Computational models for active matter

TL;DR

This review discusses various computational models for active matter across scales, highlighting their methods, challenges, and the importance of choosing appropriate levels of detail for understanding complex biological and artificial systems.

Contribution

It provides a comprehensive comparison of modeling approaches and numerical techniques for active matter, addressing current challenges and future directions.

Findings

Microscopic models influence collective behaviors significantly.

Coarse-grained and continuum models complement microscopic descriptions.

Advances are needed for real-world applications in complex media.

Abstract

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 filaments over artificial and biological swimmers on microscopic to groups of animals on macroscopic scales---mainly originate from their out-of-equilibrium character, multiscale nature, nonlinearity, and multibody interactions. In the present review, various modeling approaches and numerical techniques are addressed, compared, and differentiated to illuminate the innovations and current challenges in understanding active matter. The complexity increases from minimal microscopic models of dry active matter toward microscopic models of active matter in fluids. Complementary, coarse-grained descriptions and continuum models are elucidated. Microscopic details are often relevant and strongly affect collective behaviors, which implies that the selection of a proper level of modeling is a delicate choice, with simple models emphasizing universal properties and detailed models capturing specific features. Finally, current approaches to further advance the existing models and techniques to cope with real-world applications, such as complex media and biological environments, are discussed.