Johannes Zimmer
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View article: Well-posedness for Dean–Kawasaki models of Vlasov–Fokker–Planck type
Well-posedness for Dean–Kawasaki models of Vlasov–Fokker–Planck type Open
We consider systems of interacting particles which are described by a second-order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
View article: Deriving a GENERIC system from a Hamiltonian system
Deriving a GENERIC system from a Hamiltonian system Open
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Ha…
View article: On the generalized Langevin equation and the Mori projection operator technique
On the generalized Langevin equation and the Mori projection operator technique Open
In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the sp…
View article: Hydrodynamic Limits and Non-equilibrium Fluctuations for the Symmetric Inclusion Process with Long Jumps
Hydrodynamic Limits and Non-equilibrium Fluctuations for the Symmetric Inclusion Process with Long Jumps Open
We consider a d –dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. Wi…
View article: Interprofessional collaboration in medical rehabilitation: how can it succeed? - Results from employee's perspective
Interprofessional collaboration in medical rehabilitation: how can it succeed? - Results from employee's perspective Open
Background Given the holistic biopsychosocial treatment approach in rehabilitation, interprofessional collaboration (IPC) is essential for high-quality patient care. However, IPC regularly encounters challenges in everyday clinical routine…
View article: On the cryo-molding process and subsequent forming processes of biopolymers with low glass transition temperature
On the cryo-molding process and subsequent forming processes of biopolymers with low glass transition temperature Open
Bio-based as well as biodegradable polymers are increasingly finding their way into applications such as food packaging. Here, certain biopolymers with a high degree of crystallinity may be of interest due to their superior barrier propert…
View article: Well-Posedness for Dean-Kawasaki Models of Vlasov-Fokker-Planck Type
Well-Posedness for Dean-Kawasaki Models of Vlasov-Fokker-Planck Type Open
We consider systems of interacting particles which are described by a second order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
View article: Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps
Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps Open
We consider a d-dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. Wit…
View article: Deriving a GENERIC system from a Hamiltonian system
Deriving a GENERIC system from a Hamiltonian system Open
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Ha…
View article: Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics
Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics Open
Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recentl…
View article: On decompositions of non-reversible processes
On decompositions of non-reversible processes Open
We consider fluxes and forces in Markov chains. In physics, the concept of so-called iso-surfaces has recently been introduced. In generic cases, there are infinitely many associated iso-dissipation forces. We first show that this is due t…
View article: Second-order asymptotic expansion and thermodynamic interpretation of a fast–slow Hamiltonian system
Second-order asymptotic expansion and thermodynamic interpretation of a fast–slow Hamiltonian system Open
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast–slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging met…
View article: Effects of Short-Term Dynamic Balance Training on Postural Stability in School-Aged Football Players and Gymnasts
Effects of Short-Term Dynamic Balance Training on Postural Stability in School-Aged Football Players and Gymnasts Open
Static and dynamic balance abilities enable simple and complex movements and are determinants of top athletic performance. Balance abilities and their proficiency differ fundamentally with respect to age, gender, type of balance interventi…
View article: Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system
Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system Open
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging met…
View article: Emergence of a nonconstant entropy for a fast-slow Hamiltonian system in its second-order asymptotic expansion
Emergence of a nonconstant entropy for a fast-slow Hamiltonian system in its second-order asymptotic expansion Open
A system of ordinary differential equations describing the interaction of a fast and a slow particle is studied, where the interaction potential $U_\epsilon$ depends on a small parameter $\epsilon$. The parameter $\epsilon$ can be interpre…
View article: Orthogonality of fluxes in general nonlinear reaction networks
Orthogonality of fluxes in general nonlinear reaction networks Open
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, we adapt these results for reaction networks. In particula…
View article: Well-posedness for a regularised inertial Dean-Kawasaki model for\n slender particles in several space dimensions
Well-posedness for a regularised inertial Dean-Kawasaki model for\n slender particles in several space dimensions Open
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly\ninteracting inertial particles of finite volume, is proposed and analysed in\nany finite dimension $d\\in\\mathbb{N}$. It is a regularised and inertial version\nof …
View article: From weakly interacting particles to a regularised Dean–Kawasaki model
From weakly interacting particles to a regularised Dean–Kawasaki model Open
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 noise in divergence form. We derive a regularised Dean–Kaw…
View article: Orthogonality of Fluxes in General Nonlinear Reaction Networks
Orthogonality of Fluxes in General Nonlinear Reaction Networks Open
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, we adapt these results for reaction networks. In particula…
View article: Code for "Harnessing fluctuations to discover dissipative evolution equations"
Code for "Harnessing fluctuations to discover dissipative evolution equations" Open
This dataset contains the source codes for for the paper "Harnessing fluctuations to discover dissipative evolution equations". The code computes the macroscopic evolution operator associated with many-particle systems (hydrodynamic limit)…
View article: Effective Hamiltonian dynamics via the Maupertuis principle
Effective Hamiltonian dynamics via the Maupertuis principle Open
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in $\dim$-dimensional space. As alternative to the established approach of averaging Hamiltonian dynamics by reformulating the system as Hamilton-…
View article: A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation
A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation Open
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 uniqueness) for this class. In the second part, we establish…
View article: A Regularized Dean--Kawasaki Model: Derivation and Analysis
A Regularized Dean--Kawasaki Model: Derivation and Analysis Open
The Dean--Kawasaki model consists of a nonlinear stochastic partial differential equation featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, driven by space-time white noise; this equation describes t…
View article: A variational structure for interacting particle systems and their hydrodynamic scaling limits
A variational structure for interacting particle systems and their hydrodynamic scaling limits Open
We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functiona…
View article: Minimizing movements for oscillating energies: the critical regime
Minimizing movements for oscillating energies: the critical regime Open
Minimizing movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimizing movement scheme involves a temporal parameter τ and a spatial parameter ε , with τ describ…
View article: How to discover dissipative PDEs from particles? Particle fluctuations determine evolution operator
How to discover dissipative PDEs from particles? Particle fluctuations determine evolution operator Open
Dissipative processes abound in most areas of sciences and can often be abstractly written as $\partial_t z = K(z) \delta S(z)/\delta z$, which is a gradient flow of the entropy $S$. Although various techniques have been developed to compu…