Spatio-angular order in populations of self-aligning objects: Formation of oriented patches

Physica D: Nonlinear Phenomena

Volumn 89, Issue 3-4, 1996, Pages 346-367

  Mogilner, Alex ^a   Edelstein Keshet, Leah ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001499542     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00207-3     Document Type: Article

References (41)

1. Alt, W. and Geigant, E. (1994), private communication.
2. Abramowitz, M. and Stegun, A. eds. (1964), Handbook of Mathematical Functions (National Bureau of Standards, Washington).
3. Alt, W. (1988), Modelling of motility in biological systems, ICIAM 1987 Proceedings (SIAM, Philadelphia) pp. 15-30.
4. Civelekoglu, G. and Edelstein-Keshet, L. (1994), Models for the formation of actin structures, Bull. Math. Biol. 56, 587-616.
5. Chandrasekhar, S., Shashihad, R. and Tara, N. (1970), Theory of melting of molecular crystals: the liquid crystalline phase, Mol. Cryst. Liq. Cryst. 10, 337-358.
6. De Gennes, P.G. (1974), The Physics of Liquid Crystals (Clarendon, Oxford).
7. Edelstein-Keshet, L. and Ermentrout, G.B. (1989), Models for branching networks in two dimensions, SIAM J. Appl. Math. 49, 1136-1157.
8. Edelstein-Keshet, L. and Ermentrout, G.B. (1990), Models for contact-mediated pattern formation: cells that form parallel arrays, J. Math. Biol. 29, 33-58.
9. Edmunds, M. (1974), Defense in Animals (Longman, London).
10. Elsdale, T. (1972), Pattern formation in fibroblast cultures, an inherently precise morphogenetic process, in: Towards a Theoretical Biology, Vol. 4, C.H. Waddington, ed. (Edinburgh Univ. Press, Edinburgh).
11. Elsdale, T. and Wasoff, F. (1976), Fibroblast cultures and dermatoglyphics: the topology of two planar patterns: Wilhelm Roux's Archives, Vol. 180, pp. 121-147.
12. Ermentrout, B., Campbell, J. and Oster, G. (1986), A model for shell patterns based on neural activity, The Veliger 28, 369-388.
13. Ermentrout, G.B. and Cowan, J. (1979), A mathematical theory of visual hallucination patterns, Biol. Cybern. 34, 137-150.
14. Ermentrout, G.B. and Edelstein-Keshet, L. (1991), Cellular Automata approaches to biological modelling, J. Theor. Biol. 160, 97-133.
15. Geigant, E., Mogilner, A. and Ladizhansky, K. (1995), A nonlinear model for active alignment, in preparation.
16. Greco, F. and Marrucci, G. (1992), Rodlike molecular dynamics, the tumbling regime, Mol. Cryst. Liq. Cryst. 212, 125-137.
17. Gross, M.C. and Hohenberg, P.C. (1993), Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851-112.
18. Grunbaum, D. (1994), Swarming behaviour as an aide to Chemotaxis; in: Parrish, J. and Hammner, W., eds., 3D Animal Aggregations (Cambridge Univ. Press, Cambridge).
19. Katz, L.C., Potel, M.J. and Wasserung, R.J. (1981), Structure and mechanism of schooling in tadpoles of the clawed frog, Xenopus laevis, Anim. Behav. 29, 20-33.
20. Kuramoto, Y. (1975), Self-entrainment of a population of coupled nonlinear oscillators, in: Intern. Symp. on Mathematical Problems in Theoretical Physics, H. Araki, ed., Lecture Notes in Physics, Vol. 39 (Springer, New York) pp. 420-422.
21. Landau, L.D. and Lifshitz, E.M. (1956), Hydrodynamics (Pergamon, London).
22. Lifshitz, E.M. and Pitaevskii, L.P. (1981), Physical Kinetics (Pergamon, Oxford).
23. Macrobert, T.M. (1967), Spherical Harmonics (Pergamon, Oxford).
24. Marcus, M. and Ming, H. (1964), A Survey of Matrix Theory and Matrix Inequalities (Allyn Bacon, Boston).
25. Mogilner, A. and Edelstein-Keshet, L. (1995a), Selecting a common direction I: How orientational order can arise from simple contact responses between interacting cells, J. Math. Biol., in press.
26. Mogilner, A. and Edelstein-Keshet, L. (1995b), Selecting a common direction II: Peak-like solutions representing total alignment of cell clusters, submitted for publication.
27. Murray, J.D. (1989), Mathematical Biology (Springer, New York).
28. O'Brien, D.P. (1989), Analysis of the internal arrangement of individuals within crustacean aggregations (Euphausiacea, Mysidacea), J. Exp. Mar. Biol. Ecol. 128, 1-30.
29. Onsager, L. (1949), The effects of shape on the interaction of colloidal particles, Ann. NY Acad. Sci. 51, 627-659.
30. Othmer, H.G., Dunbar, S.R. and Alt, W. (1988), Models of dispersal in biological systems, J. Math. Biol. 26, 263-298.
31. Pfistner, B. and Alt, W. (1989), A two-dimensional random walk model for swarming behaviour, Alt, W. and Hoffmann, G., eds., in: Biological Motion (Springer, New York).
32. Segel, L. (1984), Modelling Dynamic Phenomena in Molecular and Cellular Biology (Cambridge Univ. Press, Cambridge).
33. Strogatz, S.H. (1993), Norbert Wiener's brain waves, in: Lecture Notes in Biomathematics, Vol. 100 (Springer, Berlin).
34. Strogatz, S.H. and Mirollo, R.E. (1991), Stability of incoherence in a population of coupled oscillators, J. Stat. Phys. 63, 613-635.
35. Swindale, N.V. (1980), A model for the formation of ocular dominance stripes, Proc. R. Soc. Lond. B 208, 243-264.
36. Swindale, N.V. (1982), A model for the formation of orientation columns, Proc. R. Soc. London B 215, 211-230.
37. Swindale, N.V. (1991), Coverage and the design of striate cortex, Biol. Cybern. 65, 415-424.
38. Swindale, N.V. (1992), A model for the coordinated development of columnar systems in primate striate cortex, Biol. Cybern. 66, 217-230.
39. Tabony, J. and Job, D. (1990), Spatial structures in microtubular solutions requiring a sustained energy source, Nature 346, 448-451.
40. Villard Baron, J. (1969), J. Phys. (Paris) 30 (Suppl. 34), 22.
41. Zwanzig, R. (1963), First-order phase transitions in a gas of long thin rods, J. Chem. Phys. 39, 1714-1721.