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Mathematics and Monument Conservation: Free Boundary Models of Marble Sulfation

Fabrizio Clarelli, Antonio Fasano and Roberto Natalini
SIAM Journal on Applied Mathematics
Vol. 69, No. 1 (2008), pp. 149-168
Stable URL: http://www.jstor.org/stable/40233778
Page Count: 20
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Mathematics and Monument Conservation: Free Boundary Models of Marble Sulfation
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Abstract

We introduce some free boundary problems which describe the evolution of calcium carbonate stones under the attack of atmospheric SO₂, taking into account both swelling of the external gypsum layer and the influence of humidity. Different behaviors are described according to the relative humidity of the environment, and in all cases reliable explicit quasi-steady approximations are introduced under reasonable assumptions on the data. Some numerical simulations are also performed to describe gypsum formation using experimental data, which show a good agreement with the quasi-steady solutions. The influence of the cleaning the crust and of the change in concentration of pollution is evaluated and discussed.

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