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Research interests

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.

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Gradient Flow Mathematics
Phase transitions Engineering & Materials Science
Hydrodynamic Limit Mathematics
Traveling Wave Mathematics
Large Deviation Principle Mathematics
Phase Transition Mathematics
gradients Physics & Astronomy
Lattice Model Mathematics

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Projects 2004 2021

Wolfson Merit Award - Nonequilibrium Particles & PDE

Zimmer, G.

1/05/1630/04/21

Project: Research council

Controlling Nucleation & Growth to Deliver Novel Materials Functionality

Zimmer, G.

Project: Research-related fundingInternally Funded Research

T shape
molecules
complex systems
valleys
atoms

MIDAS

Zimmer, G. & Ansini, N.

1/08/1331/01/15

Project: EU Commission

expertise
applicant
physics
biology
chemistry

Research Output 2003 2018

2 Citations
Open Access
Fluctuations (theory)
Rate Function
Markov chains
orthogonality
Orthogonality

Computing diffusivities from particle models out of equilibrium

Embacher, P., Dirr, N., Zimmer, J. & Reina, C. Apr 2018 In : Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 474, 2212, 20170694

Research output: Contribution to journalArticle

Open Access
Particle System
Diffusivity
Zero-range Process
Fluctuations
Exclusion Process

Eective Hamiltonian Dynamics via the Maupertuis Principle

Schwetlick, H., Sutton, D. & Zimmer, J. 31 Jul 2018 (Accepted/In press) In : Discrete and Continuous Dynamical Systems Series S.

Research output: Contribution to journalArticle

Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects

Guo, S. & Zimmer, J. 1 Apr 2018 In : Bulletin of the Malaysian Mathematical Sciences Society. 41, 2, p. 919-943 25 p.

Research output: Contribution to journalArticle

Open Access
File
Nonlocal Delay
Nonlocal Diffusion
Traveling Wavefronts
Nonlocal Equations
Diffusion equation

Datasets

In conversation with Edward Fraenkel

Zimmer, G. (Creator), University of Bath, 20 Mar 2018

Dataset

Codes for "Computing diffusivities from particle models out of equilibrium"

Zimmer, G. (Creator), Embacher, P. (Creator), Dirr, N. (Creator), Reina, C. (Creator), University of Bath, 11 Apr 2018

Dataset