Field-Theory of Active Chiral Hard Disks: A First-Principles Approach to Steric Interactions
Journal of Physics A: Mathematical and Theoretical(2023)
摘要
A first-principles approach for active chiral hard disks is presented, that
explicitly accounts for steric interactions on the two-body level. We derive an
effective one-body equation for the joint probability distribution of ositions
and angles of the particles. By projecting onto the angular modes, we write a
hierarchy for the lowest hydrodynamic modes, i.e. particle density,
polarisation, and nematic tensor. Introducing dimensionless variables in the
equations, we highlight the assumptions, which - though inherent - are often
included implicit in typical closure schemes of the hierarchy. By considering
different regimes of the Péclet number, the well-known models in active
matter can be obtained through our consideration. Explicitly, we derive an
effective diffusive description and by going to higher orders in the closure
scheme, we show that this first-principles approach results in the recently
introduced Active Model B +, a natural extension of the Model B for active
processes. Remarkably, here we find that chirality can change the sign of the
phenomenological activity parameters.
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