Integral Equation Theory of Continuum Percolation

• Applicant: Professorin Dr. Tanja Schilling
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2021 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 457534544

• Final Report Year: 2024

Final Report Abstract

The critical exponents which govern the percolation transition are universal. In contrast, the percolation threshold depends on specific system parameters. The central result of our project is a universal method to compute percolation thresholds, which can be applied to any system. We have used this method to study a range of discrete and continuous percolation problems. In particular, we have quantified the effect of particle shape and polydispersity on the percolation transition in colloidal suspensions. Further, as a technical application, we have analyzed the conductivity of composites made from Carbon Black dispersed in an elastomer.

Publications

• „Percolation: connecting the dots“, PhD thesis (University of Freiburg, 2022)
  F. Coupette
  
• Anomalous Underscreening in the Restricted Primitive Model. Physical Review Letters, 130(10).
  Härtel, Andreas; Bültmann, Moritz & Coupette, Fabian
  
• Polydispersity in percolation
  F. Coupette & T. Schilling
  
• Universal approach to critical percolation
  F. Coupette & T. Schilling
  
• Flowinduced anisotropy in a carbon black-filled silicone elastomer: electromechanical properties and structure
  B. Zimmer, N. Bart-Jan, F. Schaefer, F. Coupette, V. Tänzel, T. Schilling & T. Kraus