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Mathematical modeling of phase transition and separation in fluids: A unified approach
Discontinuity waves as tipping points: Applications to biological & sociological systems
1. | Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom, United Kingdom |
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show all references
References:
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G. Abramson and V. M. Kenkre, Spatiotemporal patterns in the Hantavirus infection, Physical Review E, 66 (2002), 011912.
doi: 10.1103/PhysRevE.66.011912. |
[2] |
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doi: 10.1016/j.jtbi.2009.07.009. |
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A. Aw and M. Rascale, Resurrection of "Second Order'' models of traffic flow, SIAM Journal on Applied Mathematics, 60 (2000), 916-938.
doi: 10.1137/S0036139997332099. |
[5] |
E. Barbera, C. Currò and G. Valenti, A hyperbolic reaction diffusion model for the hantavirus infection, Mathematical Methods in the Applied Sciences, 31 (2008), 481-499.
doi: 10.1002/mma.929. |
[6] |
A. D. Barnosky, E. A. Hadly, J. Bascompte, E. L. Berlow, J. H. Brown, M. Fortelius, W. M. Getz, J. Harte, A. Hastings, P. A. Marquet, N. D. Martinez, A. Mooers, P. Roopnarine, G. Vermeij, J. W. Williams, R. Gillespie, J. Kitzes, C. Marshall, N. Matzke, D. P. Mindell, E. Revilla and A. B. Smith, Approaching a state shift in Earth's biosphere, Nature, 486 (2012), 52-58.
doi: 10.1038/nature11018. |
[7] |
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doi: 10.1142/S0218202508003054. |
[8] |
N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Review, 53 (2011), 409-463.
doi: 10.1137/090746677. |
[9] |
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doi: 10.3934/nhm.2011.6.383. |
[10] |
N. Bellomo, B. Piccoli and A. Tosin, Modeling crowd dynamics from a complex system viewpoint, Math. Models Methods Appl. Sci., 22 (2012), 29 pp. 1230004.
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[11] |
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R. A. Bentley and M. J. O'Brien, Cultural evolutionary tipping points in the storage and transmission of information, Frontiers in Psychology, 3 (2013), 569.
doi: 10.3389/fpsyg.2012.00569. |
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doi: 10.1080/01495739.2010.517674. |
[16] |
I. Christov, P. M. Jordan and C. I. Christov, Nonlinear acoustic propagation in homentropic perfect gases: A numerical study, Physics Letters A, 353 (2006), 273-280.
doi: 10.1016/j.physleta.2005.12.101. |
[17] |
I. Christov, P. M. Jordan and C. I. Christov, Modelling weakly nonlinear acoustic wave propagation, Quart. Jl. Mech. Appl. Math., 60 (2007), 473-495.
doi: 10.1093/qjmam/hbm017. |
[18] |
M. Ciarletta and B. Straughan, Poroacoustic acceleration waves, Proceedings of the Royal Society A, 462 (2006), 3493-3499.
doi: 10.1098/rspa.2006.1730. |
[19] |
M. Ciarletta, B. Straughan and V. Zampoli, Thermo-poroacoustic acceleration waves in elastic materials with voids without energy dissipation, Int. J. Engng. Sci., 45 (2007), 736-743.
doi: 10.1016/j.ijengsci.2007.05.001. |
[20] |
M. Ciarletta, B. Straughan and V. Zampoli, Poroacoustic acceleration waves in a Jordan-Darcy-Cattaneo material, Int. J. Non-linear Mech., 52 (2013), 8-11.
doi: 10.1016/j.ijnonlinmec.2013.01.020. |
[21] |
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[26] |
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doi: 10.1016/0020-7225(91)90066-C. |
[27] |
T. Gultop, B. Alyavuz and M. Kopac, Propagation of acceleration waves in the johnson-segalman fluids, Mech. Res. Communications, 37 (2010), 153-157.
doi: 10.1016/j.mechrescom.2009.12.007. |
[28] |
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[29] |
R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research Part B, 36 (200), 507-535.
doi: 10.1016/S0191-2615(01)00015-7. |
[30] |
D. Iesan and A. Scalia, Thermoelastic Deformations, Kluwer, Dordrecht, 1996.
doi: 10.1007/978-94-017-3517-9. |
[31] |
C. B. Jonsson, L. T. M. Figueiredo and O. Vapalahti, A global perspective on hantavirus ecology, epidemiology, and disease, Clinical Micribiology Reviews, 23 (2010), 412-441.
doi: 10.1128/CMR.00062-09. |
[32] |
P. M. Jordan, Growth and decay of shock and acceleration waves in a traffic flow model with relaxation, Physica D, 207 (2005), 220-229.
doi: 10.1016/j.physd.2005.06.002. |
[33] |
P. M. Jordan, Growth, decay and bifurcation of shock amplitudes under the type-II flux law, Proc. Roy. Soc. London A, 463 (2007), 2783-2798.
doi: 10.1098/rspa.2007.1895. |
[34] |
P. M. Jordan, Some remarks on nonlinear poroacoustic phenomena, Math. Computers Simulation, 80 (2009), 202-211.
doi: 10.1016/j.matcom.2009.06.004. |
[35] |
P. M. Jordan, A note on Chrystal's equation, Appl. Math. Computation, 217 (2010), 933-936.
doi: 10.1016/j.amc.2010.05.095. |
[36] |
P. M. Jordan and J. K. Fulford, A note on poroacoustic travelling waves under Darcy's law: Exact solutions, Applications of Mathematics, 56 (2011), 99-115.
doi: 10.1007/s10492-011-0011-6. |
[37] |
P. M. Jordan, G. V. Norton, S. A. Chin-Bing and A. Warn-Varnas, On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids, European J. Mech., B-Fluids, 34 (2012), 56-63.
doi: 10.1016/j.euromechflu.2012.01.016. |
[38] |
P. M. Jordan and G. Saccomandi, Compact acoustic travelling waves in a class of fluids with nonlinear material dispersion, Proc. Roy. Soc. London A, 468 (2012), 3441-3457.
doi: 10.1098/rspa.2012.0321. |
[39] |
S. Kefi, M. Rietkerk, C. L. Alados, Y. Pueyo, V. P. Papanastasis, A. ElAich and P. C. de Ruiter, Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems, Nature, 449 (2007), 213-217.
doi: 10.1038/nature06111. |
[40] |
K. A. Lindsay and B. Straughan, Acceleration Waves and Second Sound in a Perfect fluid, Archive for Rational Mechanics and Analysis, 68 (1978), 53-87.
doi: 10.1007/BF00276179. |
[41] |
R. S. Mani, V. Ravi, A. Desai and S. N. Madhusudana, Emerging Viral Infections in India, Proceedings of the National Academy of Sciences, India Section B, 82 (2012), 5-21.
doi: 10.1007/s40011-011-0001-1. |
[42] |
A. Marasco, On the first-order speeds in any direction of acceleration waves in prestressed second - order isotropic, compressible, and homogeneous materials, Mathematical and Computer Modelling, 49 (2009), 1644-1652.
doi: 10.1016/j.mcm.2008.07.037. |
[43] |
A. Marasco, Second - order effects on the wave propagation in elastic, isotropic, incompressible, and homogeneous media, Int. J. Engng. Sci., 47 (2009), 499-511.
doi: 10.1016/j.ijengsci.2008.08.009. |
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