Related papers: From discrete elements to continuum fields: Extens…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain…
The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. We investigate the continuum limit of an unconfined, dense…
In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic…
In this contribution, we introduce a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes. It relies on the stationary action principle and interface geometric variables. The main ideas…
We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…
Diffusion models, and their generalization, flow matching, have had a remarkable impact on the field of media generation. Here, the conventional approach is to learn the complex mapping from a simple source distribution of Gaussian noise to…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…
These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a…
This paper presents a rigorous derivation of equations to evaluate the macroscopic stress tensor, the couple stress tensor, and the flux vector equivalent to underlying microscopic fields in continuous and discrete heterogeneous systems…
We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations…
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress $P$ in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated…
The purpose of this paper is to give an overview in the realm of numerical computations of polydispersed turbulent two-phase flows, using a mean-field/PDF approach. In this approach, the numerical solution is obtained by resorting to a…