@article{ISI:000230224600005,
 abstract = {We review the past decade's theoretical and experimental studies of
flocking: the collective, coherent motion of large numbers of
self-propelled ``particles″ (usually, but not always, living
organisms). Like equilibrium condensed matter systems, flocks exhibit
distinct ``phases″ which can be classified by their symmetries.
Indeed, the phases that have been theoretically studied to date each
have exactly the same symmetry as some equilibrium phase (e.g.,
ferromagnets, liquid crystals). This analogy with equilibrium phases of
matter continues in that all flocks in the same phase, regardless of
their constituents, have the same ``hydrodynamic″-that is,
long-length scale and long-time behavior, just as, e.g., all equilibrium
fluids are described by the Navier-Stokes equations. Flocks are
nonetheless very different from equilibrium systems, due to the
intrinsically nonequilibrium self-propulsion of the constituent
``organisms.″ This difference between flocks and equilibrium systems
is most dramatically manifested in the ability of the simplest phase of
a flock, in which all the organisms are, on average moving in the same
direction (we call this a ``ferromagnetic″ flock; we also use the
terms ``vector-ordered″ and ``polar-ordered″ for this situation)
to exist even in two dimensions (i.e., creatures moving on a plane), in
defiance of the well-known Mermin-Wagner theorem of equilibrium
statistical mechanics, which states that a continuous symmetry (in this
case, rotation invariance, or the ability of the flock to fly in any
direction) can not be spontaneously broken in a two-dimensional system
with only short-ranged interactions. The ``nematic″ phase of flocks,
in which all the creatures move preferentially, or are simply oriented
preferentially, along the same axis, but with equal probability of
moving in either direction, also differs dramatically from its
equilibrium counterpart (in this case, nematic liquid crystals).
Specifically, it shows enormous number fluctuations, which actually grow
with the number of organisms faster than the root N ``law of large
numbers″ obeyed by virtually all other known systems. As for
equilibrium systems, the hydrodynamic behavior of any phase of flocks is
radically modified by additional conservation laws. One such law is
conservation of momentum of the background fluid through which many
flocks move, which gives rise to the ``hydrodynamic backflow″ induced
by the motion of a large flock through a fluid. We review the
theoretical work on the effect of such background hydrodynamics on three
phases of flocks-the ferromagnetic and nematic phases described above,
and the disordered phase in which there is no order in the motion of the
organisms. The most surprising prediction in this case is that
``ferromagnetic″ motion is always unstable for low Reynolds-number
suspensions. Experiments appear to have seen this instability, but a
quantitative comparison is awaited. We conclude by suggesting further
theoretical and experimental work to be done. (c) 2005 Elsevier Inc. All
rights reserved.},
 author = {Toner, J and Tu, YH and Ramaswamy, S},
 doi = {10.1016/j.aop.2005.04.011},
 eissn = {1096-035X},
 issn = {0003-4916},
 journal = {ANNALS OF PHYSICS},
 month = {JUL},
 number = {1},
 pages = {170-244},
 researcherid-numbers = {Toner, John/G-9470-2015},
 times-cited = {505},
 title = {Hydrodynamics and phases of flocks},
 unique-id = {ISI:000230224600005},
 volume = {318},
 year = {2005}
}