i.e. an increasing electric field
leads to decreasing current. That behaviour is called negative
differential conductivity and is known to give rise to current
instabilities.
(Advisor: Prof. Eckehard Schöll,
Institute for
Theoretical Physics, Technische Universität
Berlin)
After my diploma I did some work on the optimization of binary sequences (so called Merit Problem) using evolutionary algorithms. That was together with Prof. Werner Ebeling at the Institute of Physics of the Humboldt-Universität Berlin.
The subject of my PhD thesis was related to
nonlinear dynamics in a more general context. I studied different
scenarios of transitions between regular and chaotic dynamics in
spatially extended systems. Among other things I modeled the
synchronization of spatio-temporal dynamics with an external
forcing using the periodically forced complex Ginzburg-Landau
equation (CGLE).
The CGLE is an amplitude equation describing the behaviour of a
spatially extended system close to the onset of an oscillatory
instability. Originally derived as a model for inhomogeneous
superconductors it turned out that the approach can be applied to a
wide class of systems.
A possible realization of a system described by the forced CGLE
can be e.g. a chemical reaction with periodically modulated light
intensity.
That work was done under Prof. Arkady Pikovsky
in the Department of
Physics at the Universität
Potsdam
I am still interested in the synchronization of spatio-temporal
dynamics. In that context I study the periodically forced complex
Ginzburg-Landau-equation in one dimension. It has been shown [5] that localized jumps of the
phase of 2 pi (so called phase kinks) lead to new dynamical regimes
with spatio-temporal intermittency. These phase kinks separate
domains with synchronized dynamics. Due to the fact that the phase
is defined modulo 2 pi the phase kinks can be seen both as fronts
and as pulses. Under certain conditions these kinks become
unstable. That instability can give rise to backfiring-like
structures, leading to characteristic patterns, similar to those
e.g. observed in the pigmentation of shells of
mollusks.
Together with Médéric Argentina we investigated mechanisms for the transitions between these dynamical regimes. We explained the underlying mechanims for the transitions and found scaling laws for the lifetime of the kinks in the backfiring-like regime.
Moreover an oscillatory instability of the phase kinks is possible. As a consequence, propagating oscillatory kinks can be observed.
That work was done in collaboration with Prof. Manuel G. Velarde in the Unidad de Fluidos at the Instituto Pluridisciplinar of the Universidad Complutense de Madrid. The work was part of the EU-TMR-Network Nonlinear Dynamics and Statistical Physics of Spatially Extended Systems .
Before joining the group of Prof.
Mikhailov I was a Postdoctoral Research Fellow in the LOCNET
project and worked with
In collaboration with the other people of the DOCS research group in Florence
I did some work about spatially-localized and time-periodic
oscillations in networks of nonlinear oscillators (so called "breathers").
[Back to the page of the Complex Systems Group group]
