PMID- 25768454
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20150625
LR  - 20150315
IS  - 1550-2376 (Electronic)
IS  - 1539-3755 (Linking)
VI  - 91
IP  - 2
DP  - 2015 Feb
TI  - Active matter beyond mean-field: ring-kinetic theory for self-propelled 
      particles.
PG  - 022103
AB  - Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field 
      kinetic theory fails to describe collective motion in soft active colloids and 
      that correlations must not be neglected. Correlation effects are also expected to 
      be essential in systems of biofilaments driven by molecular motors and in swarms 
      of midges. To obtain correlations in an active matter system from first 
      principles, we derive a ring-kinetic theory for Vicsek-style models of 
      self-propelled agents from the exact N-particle evolution equation in phase 
      space. The theory goes beyond mean-field and does not rely on Boltzmann's 
      approximation of molecular chaos. It can handle precollisional correlations and 
      cluster formation, which are both important to understand the phase transition to 
      collective motion. We propose a diagrammatic technique to perform a small-density 
      expansion of the collision operator and derive the first two equations of the 
      Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented 
      that numerically solves the evolution equation for the two-particle correlations 
      on a lattice. Agent-based simulations are performed and informative quantities 
      such as orientational and density correlation functions are compared with those 
      obtained by ring-kinetic theory. Excellent quantitative agreement between 
      simulations and theory is found at not-too-small noises and mean free paths. This 
      shows that there are parameter ranges in Vicsek-like models where the correlated 
      closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate 
      the dependence of the orientational correlations on distance in the disordered 
      phase and find that it seems to be consistent with a power law with an exponent 
      around -1.8, followed by an exponential decay. General limitations of the kinetic 
      theory and its numerical solution are discussed.
FAU - Chou, Yen-Liang
AU  - Chou YL
AD  - Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 
      01187 Dresden, Germany.
FAU - Ihle, Thomas
AU  - Ihle T
AD  - Max Planck Institute for the Physics of Complex Systems, Nothnitzer Strasse 38, 
      01187 Dresden, Germany.
AD  - Department of Physics, North Dakota State University, Fargo, North Dakota 
      58108-6050, USA.
LA  - eng
PT  - Journal Article
DEP - 20150205
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2015/03/15 06:00
MHDA- 2015/03/15 06:01
CRDT- 2015/03/14 06:00
PHST- 2014/09/24 00:00 [received]
PHST- 2015/03/14 06:00 [entrez]
PHST- 2015/03/15 06:00 [pubmed]
PHST- 2015/03/15 06:01 [medline]
AID - 10.1103/PhysRevE.91.022103 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):022103. doi: 
      10.1103/PhysRevE.91.022103. Epub 2015 Feb 5.