1998, Wolfrum, Matthias

We investigate the geometrical properties of the attractor for semilinear scalar parabolic PDEs on a bounded interval with Neumann boundary conditions. Using the nodal properties of the stationary solutions which are determined by an ordinary boundary value problem, we obtain crucial information about the long-time behavior for the full PDE. Especially, we prove a criterion for the intersection of strong- stable and unstable manifolds in the finite dimensional Morse-Smale flow on the attractor.

1999, Brüstel, U., Heinrich, A., Schumann, J., Vinzelberg, H.

[no abstract available]

1994, Borchardt, Jürgen, Grund, Friedrich, Horn, Dietmar, Uhle, Manfred

[no abstract available]

1999, Cramer, Wolfgang

[no abstract available]

1999, Pompe, S., Bubner, M., Schmeide, K., Heise, K.H., Bernhard, G., Nitsche, H.

[no abstract available]

1997, Hünlich, Rolf, Glitzky, Annegret, Röpke, Wilfried

Im Vorhaben wurden Beitraege zur Modellierung und Simulation relevanter Teilprozesse bei der Herstellung von Halbleiterbauelementen der Nanoelektronik geleistet. Behandelt wurden vorrangig Fragestellungen,die beim Verbundpartner, dem Institut fueur Halbleiterphysik Frankfurt (Oder), zur Entwicklung von SiGe--Heterojunction--Bipolartransistoren von Bedeutung waren. Schwerpunkte bildeten Fragen zur Diffusion von Fremdatomen in verspannten SiGe--Schichten sowie zu Feldeffekten bei der Diffusion elektrisch geladener Teilchen im Hochkonzentrationsfall. Gegenstand der analytischen und numerischen Untersuchungen waren verschiedene Klassen von Elektro-Reaktions-Diffusionsgleichungen in Heterostrukturen, die relevante Aufgaben aus der Halbleitertechnologie auf verschiedenen Niveaus modellieren. Hier wurden neue Aussagen zur globalen Existenz, Einzigkeit und zum asymptotischen Verhalten der Loesungen erhalten.Weiterhin wurden Diskretisierungsschemata, die Konvergenz von Naeherungsverfahren sowie die Reduktion der Modellgleichungen fuer singulaer gestoerte Faelle diskutiert.

1996, Becker, E., Schmitz, G., Geprägs, R.

We present self-consistent comparisons of axissymmetric and 3-dimensional simulations of the tropospheric circulation under idealized physical conditions. These reveal a feedback of transient eddies onto the Hadley circulation which, first, strongly depends on equatorial heating and, second, is in case of realistic heating quite different from prescribed eddy forcing. A quantitative estimation for the eddy-induced mixing of vorticity into the poleward flow of the Hadley cell is given. The proposed relation is in accordance with observations. It is derived from the computational result that eddy momentum flux convergence is of the same order as the equatorward flux of relative vorticity generated by the Hadley circulation. Evaluation of the local budgets of sensible heat gives rise to a clear picture of how the poleward heat transports due to Hadley circulation and transient eddies interlock. This mechanism is found to be essential for an interpretation of the eddy feedback.

1999, Becker, E., Schmitz, G.

Several experiments performed with an idealized troposphere–stratosphere GCM are comparedto estimate the impact of orography and prescribed local heat sources on the residual circulationin the northern winter stratosphere. It is found that only the combined action of orographicand thermal wave forcing in northern midlatitudes is capable of inducing a residual circulationreaching continuously from tropical to polar latitudes at stratospheric altitudes. Intensificationsof the residual circulation in response to modified forcing of stationary waves are generallyassociated with, firstly, a reduced polar night jet accompanied by enhanced easterlies inlow and summer hemispheric latitudes and, secondly, substantial warming of the polar nightstratosphere completely compensated by cooling in the tropics and subtropics.