Computational models for active matter

Abstract

Active matter, which ranges from molecular motors to groups of animals, exists at different length scales and timescales, and various computational models have been proposed to describe and predict its behaviour. The diversity of the methods and the challenges in modelling active matter primarily originate from the out-of-equilibrium character, lack of detailed balance and of time-reversal symmetry, multiscale nature, nonlinearity and multibody interactions. Models exist for both dry active matter and active matter in fluids, and can be agent-based or continuum-level descriptions. They can be generic, emphasizing universal features, or detailed, capturing specific features. We compare various modelling approaches and numerical techniques to illuminate the innovations and challenges in understanding active matter.

Key points

  • Active matter exhibits a wide range of emergent non-equilibrium phenomena, theoretical studies of which often require computer simulations.

  • Active matter encompasses synthetic and living systems, including active gels and the cytoskeleton, cells and tissues, nanorobots and microrobots, synthetic and biological microswimmers, and animal herds.

  • Active matter is characterized by out-of-equilibrium behaviour, nonlinearity, multibody interactions, lack of detailed balance or time-reversal symmetry and, generically, absence of an equation of state.

  • The wide spectrum of systems and phenomena requires a multitude of models and simulation techniques, from agent-based to continuum-level approaches, and combinations thereof.

  • Active agents can interact in many ways, such as volume exclusion, contact attraction, visual information and hydrodynamics. Hydrodynamic interactions are ubiquitous for self-propelled particles in an aqueous environment, which implies a classification into dry and wet active matter.

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Fig. 1: Modelling active matter.
Fig. 2: Models of dry active matter.

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Acknowledgements

M.R.S., A.W. and H.R. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) within SFB 1027 (A3, A7). R.G.W. and G.G. acknowledge funding by DFG within the priority programme SPP 1726 “Microswimmers — from Single Particle Motion to Collective Behaviour”.

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All authors contributed to all aspects of manuscript preparation, revision and editing.

Correspondence to M. Reza Shaebani or Gerhard Gompper or Heiko Rieger.

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Shaebani, M.R., Wysocki, A., Winkler, R.G. et al. Computational models for active matter. Nat Rev Phys (2020). https://doi.org/10.1038/s42254-020-0152-1

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