Related papers: Coarse-graining two-dimensional turbulence via dyn…

Constructing atom-resolved states from low-resolution data is of practical importance in many areas of science and engineering. This problem is addressed in this paper in the context of multiscale factorization methods for molecular…

Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to…

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Starting from the stochastic thermodynamics description of two coupled underdamped Brownian particles, we showcase and compare three different coarse-graining schemes leading to an effective thermodynamic description for the first of the…

Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically…

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli using a coarse-graining procedure. We study this process for a simple…

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…

Molecular discovery within the vast chemical space remains a significant challenge due to the immense number of possible molecules and limited scalability of conventional screening methods. To approach chemical space exploration more…

The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from…

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster…

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas…

We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a quasi-equilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the…

We investigate the direct enstrophy cascade of two-dimensional decaying turbulence in a flowing soap film channel. We use a coarse-graining approach that allows us to resolve the nonlinear dynamics and scale-coupling simultaneously in space…

This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…

We study the sub-grid scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multi-dimensional upwind scheme for the vorticity transport equations and establish its properties…

We consider the modeling of the effect of unresolved scales, for two-dimensional and geophysical flows. We first show that the effect of small scales on a coarse-grained field, can be approximated at leading order, by the effect of the…

Volume conserving surface (VCS) models without deposition and evaporation, as well as ideal molecular-beam epitaxy models, are prototypes to study the symmetries of conserved dynamics. In this work we study two similar VCS models with…

This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…

We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is non-local both in space and time, i.e. the closure terms are…