Active gels on surfaces

• Applicants: Professor Dr. Ivo Sbalzarini; Professor Dr. Axel Voigt
• Subject Area: Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 417223351

• Final Report Year: 2022

Final Report Abstract

Active polar and nematic gels on surfaces embody a tight coupling between topology, geometry, deformation, and hydrodynamics. This coupling is hypothesized to be essential for morphogenetic processes in living systems. In this project, we have derived the model equations by two different approaches: a thin-film limit of established 3D active gel models, as well as intrinsic balance laws. The correct coupling between surface deformation in the normal direction and internal fluid properties, such as orientational and flow fields, is thereby of particular importance. The issue of how to transport vector (director) fields and tensor (Q-tensor) fields on evolving surfaces has also been addressed. Numerically, we have tackled the problem by surface finite-element approaches. Due to the complexity of the equations, only parts could be addressed analytically in cooperation with Reusken/Voigt. Therefore, we have provided validation by qualitative comparison with experimental results. Close cooperations exist with Bartels/Neukamm for modeling liquid crystals, and their coupling with surface shape changes. In addition, continuous particle methods have been considered, which will be further developed to be applicable to these problems and the proposed specific biological application.

Publications

• Hydrodynamic interactions in polar liquid crystals on evolving surfaces. Physical Review Fluids, 4(4).
  Nitschke, Ingo; Reuther, Sebastian & Voigt, Axel
  
• Liquid crystals on deformable surfaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2241).
  Nitschke, Ingo; Reuther, Sebastian & Voigt, Axel
  
• Defects in Active Nematics – Algorithms for Identification and Tracking. Computational Methods in Applied Mathematics, 21(3), 683-692.
  Wenzel, Dennis; Nestler, Michael; Reuther, Sebastian; Simon, Maximilian & Voigt, Axel
  
• Multiphase field models for collective cell migration. Physical Review E, 104(5).
  Wenzel, D. & Voigt, A.
  
• Active Nematodynamics on Curved Surfaces – The Influence of Geometric Forces on Motion Patterns of Topological Defects. Communications in Computational Physics, 31(3), 947-965.
  Nestler, Michael & Voigt, Axel
  
• Deformable active nematic particles and emerging edge currents in circular confinements. The European Physical Journal E, 45(2).
  Krause, Veit & Voigt, Axel
  
• Effects of curvature on epithelial tissue —Coordinated rotational movement and other spatiotemporal arrangements. Europhysics Letters, 138(6), 67002.
  Happel, L.; Wenzel, D. & Voigt, A.
  
• Impact of contact inhibition on collective cell migration and proliferation. Physical Review E, 105(3).
  Jain, H. P.; Wenzel, D. & Voigt, A.
  
• Observer-invariant time derivatives on moving surfaces. Journal of Geometry and Physics, 173(c(2022, 3)), 104428.
  Nitschke, Ingo & Voigt, Axel
  
• A Meshfree Collocation Scheme for Surface Differential Operators on Point Clouds. Journal of Scientific Computing, 96(3).
  Singh, Abhinav; Foggia, Alejandra; Incardona, Pietro & Sbalzarini, Ivo F.