Johannes Zimmer University of Bath
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. ………..