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Inhalt des Dokuments

Seminar "Dünne Schichten", Wintersemester 2011/12

Organisation
Koordination:
Prof. Dr. Barbara Wagner, Dr. Kersten Schmidt
Termine:
Do, 14-16 Uhr in MA 645
Inhalt:
Vorträge von Gästen, Mitarbeitern und Studenten zu dünnen Schichten und anderen Themen der asymptotischen Analysis
Termine
Datum
Uhrzeit
Raum
Vortragende(r)
Titel
27.10.2011
14.15 Uhr
MA 645
Dr. Kersten Schmidt (TU Berlin)
High order transmission conditions for conductive thin sheets, Part I
03.11.2011
14.15 Uhr
MA 645
Dr. Kersten Schmidt (TU Berlin)
High order transmission conditions for conductive thin sheets, Part II
10.11.2011
14.15 Uhr
MA
645
Sebastian Jachalski (WIAS)
Stationary solutions for two-layer lubrication equation
17.11.2011
14.15 Uhr
MA
645
Dr. Anastasia Thöns-Zueva (TU Berlin)
High Order Asymptotic Expansion for Viscous Acoustic Equations Close to Rigid Walls (Abstract)
24.11.2011 
14.15 Uhr
MA 645
Dr. Dirk Peschka (WIAS)
Numerical algorithms and variational formulations for multiphase flows

01.12.2011
14.15 Uhr
MA 645
Dr. Maciek Korzec (TU Berlin)
Evolution of thin solid films and interfaces in photovoltaic devices
08.12.2011
14.15 Uhr
MA 645
Dr. Andreas Münch (University of Oxford)
A multiple scales approach to evaporation induced Marangoni convection
15.12.2011
14.15 Uhr
MA 645
Dr. Andreas Pflug (Fraunhofer IST, Braunschweig) 
Gasfluss- und Plasmasimulation für die
Dünnschichttechnik
12.01.2012
14.15 Uhr
MA 645
Dirk Klindworth (TU Berlin)
Computation of guided modes in photonic crystal wave guides
19.01.2012
Geänderter
Raum
und 
Uhrzeit!
12.15 Uhr
MA 542
Dr. Bérangère Delourme (Caltech)
Asymptotic models for thin periodic layers in electromagnetism (Abstract)
26.01.2012
14.15 Uhr
MA 645 
Dr. Georgy Kitavtsev (MPI Leizig) 
Coarsening rates for liquid droplets in the presence of strong slippage
02.02.2012
14.15 Uhr
MA 645
Marion Dzwinik (TU Berlin) 
Surface diffusion dewetting of thin solid films
09.02.2012
Geänderter
Raum
und 
Uhrzeit!
12.15 Uhr
MA 542
Matthias Liero (WIAS) 
Interface conditions in Reaction-diffusion equations
16.02.2012
14.15 Uhr
MA 645
tba
tba

Abstracts

Bérangère Delourme

Asymptotic models for thin periodic layers in electromagnetism
Donnerstag, 19. Januar 2011, 12:15 in MA 542

My talk is dedicated to the study of asymptotic models associated with electromagnetic waves scattering from a complex periodic ring, made of a dielectric ring containing two layers of wires winding around it. This is a joined work with P. Joly and H. Haddar. We are interested in situations where both the thickness of the ring and the distance between two consecutive wires are very small compared to the wavelength λ of the incident wave and the diameter of the ring. In these cases, numerical computations of the solution would become prohibitive as the small scale parameter (denoted by δ) goes to 0, since the mesh used needs to accurately follow the geometry of the heterogeneities. In order to overcome this difficulty, we shall derive approximate models where the periodic ring is replaced by e ffective transmission conditions on the mean interface Γ. The numerical discretization of approximate problems is expected to be much less expensive than the exact one, since the mesh no longer needs to be constrained by the small scale. From a technical point of view, these approximate models are derived from the asymptotic expansion of the solution with respect to the small parameter δ. Our method mixes matched asymptotic expansions and homogenization. We build the approximate transmission conditions from the truncated expansion.We pay particular attention to the justification of the asymptotic expansion and to the stabilization of the eff ective transmission conditions. Error estimates and numerical simulations are carried out to validate the accuracy of the models.

Keywords : matched asymptotic expansions, periodic homogenization, approximate transmission conditions, Maxwell's equations, Helmholtz equation.

Anastasia Thöns-Zueva

High Order Asymptotic Expansion for Viscous Acoustic Equations Close to Rigid Walls

Donnerstag, 17. November 2011, 14:15 in MA 645

In this study we are investigating the acoustic equations as a perturbation of the Navier-Stokes equations around a stagnant  uniform fluid and without heat flux. For gases the viscosities η and η' are very small and lead to viscosity boundary layers close to walls.  We will restrict our attention on those viscosity boundary layers and do not consider non-linear convection.

As there is a small factor η comes out in front of the curl curl operator in governing equations, the system is singularly perturbed, i.e.,  first, its formal limit η→ 0 does not provide a meaningful solution, and secondly, a boundary layer close to the wall ∂Ω appears. The choice of asymptotic expansion method seems to be the best adapted to this case.

In this approach we separate the solution in far field and correcting near field, where far field represents the area away the wall and exhibits no boundary layer, at the same time near field decays exponentially outside the zone of size O(√η) from the boundary.

To complete the solution, effective (impedance) boundary conditions are derived for the far field.

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