Combing the Hairy Ball Using a Vector Field Without Equilibria

Carvalho, Tiago; Gonçalves, Luiz Fernando

doi:10.1007/s10883-019-09446-5

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…In nature however, the air or water surrounding an organism can be very still, and may not provide a reliable directional cue [Crall et al, 2017, Houle and van Breugel, 2023, Carvalho and Gonc ¸alves, 2020.…”

Section: Introductionmentioning

confidence: 99%

“…In nature however, the air or water surrounding an organism is rarely consistent, and can be very still or turbulent [Crall et al, 2017, Houle and van Breugel, 2023, Carvalho and Gonc ¸alves, 2020. How then should a flying organism track a plume when ambient flow is below detection thresholds?…”

Section: Introductionmentioning

confidence: 99%

“…For both swimming and flying animals engaged in olfactory search, turning into the direction of oncoming wind or water current is often a critical first step [Marsh et al, 1978, Carton and Montgomery, 2003]. However, in nature, wind and water currents may not always provide a reliable directional cue [Crall et al, 2017, Houle and van Breugel, 2023, Carvalho and Gonçalves, 2020], and it is unclear how organisms adjust their search strategies accordingly due to the challenges of separately controlling flow and chemical encounters. Here, we use the genetic toolkit of Drosophila melanogaster , a model organism for olfaction [Benton, 2022], to develop an optogenetic paradigm to deliver temporally precise “virtual” olfactory experiences in free-flying animals while independently manipulating the wind conditions.…”

mentioning

confidence: 99%

“…For both swimming and flying animals engaged in olfaction driven search, turning into the direction of oncoming wind or water current is often a critical first step 1, 2 . However, in nature, wind and water currents may not always provide a reliable directional cue 3, 4, 5 . It is unclear how organisms adjust their search strategies accordingly due to the challenges of separately controlling flow and chemical encounters.…”

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confidence: 99%

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Wind Gates Olfaction Driven Search States in Free Flight

Stupski,

van Breugel

2023

Preprint

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For any organism tracking a chemical cue to its source, the motion of its surrounding fluid provides crucial information for success. For both swimming and flying animals engaged in olfactory search, turning into the direction of oncoming wind or water current is often a critical first step [Marsh et al., 1978, Carton and Montgomery, 2003]. However, in nature, wind and water currents may not always provide a reliable directional cue [Crall et al., 2017, Houle and van Breugel, 2023, Carvalho and Gonçalves, 2020], and it is unclear how organisms adjust their search strategies accordingly due to the challenges of separately controlling flow and chemical encounters. Here, we use the genetic toolkit ofDrosophila melanogaster, a model organism for olfaction [Benton, 2022], to develop an optogenetic paradigm to deliver temporally precise “virtual” olfactory experiences in free-flying animals while independently manipulating the wind conditions. We show that in free flight,Drosophila melanogasteradopt distinct search routines that are gated by whether they are flying in laminar wind or in still air. We first confirm that in laminar wind flies turn upwind, and further, we show that they achieve this using a rapid turn. In still air, flies adopt remarkably stereotyped “sink and circle” search state characterized by ∼60°turns at 3-4 Hz, biased in a consistent direction. In both laminar wind and still air, immediately after odor onset, flies decelerate and often perform a rapid turn. Both maneuvers are consistent with predictions from recent control theoretic analyses for how insects may estimate properties of wind while in flight [van Breugel, 2021, van Breugel et al., 2022]. We suggest that flies may use their deceleration and “anemometric” turn as active sensing maneuvers to rapidly gauge properties of their wind environment before initiating a proximal or upwind search routine.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Wind Gates Olfaction Driven Search States in Free Flight

Stupski,

van Breugel

2023

Preprint

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“…However, by Theorem 1.1 we get a discontinuous vector field tangent to S 2 without equilibria (note that an equilibrium point is a minimal set). This problem was addressed in [5].…”

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confidence: 99%

A flow on $ S^2 $ presenting the ball as its minimal set

Carvalho¹,

Gonçalves²

2021

DCDS-B

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The main goal of this paper is to present the existence of a vector field tangent to the unit sphere S 2 such that S 2 itself is a minimal set. This is reached using a piecewise smooth (discontinuous) vector field and following the Filippov's convention on the switching manifold. As a consequence, none regularization process applied to the initial model can be topologically equivalent to it and we obtain a vector field tangent to S 2 without equilibria.

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