An SDE model for deterioration of rock surfaces

References

• Camuffo, D. (1986). Deterioration processes of historical monuments. In: Schneider, T, ed. Acidification and Its Policy Implications. Amsterdam: Elsevier Science Publishers, p 189–221.
   Google Scholar
• Carroll, D. (1970). Rock Weathering. New York: Plenum Press.
   Google Scholar
• Huggett, R. J. (2011). Fundamentals of Geomorphology. 3rd ed. London: Routledge, Taylor and Francis Group.
   Google Scholar
• Anderson, R. S., Anderson, S. P. (2010). Geomorphology: The Mechanics and Chemistry of Landscapes. Cambridge: Cambridge University Press.
   Google Scholar
• Allen, E. J., Allen, L. J. S., Arciniega, A., Greenwood, P. E. (2008). Construction of equivalent stochastic differential equation models. Stoch. Anal. Appl. 26(2):274–297. DOI:10.1080/07362990701857129.
   Web of Science ®Google Scholar
• Allen, E. J. (2016). Environmental variability and mean-reverting processes. Discrete Continuous Dyn. Syst. Ser. B 21(7):2073–2089. DOI:10.3934/dcdsb.2016037.
   Web of Science ®Google Scholar
• Allen, E. J. (2016). Stochastic differential equation models for the wear of coins in circulation. Tribol. Lett. 64(3):1–8. DOI:10.1007/s11249-016-0780-x.
   Web of Science ®Google Scholar
• Allen, E. J. (2018). SDE models with exponential drift and diffusion for approximating fatigue crack growth dynamics. Eng. Fract. Mech.. 200:75–85. DOI:10.1016/j.engfracmech.2018.07.013.
   Web of Science ®Google Scholar
• Allen, L. J. S. (2010). An Introduction to Stochastic Processes with Applications to Biology. 2nd ed. Boca Raton, FL: CRC Press, Chapman & Hall Publishers.
   Google Scholar
• Ladde, A. G., Ladde, G. S. (2013). An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis. Vol. 2. Singapore: World Scientific Publishing Company.
   Google Scholar
• Domokos, G., Gibbons, G. W. (2013). Geometrical and physical models of abrasion. Available at http://arxiv.org/abs/1307.5633
   Google Scholar
• Greeley, R., Leach, R. N., Williams, S. H., White, B. R., Pollack, J. B., Krinsley, D. H., Marshall, J. R. (1982). Rate of wind abrasion on mars. J. Geophys. Res. 87(B12):10009–10024. DOI:10.1029/JB087iB12p10009.
   Web of Science ®Google Scholar
• Vákonyi, P. L., Domokos, G. (2011). A general model for collision-based abrasion processes. IMA J. Appl. Math. 76:47–56. DOI:10.1093/imamat/hxq066.
   Web of Science ®Google Scholar
• Vákonyi, P. L., Laity, J. E. (2011). Formation of surface features on ventifacts: Modeling the role of sand grains rebounding within cavities. Geomorphology 139:220–229. DOI:10.1016/j.geomorph.2011.10.021.
   Web of Science ®Google Scholar
• Vákonyi, P. L., Laity, J. E., Domokos, G. (2016). Quantitative modeling of facet development in ventifacts by sand abrasion. Aeolian Res. 20:25–33. DOI:10.1016/j.aeolia.2015.10.006.
   Web of Science ®Google Scholar
• Wang, Z.-T., Wang, H.-T., Niu, Q.-H., Dong, Z.-B., Wang, T. (2011). Abrasion of yardangs. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(3 Pt 1):031304. DOI:10.1103/PhysRevE.84.031304.
   PubMed Web of Science ®Google Scholar
• Wittel, F. K., Carmona, H. A., Kun, F., Herrmann, H. J. (2008). Mechanisms in impact fragmentation. Int. J. Fract. 154(1-2):105–117. DOI:10.1007/s10704-008-9267-6.
   Web of Science ®Google Scholar
• Sipos, A. A., Domokos, G., Wilson, A., Hovius, N. (2011). A discrete random model describing bedrock profile abrasion. Math. Geosci. 43(5):583–591. DOI:10.1007/s11004-011-9343-8.
   Web of Science ®Google Scholar
• Domokos, G., Gibbons, G. W. (2012). The evolution of pebble shape in space and time. Proc. R. Soc. Lond. 468(2146):3059–3079. DOI:10.1098/rspa.2011.0562.
   Web of Science ®Google Scholar
• Åström, J. A. (2006). Statistical models of brittle fragmentation. Adv. Phys. 55(3-4):247–278. DOI:10.1080/00018730600731907.
   Web of Science ®Google Scholar
• Domokos, G., Kun, F., Sipos, A. Á., Szabó, T. (2015). Universality of fragment shapes. Sci. Rep. 5:9147. DOI:10.1038/srep09147.
   PubMed Web of Science ®Google Scholar
• Sklar, L. S., Riebe, C. S., Marshall, J. A., Genetti, J., Leclere, S., Lukens, C. L., Merces, V. (2017). The problem of predicting the particle size distribution of sediment supplied by hillslopes to rivers. Geomorphology 277:31–49. DOI:10.1016/j.geomorph.2016.05.005.
   Web of Science ®Google Scholar
• Åström, J. A., Linna, R. P., Timonen, J., Møller, P. F., Oddershede, L. (2004). Exponential and power-law mass distributions in brittle fragmentation. Phys. Rev. E 70(2):026104. DOI:10.1103/PhysRevE.70.026104.
   Web of Science ®Google Scholar
• Firey, W. J. (1974). Shapes of worn stones. Mathematika 21(1):1–11. DOI:10.1112/S0025579300005714.
   Web of Science ®Google Scholar
• Suzuki, T., Takahashi, K. (1981). An experimental study of wind abrasion. J. Geol. 89(4):509–522. DOI:10.1086/628617.
   Web of Science ®Google Scholar
• Szabó, T., Fityus, S., Domokos, G. (2013). Abrasion model of downstream changes in grain shape and size along the williams river, Australia. J. Geophys. Res. Earth Surf. 118:2059–2071. DOI:10.1002/jgrf.20142.
   Web of Science ®Google Scholar
• Barchyn, T. E. (2018). Modeling the mechanisms behind yardang evolution. J. Geophys. Res. Earth Surf. 123:618–621. DOI:10.1002/2018JF004629.
   Web of Science ®Google Scholar
• Pelletier, J. D., Kapp, P. A., Abell, J. (2018). Controls on yardang development and morphology: 1. Field observations and measurements at ocotillo wells, California. J. Geophys. Res. EarthSurf. 123:694–722. DOI:10.1002/2017JF004461.
   Web of Science ®Google Scholar
• Pelletier, J. D. (2018). Controls on yardang development and morphology: 2. Numerical modeling. J. Geophys. Res. EarthSurf. 123:723–743. DOI:10.1002/2017JF004462.
   Web of Science ®Google Scholar
• López, A., Stickland, M. T., Dempster, W. M. (2018). CFD study of fluid flow changes with erosion. Comput. Phys. Commun. 227:27–41. DOI:10.1016/j.cpc.2018.02.002.
   Web of Science ®Google Scholar
• Quaife, B. D., Moore, M. (2018). A boundary-integral framework to simulate viscous erosion of a porous medium. Comput. Phys. 375:1–21. DOI:10.1016/j.jcp.2018.07.037.
   Google Scholar
• Allen, E. J. (2009). Derivation of stochastic partial differential equations for size- and age-structured populations. J. Biol. Dyn. 3(1):73–86. DOI:10.1080/17513750802162754.
   PubMedGoogle Scholar
• Fornós, J. J., Gómez-Pujol, L., Cifre, J., Hierro, F. (2011). First steps in limestone weathering and erosion: an atomic force microscopy (AFM) and scanning electron microscopy (SEM) approach. Acta Carsologica 40(2):275–282. DOI:10.3986/ac.v40i2.12.
   Web of Science ®Google Scholar
• McCarroll, D., Nesje, A. (1996). Rock surface roughness as an indicator of degree of rock surface weathering. Earth Surf. Process. Landforms 21(10):963–977. DOI:10.1002/(SICI)1096-9837(199610)21:10<963::AID-ESP643>3.0.CO;2-J.
   Web of Science ®Google Scholar
• Birginie, J. M. (2000). Sea water absorption, permeability evolution and deterioration assessment of building stones subjected to marine exposure. In: Fassina, V., ed. Proceedings of the 9th International Congress on Deterioration and Conservation of Stone. Amsterdam: Elsevier Science, p. 313–321.
   Google Scholar
• Kloeden, P. E., Platen, E., Schurz, H. (1994). Numerical Solution of SDE through Computer Experiments. Berlin: Springer.
   Google Scholar
• Mathur, S. M. (2008). Elements of Geology. Delhi, India: PHI Learning.
   Google Scholar