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All issues Volume 18 (2023) Math. Model. Nat. Phenom., 18 (2023) 27 References
Open Access
Review
Issue
Math. Model. Nat. Phenom.
Volume 18, 2023
Article Number 27
Number of page(s) 30
Section Mathematical methods
DOI https://doi.org/10.1051/mmnp/2023031
Published online 17 October 2023
  1. A. Ababneh, F. Benboudjema and Y. Xi, Chloride penetration in nonsaturated concrete. J. Mater. Civ. Eng. 15 (2003) 183–191. [CrossRef] [Google Scholar]
  2. A.B. Abell, K.L. Willis and D.A. Lange, Mercury intrusion porosimetry and image analysis of cement-based materials. J. Colloid Interface Sci. 211 (1999) 39–44. [CrossRef] [Google Scholar]
  3. A.A. Abubakar, S.S. Akhtar and A.F.M. Arif, Phase field modeling of V2O5 hot corrosion kinetics in thermal barrier coatings. Comput. Mater. Sci. 99 (2015) 105–116. [CrossRef] [Google Scholar]
  4. Z. Ahmad, Principles of Corrosion Engineering and Corrosion Control. Elsevier (2006). [Google Scholar]
  5. G. Alì, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. I. Modeling and qualitative analysis. Transp. Porous Media 69 (2007) 109–122. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Alì, V. Furuholt, R. Natalini and I. Torcicollo, A mathematical model of sulphite chemical aggression of limestones with high permeability. II. Numerical approximation. Transp. Porous Media 69 (2007) 175–188. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Alì, R. Natalini and I. Torcicollo, Global existence for a 1D parabolic-elliptic model for chemical aggression in permeable materials. Nonlinear Anal. Real World Appl. 21 (2015) 1–12. [CrossRef] [MathSciNet] [Google Scholar]
  8. D. Aregba-Driollet, F. Diele and R. Natalini, A mathematical model for the sulphur dioxide aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J. Appl. Math. 64 (2004) 1636–1667. [CrossRef] [MathSciNet] [Google Scholar]
  9. D.J. Atha and M.R. Jahanshahi, Evaluation of deep learning approaches based on convolutional neural networks for corrosion detection. Struct. Health Monit. 17 (2018) 1110–1128. [CrossRef] [Google Scholar]
  10. S. Balakrishna and G. Shankar Narayana, A simple method for measuring porosity in rocks, Proc. Indian Acad. Sci. A 51 (1960) 265–269. [CrossRef] [Google Scholar]
  11. E. Bastidas-Arteaga, C.-P. El Soueidy, O. Amiri and P.T. Nguyen, Polynomial chaos expansion for lifetime assessment and sensitivity analysis of reinforced concrete structures subjected to chloride ingress and climate change. Struct. Concr. 21 (2020) 1396–1407. [CrossRef] [Google Scholar]
  12. C. Bataillon, F. Bouchon, C. Chainais-Hillairet, C. Desgranges, E. Hoarau, F. Martin, S. Perrin, M. Tupin and J. Talandier, Corrosion modelling of iron based alloy in nuclear waste repository. Electrochim. Acta 55 (2010) 4451–4467. [CrossRef] [Google Scholar]
  13. C. Bataillon, F. Bouchon, C. Chainais-Hillairet, J. Fuhrmann, E. Hoarau and R. Touzani, Numerical methods for the simulation of a corrosion model with moving oxide layer. J. Comput. Phys. 231 (2012) 6213–6231. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Bonetti, C. Cavaterra, F. Freddi, M. Grasselli and R. Natalini, A nonlinear model for marble sulphation including surface rugosity: theoretical and numerical results. Commun. Pure Appl. Anal. 18 (2019) 977–998. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Bonetti, C. Cavaterra, F. Freddi, M. Grasselli and R. Natalini, Chemomechanical degradation of monumental stones: preliminary Results, in Mathematical Modeling in Cultural Heritage, Vol. 41 of Springer INdAM Series. Springer, Cham (2021) 59–72. [CrossRef] [Google Scholar]
  16. L. Brugnano, G. Frasca-Caccia and F. Iavernaro, Line integral solution of Hamiltonian PDEs. Mathematics 7 (2019) 275. [CrossRef] [Google Scholar]
  17. L. Brugnano and F. Iavernaro, Line Integral Methods for Conservative Problems, Vol. 13. CRC Press (2016). [CrossRef] [Google Scholar]
  18. D. Camuffo, M. Del Monte and C. Sabbioni, Origin and growth mechanisms of the sulfated crusts on urban limestone. Water Air Soil Pollut. 19 (1983) 351–359. [CrossRef] [Google Scholar]
  19. A. Cardone, R. D’Ambrosio and B. Paternoster, Exponentially fitted imex methods for advection–diffusion problems. J. Comput. Appl. Math. 316 (2017) 100–108. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Casillo, F. Colace, D. Conte, M. Lombardi, D. Santaniello and C. Valentino, Context-aware recommender systems and cultural heritage: a survey. J. Ambient Intell. Humaniz. Comput. 14 (2021) 3109–3127. [Google Scholar]
  21. M. Casillo, D. Conte, M. Lombardi, D. Santaniello, A. Troiano and C. Valentino, A content-based recommender system for hidden cultural heritage sites enhancing. Lect. Notes Netw. Syst. 217 (2022) 97–109. [CrossRef] [Google Scholar]
  22. M. Casillo, M. De Santo, M. Lombardi, R. Mosca, D. Santaniello and C. Valentino, Recommender systems and digital storytelling to enhance tourism experience in cultural heritage sites, in Proceedings – 2021 IEEE International Conference on Smart Computing, SMARTCOMP 2021 (2021) 323–328. [CrossRef] [Google Scholar]
  23. M.J. Castro and C. Parés, Well-balanced high-order finite volume methods for systems of balance laws. J. Sci. Comput. 82 (2020) 1–48. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Celledoni, V. Grimm, R.I. McLachlan, D.I. McLaren, D. O’Neale, B. Owren and G.R.W. Quispel, Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. J. Comput. Phys. 231 (2012) 6770–6789. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Chainais-Hillairet, P.-L. Colin and I. Lacroix-Violet, Convergence of a finite volume scheme for a corrosion model. Int. J. Finite 12 (2015) 27. [Google Scholar]
  26. C. Chainais-Hillairet and I. Lacroix-Violet, On the existence of solutions for a drift-diffusion system arising in corrosion modeling. Discrete Contin. Dyn. Syst. Ser. B 20 (2015) 77–92. [MathSciNet] [Google Scholar]
  27. V. Chalupecký and A. Muntean, Semi-discrete finite difference multiscale scheme for a concrete corrosion model: a priori estimates and convergence. Jpn. J. Ind. Appl. Math. 29 (2012) 289–316. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Chapwanya, J.M.-S. Lubuma and R.E. Mickens, Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences. Comput. Math. with Appl. 68 (2014) 1071–1082. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Chianese and F. Piccialli, Designing a smart museum: When cultural heritage joins IoT, in Proceedings – 2014 8th International Conference on Next Generation Mobile Applications, Services and Technologies, NGMAST 2014 (2014), 300–306. [Google Scholar]
  30. F. Clarelli, B. De Filippo and R. Natalini, Mathematical model of copper corrosion. Appl. Math. Model. 38 (2014) 4804–4816. [CrossRef] [MathSciNet] [Google Scholar]
  31. F. Clarelli, A. Fasano and R. Natalini, Mathematics and monument conservation: free boundary models of marble sulfation. SIAM J. Appl. Math. 69 (2008) 149–168. [CrossRef] [MathSciNet] [Google Scholar]
  32. A. Coco, M. Donatelli, M. Semplice and S. Serra-Capizzano, Numerical simulations of marble sulfation, in Mathematical Modeling in Cultural Heritage, Vol. 41 of Springer INdAM Series. Springer, Cham (2021) 107–122. [CrossRef] [Google Scholar]
  33. A. Coco, M. Semplice and S. Serra Capizzano, A level-set multigrid technique for nonlinear diffusion in the numerical simulation of marble degradation under chemical pollutants. Appl. Math. Comput. 386 (2020) 125503. [MathSciNet] [Google Scholar]
  34. F. Colace, C. Elia, C.G. Guida, A. Lorusso, F. Marongiu and D. Santaniello, An IOT-based framework to protect cultural heritage buildings, in Proceedings – 2021 IEEE International Conference on Smart Computing, SMARTCOMP 2021 (2021) 377–382. [CrossRef] [Google Scholar]
  35. J.B. Collins and H. Levine, Diffuse interface model of diffusion-limited crystal growth. Phys. Rev. B Condens. Matter 31 (1985) 6119–6122. [CrossRef] [PubMed] [Google Scholar]
  36. V. Comite and P. Fermo, The damage induced by atmospheric pollution on stone surfaces: the chemical characterization of black crusts, in Mathematical Modeling in Cultural Heritage, Vol. 41 of Springer INdAM Series. Springer, Cham (2021) 123–134. [CrossRef] [Google Scholar]
  37. D. Conte, R. D’Ambrosio, G. Giordano and B. Paternoster, Regularized exponentially fitted methods for oscillatory problems. J. Phys. Conf. Ser. 1564 (2020) 012013. [CrossRef] [Google Scholar]
  38. D. Conte and G. Frasca-Caccia, A MATLAB code for the computational solution of a phase field model for pitting corrosion. Dolomites Res. Notes Approx. 15 (2022) 47–65. [MathSciNet] [Google Scholar]
  39. D. Conte and G. Frasca-Caccia, Exponentially fitted methods with a local energy conservation law. Adv. Comput. Math. 49 (2023) 49. [CrossRef] [Google Scholar]
  40. D. Conte, N. Guarino, G. Pagano and B. Paternoster, On the advantages of nonstandard finite difference discretizations for differential problems. Numer. Anal. Appl. 15 (2022) 219–235. [CrossRef] [MathSciNet] [Google Scholar]
  41. D. Conte, N. Guarino, G. Pagano and B. Paternoster, Positivity-preserving and elementary stable nonstandard method for a COVID-19 SIR model. Dolomites Res. Notes Approx. 15 (2022) 65–77. [MathSciNet] [Google Scholar]
  42. D. Conte, F. Mohammadi, L. Moradi and B. Paternoster, Exponentially fitted two-step peer methods for oscillatory problems. Comput. Appl. Math. 39 (2020) 1–19. [Google Scholar]
  43. S. Cuomo, P. De Michele, A. Galletti and F. Piccialli, A cultural heritage case study of visitor experiences shared on a social network. in Proceedings - 2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing, 3PGCIC 2015, (2015) 539–544. [Google Scholar]
  44. S. Cuomo, P.D. Michele, F. Piccialli, A. Galletti and J.E. Jung, Iot-based collaborative reputation system for associating visitors and artworks in a cultural scenario. Expert Syst. Appl. 79 (2017) 101–111. [CrossRef] [Google Scholar]
  45. N. Daengprathum, R. Onchang, K. Nakhapakorn, O. Robert, A. Tipayarom and Peter J.S. Estimation of effects of air pollution on the corrosion of historical buildings in Bangkok. Environ. Nat. Resour. J. 20 (2022) 505–514. [CrossRef] [Google Scholar]
  46. R. D’Ambrosio and B. Paternoster, Exponentially fitted singly diagonally implicit Runge–Kutta methods. J. Comput. Appl. Math. 263 (2014) 277–287. [CrossRef] [MathSciNet] [Google Scholar]
  47. D.H. Davis, Estimating porosity of sedimentary rocks from bulk density. J. Geol. 62 (1954) 102–107. [CrossRef] [Google Scholar]
  48. A. Di Filippo, M. Lombardi, F. Marongiu, A. Lorusso and D. Santaniello, Generative design for project optimization, in Proceedings – DMSVIVA 2021: 27th International DMS Conference on Visualization and Visual Languages (2021) 110–115. [Google Scholar]
  49. M. Donatelli, M. Semplice and S. Serra-Capizzano, AMG preconditioning for nonlinear degenerate parabolic equations on nonuniform grids with application to monument degradation. Appl. Numer. Math. 68 (2013) 1–18. [CrossRef] [MathSciNet] [Google Scholar]
  50. P. Ernst and R.C. Newman, Pit growth studies in stainless steel foils. I. introduction and pit growth kinetics. Corros. Sci. 44 (2002) 927–941. [CrossRef] [Google Scholar]
  51. T. Fatima, N. Arab, E.P. Zemskov and A. Muntean, Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains. J. Eng. Math. 69 (2011) 261–276. [CrossRef] [Google Scholar]
  52. D. Ferretti and Z.P. Bažant, Stability of ancient masonry towers: Moisture diffusion, carbonation and size effect. Cem. Concr. Res. 36 (2006) 1379–1388. [CrossRef] [Google Scholar]
  53. G.J. Fix, Phase field methods for free boundary problems, in Free Boundary Problems: Theory and Applications. Pitman (Advanced Publishing Program). Boston, Mass.-London (1983) 580. [Google Scholar]
  54. G. Frasca-Caccia and P.E. Hydon, Locally conservative finite difference schemes for the modified KdV equation. J. Comput. Dyn. 6 (2019) 307–323. [CrossRef] [MathSciNet] [Google Scholar]
  55. G. Frasca-Caccia and P.E. Hydon, Simple bespoke preservation of two conservation laws. IMA J. Numer. Anal. 40 (2020) 1294–1329. [CrossRef] [MathSciNet] [Google Scholar]
  56. G. Frasca-Caccia and P.E. Hydon, A new technique for preserving conservation laws. Found. Comput. Math. 22 (2021) 477–506. [Google Scholar]
  57. G. Frasca-Caccia and P.E. Hydon, Numerical preservation of multiple local conservation laws. Appl. Math. Comput. 403 (2021) 126203. [Google Scholar]
  58. H. Gao, L. Ju, R. Duddu and H. Li. An efficient second-order linear scheme for the phase field model of corrosive dissolution. J. Comput. Appl. Math. 367 (2020) 112472. [CrossRef] [MathSciNet] [Google Scholar]
  59. H. Gao, L. Ju, X. Li and R. Duddu, A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion. J. Comput. Phys. 406 (2020) 109191. [CrossRef] [MathSciNet] [Google Scholar]
  60. C. Giavarini, M.L. Santarelli, R. Natalini and F. Freddi, A non-linear model of sulphation of porous stones: numerical simulations and preliminary laboratory assessments. J. Cult. Herit. 9 (2008) 14–22. [CrossRef] [Google Scholar]
  61. F.R. Guarguaglini and R. Natalini, Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones. Nonlinear Anal. Real World Appl. 6 (2005) 477–494. [CrossRef] [MathSciNet] [Google Scholar]
  62. F.R. Guarguaglini and R. Natalini, Nonlinear transmission problems for quasilinear diffusion systems. Netw. Heterog. Media 2 (2007) 359–381. [CrossRef] [MathSciNet] [Google Scholar]
  63. E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration, Vol. 31 of Springer Series in Computational Mathematics, 2nd ed. Springer-Verlag, Berlin (2006). [Google Scholar]
  64. C. Hall and A. Hamilton, Porosities of building limestones: using the solid density to assess data quality. Mater. Struct. 49 (2016) 3969–3979. [CrossRef] [Google Scholar]
  65. R. Hamilton and H. Crabbe, Environment, pollution and effects, In The Effects of Air Pollution on Cultural Heritage. Springer (2009) 1–27. [Google Scholar]
  66. M.E. Haque and K.V. Sudhakar, Prediction of corrosion-fatigue behavior of dp steel through artificial neural network. Int. J. Fatigue 23 (2001) 1–4. [CrossRef] [Google Scholar]
  67. A. Heibig, A. Petrov and C. Reichert, Solvability for a drift-diffusion system with Robin boundary conditions. J. Differ. Equ. 267 (2019) 2331–2356. [CrossRef] [Google Scholar]
  68. D. Hilhorst, R. van der Hout and L.A. Peletier, The fast reaction limit for a reaction-diffusion system. J. Math. Anal. Appl. 199 (1996) 349–373. [CrossRef] [MathSciNet] [Google Scholar]
  69. N.-D. Hoang, Image processing-based pitting corrosion detection using metaheuristic optimized multilevel image thresholding and machine-learning approaches. Math. Probl. Eng. 2020 (2020) 6765274. [Google Scholar]
  70. N.-D. Hoang and V.-D. Tran, Image processing-based detection of pipe corrosion using texture analysis and metaheuristic- optimized machine learning approach. Comput. Intell. Neurosci. 2020 (2019) 6765274. [Google Scholar]
  71. L. Gr Ixaru and G. Vanden Berghe. Exponential Fitting, Vol. 568. Springer Science & Business Media (2004). [CrossRef] [Google Scholar]
  72. J.B. Keller and S.I. Rubinow, Recurrent precipitation and liesegang rings. J. Chem. Phys. 74 (1981) 5000–5007. [CrossRef] [MathSciNet] [Google Scholar]
  73. S.G. Kim, W.T. Kim and T. Suzuki, Phase-field model for binary alloys. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60 (1999) 7186–7197. [Google Scholar]
  74. N.P. Kulshreshtha, A.R. Punuru and K.L. Gauri, Kinetics of reaction of so2 with marble. J. Mater. Civ. Eng. 1 (1989) 60–72. [CrossRef] [Google Scholar]
  75. J.S. Langer, Models of pattern formation in first-order phase transitions, in Directions in Condensed Matter Physics, Vol. 1 of World Sci. Ser. Dir. Condensed Matter Phys.. World Sci. Publishing, Singapore (1986) 165–186. [Google Scholar]
  76. T. Li and H.-H. Huang, Probabilistic quantitative analysis on the contents of sulfate corrosion products in concrete. Constr. Build. Mater. 275 (2021). [Google Scholar]
  77. L. Liu, E. Tan, Y. Zhen, X.J. Yin and Z.Q. Cai, AI-facilitated coating corrosion assessment system for productivity Enhancement, in Proceedings of the 13th IEEE Conference on Industrial Electronics and Applications, ICIEA 2018 (2018) 606–610. [Google Scholar]
  78. W. Mai, S. Soghrati and R.G. Buchheit, A phase field model for simulating the pitting corrosion. Corros. Sci. 110 (2016) 157–166. [CrossRef] [Google Scholar]
  79. R.I. McLachlan and G.R.W. Quispel, Discrete gradient methods have an energy conservation law. Discrete Contin. Dyn. Syst. 34 (2013) 1099–1104. [Google Scholar]
  80. A. Michel, G. Mette Rica, M. Lepech and H. Stang, Coupled hygrothermal, electrochemical, and mechanical modelling for deterioration prediction in reinforced cementitious materials, in Coupled Problems in Science and Engineering VII (2017) 345–356. [Google Scholar]
  81. R.E. Mickens, Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Numer. Methods Partial Differ. Equ. 23 (2007) 672–691. [CrossRef] [Google Scholar]
  82. A. Muntean, Multiscale carbonation reactions: status of things and two modeling exercises related to cultural heritage, in INdAM Workshop: Mathematical modeling and Analysis of Degradation and Restoration in CULTURAL HERITAGE (2021) 175–185. [Google Scholar]
  83. J. Niesen and W. Wright, Algorithm 919: a Krylov subspace algorithm for evaluating the φ-functions appearing in exponential integrators. ACM Trans. Math. Softw. 38 (2012) 1–19. [CrossRef] [Google Scholar]
  84. A. Pelle, B. Briseghella, A.V. Bergami, G. Fiorentino, G.F. Giaccu, D. Lavorato, G. Quaranta, A. Rasulo and C. Nuti, Time-dependent cyclic behavior of reinforced concrete bridge columns under chlorides-induced corrosion and rebars buckling. Struct. Concr. 23 (2019) 81–103. [Google Scholar]
  85. G.R.W. Quispel and D.I. McLaren, A new class of energy-preserving numerical integration methods. J. Phys. A. 41 (2008) 045206. [CrossRef] [MathSciNet] [Google Scholar]
  86. R. Reale, L. Campanella, M.P. Sammartino, G. Visco, G. Bretti, M. Ceseri, R. Natalini and F. Notarnicola, A mathematical, experimental study on iron rings formation in porous stones. J. Cult. Herit. 38 (2019) 158–166. [CrossRef] [Google Scholar]
  87. P. Roberge, Corrosion engineering. McGraw-Hill Education, 2008. [Google Scholar]
  88. T. Ruotsalo, K. Haav, A. Stoyanov, S. Roche, E. Fani, R. Deliai, E. Mäkelä, T. Kauppinen and E. Hyvönen, Smartmuseum: a mobile recommender system for the web of data. Web Semant. 20 (2013) 50–67. [CrossRef] [Google Scholar]
  89. G. Russo and A. Khe, High order well balanced schemes for systems of balance laws, in Hyperbolic Problems: Theory, Numerics and Applications, Vol. 67 of Proc. Sympos. Appl. Math. Am. Math. Soc., Providence, RI (2009) 919–928. [CrossRef] [Google Scholar]
  90. A.V. Saetta, B.A. Schrefler and R.V. Vitaliani, The carbonation of concrete and the mechanism of moisture, heat and carbon dioxide flow through porous materials. Cem. Concr. Res. 23 (1993) 761–772. [CrossRef] [Google Scholar]
  91. A.V. Saetta, B.A. Schrefler and R.V. Vitaliani, 2D model for carbonation and moisture/heat flow in porous materials. Cem. Concr. Res. 25 (1995) 1703–1712. [CrossRef] [Google Scholar]
  92. A.V. Saetta and R.V. Vitaliani, Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures part i: Theoretical formulation. Cem. Concr. Res. 34 (2004) 571–579. [CrossRef] [Google Scholar]
  93. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian problems, Vol. 7 of Applied Mathematics and Mathematical Computation. Chapman & Hall, London (1994). [Google Scholar]
  94. M. Semplice, Preconditioned implicit solvers for nonlinear PDEs in monument conservation. SIAM J. Sci. Comput. 32 (2010) 3071–3091. [CrossRef] [MathSciNet] [Google Scholar]
  95. L.F. Shampine, Numerical Solution of Ordinary Differential Equations. Chapman & Hall, New York (1994). [Google Scholar]
  96. R. Sidje, Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Softw. 24 (1998) 130–156. [CrossRef] [Google Scholar]
  97. T. Skoulikidis and D. Charalambous, Mechanism of sulphation by atmospheric SO2 of the limestones and marbles of the ancient monuments and statues: II. Hypothesis concerning the rate determining step in the process of sulphation, and its experimental confirmation. Br. Corros. J. 16 (1981) 70–77. [CrossRef] [Google Scholar]
  98. T. Skoulikidis and P. Papakonstantinou-Ziotis, Mechanism of sulphation by atmospheric SO2 of the limestones and marbles of the ancient monuments and statues. I. Observations in situ (acropolis) and laboratory measurements. Br. Corros. J. 16 (1981) 63–69. [CrossRef] [Google Scholar]
  99. A. Steffens, D. Dinkler and H. Ahrens, Modeling carbonation for corrosion risk prediction of concrete structures. Cem. Concr. Res. 32 (2002) 935–941. [CrossRef] [Google Scholar]
  100. Ø.D. Trier, J.H. Reksten and K. Løseth, Automated mapping of cultural heritage in Norway from airborne lidar data using faster r-cnn. Int. J. Appl. Earth Obs. Geoinf. 95 (2021) 102241. [Google Scholar]
  101. X. Tu, J. Di, C. Pang and X. Xu, Numerical study on diffusion of chloride and induced rebar corrosion by two-dimensional multiscale approach. Model. Simul. Eng. 2018 (2018) 1–20. [CrossRef] [Google Scholar]
  102. K. Van Balen, Carbonation reaction of lime, kinetics at ambient temperature. Cem. Concr. Res. 35 (2005) 647–657. [CrossRef] [Google Scholar]
  103. K. Van Balen and D. Van Gemert, Modelling lime mortar carbonation. Mater. Struct. 27 (1994) 393–398. [CrossRef] [Google Scholar]
  104. A.J. Vromans, A. Muntean and F. van de Ven, A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics. Pac. J. Math. Ind. 10 (2018) Art. 5. [CrossRef] [Google Scholar]
  105. F.C. Walsh, Faraday and his laws of electrolysis: An appreciation. Bull. Electrochem. 7 (1992) 481–484. [Google Scholar]
  106. A.T.S. Wan, A. Bihlo and J.-C. Nave, The multiplier method to construct conservative finite difference schemes for ordinary and partial differential equations. SIAM J. Numer. Anal. 54 (2016) 86–119. [CrossRef] [MathSciNet] [Google Scholar]
  107. Y. Wang, Y. Bai and Y. Xi, Analytical solutions of moisture-chloride ion coupled transport in unsaturated concrete. J. Am. Ceram. Soc. 104 (2021) 5883–5897. [CrossRef] [Google Scholar]
  108. Y. Wang, N. Stash, L. Aroyo, P. Gorgels, L. Rutledge and G. Schreiber, Recommendations based on semantically enriched museum collections. Web Semant. 6 (2008) 283–290. [CrossRef] [Google Scholar]
  109. S.S. Yerrapragada, S.R. Chirra, J.H. Jaynes, S. Li, J.K. Bandyopadhyay and K.L. Gauri, Weathering rates of marble in laboratory and outdoor conditions. Int. J. Environ. Eng. 122 (1996) 856–863. [Google Scholar]
  110. N.G. Zamani, J.F. Porter and A.A. Mufti, A survey of computational efforts in the field of corrosion engineering. Int. J. Numer. Methods Eng. 23 (1986) 1295–1311. [CrossRef] [Google Scholar]

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