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

Head:
Marita Thomas

Coworkers:
Dirk Peschka, Sven Tornquist, Andrea Zafferi

Secretary:
Andrea Eismann


Upcoming Events:

• Mathematical Models for Biological Multiscale Systems, 12 -- 14 September 2022

• 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.

Past Events:
• 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 (WIAS Berlin)
  Section S14 ”Applied analysis” organised by D. Knees (University of Kassel), M. Thomas (WIAS Berlin)
• 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
• PDE 2019: Partial Differential Equations in Fluids and Solids, WIAS Berlin, 9th -- 13rd September, 2019
• A. Münch (University of Oxford) and D. Peschka (Weierstrass Group) 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, 15th -- 19th July, 2019.
• From 1 June to 31 July, 2019, L. Heltai, (SISSA, Trieste) was a visitor of the Weierstrass Group 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