2015
DOI: 10.1007/s00332-015-9262-9
|View full text |Cite
|
Sign up to set email alerts
|

Pursuit and Synchronization in Hydrodynamic Dipoles

Abstract: We study theoretically the behavior of a class of hydrodynamic dipoles. This study is motivated by recent experiments on synthetic and biological swimmers in microfluidic Hele-Shaw type geometries. Under such confinement, a swimmer's hydrodynamic signature is that of a potential source dipole, and the long-range interactions among swimmers are obtained from the superposition of dipole singularities. Here, we recall the equations governing the positions and orientations of interacting asymmetric swimmers in dou… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

1
8
0

Year Published

2018
2018
2021
2021

Publication Types

Select...
3
1

Relationship

1
3

Authors

Journals

citations
Cited by 4 publications
(9 citation statements)
references
References 22 publications
(62 reference statements)
1
8
0
Order By: Relevance
“…is the unit vector orthogonal tov f (t) forming a local right-handed coordinate system and ∇ is the gradient operator in the global coordinate system. With respect to the paper by Filella et al (2018), we note the difference in sign between ( 8) and ( 5) therein, which arises from our choice to work with transverse versus aligned dipoles, that is, T-dipoles instead of A-dipoles, as defined by Kanso & Tsang, 2014. One can verify that the sign is indeed negative by considering a fish swimming in the x-direction ( f = 0,v f =î, andv ⊥ f =ĵ) in a shear flow (U f = Yî with > 0); in this case, the turn rate in ( 8) is − such that the fish will turn clockwise, as one would expect also based on the work of Tchieu et al (2012).…”
Section: E7-5mentioning
confidence: 99%
“…is the unit vector orthogonal tov f (t) forming a local right-handed coordinate system and ∇ is the gradient operator in the global coordinate system. With respect to the paper by Filella et al (2018), we note the difference in sign between ( 8) and ( 5) therein, which arises from our choice to work with transverse versus aligned dipoles, that is, T-dipoles instead of A-dipoles, as defined by Kanso & Tsang, 2014. One can verify that the sign is indeed negative by considering a fish swimming in the x-direction ( f = 0,v f =î, andv ⊥ f =ĵ) in a shear flow (U f = Yî with > 0); in this case, the turn rate in ( 8) is − such that the fish will turn clockwise, as one would expect also based on the work of Tchieu et al (2012).…”
Section: E7-5mentioning
confidence: 99%
“…Existing mathematical models of flow interactions in fish schools vary in the degree of fidelity to the fluid dynamics and sensory-feedback control at the swimmer level. Ideal flow models – based on a dipolar far-field approximation (Tchieu, Kanso & Newton 2012) – with no feedback control have been used to assess the effect of passive flow interactions on the stability of pairwise (Kanso & Tsang 2014, 2015) and diamond lattice formations (Tsang & Kanso 2013) and the advantages of flapping out of phase (Kanso & Newton 2009). This far-field flow model coupled to visual feedback control, either in the form of behavioural rules (Filella et al.…”
Section: Introductionmentioning
confidence: 99%
“…Reference [213] proposed a model with a set of equations for cell cell interaction through hydrodynamics which agrees with the experimental observation of vertex arrays. Hydrodynamic interactions of dipoles in confined space were analytically and numerically studied [215,216,217].…”
Section: Recommendation For Future Workmentioning
confidence: 99%
“…In reference [217], a dipole is comprised of a head and a tail connected by a rod of invariant length. Analysis shows that when the tail of the dipole is larger than the head, pursuit mode (one dipole follows another) is stable and when the head is larger than the tail, synchronization mode (dipoles swim in parallel) is stable.…”
Section: Recommendation For Future Workmentioning
confidence: 99%
See 1 more Smart Citation