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Volumn 86, Issue 2, 2012, Pages

Going from microscopic to macroscopic on nonuniform growing domains

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MODEL; DOMAIN GROWTH; FUNCTIONAL SPECIFICATION; GROWING DOMAINS; INDIVIDUAL PARTICLES; INDIVIDUAL-BASED; LATTICE ELEMENTS; MASTER EQUATIONS; MORPHOGENS; PARTICLE DENSITIES; PARTICLE DIFFUSION; PARTICLE MIGRATION; PDE MODEL; SPATIOTEMPORAL DISTRIBUTIONS; TRANSITION RATES;

EID: 84865583080     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.021921     Document Type: Article
Times cited : (42)

References (36)
  • 1
    • 0031207030 scopus 로고    scopus 로고
    • SMJMAP 0036-1399 10.1137/S0036139995288976
    • H. G. Othmer and A. Stevens, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139995288976 57, 1044 (1997).
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1044
    • Othmer, H.G.1    Stevens, A.2
  • 3
    • 57349137121 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2008.10.038
    • M. J. Simpson, K. A. Landman, and B. D. Hughes, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.10.038 388, 399 (2009).
    • (2009) Physica A , vol.388 , pp. 399
    • Simpson, M.J.1    Landman, K.A.2    Hughes, B.D.3
  • 8
  • 10
    • 35348964624 scopus 로고    scopus 로고
    • Continuous macroscopic limit of a discrete stochastic model for interaction of living cells
    • DOI 10.1103/PhysRevLett.99.168102
    • M. Alber, N. Chen, P. M. Lushnikov, and S. A. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.168102 99, 168102 (2007). (Pubitemid 47613326)
    • (2007) Physical Review Letters , vol.99 , Issue.16 , pp. 168102
    • Alber, M.1    Chen, N.2    Lushnikov, P.M.3    Newman, S.A.4
  • 11
    • 63049107118 scopus 로고    scopus 로고
    • JMBLAJ 0303-6812 10.1007/s00285-008-0201-3
    • T. Hillen and K. J. Painter, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s00285-008-0201-3 58, 183 (2009).
    • (2009) J. Math. Biol. , vol.58 , pp. 183
    • Hillen, T.1    Painter, K.J.2
  • 12
    • 0034917420 scopus 로고    scopus 로고
    • SMJMAP 0036-1399 10.1137/S0036139999358167
    • T. Hillen and H. G. Othmer, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139999358167 61, 751 (2000).
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 751
    • Hillen, T.1    Othmer, H.G.2
  • 13
    • 0036553052 scopus 로고    scopus 로고
    • SMJMAP 0036-1399 10.1137/S0036139900382772
    • H. G. Othmer and T. Hillen, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139900382772 62, 1222 (2002).
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1222
    • Othmer, H.G.1    Hillen, T.2
  • 14
    • 77952668745 scopus 로고    scopus 로고
    • BMTBAP 0092-8240 10.1007/s11538-009-9467-x
    • R. E. Baker, C. A. Yates, and R. Erban, Bull. Math. Biol. BMTBAP 0092-8240 10.1007/s11538-009-9467-x 72, 719 (2010).
    • (2010) Bull. Math. Biol. , vol.72 , pp. 719
    • Baker, R.E.1    Yates, C.A.2    Erban, R.3
  • 16
    • 0036154068 scopus 로고    scopus 로고
    • BIOJAU 0006-3495 10.1016/S0006-3495(02)75426-X
    • K. Kruse, Biophys. J. BIOJAU 0006-3495 10.1016/S0006-3495(02)75426-X 82, 618 (2002).
    • (2002) Biophys. J. , vol.82 , pp. 618
    • Kruse, K.1
  • 17
    • 84865595288 scopus 로고    scopus 로고
    • See Supplemental Material at
    • See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevE.86.021921 for more details and movies.
  • 20
    • 33645429016 scopus 로고
    • JPCHAX 0022-3654 10.1021/j100540a008
    • D. T. Gillespie, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100540a008 81, 2340 (1977).
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340
    • Gillespie, D.T.1
  • 21
    • 0040261379 scopus 로고
    • ADMTA4 0001-8708 10.1016/0001-8708(70)90034-4
    • F. Spitzer, Adv. Math. ADMTA4 0001-8708 10.1016/0001-8708(70)90034-4 5, 246 (1970).
    • (1970) Adv. Math. , vol.5 , pp. 246
    • Spitzer, F.1
  • 22
    • 25444471803 scopus 로고    scopus 로고
    • Derivation of macroscopic equations for individual cell-based models: A formal approach
    • DOI 10.1002/mma.638
    • M. Bodnar and J. J. L. Velazquez, Math. Methods Appl. Sci. MMSCDB 0170-4214 10.1002/mma.638 28, 1757 (2005). (Pubitemid 41360038)
    • (2005) Mathematical Methods in the Applied Sciences , vol.28 , Issue.15 , pp. 1757-1779
    • Bodnar, M.1    Velazquez, J.J.L.2
  • 25
    • 0004232671 scopus 로고
    • Princeton University Press, Princeton
    • H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, 1993).
    • (1993) Random Walks in Biology
    • Berg, H.C.1
  • 28
    • 67649365828 scopus 로고    scopus 로고
    • SMJMAP 0036-1399 10.1137/070705039
    • S. A. Isaacson, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/070705039 70, 77 (2009).
    • (2009) SIAM J. Appl. Math. , vol.70 , pp. 77
    • Isaacson, S.A.1
  • 32
    • 0029163545 scopus 로고    scopus 로고
    • NATUAS 0028-0836 10.1038/376765a0
    • S. Kondo and R. Asai, Nature NATUAS 0028-0836 10.1038/376765a0 376, 765 (2002).
    • (2002) Nature , vol.376 , pp. 765
    • Kondo, S.1    Asai, R.2
  • 33
    • 0037340207 scopus 로고    scopus 로고
    • Mathematical models of cell colonization of uniformly growing domains
    • DOI 10.1016/S0092-8240(02)00098-8
    • K. A. Landman, G. J. Pettet, and D. F. Newgreen, Bull. Math. Biol. BMTBAP 0092-8240 10.1016/S0092-8240(02)00098-8 65, 235 (2003). (Pubitemid 36333242)
    • (2003) Bulletin of Mathematical Biology , vol.65 , Issue.2 , pp. 235-262
    • Landman, K.A.1    Pettet, G.J.2    Newgreen, D.F.3
  • 34
    • 67649970513 scopus 로고    scopus 로고
    • JTBIAP 0022-5193 10.1016/j.jtbi.2009.04.025
    • B. J. Binder and K. A. Landman, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2009.04.025 259, 541 (2009).
    • (2009) J. Theor. Biol. , vol.259 , pp. 541
    • Binder, B.J.1    Landman, K.A.2


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