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07.01.2019 15:00 Uwe Thiele (Uni Münster):
Straightening and moving the snake - localised clusters in passive and active Phase Field Crystal modelsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

First, we consider the bifurcation structure of localised solutions for the standard (passive or thermodynamic) phase field crystal (PFC) model [aka conserved Swift-Hohenberg (cSH) equation with cubic nonlinearity] that may be obtained as a local approximation of a dynamical density functional theory (DDFT). It is thought to provide the simplest microscopic continuum description of the thermodynamic transition from a fluid state to a crystalline state and is frequently used to model colloidal crystallisation [1].

After introducing the cSH equation as an example of a conserved dynamics, its steady states and their bifurcations are analysed. In particular, We focus on the variety of spatially localized structures, that are found in addition to periodic structures. The location of these structures in the temperature versus mean concentration plane is determined using a combination of numerical continuation in one and two dimensions and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard aligned homoclinic snaking when the solutions are plotted employing the chemical potential as main control parameter [2]. We also show how the localised states are related to the Maxwell construction of the crystallisation isotherm.

Second, We consider the active phase field crystal (aPFC) model [3] that results as a combination of the passive PFC model and the Toner-Tu theory for self-propelled particles. It is considered a simple model that describes the transition between resting and traveling ('living') crystals. In the linear regime, analytical expressions for the transitions from the liquid state to both types of space-filling crystals are obtained and the resulting phase-diagram is discussed [4]. In the nonlinear regime, we describe a variety of localized resting and travelling clusters that may exist besides spatially extended crystals. We provide a semi-analytical criterion for the onset of motion in the nonlinear regime, that corresponds to drift pitchfork and drift transcritical bifurcations [5]. Numerical continuation is applied to follow resting and traveling localized states while varying the activity and the mean concentration as well as to determine their regions of existence. Based on this information we finally discuss teh scattering behaviour of the found travelling localised states.

[1] H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G. Toth, G. Tegze, and L. Granasy, Adv. Phys. 61, 665 (2012). [2] U. Thiele, A. J. Archer, M. J. Robbins, H. Gomez, and E. Knobloch, Phys. Rev. E. 87, 042915 (2013). [3] A. M. Menzel and H. Löwen, Phys. Rev. Lett. 110, 055702 (2013). [4] A. I. Chervanyov, H. Gomez and U. Thiele, EPL 115, 68001 (2016). [5] L. Ophaus, S. V. Gurevich and U. Thiele, PRE 98, 022608 (2018).

10.01.2019 15:45 Gianni Dal Maso (SISSA, Triest):
TBAMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

10.01.2019 16:30 Hélène Esnault (Freie Universität Berlin):
Verschiedene Aspekte von Differentialgleichungen in arithmetischer Geometrie - Mathematisches Kolloquium der LMUA027 (Haus B , 80333 Theresienstr. 39)

Wir geben einen Überblick über die Reduktion modulo einer Primstelle von Differentialgleichungen, mit Hinblick auf Grothendiecks p-Krümmung Vermutung (noch offen) und Simpsons motivische Vermutungen (einige Punkte sind hier seit kurzem bekannt).

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

10.01.2019 17:15 Örs Legeza (Wigner Research Center Budapest):
TBAMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

14.01.2019 16:15 Per von Soosten (TUM):
tbaMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

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14.01.2019 16:30 Volker Betz (TU Darmstadt):
TBAB 252 (Theresienstr. 39, 80333 München)

TBA

17.01.2019 15:00 Katharina Schratz (Karlsruher Institut für Technologie):
TBARoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

17.01.2019 16:30 TBA:
TBARoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

21.01.2019 16:15 Matthia Sensi (Universität Trento):
tbaMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

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21.01.2019 16:30 Alexander Drewitz (University of Cologne) :
TBAB 252 (Theresienstr. 39, 80333 München)

TBA

21.01.2019 17:00 Daniel Wachsmuth (Universität Würzburg):
Second-order optimality conditions in optimal control problemsGebäude 33, Raum 1401 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

In the talk we give a review on second-order optimality conditions for optimal control problems subject to partial differential equations and variational inequalities. Such conditions imply, e.g., local optimality, local uniqueness of critical points, and stability of solutions with respect to perturbations. In addition, they are crucial in proofs of a-priori and a-posteriori error estimates for numerical approximations.

22.01.2019 16:30 Robert Didier (Universität Nantes, FR):
tbaMI 03.10.011 (Boltzmannstr. 3, 85748 Garching)

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28.01.2019 14:15 Prof. Pierre Devolder:
TBABC1 2.02.01 (Parkring 11, 85748 Garching)

TBA

28.01.2019 15:00 Dr. Axel Bücher:
TBABC1 2.02.01 (Parkring 11, 85748 Garching)

TBA

28.01.2019 16:00 Jean-David Fermanian:
TBABC1 2.02.01 (Parkring 11, 85748 Garching)

TBA

28.01.2019 16:15 Nikolay Martinchuk (RUG):
tbaMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

tba