EDP Sciences logo
Subscriber Authentication Point
Sciengine logo
Search
Menu
All issues Volume 21 (2026) Math. Model. Nat. Phenom., 21 (2026) 17 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 21, 2026
Article Number 17
Number of page(s) 32
Section Mathematical methods
DOI https://doi.org/10.1051/mmnp/2026011
Published online 22 April 2026
  1. L. Philippot, J.M. Raaijmakers, P. Lemanceau and W.H. Van Der Putten, Going back to the roots: the microbial ecology of the rhizosphere. Nat. Rev. Microbiol. 11 (2013) 789–799. [Google Scholar]
  2. R.D. Bardgett and W.H. Van Der Putten, Belowground biodiversity and ecosystem functioning. Nature 515 (2014) 505–511. [Google Scholar]
  3. N. Fierer, Embracing the unknown: disentangling the complexities of the soil microbiome. Nat. Rev. Microbiol. 15 (2017) 579–590. [Google Scholar]
  4. P.C. Baveye, W. Otten, A. Kravchenko, M. Balseiro-Romero, E. Beckers, M. Chalhoub, C. Darnault, T. Eickhorst, P. Garnier, S. Hapca and S. Kiranyaz, Emergent properties of microbial activity in heterogeneous soil microenvironments: different research approaches are slowly converging, yet major challenges remain. Front. Microbiol. 9 (2018) Art. no. 367238. [Google Scholar]
  5. A. Genty and V. Pot, Numerical simulation of 3D liquid-gas distribution in porous media by a two-phase TRT lattice Boltzmann method. Transport Porous Media 96 (2013) 271–294. [Google Scholar]
  6. O. Monga, M. Bousso, P. Garnier and V. Pot, 3D geometric structures and biological activity: application to microbial soil organic matter decomposition in pore space. Ecol. Model. 216 (2008) 291–302. [Google Scholar]
  7. O. Monga, F. Hecht, M. Serge, M. Klai, M. Bruno, J. Dias, P. Garnier and V. Pot, Generic tool for numerical simulation of transformation-diffusion processes in complex volume geometric shapes: application to microbial decomposition of organic matter. Comput. Geosci. 169 (2022) 105240. [Google Scholar]
  8. M. Klai, O. Monga, M.S. Jouini and V. Pot, A voxel-based approach for simulating microbial decomposition in soil: comparison with LBM and improvement of morphological models. PLoS One 20 (2025) e0313853. [Google Scholar]
  9. M. Klai, Simulation and Analysis of Joint Transformation and Diffusion Dynamics in Irregular Domains: Application to Computational Modeling of Microbial Decomposition in Porous Media. Ph.D. Thesis, Sorbonne Universite (Paris, France); Universite Cadi Ayyad (Marrakech, Maroc) (2025). [Google Scholar]
  10. Z. Belghali, O. Monga, M. Klai, E.H. Abdelwahed, L. Druoton, V. Pot and P.C. Baveye, Geometric modelling of 3D pore space using curve skeleton: Application to computational microbiology of soil organic matter mineralization. PLoS One 20 (2025) e0331031. [Google Scholar]
  11. B. Leye, D. Nguyen-Ngoc, O. Monga, P. Garnier and N. Nunan, Simulating biological dynamics using partial differential equations: application to decomposition of organic matter in 3D soil structure. Vietnam J. Math. 43 (2015) 801–817. [Google Scholar]
  12. J.K. Hale, Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs, Am. Math. Soc., 25 (2010), 198. [Google Scholar]
  13. J. Milnor, On the Concept of Attractor. The Theory of Chaotic Attractors. Springer, New York, NY (1985) 243–264. [Google Scholar]
  14. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44, Springer Science & Business Media (2012). [Google Scholar]
  15. V.A. Pliss, Nonlocal Problems of the Theory of Oscillations. Academic Press (1966). [Google Scholar]
  16. G.R. Sell and Y. You, Dynamics of evolutionary equations. Vol. 143. New York: Springer, 2002. [Google Scholar]
  17. T. Yoshizawa, Stability Theory by Liapunov's Second Method. Vol. 9. Mathematical Society of Japan (1966). [Google Scholar]
  18. D. Nguyen-Ngoc, et al., Modeling microbial decomposition in real 3d soil structures using partial differential equations. Int. J. Geosci. 4 (2013) 15–26. [Google Scholar]
  19. C.M. Dafermos, Semiflows associated with compact and uniform processes. Math. Syst. Theory 8 (1974) 142–149. [Google Scholar]
  20. D.D. Bainov and P.S. Simeonov, Integral Inequalities and Applications, vol. 57. Springer Science & Business Media (2013). [Google Scholar]
  21. W.M. Haddad and V. Chellaboina, Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems. Nonlinear Anal. Real World Appl. 6 (2005) 35–65. [Google Scholar]
  22. A. Batkai, M.K. Fijavz and A. Rhandi, Positive Operator Semigroups. Operator Theory: Advances and Applications, vol. 257 (2017). [Google Scholar]
  23. A. Juyal, T. Eickhorst, R. Falconer, P.C. Baveye, A. Spiers and W. Otten, Control of pore geometry in soil microcosms and its effect on the growth and spread of Pseudomonas and Bacillus sp. Front. Environ. Sci. 6 (2018) Article 73. [Google Scholar]
  24. O. Monga, F.N. Ngom and J.F. Delerue, Representing geometric structures in 3D tomography soil images: application to pore-space modelling. Comput. & Geosci. 33 (2007) 1140–1161. [Google Scholar]
  25. T. Bultreys, L.V. Hoorebeke and V. Cnudde, Multi-scale, micro-computed tomography-based pore network models to simulate drainage in heterogeneous rocks. Adv. Water Resources 78 (2015) 36–49. [Google Scholar]
  26. A.T. Kemgue, O. Monga, S. Moto, V. Pot, P. Garnier, P.C. Baveye and A. Bouras, From spheres to ellipsoids: Speeding up considerably the morphological modeling of pore space and water retention in soils. Comput. & Geosci. 123 (2019) 20–37. [Google Scholar]
  27. N.F. Ngom, O. Monga, et al., 3D shape extraction segmentation and representation of soil microstructures using generalized cylinders. Comput. Geosci. 39 (2012) 50–63. [Google Scholar]
  28. O. Monga, P. Garnier, V. Pot, E. Coucheney, N. Nunan, W. Otten and C. Chenu, Simulating microbial degradation of organic matter in a simple porous system using the 3-D diffusion-based model MOSAIC. Biogeosciences 11 (2014) 2201–2209. [Google Scholar]
  29. B. Mbe, O. Monga, V. Pot, W. Otten, F. Hecht, X. Raynaud, N. Nunan, C. Chenu, P.C. Baveye and P. Garnier, Scenario modelling of carbon mineralization in 3D soil architecture at the microscale: toward an accessibility coefficient of organic matter for bacteria. Eur. J. Soil Sci. 73 (2022) e13144. [Google Scholar]
  30. X. Raynaud and N. Nunan, Spatial ecology of bacteria at the microscale in soil. PLoS One 9 (2014) e87217. [Google Scholar]
  31. J.L. Soong, L. Fuchslueger, S. Maranon-Jimenez, et al., Microbial carbon limitation: The need for integrating microorganisms into our understanding of ecosystem carbon cycling. Glob Change Biol. 26 (2020) 1953–1961. [Google Scholar]
  32. T.W. Walker, C. Kaiser, F. Strasser et al., Microbial temperature sensitivity and biomass change explain soil carbon loss with warming. Nat. Climate Change 8 (2018) 885–889. [Google Scholar]
  33. B. Leye, C. Goudjo and M. Sy, Convergence analysis of a parabolic nonlinear system arising in biology. Afr. Mat. 24 (2013) 179–194. [Google Scholar]
  34. A.V. Fick, On liquid diffusion. Lond. Edinb. Dublin Philos. Mag. J. Sci. 10 (1855) 30–39. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.