## Johannes Zimmer University of Bath

# Johannes Zimmer

## Profile

A central research interest of mine is the development of multi-scale methods for dynamic problems.

In particular, I am interested in the derivation of macroscopic descriptions for processes out of equilibrium. This includes entropy-driven processes, such as the description of diffusive processes as a gradient flow of an entropy, energy-driven processes and processes which combine energetic and entropic effects. One aspect of my work concerns the derivation of such thermodynamic descriptions from micro- or mesoscopic models.

Methodologically, this scale-bridging combines tools from mathematical analysis (partial differential equations, calculus of variations) with probabilistic ones. I enjoy interdisciplinary research with physicists, material scientists and researchers in mechanics.

### Johannes Zimmer University of Bath, Publications

Guo, S. and Zimmer, J., 2017. Forthcoming. Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects.*Bulletin of the Malaysian Mathematical Sciences Society*

Dirr, N., Stamatakis, M. and Zimmer, J., 2016. Entropic and gradient flow formulations for nonlinear diffusion.*Journal of Mathematical Physics*, 57 (8), 081505.

Zimmer, G. and Reina, C., 2015. Entropy production and the geometry of dissipative evolution equations.*Physical Review E (PRE)*, 92 (5), 052117.

Guo, S. and Zimmer, J., 2015. Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects.*Nonlinearity*, 28 (2), pp. 463-492.

Schwetlick, H., Sutton, D. C. and Zimmer, J., 2015. On the Γ-limit for a non-uniformly bounded sequence of two-phase metric functionals.*Discrete and Continuous Dynamical Systems – Series A*, 35 (1), pp. 411-426. ………..