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All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 30 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 30
Number of page(s) 23
DOI https://doi.org/10.1051/mmnp/2022034
Published online 18 August 2022
  1. J.R. Banavar, A. Maritan and A. Rinaldo, Size and form in efficient transportation networks. Nature 399 (1999) 130–132. [CrossRef] [PubMed] [Google Scholar]
  2. D.A. Beard and J.B. Bassingthwaighte, Advection and diffusion of substances in biological tissues with complex vascular networks. Ann. Biomed. Eng. 28 (2000) 253–268. [CrossRef] [PubMed] [Google Scholar]
  3. Ö. Bodin, M. Tengö, A. Norman, J. Lundberg and T. Elmqvist, The value of small size: loss of forest patches and ecological thresholds in southern Madagascar. Ecol. Appl. 16 (2006) 440–451. [CrossRef] [PubMed] [Google Scholar]
  4. J.W.G. Cairney, Translocation of solutes in ectomycorrhizal and saprotrophic rhizomorphs. Mycolog. Res. 96 (1992) 135–141. [CrossRef] [Google Scholar]
  5. R.S. Cantrell, C. Cosner and Y. Lou, Movement toward better environments and the evolution of rapid diffusion. Math. Biosci. 204 (2006) 199–214. [CrossRef] [MathSciNet] [Google Scholar]
  6. R.S. Cantrell, C. Cosner and Y. Lou, Advection-mediated coexistence of competing species. Proc. Roy. Soc. Edinb. Sect. A 137 (2007) 497–518. [CrossRef] [Google Scholar]
  7. A. Chapman, Semi-Autonomous Networks: Effective Control of Networked Systems through Protocols, Design, and Modeling. Springer Theses. 2015, pp. 6–13. [Google Scholar]
  8. A. Chapman and M. Mesbahi, Advection on graphs. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, IEEE, (2011), pp. 1461–1466. [CrossRef] [Google Scholar]
  9. A. Chapman, E. Schoof and M. Mesbahi, Advection on networks with an application to decentralized load balancing. 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (2012). [Google Scholar]
  10. C. Cosner, Reaction-diffusion-advection models for the effects and evolution of dispersal. Discr. Continu. Dyn. Syst. 34 (2014) 1701. [CrossRef] [Google Scholar]
  11. P. Erdős and A. Rényi, On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci 5 (1960) 17–60. [Google Scholar]
  12. E. Estrada, The structure of complex networks: theory and applications. Oxford University Press (2012). [Google Scholar]
  13. E. Estrada, Combinatorial study of degree assortativity in networks. Phys. Rev. E 84 (2011) 047101. [CrossRef] [PubMed] [Google Scholar]
  14. E. Estrada, ‘Hubs-repelling’ Laplacian and related diffusion on graphs/networks. Linear Algebr. Appl. 596 (2020) 256–280. [CrossRef] [Google Scholar]
  15. E. Estrada and D. Mugnolo, Hubs-biased resistance distances on graphs and networks. J. Math. Anal. Appl. 507 (2022) 125728. [CrossRef] [Google Scholar]
  16. W.F. Fagan et al., Perceptual ranges, information gathering, and foraging success in dynamic landscapes. Am. Natural. 189 (2017) 474–489. [CrossRef] [PubMed] [Google Scholar]
  17. W.F. Fagan et al., Improved foraging by switching between diffusion and advection: benefits from movement that depends on spatial context. Theor. Ecol. 13 (2020) 127–136. [CrossRef] [Google Scholar]
  18. L.V. Gambuzza, M. Frasca and E. Estrada, Hubs-attracting Laplacian and related synchronization on networks. SIAM J. Appl. Dyn. Syst. 19 (2020) 1057–1079. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.U. Ganzhorn, J. Fietz, E. Rakotovao, D. Schwab and D. Zinner, Lemurs and the regeneration of dry deciduous forest in Madagascar. Conserv. Biol. 13 (1999) 794–804. [CrossRef] [Google Scholar]
  20. R.W. Gillham et al., An advection-diffusion concept for solute transport in heterogeneous unconsolidated geological deposits. Water Resour. Res. 20 (1984) 369–378. [CrossRef] [Google Scholar]
  21. D. Goldman, Theoretical models of microvascular oxygen transport to tissue. Microcirculation 15 (2008) 795–811. [CrossRef] [PubMed] [Google Scholar]
  22. D. Goldman and A.S. Popel, A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport. J. Theor. Biol. 206 (2000) 181–194. [CrossRef] [Google Scholar]
  23. D. Grunbaum, Using spatially explicit models to characterize foraging performance in heterogeneous landscapes. Am. Natural. 151 (1998) 97–113. [CrossRef] [PubMed] [Google Scholar]
  24. D. Grünbaum, Advection–diffusion equations for generalized tactic searching behaviors. J. Math. Biol. 38 (1999) 169–194. [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Hanski, A practical model of metapopulation dynamics. J. Animal Ecol. 63 (1994) 151–162. [CrossRef] [Google Scholar]
  26. L.L. Heaton et al., Advection, diffusion, and delivery over a network. Phys. Rev. E 86 (2012) 021905. [CrossRef] [PubMed] [Google Scholar]
  27. R. Hošek and J. Volek, Discrete advection–diffusion equations on graphs: maximum principle and finite volumes. Appl. Math. Comput. 361 (2019) 630–644. [MathSciNet] [Google Scholar]
  28. D.H. Jennings, Translocation of solutes in fungi. Biolog. Rev. 62 (1987) 215–243. [CrossRef] [Google Scholar]
  29. J.P. Kirkpatrick, D.M. Brizel and M.W. Dewhirst, A mathematical model of tumor oxygen and glucose mass transport and metabolism with complex reaction kinetics. Radiat. Res. 159 (2003) 336–344. [CrossRef] [PubMed] [Google Scholar]
  30. K.A. McCulloh, J.S. Sperry and F.R. Adler, Water transport in plants obeys Murray’s law. Nature 421 (2003) 939–942. [CrossRef] [PubMed] [Google Scholar]
  31. R. Merris, Laplacian matrices of graphs: a survey. Linear Algebr. Appl. 197 (1994) 143–176. [CrossRef] [Google Scholar]
  32. N.W. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89 (2002) 208701. [CrossRef] [PubMed] [Google Scholar]
  33. Rak, Advection on graphs.(Doctoral dissertation) 2017. http://nrs.harvard.edu/urn-3:HUL.InstRepos:38779537 [Google Scholar]
  34. L. Sack and N.M. Holbrook, Leaf hydraulics. Annu. Rev. Plant Biol. 57 (2006) 361–381. [CrossRef] [PubMed] [Google Scholar]
  35. S. Sadhukhan and S.K. Basu, Anomalous advection–diffusion models for Avascular tumour growth. Preprint arXiv:1905.05706 (2019). [Google Scholar]
  36. R.J. Shipley and S.J. Chapman, Multiscale modelling of fluid and drug transport in vascular tumours. Bull. Math. Biol. 72 (2010) 1464–1491. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  37. G.T. Skalski and J.F. Gilliam, A diffusion-based theory of organism dispersal in heterogeneous populations. Am. Natural. 161 (2003) 441–458. [CrossRef] [PubMed] [Google Scholar]
  38. R.C. Tyson, J.B. Wilson and W.D. Lane, Beyond diffusion: modelling local and long-distance dispersal for organisms exhibiting intensive and extensive search modes. Theor. Populat. Biol. 79 (2011) 70–81. [CrossRef] [Google Scholar]
  39. J.H. Young, R.F. Evert and W. Eschrich, On the volume-flow mechanism of phloem transport. Planta 113 (1973) 355–366. [CrossRef] [PubMed] [Google Scholar]
  40. J. Yellen, Basic digraph models and properties. In Handbook of Graph Theory (Discrete Mathematics and Its Applications), edited by J. L. Gross, J. Yellen, P. Zhang, Chapman and Hall/CRC (2013) 164–179. [CrossRef] [Google Scholar]
  41. Y. Yuan, J. Yan and P. Zhang, Assortativity measures for weighted and directed networks. J. Complex Netw. 9 (2021) cnab017. [CrossRef] [Google Scholar]

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