Abstract
Active matter is made of active particles which are able to convert energy from the environment into directed persistent motion. They can be modelled by stochastic differential equations subject to persistent noise. Run and tumble and active Brownian particle (ABP) models have been first proposed and still are considered closer to experimental observations but do not allow for much analytical progress. The Gaussian coloured noise (GCN) model, introduced as a time coarse-grained version of the ABP can be tuned to have the same variance of the active force as the ABP, which leads to a simpler analytical treatment. Finally, the UCNA can be considered as a Markovian reduction of the GCN. We give a simple derivation of the governing equation and analyse some of its recent applications ranging from the study of the swim pressure, its relation to the mobility, to the state induced by a moving object.
Highlights
The aim of this chapter is to provide an overview of some recent advances and open problems in the statistical description of active particles
We present a description of a model of N mutually interacting active particles in the presence of external fields and characterise its steady state behaviour
Within the UCNA, we show that it is possible to develop a statistical mechanical approach similar to the one employed in the study of equilibrium liquids and to obtain the explicit form of the many-particle distribution function by means of the multidimensional unified coloured noise approximation
Summary
The aim of this chapter is to provide an overview of some recent advances and open problems in the statistical description of active particles. Active matter is composed of systems which are able to convert energy from the environment into directed motion. Every element of an active matter system can be considered out of equilibrium, in contrast to boundary driven systems, like those subject to a concentration gradient which are locally equilibrated [1–3]. Active systems abound in nature, ranging from flock of birds, structure-forming cytoskeletons of cells to bacterial colonies, but can be man-made in a laboratory using biological building blocks or synthetic components. We shall discuss active systems whose behaviour is assimilable to that of some bacteria or self-propelled particles and whose constituents are driven by an external random force and constantly spend energy to move through a viscous medium
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