John Toner
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View article: The Order-disorder Transition in Incompressible Polar Active Fluids with an Easy Axis
The Order-disorder Transition in Incompressible Polar Active Fluids with an Easy Axis Open
Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar a…
View article: Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks
Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks Open
We study the hydrodynamic behavior of two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. We show that, in the absence of fluctuations, such systems gener…
View article: Only the Ambidextrous Can Flock: Two-dimensional Chiral Malthusian Flocks, Time Cholesterics, and the KPZ Equation
Only the Ambidextrous Can Flock: Two-dimensional Chiral Malthusian Flocks, Time Cholesterics, and the KPZ Equation Open
We study two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. In the absence of fluctuations, these form a ``time cholesteric", in which the velocity rotat…
View article: Response to the comment on The inconvenient truth about flocks by Chaté and Solon
Response to the comment on The inconvenient truth about flocks by Chaté and Solon Open
This is our response to the comment arXiv:2504.13683 posted by Chaté and Solon in reference to our preprint arXiv:2503.17064
View article: The inconvenient truth about flocks
The inconvenient truth about flocks Open
We reanalyze the hydrodynamic theory of "flocks" that is, polar ordered "dry" active fluids in two dimensions. For "Malthusian" flocks, in which birth and death cause the density to relax quickly, thereby eliminating density as a hydrodyna…
View article: Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions
Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions Open
I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all h…
View article: Dynamics of packed swarms: Time-displaced correlators of two-dimensional incompressible flocks
Dynamics of packed swarms: Time-displaced correlators of two-dimensional incompressible flocks Open
We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the roughne…
View article: Phase separation in ordered polar active fluids: A new Universality class
Phase separation in ordered polar active fluids: A new Universality class Open
We show that phase separation in ordered polar active fluids belongs to a new universality class. This describes large collections of self-propelled entities (``flocks"), all spontaneously moving in the same direction, in which attractive …
View article: Coulomb universality
Coulomb universality Open
Motivated by a number of realizations of long-range interacting systems, including ultra-cold atomic and molecular gases, we study a neutral plasma with power-law interactions longer-ranged than Coulombic. We find that beyond a crossover l…
View article: Following your nose: Autochemotaxis and other mechanisms for spinodal decomposition in flocks
Following your nose: Autochemotaxis and other mechanisms for spinodal decomposition in flocks Open
We develop the hydrodynamic theory of dry, polar ordered, active matter (``flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We fin…
View article: Spinodal decomposition and phase separation in polar active matter
Spinodal decomposition and phase separation in polar active matter Open
We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (…
View article: Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks
Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks Open
We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the ``rough…
View article: Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems
Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems Open
I show that non-equilibrium two-dimensional interfaces between three dimensional phase separated fluids exhibit a peculiar "sub-logarithmic" roughness. Specifically, an interface of lateral extent $L$ will fluctuate vertically (i.e., norma…
View article: Packed Swarms on Dirt: Two-Dimensional Incompressible Flocks with Quenched and Annealed Disorder
Packed Swarms on Dirt: Two-Dimensional Incompressible Flocks with Quenched and Annealed Disorder Open
We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed disorder (i.e., time-dependent random whit…
View article: Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder
Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder Open
We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We…
View article: Broken living layers: dislocations in active smectics
Broken living layers: dislocations in active smectics Open
We show that dislocations in active 2d smectics with underlying rotational symmetry are always unbound in the presence of noise, meaning the active smectic phase does not exist for non-zero noise in $d=2$. The active smectic phase can, lik…
View article: Susceptibility of Polar Flocks to Spatial Anisotropy
Susceptibility of Polar Flocks to Spatial Anisotropy Open
We consider the effect of spatial anisotropy on polar flocks by investigating active $q$-state clock models in two dimensions. In contrast to what happens in equilibrium, we find that, in the large-size limit, any amount of anisotropy chan…
View article: Incompressible polar active fluids with quenched disorder in dimensions $d> 2$
Incompressible polar active fluids with quenched disorder in dimensions $d> 2$ Open
We present a hydrodynamic theory of incompressible polar active fluids with quenched disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a non…
View article: Long-ranged order and flow alignment in sheared $p-$atic liquid crystals
Long-ranged order and flow alignment in sheared $p-$atic liquid crystals Open
We formulate a hydrodynamic theory of $p-$atic liquid crystals, namely two-dimensional anisotropic fluids endowed with generic $p-$fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discre…
View article: Hydrodynamic theory of $p-$atic liquid crystals
Hydrodynamic theory of $p-$atic liquid crystals Open
We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic $p-$fold rotational symmetry, also known as $p-$atics, of which mematics $(p=2)$ and hexatics $(p=6)$ are the two best known examples. Previou…
View article: Darcy’s Law without Friction in Active Nematic Rheology
Darcy’s Law without Friction in Active Nematic Rheology Open
We study the dynamics of a contractile active nematic fluid subjected to a Poiseuille flow. In a quasi-1D geometry, we find that the linear rheology of this material is reminiscent of Darcy's law in complex fluids, with a pluglike flow dec…
View article: Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes
Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes Open
We show that inversion-asymmetric tethered membranes exhibit a new double-spiral phase with long range orientational order not present in symmetric membranes. We calculate the universal algebraic spiral shapes of these membranes in this ph…
View article: Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases
Statistical mechanics of asymmetric tethered membranes: Spiral and crumpled phases Open
We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends on the local in-plane…
View article: Swarming in the Dirt: Ordered Flocks with Quenched Disorder
Swarming in the Dirt: Ordered Flocks with Quenched Disorder Open
The effect of quenched (frozen) disorder on the collective motion of active particles is analyzed. We find that active polar systems are far more robust against quenched disorder than equilibrium ferromagnets. Long-ranged order (a nonzero …
View article: Hydrodynamic theory of flocking in the presence of quenched disorder
Hydrodynamic theory of flocking in the presence of quenched disorder Open
The effect of quenched (frozen) orientational disorder on the collective\nmotion of active particles is analyzed. We find that, as with annealed disorder\n(Langevin noise), active polar systems are far more robust against quenched\ndisorde…
View article: Why walking is easier than pointing: Hydrodynamics of dry active matter
Why walking is easier than pointing: Hydrodynamics of dry active matter Open
Although human beings have known about the phenomenon of "flocking"- that is, the coherent movement of large numbers of creatures (flocks of birds, schools of fish, herds of woolly mammoths, etc.)- since prehistoric times, it is only in th…
View article: Squeezed in three dimensions, moving in two: Hydrodynamic theory of three-dimensional incompressible easy-plane polar active fluids
Squeezed in three dimensions, moving in two: Hydrodynamic theory of three-dimensional incompressible easy-plane polar active fluids Open
We study the hydrodynamic behavior of three-dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with nonzero average velocity, hereafter called 3D easy-plane incompressible pola…
View article: Long-time anomalous swimmer diffusion in smectic liquid crystals
Long-time anomalous swimmer diffusion in smectic liquid crystals Open
The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid …
View article: Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media
Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media Open
Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the trans…