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Wildebeest Herds on Rolling Hills: Flocking on Arbitrary Curved Surfaces

Hueschen, Christina L. and Dunn, Alexander R. and Phillips, Rob (2022) Wildebeest Herds on Rolling Hills: Flocking on Arbitrary Curved Surfaces. . (Unpublished)

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The collective behavior of active agents, whether herds of wildebeest or microscopic actin filaments propelled by molecular motors, is an exciting frontier in biological and soft matter physics. Almost three decades ago, Toner and Tu developed a hydrodynamic theory of the collective action of flocks, or herds, that helped launch the modern field of active matter. One challenge faced when applying continuum active matter theories to living phenomena is the complex geometric structure of biological environments. Both macroscopic and microscopic herds move on asymmetric curved surfaces, like undulating grass plains or the surface layers of cells or embryos, which can render problems analytically intractable. In this work, we present a formulation of the Toner-Tu flocking theory that uses the finite element method to solve the governing equations on arbitrary curved surfaces. First, we test the developed formalism and its numerical implementation in channel flow with scattering obstacles and on cylindrical and spherical surfaces, comparing our results to analytical solutions. We then progress to surfaces with arbitrary curvature, moving beyond previously accessible problems to explore herding behavior on a variety of landscapes. Our approach allows the investigation of transients and dynamic solutions not revealed by analytic methods. It also enables versatile incorporation of new geometries and boundary conditions and efficient sweeps of parameter space. Looking forward, the work presented here lays the groundwork for a dialogue between Toner-Tu theory and data on collective motion in biologically-relevant geometries, from drone footage of migrating animal herds to movies of microscopic cytoskeletal flows within cells.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Discussion Paper
Hueschen, Christina L.0000-0002-3437-2895
Dunn, Alexander R.0000-0001-6096-4600
Phillips, Rob0000-0003-3082-2809
Additional Information:The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license. We are deeply grateful to a number of generous colleagues who have carefully described their thinking and work on the formulation of continuum descriptions on surfaces, and to others who have provided invaluable feedback on this work. We especially thank Ashutosh Agarawal, Marino Arroyo, David Bensimon, Mark Bowick, Markus Deserno, Soichi Hirokawa, Greg Huber, Alexei Kitaev (who showed us how to solve the half space problem), Jane Kondev, Elgin Korkmazhan, Deepak Krishnamurthy, Kranthi Mandadapu, Madhav Mani, Cristina Marchetti, Walker Melton, Alexander Mietke, Phil Nelson, Silas Nissen, Manu Prakash, Sriram Ramaswamy, Suraj Shankar, Mike Shelley, Sho Takatori, John Toner, Yuhai Tu, and Vincenzo Vitelli. We thank Nigel Orme for his work on Figures 1 and 2. This work was supported by a Damon Runyon Fellowship Award (C.L.H.), a Burroughs Wellcome Career Award at the Scientific Interface (C.L.H.), NIH R35GM130332 (A.R.D.), an HHMI Faculty Scholar Award (A.R.D.), NIH MIRA 1R35GM118043 (R.P.), and the Chan Zuckerberg Biohub (R.P.). Authors declare that they have no competing interests.
Funding AgencyGrant Number
Damon Runyon Cancer Research FoundationUNSPECIFIED
Burroughs Wellcome FundUNSPECIFIED
Howard Hughes Medical Institute (HHMI)UNSPECIFIED
Chan Zuckerberg BiohubUNSPECIFIED
Record Number:CaltechAUTHORS:20220706-965496000
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Official Citation:Wildebeest Herds on Rolling Hills: Flocking on Arbitrary Curved Surfaces Christina L. Hueschen, Alexander R. Dunn, Rob Phillips bioRxiv 2022.06.22.497052; doi:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115353
Deposited By: George Porter
Deposited On:08 Jul 2022 22:39
Last Modified:25 Jul 2022 23:13

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