Existence and stability of unidirectional flocks in hydrodynamic Euler Alignment systems
In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in multi-dimensional settings subject to a threshold condition similar to the...
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| Published in | arXiv.org |
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| Main Authors | , |
| Format | Paper Journal Article |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
25.11.2019
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| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.1911.10661 |
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| Abstract | In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in multi-dimensional settings subject to a threshold condition similar to the one dimensional case. We develop the flocking and stability theory of these solutions and show long time convergence to traveling wave with rapidly aligned velocity field. In the context of multi-scale models introduced in \cite{ST-multi} our solutions can be superimposed into Mikado formations -- clusters of unidirectional flocks pointing in various directions. Such formations exhibit multiscale alignment phenomena and resemble realistic behavior of interacting large flocks. |
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| AbstractList | Analysis & PDE 15 (2022) 175-196 In this note we reveal new classes of solutions to hydrodynamic Euler
alignment systems governing collective behavior of flocks. The solutions
describe unidirectional parallel motion of agents, and are globally well-posed
in multi-dimensional settings subject to a threshold condition similar to the
one dimensional case. We develop the flocking and stability theory of these
solutions and show long time convergence to traveling wave with rapidly aligned
velocity field.
In the context of multi-scale models introduced in \cite{ST-multi} our
solutions can be superimposed into Mikado formations -- clusters of
unidirectional flocks pointing in various directions. Such formations exhibit
multiscale alignment phenomena and resemble realistic behavior of interacting
large flocks. In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in multi-dimensional settings subject to a threshold condition similar to the one dimensional case. We develop the flocking and stability theory of these solutions and show long time convergence to traveling wave with rapidly aligned velocity field. In the context of multi-scale models introduced in \cite{ST-multi} our solutions can be superimposed into Mikado formations -- clusters of unidirectional flocks pointing in various directions. Such formations exhibit multiscale alignment phenomena and resemble realistic behavior of interacting large flocks. |
| Author | Shvydkoy, Roman Lear, Daniel |
| Author_xml | – sequence: 1 givenname: Daniel surname: Lear fullname: Lear, Daniel – sequence: 2 givenname: Roman surname: Shvydkoy fullname: Shvydkoy, Roman |
| BackLink | https://doi.org/10.48550/arXiv.1911.10661$$DView paper in arXiv https://doi.org/10.2140/apde.2022.15.175$$DView published paper (Access to full text may be restricted) |
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| DOI | 10.48550/arxiv.1911.10661 |
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| Snippet | In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe... Analysis & PDE 15 (2022) 175-196 In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of... |
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| SubjectTerms | Alignment Dimensional stability Mathematics - Analysis of PDEs Scale models Traveling waves Velocity distribution Well posed problems |
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| Title | Existence and stability of unidirectional flocks in hydrodynamic Euler Alignment systems |
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