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Events
3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics

Black text on a green, yellow, orange gradient: ‘Conference - 3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics’

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

16.02.26 18.02.26

3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics

conference

16.02.26 18.02.26

3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics

Recent years have witnessed significant advancements in the derivation, analysis, and simulation of fluctuations within non-equilibrium systems, particularly through the utilization of reduced models governed by nonlinear stochastic partial differential equations (SPDEs), such as Dean-Kawasaki or Kardar-Parisi-Zhang (KPZ)/Burgers type equations. The applicability of these methods extends beyond physically motivated classical particle models to the realm of sociophysics and opinion dynamics. in these systems, where the population of interacting agents is large yet finite, fluctuation effects are non-negligible and play a governing role in system evolution.

Fluctuating Hydrodynamics (FHD) inherently sits at the intersection of stochastic analysis, numerical analysis, theoretical physics, and mathematical modeling. Consequently, the primary objective of this workshop is to cultivate an interdisciplinary environment that bridges these distinct fields. By convening researchers from diverse backgrounds, we aim to establish a common language, facilitate the exchange of methodological challenges, and catalyze new collaborative research trajectories.

This event is the third installment in the series initiated by the 2019 Berlin-Leipzig Workshop on Fluctuating Hydrodynamics. We aim to perpetuate this successful collaboration through alternating venues in Leipzig and Berlin.

This event is supported by TRR388, IRTG 2544, MATH+, CRC 1114, ERC FluCo.

WARNING: Please be wary if a company directly contacts you regarding payment for accommodation in Leipzig: this is fraud / phishing.

Registration closes on February 4.

Program

11:30 - 12:00	Welcome Coffee
12:00 - 12:45	Michela Ottobre Multiscale interacting particle systems In this talk we will consider SDE systems that are multiscale in time, in the regime of interest for stochastic averaging theory. When applying averaging methods a key assumption is that the dynamics for the fast scale is ergodic, i.e. that it has a unique equilibrium (invariant measure). If the fast scale has multiple invariant measures (which is a rather common occurrence in many scenarios, for example for McKean-Vlasov SDEs) then truly very little is known. In particular both averaging and homogenization theory are currently not very equipped to help tackle this problem. In this talk we will present situations in which this scenario occurs, with particular reference to multiscale interacting particle systems, summarise recent progress and point out gaps in current theory.
12:45 - 13:30	Lucio Galeati Fluctuation for mean field limits of particle systems driven by fBm Consider a system of $N$ particles, subject to a mean-field type pairwise interaction kernel $K$, each driven by an independent fractional Brownian motion (idiosyncratic noises). Previous works established that, for a large class of non-Lipschitz, possibly singular kernels, the associated McKean-Vlasov equation is well-posed, and the empirical measure converges to its law as $N\to\infty$, with rate of order $N^{-1/2}$ in suitable negative Sobolev norms. In this talk I will present results concerning the Gaussian fluctuations underlying this mean field convergence, validating the optimality of this rate; they are valid for both first order interactions and for kinetic systems. The proofs are based on the use of Girsanov transform and the method of U-statistics first introduced by Sznitman. Based on ongoing joint work with Avi Mayorcas (Bath) and Johanna Weinberger (Technion).
13:30 - 14:30	Lunch Break
14:30 - 15:15	Oana Lang Stochastic Stabilization of Fluid Dynamics Models We introduce a carefully designed stochastic perturbation whose diffusion coefficient depends super-linearly on the solution norm. This noise acts selectively, becoming active when the norm approaches blow-up, and its quadratic variation produces a stabilizing second-order effect. Under suitable structural assumptions on the drift, we prove that the associated SPDE admits global strong solutions almost surely in three regimes of initial regularity. In particular, the stochastic control extends the lifespan of solutions to infinite time, including in situations where no global deterministic solution is known. This is joint work with Dan Crisan, based on the paper Lang, O., Crisan, D. Global solutions for stochastically controlled fluid dynamics models. Stoch PDE: Anal Comp (2025).
15:15 - 16:00	Lorenzo Dello Schiavo Massive Particle Systems, Wasserstein Brownian Motions, and the Dean--Kawasaki SPDE Let W be a conservative, ergodic Markov diffusion on some arbitrary state space M, converging exponentially fast to equilibrium. We consider: (1) Systems of up to countably many massive particles in M, with finite total mass. Each particle is subject to an independent instance of the noise W, with volatility the inverse mass carried by the particle. We prove that the corresponding infinite system of SDEs has a unique solution, for every starting configuration and every distribution of the masses in the infinite simplex. (2) Solutions to the Dean--Kawasaki SPDE with singular drift, driven by the generator L of W. We prove that the equation may be given rigorous meaning on M, and that it has a unique `distributional’ solution. This extends Konarovskyi--Lehmann--von Renesse's `ill-posedness vs. triviality' to the case of infinitely many massive particles. (3) Diffusions with values in the space P of all probability measures on M, driven by the geometry induced by L. (4) In the case when M is a manifold, differential-geometric and metric-measure Brownian motions on P induced by the geometry of optimal transportation and reversible for a normalized completely random measure. We show that all these objects coincide. Based on arXiv:2411.14936
16:00 - 16:30	Coffee Break
16:30 - 17:15	Franca Hoffmann Nonlinear Stability for chemotactic clustering with discontinuous advection Bacterial chemotaxis describes the ability of single-cell organisms to respond to chemical signals. In the case where the bacterial response to these chemical signals is sharp, the corresponding chemotaxis model for bacterial self-organization exhibits a discontinuous advection speed. This is a key challenge for analysis. We present a perturbative approach, both from a macroscopic and a kinetic viewpoint, where the shape of the cellular profile is clearly separated from its global motion. As a result, we obtain exponential relaxation to equilibrium with an explicit rate. This is joint work with Vincent Calvez and Gianluca Favre.
17:15 - 18:00	Antonin Brossollet Informatic entropy production rate from density field theories A defining feature of non-equilibrium systems is the breakdown of time-reversal symmetry. Several approaches exist to quantify this breakdown, this talk will focus on computing the informatic entropy production rate, using the Onsager-Machlup path integral formulation, as a way to compute the probability of a given stochastic path. The approach presented here is applicable to a rather general set of stochastic equation, from the exact equation for microscopic densities (Dean-Kawasaki equation), to coarse-grained fluctuating hydrodynamics models with density-dependent mobility. We will show how a careful treatment of the so-called spurious drift, and proper time and space discretizations, we recover and generalize results obtained via other routes, such as ones from Doi-Peliti field theories. The quite direct computation presented in this talk indicates that it is possible to operate directly at the level of stochastic density consistently, which was not previously clear.

10:00 - 10:45	Daniel Heydecker The Porous Medium Equation: Multiscale Integrability in Large Deviations We consider a zero-range process $\eta^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12\Delta u^\alpha, \alpha>1$. As a main result we obtain a large deviation principle in any scaling regime of vanishing particle size $\chi_N\to 0$. The key challenge is to develop uniform integrability estimate on the nonlinearity $(\eta^N(x))^\alpha$ in a situation where neither pathwise regularity nor Dirichlet-form based regularity is readily available. We resolve this by introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales.
10:45 - 11:30	Julian Fischer A multilevel Monte Carlo method for the Dean-Kawasaki equation from fluctuating hydrodynamics The Dean-Kawasaki equation is one of the most basic models of fluctuating hydrodynamics; it provides an SPDE description of density fluctuations in systems of weakly interacting diffusing particles. While typically substantially faster to simulate than the particle system itself, the computation of statistical properties of fluctuations via the Dean-Kawasaki equation is still expensive, as it involves solving the SPDE for a large number of realizations of the noise. We propose and analyse a multilevel Monte Carlo scheme for the Dean-Kawasaki equation, enabling the computation of the statistics of density fluctuations at a reduced computational complexity.
11:30 - 12:00	Coffee Break
12:00 - 12:45	Johannes Zimmer Learning gradient flows via fluctuating hydrodynamics from particles The aim is to learn gradient flow evolution from underlying particle models. Specifically, we will discuss how the mobility and the evolution operator of suitable diffusive processes can be learned from particle data. As rigorous result, error estimates for the mobility associated with the simple exclusion process are presented. Methodologically, fluctuating hydrodynamics, seen as "thermodynamically correct" stochastic perturbation of a deterministic gradient flow, will play a central role.
12:45 - 13:30	Nicolas Dirr tba
13:30 - 14:30	Lunch Break
14:30 - 15:15	Rupert Klein MD -- FHD -- HD
15:15 - 16:00	André Schlichting Cluster Formation and coarsening in locally attractive interacting particle systems We investigate the behavior of weakly interacting diffusions on the one-dimensional torus subject to finite-range attractive interactions. In particular, we study the emergence of clusters and the subsequent coarsening of multi-cluster configurations into a single-cluster state. Depending on the parameter regime, this coarsening is driven by two competing mechanisms: (1) coalescence, whereby whole clusters move and merge in a manner analogous to coalescing Brownian motions; and (2) mass exchange, in which individual particles detach from one cluster and attach to another, leading to an effective transfer of mass between clusters. Based on an Eyring–Kramers-type asymptotic analysis, we propose a unified effective model capturing the interplay between these mechanisms and argue that the associated deterministic mean-field PDE exhibits dynamical metastability induced by mass exchange. In addition, we introduce a new variant of the strict Riesz rearrangement inequality to characterize the global minimizers of the free energy, showing that they are either spatially uniform or single-cluster states, i.e., symmetrically decreasing. Joint work with N. Gerber, R. Gvalani, M. Hairer, and G. Pavliotis.
16:00 - 16:30	Coffee Break
16:30 - 17:15	Bálint András Tóth Hyperbolic hydrodynamic limits for interacting particle systems with several conservation laws - survey and outlook The typical and much studied model of interacting particles with one single conservation law is the asymmetric simple exclusion which leads, under Eulerian scaling, to the Burgers equation as hydrodynamic limit. This one, and similar settings have been fully understood since the 1990-s. When there are more than one conserved observables (like, e.g., several types of interacting particles, or particle number and a kind of momentum) the limit and the limiting procedure are much more complex. Hyperbolic systems of conservation laws arise and the status of the limiting procedure is less understood. I will survey old work in this context (joint with Benedek Valkó and József Fritz) and flash up some recent projects in a very early stage (joint with Balázs Maga).
19:00 -	Dinner

10:00 - 10:45	Marco De Corato Finite element formulations for nonequilibrium transport problems using fluctuating hydrodynamics Nonequilibrium transport at micro- and mesoscopic scales plays a central role in many modern engineering systems, making accurate modeling of these processes essential. At such small scales, thermal fluctuations can significantly influence transport behavior and thus their effect must be taken into account by transport models. Fluctuating hydrodynamics provides a systematic framework for incorporating thermal noise into the conservation laws of mass, momentum, and energy, leading to stochastic transport equations. In this seminar, we discuss engineering applications where this modeling framework is especially relevant, and we present finite element formulations for nonequilibrium transport based on fluctuating hydrodynamics. In particular, we focus on how to address the challenge of solving transport problems accurately when the solution has both long-ranged and short-ranged (delta-correlated) correlations, a common feature of nonequilibrium transport phenomena in engineering contexts. To illustrate this, we analyze the solution of a nonhomogeneous Fourier equation and demonstrate that decoupling local and non-local fluctuations is essential for achieving convergence. Finally, as a practical application, we present a finite element study of the rotational dynamics of an active colloid in a complex fluid. These, simulations are based on an advection-diffusion model with thermal fluctuations are conducted in a two-dimensional domain. The results indicate that this numerical approach successfully captures the key features observed in experimental studies of active colloids in polymer solutions.
10:45 - 11:30	Vitalii Konarovskyi A quantitative central limit theorem for the simple symmetric exclusion process We prove a quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a multidimensional discrete torus in local equilibrium. Our main result establishes the optimal rate of convergence of the density fluctuation field to the generalized Ornstein–Uhlenbeck process. The proof is based on a detailed comparison of the generators of the SSEP fluctuation field and the limiting Ornstein–Uhlenbeck dynamics. The main ingredients are a careful control of the resulting error terms, regularity properties of the Ornstein–Uhlenbeck semigroup, and an infinite-dimensional Berry–Esseen bound for the initial particle fluctuations. This is joint work with Benjamin Gess.
11:30 - 12:00	Coffee Break

3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics

3rd Berlin - Leipzig Workshop on Fluctuating Hydrodynamics

Program

Participants

Antonin Brossollet

Javier Castro

Xiaopeng Cheng

Nelly Coulonges

Ana Damnjanović

Marco De Corato

Guilherme de Lima Feltes

Lorenzo Dello Schiavo

Nicolas Dirr

Ana Djurdjevac

Bernhard Eisvogel

Julian Fischer

Lucio Galeati

Nicolai Gerber

Benjamin Gess

Nicholas Graham

Daniel Heydecker

Franca Hoffmann

Shanshan Hu

Dave Jacobi

Rupert Klein

Vitalii Konarovskyi

Sefika Kuzgun

Oana Lang

Francis Lörler

Adrian Martini

Abdulwahab Mohamed

Felix Otto

Michela Ottobre

Matteo Palmieri

Nicolas Perkowski

Shyam Popat

Max Sauerbrey

André Schlichting

Rhys Steele

Ran Tao

Bálint András Tóth

Sanjay Verma

Max von Renesse

Zhengyan Wu

Johannes Zimmer

Organizers

Ana Djurdjevac

Benjamin Gess

Nicolas Perkowski

Max von Renesse

Administrative Contact

Katja Heid