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Stochastic Differential Equation Models for the Wear of Coins in Circulation

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Abstract

The wear of coins in circulation is mathematically examined. It is assumed that high points on the coin surface wear at a greater rate than low points. Based on this hypothesis, deterministic and stochastic differential equation models for the dynamical wear of coins in circulation are derived from physical principles. The mathematical models are solved and compared. The models agree with and explain the actual weight loss behavior of coins in circulation. As an application of the models, a quantitative parameter of coin condition is studied.

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Acknowledgements

The author is grateful to the referees for their careful, thorough reviews and their helpful comments.

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  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409-1042, USA

    Edward Allen

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  1. Edward Allen
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Correspondence to Edward Allen.

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Allen, E. Stochastic Differential Equation Models for the Wear of Coins in Circulation. Tribol Lett 64, 45 (2016). https://doi.org/10.1007/s11249-016-0780-x

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  • DOI: https://doi.org/10.1007/s11249-016-0780-x

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