A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.
REFERENCES
1.
S.
Ramaswamy
, Annu. Rev. Condens. Matter Phys.
1
, 323
(2010
).2.
3.
M.
Badoual
, F.
Jülicher
, and J.
Prost
, Proc. Natl. Acad. Sci. U. S. A.
99
, 6696
(2002
).4.
J. L.
Souman
, I.
Frissen
, M. N.
Sreenivasa
, and M. O.
Ernst
, Curr. Biol.
19
, 1538
(2009
).5.
S.
Nakata
, Y.
Iguchi
, S.
Ose
, M.
Kuboyama
, T.
Ishii
, and K.
Yoshikawa
, Langmuir
13
, 4454
(1997
).6.
H.
Jin
, A.
Marmur
, O.
Ikkala
, and R. H. A.
Ras
, Chem. Sci.
3
, 2526
(2012
).7.
J. R.
Howse
, R. A. L.
Jones
, A. J.
Ryan
, T.
Gough
, R.
Vafabakhsh
, and R.
Golestanian
, Phys. Rev. Lett.
99
, 048102
(2007
).8.
W. F.
Paxton
, A.
Sen
, and T. E.
Mallouk
, Chem.–Eur. J.
11
, 6462
(2005
).9.
H.-R.
Jiang
, N.
Yoshinaga
, and M.
Sano
, Phys. Rev. Lett.
105
, 268302
(2010
).10.
R.
Kapral
, J. Chem. Phys.
138
, 020901
(2013
).11.
F.
Kümmel
, B.
ten Hagen
, R.
Wittkowski
, I.
Buttinoni
, R.
Eichhorn
, G.
Volpe
, H.
Löwen
, and C.
Bechinger
, Phys. Rev. Lett.
110
, 198302
(2013
);
[PubMed]
F.
Kümmel
, B.
ten Hagen
, R.
Wittkowski
, D.
Takagi
, I.
Buttinoni
, R.
Eichhorn
, G.
Volpe
, H.
Löwen
, and C.
Bechinger
, Phys. Rev. Lett.
113
, 029802
(2014
).
[PubMed]
12.
K.
Yoshikawa
and N.
Magome
, Bull. Chem. Soc. Jpn.
66
, 3352
(1993
).13.
P. K.
Ghosh
, V. R.
Misko
, F.
Marchesoni
, and F.
Nori
, Phys. Rev. Lett.
110
, 268301
(2013
).14.
Y.
Fily
, A.
Baskaran
, and M. F.
Hagan
, Soft Matter
10
, 5609
(2014
).15.
Y.
Sumino
, N.
Magome
, T.
Hamada
, and K.
Yoshikawa
, Phys. Rev. Lett.
94
, 068301
(2005
).16.
Y.
Hayashima
, M.
Nagayama
, and S.
Nakata
, J. Phys. Chem. B
105
, 5353
(2001
).17.
F.
Takabatake
, K.
Yoshikawa
, and M.
Ichikawa
, J. Chem. Phys.
141
, 051103
(2014
).18.
Y.
Sumino
and K.
Yoshikawa
, Chaos
18
, 026106
(2008
).19.
F.
Domingues Dos Santos
and T.
Ondarçuhu
, Phys. Rev. Lett.
75
, 2972
(1995
).20.
T.
Ohta
and T.
Ohkuma
, Phys. Rev. Lett.
102
, 154101
(2009
).21.
P.
de Buyl
, A. S.
Mikhailov
, and R.
Kapral
, Europhys. Lett.
103
, 60009
(2013
).22.
K.
Nagai
, Y.
Sumino
, H.
Kitahata
, and K.
Yoshikawa
, Phys. Rev. E
71
, 065301
(2005
).23.
M.
Nagayama
, S.
Nakata
, Y.
Doi
, and Y.
Hayashima
, Physica D
194
, 151
(2004
).24.
V.
Pimienta
, M.
Brost
, N.
Kovalchuk
, S.
Bresch
, and O.
Steinbock
, Angew. Chem., Int. Ed.
50
, 10728
(2011
).25.
T.
Ban
, Y.
Hatada
, and K.
Takahashi
, Phys. Rev. E
79
, 031602
(2009
).26.
S.
Yabunaka
, T.
Ohta
, and N.
Yoshinaga
, J. Chem. Phys.
136
, 074904
(2012
).27.
N.
Yoshinaga
, K. H.
Nagai
, Y.
Sumino
, and H.
Kitahata
, Phys. Rev. E
86
, 016108
(2012
).28.
See Ref. 26 for the description of a concrete model.
29.
30.
I. S.
Gradshteyn
and I. M.
Ryzhik
, Table of Integrals, Series, and Products
(Academic Press
, Burlington
, 2007
).31.
W. L.
Keith
and R. H.
Rand
, Int. J. Non-Linear Mech.
20
, 325
(1985
).32.
See supplementary material at http://dx.doi.org/10.1063/1.4923421 for details of the numerical calculations.
33.
34.
B.
van der Pol
, Philos. Mag.
3
, 65
(1927
).35.
A.
Mikhailov
and V.
Calenbuhr
, From Cells to Societies
(Springer-Verlag
, Berlin
, 2002
).36.
U.
Erdmann
, W.
Ebeling
, L.
Schimansky-Geier
, and F.
Schweitzer
, Eur. Phys. J. B
15
, 105
(2000
).37.
38.
F.
Schweitzer
, W.
Ebeling
, and B.
Tilch
, Phys. Rev. Lett.
80
, 5044
(1998
).39.
40.
R. H.
Rand
and P. J.
Holmes
, Int. J. Non-Linear Mech.
15
, 387
(1980
).41.
L. A.
Low
, P. G.
Reinhall
, and D. W.
Storti
, J. Vib. Acoust.
125
, 162
(2003
).© 2015 AIP Publishing LLC.
2015
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