64 citations · 370 across the 28 of their papers we have counts for
35 papers
On decompositions of non-reversible processes
M. H. Duong, J. Zimmer
Markov chains are studied in a formulation involving forces and fluxes. First, the iso-dissipation force recently introduced in the physics literature is investigated; we show that…
Second-order fast-slow dynamics of non-ergodic Hamiltonian systems: Thermodynamic interpretation and simulation
Matthias Klar, Karsten Matthies, Celia Reina +1
A class of fast-slow Hamiltonian systems with potential describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varep…
Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system
Matthias Klar, Karsten Matthies, Johannes Zimmer
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical tec…
Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions
Federico Cornalba, Tony Shardlow, Johannes Zimmer
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\ma…
Orthogonality of Fluxes in General Nonlinear Reaction Networks
Johannes Zimmer, D. R. Michiel Renger
We consider the chemical reaction networks and study currents in these systems. Reviewing recent decomposition of rate functionals from large deviation theory for Markov processes,…
A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation
Jin Feng, Toshio Mikami, Johannes Zimmer
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying u…
From weakly interacting particles to a regularised Dean--Kawasaki model
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative…
How to find the evolution operator of dissipative PDEs from particle fluctuations?
Xiaoguai Li, Nicolas Dirr, Peter Embacher +2
Dissipative processes abound in most areas of sciences and can often be abstractly written as , which is a gradient flow of the entropy . Although…
A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits
Marcus Kaiser, Robert L. Jack, Johannes Zimmer
We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range process…
A regularised Dean-Kawasaki model: derivation and analysis
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The Dean-Kawasaki model consists of a nonlinear stochastic partial differential equation featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, a…
Effective Hamiltonian Dynamics via the Maupertuis Principle
Hartmut Schwetlick, Daniel C. Sutton, Johannes Zimmer
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in -dimensional space. As alternative to the established approach of averaging Ha…
Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics
Robert L. Jack, Marcus Kaiser, Johannes Zimmer
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider…
Computing diffusivities from particle models out of equilibrium
Peter Embacher, Nicolas Dirr, Johannes Zimmer +1
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy req…
Canonical structure and orthogonality of forces and currents in irreversible Markov chains
Marcus Kaiser, Robert L. Jack, Johannes Zimmer
We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, a…
Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance
Marcus Kaiser, Robert L. Jack, Johannes Zimmer
We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limi…
Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles
Nicolas Dirr, Marios G. Stamatakis, Johannes Zimmer
Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a d…
A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
D. Hömberg, F. S. Patacchini, K. Sakamoto +1
The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in mul…
Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential
Boris Buffoni, Hartmut Schwetlick, Johannes Zimmer
The Frenkel-Kontorova model for dislocation dynamics from 1938 is given by a chain of atoms, where neighbouring atoms interact through a linear spring and are exposed to a smooth p…
Minimising movements for oscillating energies: the critical regime
Nadia Ansini, Andrea Braides, Johannes Zimmer
Minimising movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimising movement scheme involves a temp…
Entropic and gradient flow formulations for nonlinear diffusion
Nicolas Dirr, Marios Stamatakis, Johannes Zimmer
Nonlinear diffusion is considered for a class of nonlinearities . It is shown that for suitable choices of , an associated Lyapunov functional can be…
Travelling waves for a Frenkel-Kontorova chain
Boris Buffoni, Hartmut Schwetlick, Johannes Zimmer
In this article, the Frenkel-Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spin…
Entropy production and the geometry of dissipative evolution equations
Celia Reina, Johannes Zimmer
Purely dissipative evolution equations are often cast as gradient flow structures, , where the variable of interest evolv…
A convergent string method: Existence and approximation for the Hamiltonian boundary-value problem
Hartmut Schwetlick, Johannes Zimmer
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is,…
Stability of traveling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects
Shangjiang Guo, Johannes Zimmer
This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green…