Research Group
CHeSs  Complex Heterogeneous Systems
Group
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 stateoftheart 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 blowup solutions

Homogenization: asymptotic twoscale expansion, twoscale 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