of active particles: polar active fluid (left) formed by polar particles (a) with polar interactions; active nematic fluid (center) formed by apolar particles (b) with apolar interactions; self-propelled active nematic fluid (right) formed by self-propelled particles (c) with apolar interactions.[]{data-label="Fig1"}](Fig0-v2.pdf){width="8cm"}

One can envisage a third class of active fluids that consists of SP particles whose emergent macrostates are nematic in symmetry. A realization of this is self-propelled particles with physical interactions, such as steric repulsion or hydrodynamic interactions among swimmers in a suspension. It has been shown that these interactions lead to nematic, rather than polar order [@Baskaran2008a; @Baskaran2009]. What is key is the fact that interactions such as steric collisions or hydrodynamic couplings individually conserve momentum and hence cannot lead to the development of a macroscopic momentum for the system. The ordered state of these systems has nematic symmetry, but as we will see below its properties are distinct from those of active nematics composed of apolar particles. Here we refer to this third class of active systems as *self-propelled nematic* fluids. Further, it has recently become apparent that models of polar particles with apolar interactions may be relevant to a number of physical systems, including gliding myxobacteria [@Peruani2012], 