complexity of the large-scale structures observed in systems of repulsive self-propelled particles.'
author:
- 'Aitor Martín-Gómez'
- Demian Levis
- 'Albert Díaz-Guilera'
- Ignacio Pagonabarraga
bibliography:
- 'AITOR.bib'
title: Collective motion of Active Brownian Particles with polar alignment
---

Introduction {#sec:Introduction}
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Flocks of birds, bacterial colonies, synthetic diffusio-phoretic colloidal suspensions or dense assemblies of actin filaments are all examples of active matter systems, where the individual constituents, or ’active particles’, pump energy from the environment to convert it into directed motion. In the presence of interactions, this ability to self-propel leads to interesting out-of-equilibrium many-body phenomena, such as the emergence of collective motion (or flocking), observed in populations of active particles (both in living and man-made systems) across a broad range of scales: from vertebrates down to motile bacteria or intracellular filaments driven by molecular motors [@VicsekRev; @BechingerRev]. From a general, fundamental perspective, the emergence of collective motion is understood as arising from the presence of velocity-alignment interactions between self-propelled ’point-like’ agents, as put forward by the celebrated Vicsek model [@Vicsek1995] and its fore-coming refinements and extensions [@VicsekRev; @Toner1995; @Toner2005; @Ramaswamy2010]. A salient feature of this non-equilibrium symmetry breaking phase transition, is the spontaneous formation of large-scale structures in 