Related papers: Learning hydrodynamic equations for active matter …
We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse-graining in both space and time to bridge microscopic particle dynamics with macroscopic…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
In the quest to understand large-scale collective behavior in active matter, the complexity of hydrodynamic and phoretic interactions remains a fundamental challenge. To date, most works either focus on minimal models that do not (fully)…
We present a principled data-driven strategy for learning deterministic hydrodynamic models directly from stochastic non-equilibrium active particle trajectories. We apply our method to learning a hydrodynamic model for the propagating…
Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such hydrodynamic parameters are difficult to derive from microscopics. Seldom is this challenge more…
Biological systems are non-linear, include unobserved variables and the physical principles that govern their dynamics are partly unknown. This makes the characterization of their behavior very challenging. Notably, their activity occurs on…
In this review we discuss the recent progress in the simulation of soft active matter systems and in particular the hydrodynamics of microswimmers using the method of multiparticle collision dynamics, which solves the hydrodynamic flows…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from…
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic…
Some nonequilibrium systems exhibit anomalous suppression of the large-scale density fluctuations, so-called hyperuniformity. Recently, hyperuniformity was found numerically in a simple model of chiral active fluids [Q.-L. Lei et al., Sci.…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this work, we show a novel approach where the latest version of the…
We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on…
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology,…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…