Eliminating inertia in a stochastic model of a micro-swimmer with constant speed
Tóm tắt
We are concerned with the dynamical description of the motion of a stochastic micro-swimmer with constant speed and fluctuating orientation in the long time limit by adiabatic elimination of the orientational variable. Starting with the corresponding full set of Langevin equations, we eliminate the memory in the stochastic orientation and obtain a stochastic equation for the position alone in the overdamped limit. An equivalent procedure based on the Fokker-Planck equation is presented as well.
Tài liệu tham khảo
H. Niwa, J. Theor. Biol. 171, 123 (1994)
T. Vicsek, A. Czirók, E.Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)
P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. Special Topics 202, 1 (2012)
M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013)
M.J.B. Hauser, L. Schimansky-Geier, Eur. Phys. J. Special Topics 224, 1147 (2015)
M. Schienbein, H. Gruler, Bull. Math. Biol. 55, 585 (1993)
S. van Teeffelen, H. Löwen, Phys. Rev. E 78, 020101 (2008)
D. Selmeczi, L. Li, L.I. Pedersen, S.F. Nørrelykke, P.H. Hagedorn, S. Mosler, N.B. Larsen, E.C. Cox, H. Flyvbjerg, Eur. Phys. J. Special Topics 157, 1 (2008)
H. Bödeker, C. Beta, T. Frank, E. Bodenschatz, Europhys. Lett. 90, 28005 (2010)
L. Li, S.F. Nørrelykke, E.C. Cox, PLoS ONE 3, e2093 (2008)
G. Amselem, M. Theves, A. Bae, E. Bodenschatz, C. Beta, PLoS ONE 7, e37213 (2012)
R. Dilao, M.J.B. Hauser, Comptes Rendus Biologies 336, 565 (2013)
B. Rodiek, M.J.B. Hauser, Eur. Phys. J. Special Topics 224, 1199 (2015)
S. Bazazi, P. Romanczuk, S. Thomas, L. Schimansky-Geier, J.J. Hale, G.A. Miller, G.A. Sword, S.J. Simpson, I.D. Couzin, Proc. R. Soc. B 278, 356 (2011)
P. Romanczuk, M. Romensky, D. Scholz, V. Lobaskin, L. Schimansky-Geier, Eur. Phys. J. Special Topics 224, 1215 (2015)
W.F. Paxton, K.C. Kistler, C.C. Olmeda, A. Sen, S.K.S. Angelo, Y. Cao, T.E. Mallouk, P.E. Lammert, V.H. Crespi, J. Am. Chem. Soc. 126, 13424 (2004)
J.R. Howse, R.A.L. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007)
G. Ruckner, R. Kapral, Phys. Rev. Lett. 98, 150603 (2007)
K.V. Kumar, S. Ramaswamy, M. Rao, Phys. Rev. E 77, 020102 (2008)
A. Kudrolli, G. Lumay, D. Volfson, L.S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008)
P. Tierno, R. Albalat, F. Sagués, Small 6, 1749 (2010)
H. Ke, S. Ye, R.L. Carroll, K. Showalter, J. Phys. Chem. A 114, 5462 (2010)
D. Takagi, A.B. Braunschweig, J. Zhang, M.J. Shelley, Phys. Rev. Lett. 110, 038301 (2013)
G. Grègoire, H. Chate, Phys. Rev. Lett. 92, 025702 (2004)
H. Chate, F. Ginelli, R. Montagne, Phys. Rev. Lett. 96, 180602 (2006)
J. Buhl, D.J.T. Sumpter, I.D. Couzin, J.J. Hale, E. Despland, E.R. Miller, S.J. Simpson, Science 312, 1402 (2006)
E. Bertin, M. Droz, and G. Grègoire, Phys. Rev. E 74, 0222101 (2006)
T. Ihle, Phys. Rev. E 83, 030901 (2011)
T. Ihle, Phys. Rev. E 88, 040303 (2013)
R. Großmann, L. Schimansky-Geier, P. Romanczuk, Phys. Rev. Lett. 113, 258104 (2014)
R. Großmann, F. Peruani, M. Bär, New J. Phys. 18, 043009 (2016)
H. Seyed-Allaei, L. Schimansky-Geier, M.R. Ejtehadi, Phys. Rev. E 94, 062603 (2016)
A. Patch, D. Yllanes, M.C. Marchetti, Phys. Rev. E 95, 012601 (2017)
F. Schweitzer, W. Ebeling, B. Tilch, Phys. Rev. Lett. 80, 5044 (1998)
F. Schweitzer, Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences, Synergetics (Springer, 2003)
A. Mikhailov, D. Meinköhn, in Stochastic Dynamics, edited by L. Schimansky-Geier, T. Pöschel (Springer, 1997)
F. Peruani, L.G. Morelli, Phys. Rev. Lett. 99, 10602 (2007)
P. Langevin, C.R. Acad. Sci (Paris) 146, 530 (1908)
P.M. Kareiva, N. Shigesada, Oecologia 56, 234 (1983)
A. Okubo, S.A. Levin, Diffusion and Ecological Problems: Modern Developments, 2nd edition, Interdisciplinary Applied Mathematics, Vol. 14 (Springer Science + Business Media, New York, 2001)
W. Ebeling, F. Schweitzer, B. Tilch, Biosystems 49, 17 (1999)
U. Erdmann, W. Ebeling, L. Schimansky-Geier, F. Schweitzer, Eur. Phys. J. B 15, 105 (2000)
P. Romanczuk, L. Schimansky-Geier, Phys. Rev. Lett. 106, 230601 (2011)
F.J. Sevilla, L.A. Gomez Nava, Phys. Rev. E 90, 022130 (2014)
H.A. Kramer, Physica 7, 284 (1940)
R. Becker, Theorie der Wärme (Springer, Berlin, 1955), Chap. VI B
Yu.B. Rumer, M.Sh. Rivkin, Thermodynamics, Statistical Physics and Kinetics (Mir Publishers, Moscow, 1980)
L. Haeggqwist, L. Schimansky-Geier, I.M. Sokolov, F. Moss, Eur. Phys. J. Special Topics 157, 33 (2008)
C. Weber, P.K. Radtke, L. Schimansky-Geier, P. Hänggi, Phys. Rev. E 84, 011132 (2011)
C. Weber, I.M. Sokolov, L. Schimansky-Geier, Phys. Rev. E 85, 052101 (2012)
F. Thiel, L. Schimansky-Geier, I.M. Sokolov, Phys. Rev. E 86, 021117 (2012)
J. Nötel, I.M. Sokolov, L. Schimansky-Geier, J. Phys. A: Math. Theor. 50, 034033 (2017)
M. Mijalkov, G. Volpe, Soft Matter 9, 6376 (2013)
G. Volpe, S. Gigan, G. Volpe, Am. J. Phys. 82, 659 (2014)
A. Geiseler, P. Hänggi, F. Marchesoni, C. Mulhern, S. Savel’ev, Phys. Rev. E 94, 012613 (2016)
A. Geiseler, P. Hänggi, G. Schmid, Eur. Phys. J. B 89, 175 (2016)
D. Debnath, P.K. Ghosh, Y. Li, F. Marchesoni, B. Li, Soft Matter 12, 2017 (2016)
B. ten Hagen, S. van Teeffelen, H. Löwen, J. Phys.: Condens. Matter 23, 194119 (2011)
S. Babel, B. ten Hagen, H. Löwen, J. Stat. Mech. 2014, P02011 (2014)
A. Einstein, Ann. Phys. 17, 549 (1905)
M. von Smoluchowski, Ann. Phys. 326, 756 (1906)
P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)
L. H’walisz, P. Jung, P. Hänggi, P. Talkner, L. Schimansky-Geier, Z. Phys. B 77, 471 (1989)
H. Haken, Synergetics-an Introduction, 2nd edition (Springer, Berlin, 1978), Chap. 7
C.W. Gardiner, Handbook of Stochastic Methods (Springer, 1983)
C.W. Gardiner, Phys. Rev. A 29, 2814 (1984)
P. Jung, P. Hänggi, Phys. Rev. A 35, 4464 (1987)
L. Schimansky-Geier, P. Talkner, in Stochastic Dynamics of Reacting Macromolecules, edited by W. Ebeling, L. Schimansky-Geier, Yu.M. Romanovsky (World Sientific, Singapore, 2002)
J.M. Sancho, Phys. Rev. E 84, 062102 (2011)
R.L. Stratonovich, SIAM J. Control, 4, 362 (1966)
R.L. Stratonovich, Topics in the Theory of Random Noise 1 (Gordon and Breach, New York, 1963), pp. 89ff
N.G. van Kampen, J. Stat. Phys 24, 175 (1981)
I.M. Sokolov, Chem. Phys. 375, 359 (2010)
R.L. Stratonovich, in Noise in Nonlinear Dynamical Systems, edited by F. Moss, P.V.E. McClintock, Vol. 1 (Cambridge University Press, 1989)
V.I. Tikhonov, M.A. Mironov, Markovian Processes (in Russian), (Soviet Radio, Moscow, 1977)