| Nov 3, 2009 |
Prof. Dr. Sergei Pilyugin
(St.Petersburg University) |
Structural stability of diffeomorphisms and shadowing properties |
We will discuss several new results concerning relations between
structural stability, Ω-stability, and
some shadowing properties of diffeomorphisms of smooth closed manifolds.
- Variational shadowing property is equivalent to structural stability.
- Lipschitz shadowing property is equivalent to structural stability.
- Lipschitz periodic shadowing property is equivalent to Ω-stability.
Some of these results are joint with A. Osipov and S. Tikhomirov.
|
| Nov 10, 2009 |
Dr. Laurette Tuckermann
(PMMH, ESPCI Paris) |
Turbulent-laminar patterns in plane Couette flow |
The greatest mystery in fluid dynamics is probably transition to turbulence.
The simplest shear flow, plane Couette flow -- the flow between parallel
plates moving at different velocities -- is linearly stable for all Reynolds
numbers, but nevertheless undergoes sudden transition to 3D turbulence at
Re near 325. At just these Reynolds numbers, it was recently discovered
experimentally at CEA-Saclay that the flow takes the form of a steady
and regular pattern of wide oblique turbulent and laminar bands.
We have been able to reproduce these remarkable flows in numerical simulations
of the Navier-Stokes equations. Simulations display a rich variety of variants
of these patterns, including spatio-temporal intermittency, branching and
travelling states, and localized states analogous to spots. Quantitative
analysis of the Reynolds-averaged equations reveals that both the mean flow
and the turbulent force are centrosymmetric and can be described by only three
trigonometric functions, leading to a model of 6 ODEs. We find that the
transition is best described as a bifurcation in the probability distribution
function of the power spectrum.
|
| SFB 647 |
| Nov 17, 2009 |
Julia Ehrt
(WIAS / FU Berlin) |
Promotionsvortrag / Dissertation Defense
Mathmatics of Cell Motility |
| 15:15,
Free Unversity Berlin, Room 140, Arnimallee 7 (rear building), 14195 Berlin |
|
The talk will investigate mathematical and modelling aspects of cell motility.
After giving a brief overview on the bio-chemical processes of cell motility in general
I will focus on crawling cells.
The different processes involved in crawling cells have posed challenging problems in terms of
their physical and chemical background. In addition crawling cells pose a rich field in terms of
mathematical modelling.
Several aspects of the physical and chemical background and the difficulties in modeling these will be
adressed in the talk.
In the last part I will present a very recent model investigated by Gholami, Falcke and Frey (2008)
in which interesting mathematical questions arise.
I will explain the model and investigate its mathematical background.
|
| Nov 24, 2009 |
Dr. Nikolay Zhuravlev
(Peoples' Friendship University of Russia) |
Methoden zur qualitativen Untersuchung periodischer Lösungen von
Funktionaldifferentialgleichungen |
|
Die Eigenwerte des Monodromie-Operators beschreiben das Verhalten der
Trajektorien in der Naehe einer periodischen Loesung. Im Gegensatz zu
gewoehnlichen Differentialgleichungen fuehren
Funktionaldifferentialgleichungen jedoch auf Operatoren zwischen
unendlich-dimensionalen Raeumen. Es ist daher viel schwieriger, die
Eigenwerte des Monodromie-Operators zu bestimmen.
Im Vortrag werde ich ueber Methoden zur Bestimmung dieser Eigenwerte
berichten.
|
| Dec 1, 2009 |
SFB 647 |
| Dec 8, 2009 |
Dr. Georgy Kitavtsev
(WIAS Berlin) |
Reduced ODE models describing coarsening dynamics of slipping droplets |
|
In this talk the topic of reduced ODE models corresponding to a family of one-dimensional
lubrication equations derived by M"unch et al. '06 is addressed.
This family describes the dewetting process of nanoscopic thin liquid ?lms on hydrophobized
polymer substrates due to the presence of several intermolecular forces and takes
account of different ranges of slip-lengths at the polymer substrate interface. Reduced
ODE models derived from underlying lubrication equations allow for an efficient analytical
and numerical investigation of the latest stage of the dewetting process: coarsening
dynamics of the remaining droplets. We present a new geometric approach which can
be used for an alternative derivation and justi?cation of above reduced ODE models
and is based on a center-manifold reduction recently applied by Mielke and Zelik '08
to a certain class of semilinear parabolic equations. One of the main problems for
a rigorous justi?cation of this approach is investigation of the spectrum of a lubrication
equation linearized at the stationary solution, which describes physically a single
droplet. The corresponding eigenvalue problem turns out to be a singularly perturbed
one with respect to a small parameter ε tending to zero. For this problem we show existence
of an ε-dependent spectral gap between a unique exponentially small eigenvalue
and the rest of the spectrum.
|
| Dec 15, 2009 |
SFB 647 |
| Jan 12, 2010 |
SFB 647 |
| Jan 26, 2010 |
Prof.Dr. Sergei Shapiro
(Freie Universität Berlin, FR Geophysik) |
Fluid-induced seismicity and pore-pressure diffusion in rocks |
Dr. Marc Timme
(MPI Dynamics&Selforganization, Göttingen) |
Spatio-Temporal Patterns in the Brain: Neural Networks with Nonlinear Dendrites |
| Feb 2, 2010 |
Prof. Dr. Flavio Abdenur
(PUC, Rio de Janeiro) |
Geometric mechanisms for robust transitivity |
| 14:15,
Free Unversity Berlin, Room 140, Arnimallee 7 (rear building), 14195 Berlin |
|
The existence of robustly transitive but non-Anosov
diffeomorphisms has been known ever since Shub's construction in the
early seventies. In the past 15 years or so, new examples have been
given, many of which rely on the blender studied by Diaz and Bonatti. In
addition, for the first time general necessary properties of such
systems have been obtained: "robust transitivity implies such-and-such a
condition". In this talk I will briefly survey the literature and then
discuss some ongoing work that goes in the opposite direction: we ask
which conditions are sufficient for - and hopefully in some sense
characterize - the phenomenon of robust transitivity. This involves
ongoing joint work with S. Crovisier.
|
| SFB 647 |
| Feb 9, 2010 |
Dr. Przemyslaw Perlikowski
(Technical University of Lodz) |
Dynamics in a ring of delayed coupled Stuart-Landau oscillators |
|
Results presented in the talk consider the ring of unidirectionally
delayed coupled Stuart-Landau oscillators. Firstly, we show
investigations of steady state stability, we present its properties with
respect to delay in coupling and number of oscillators in the ring. To
cope with small and large delay in the coupling we applied analytical
techniques, while for intermediate delay we use Lambert function. Then, we
present the influence of time delay and size of the ring on appearance of
periodic solutions. We find coexisting stable periodic solutions (here,
rotating waves), which correspond to Eckhaus instability. Presented
results are ongoing joint work with S. Yanchuk.
|
Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !
Last change: Feb. 8, 2010
