Modeling, Analysis, and Scaling Limits for Bulk-Interface Processes

• We congratulate M. Thomas on her appointment as university professor at the Department of Applied Analysis at the Freie Universität Berlin on 11 August 2022! We are also pleased to announce that she will continue to head Weierstrass Group 1 until the end of its funding period!

From left to right: Dirk Peschka, Marita Thomas, Sven Tornquist, Andrea Zafferi.

Highlights & Events in the Past:
• Mathematical Models for Biological Multiscale Systems, 12 -- 14 September 2022
• On 11 July 2022, the German Research Foundation approved the funding of the project "Mathematical modeling and simulation of substrate-flow interaction using generalized gradient flows" by D. Peschka in the second funding period of the SPP 2171 "Dynamic Wetting of Flexible, Adaptive and Switchable Surfaces".
• On 25 May 2022, the German Research Foundation has approved the third funding period of the CRC 1114 "Scaling Cascades in Complex Systems"! Weierstrass Group 1 is involved in the two new projects "B09 - Materials with discontinuities on many scale" (jointly with RG 1) and "C02 - Interface dynamics: Bridging stochastic and hydrodynamic descriptions" (jointly with RG 5 and the Freie Universität Berlin). Besides, the project period of "C09 - Dynamics of rock dehydration on multiple scales" has been successfully prolonged.
• Congratulations! M. H. Farshbaf Shaker begins his W2 Professorship of Mathematics in Engineering at HTW Berlin (University of Applied Sciences for Engineering and Economics Berlin) on 1 April 2022.
• SIAM Conference on Analysis of Partial Differential Equations, 14 -- 18 March 2022
  Minisymposium MS80 "Energy-Based Mathematical Methods and Thermodynamics" hosted by D. Peschka, M. Thomas, and M. Liero (RG 1).
• GAMM 2021, 91st Annual GAMM Meeting, Kassel, 15 -- 19 March 2021
  Section S11 ”Interfacial flows” organised by M. Scholle (Hochschule Heilbronn), D. Peschka
  Section S14 ”Applied analysis” organised by D. Knees (University of Kassel), M. Thomas
• 2nd Conference of CRC 1114 "Scaling Cascades in Complex Systems", 1 -- 3 March 2021
  Mini symposium "MSDI4: Modeling and analysis of geological fluid flows", organised by M. Thomas (WIAS Berlin) and T. John (FU Berlin)
  
• Closing Conference (23rd -- 25th February 2021) "Structures in Evolution: Theory and Applications" within the Thematic Einstein Semester, winter term 2020/21
• TES-Seminar on Energy-based Mathematical Methods and Thermodynamics within the Thematic Einstein Semester, winter term 2020/21
  
• "MA4M: Mathematical Analysis for Mechanics" (23 -- 25 November 2020) within the Thematic Einstein Semester, winter term 2020/21
• "Kick-off Conference" (26 -- 30 October 2020) within the Thematic Einstein Semester, winter term 2020/21
• "Student Compact Course" (12 -- 23 October 2020) within the Thematic Einstein Semester, winter term 2020/21
• Weierstrass Group 1 was evaluated on the basis of internal and external reviews in June 2020 and subsequently prolonged for another three years. Its first funding period was rated as a complete success.
• PDE 2019: Partial Differential Equations in Fluids and Solids, WIAS Berlin, 9 -- 13 September 2019
• A. Münch (University of Oxford) and D. Peschka organised the minisymposium ”Recent advances in understanding suspensions and granular media flow” at the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019) in Valencia, Spain, 15 -- 19 July 2019.
• From 1 June to 31 July 2019, L. Heltai, (SISSA, Trieste) was a visitor of the Weierstrass Group 1 and researched on the subject of FEM-based discretization methods.
• On 31 January and 1 February 2019, the kickoff meeting of the ECMI Special Interest Group ”Modelling, Simulation and Optimization in Electrical Engineering” took place at WIAS; the meeting was organised by N. Rotundo (RG1), P. Farrell (RG3) and D. Peschka.
• Analysis of Evolutionary and Complex Systems (ALEX2018), 24 -- 28 September 2018



Overview

Research goal of the group is the development of mathematical methods for systems with bulk-interface processes for the
• thermodynamically consistent modeling of bulk-interface interaction with dissipative, Hamiltonian, and coupled dynamics,
• theory for the existence and qualitative properties of solutions,
• derivation and justification of interfacial processes and coupling conditions.

The analytical results form the basis for the development of numerical algorithms supporting simulations for applications with bulk-interface interaction.

Currently, the following applications are treated within the group:
• dissipative processes in elastic solids with bulk-interface interaction (M. Thomas, S. Tornquist), such as e.g. damage, fracture, plastification,
• optoelectronic processes in semiconductor devices (M. Thomas, D. Peschka),
• viscous flows with free boundaries and contact lines (D. Peschka, M. H. Farshbaf Shaker, M. Thomas, A. Zafferi).




Mechanical stresses and progression of damage for a tension test with a notched bar using a BV-regularized damage model	Cross-section through a laser-device: The optically active germanium region displays the hole currents (colors) and the contour lines of the main mode (red lines)	P1 FEM solution of free boundary problem showing thin droplets sliding down an inclined plane