@article{ISI:000515350300016, abstract = {We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.}, article-number = {028002}, author = {Maitra, Ananyo and Srivastava, Pragya and Marchetti, M. Cristina and Ramaswamy, Sriram and Lenz, Martin}, doi = {10.1103/PhysRevLett.124.028002}, eissn = {1079-7114}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, month = {JAN 16}, number = {2}, orcid-numbers = {Maitra, Ananyo/0000-0003-3701-6981}, times-cited = {3}, title = {Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order}, unique-id = {ISI:000515350300016}, volume = {124}, year = {2020} }