Research Group

CHeSs - Complex Heterogeneous Systems

Our general motivation is to develop a reliable, theoretical, and computational framework for transport and reactions in complex heterogeneous multiphase systems based on mathematical, physical, and thermodynamic principles. We combine rigorous, mathematical and physical modelling strategies with state-of-the-art methodologies such as variational and thermodynamic analysis, optimization, gradient flows, statistical mechanics, stochastic analysis, and novel computational approaches allowing for the reliable and efficient discretisation of complex heterogeneous multiphase systems.

Research Interests:
Interdisciplinary and Applied Mathematics

  • Analysis of PDEs: existence and uniqueness of weak solutions, energy and entropy laws, existence of blow-up solutions
  • Homogenization: asymptotic two-scale expansion, two-scale convergence, porous media approximations, error estimates, stochastic/random media, stochastic homogenization
  • Numerical Analysis & Computations: existence and uniqueness of discrete solutions, convergence of iterates of nonlinear problems, finite difference/element/volume methods, preservation of physical properties of solutions, discrete energy and entropy laws, stochastic mode reduction
  • Stochastic/Probability: stochastic mode reduction, emergence of randomness in seemingly deterministic systems, random media, stochastic homogenization, maximum entropy principle
  • Thermodynamics & Statistical Mechanics: many particle systems, complex heterogeneous multiphase systems, fluids
  • Electrochemistry & Materials Science: batteries, fuel cells, catalysts, intercalation crystals, electrolytes, metals, fluids
  • Quantum Information & Computing: understanding and developing basic ideas and principles for possible future quantum computations and simulations, quantum alogrithms and information theory