Skip to main content
Erweiterte Suche
Anmelden
nach oben
Tribology Letters
Erschienen in:

01.12.2016 | Original Paper

Stochastic Differential Equation Models for the Wear of Coins in Circulation

verfasst von: Edward Allen

Erschienen in: Tribology Letters | Ausgabe 3/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.
Vorheriger Artikel Transition Between Mixed Lubrication and Elastohydrodynamic Lubrication with Randomly Rough Surfaces
Nächster Artikel The Tribofilm Formation of ZDDP Under Reciprocating Pure Sliding Conditions

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Allen, E.J.: Modeling with Itô Stochastic Differential Equations. Springer, Dordrecht (2007)
2.
Allen, L.J.S.: An Introduction to Stochastic Processes with Applications to Biology, 2nd edn. Chapman & Hall, Boca Raton (2010). CRC Press
3.
Archard, J.F.: Wear theory and mechanisms. In: Peterson, M.B., Winer, W.O. (eds.) Wear Control Handbook, pp. 35–80. American Society of Mechanical Engineers, New York (1980)
4.
Baboian, R., Haynes, G.S.: Development of an Environmental Wear Corrosion Test for Coinage Materials. ASTM STP 866, Philadelphia (1985)
5.
6.
Chattopadhyay, R.: Surface Wear: Analysis, Treatment, and Prevention. ASM International, Materials Park (2001)
7.
Cope, R.G.: The wear of U.K. coins in circulation. Wear 13, 217–224 (1969)CrossRef
8.
Gard, T.C.: Introduction to Stochastic Differential Equations. Marcel Decker, New York (1987)
9.
Ghanbarzadeh, A., Wilson, M., Morina, A., Dowson, D., Neville, A.: Development of a new mechano-chemical model in boundary lubrication. Tribol. Int. 93, 573–582 (2016)CrossRef
10.
Ghanbarzadeh, A., Parsaeian, P., Morina, A., Wilson, M.C.T., van Eijk, M.C.P., Nedelcu, I., Dowson, D., Neville, A.: Semi-deterministic wear model considering the effect of zinc dialkyl dithiophosphate tribofilm. Tribol. Lett. (2016). doi:10.​1007/​s11249-015-0629-8
11.
12.
Jevons, W.S.: Investigations in Currency and Finance. Macmillan and Company, London (1884)
13.
Kloeden, P.E., Platen, E., Schurz, H.: Numerical Solution of SDE Through Computer Experiments. Springer, Berlin (1994)CrossRef
14.
Ladde, A.G., Ladde, G.S.: An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis, vol. 2. World Scientific, Singapore (2013)CrossRef
15.
Müller, J.W.: Quelques remarques sur le poids original de monnaies usées. Revue numismatique 6, 190–198 (1977)CrossRef
16.
17.
Rosenhain, W.: Metallurgy: An Introduction to the Study of Physical Metallurgy. D. Van Nostrand Company, New York (1914)
18.
Rowe, W.B.: Principles of Modern Grinding Technology. Elsevier, Oxford (2009)
19.
Slade, P.G.: Electrical Contacts: Principles and Applications, 2nd edn. CRC Press, Boca Raton (2013)
20.
21.
22.
Tong, G., Jin, X.: Study on the simulation of radial tire wear characteristics. WSEAS Trans. Syst. 11, 419–429 (2012)
23.
Totten, G.E., Liang, H.: Surface Modification and Mechanisms: Friction, Stress, and Reaction Engineering. Marcel Dekker, New York (2004)
24.
Velde, F.R.: On the Evolution of Specie: Circulation and Weight Loss in the 18th and 19th Century Coinage. Document de travail no. 422, Direction Générale des Études et des Relations Internationales. Banque de France, Paris (2013)
25.
Wen, S., Huang, P.: Principles of Tribology. Wiley, New York (2012)
26.
27.
Yeoman, R.S.: A Guide Book of United States Coins, 36th edn. Western Publishing Company, Racine (1982)
28.
Zmitrowicz, A.: Wear patterns and laws of wear a review. J. Theor. Appl. Mech. 44, 219–253 (2006)
Metadaten
Titel
Stochastic Differential Equation Models for the Wear of Coins in Circulation
verfasst von
Edward Allen
Publikationsdatum
01.12.2016
Verlag
Springer US
Erschienen in
Tribology Letters / Ausgabe 3/2016
Print ISSN: 1023-8883
Elektronische ISSN: 1573-2711
DOI
https://doi.org/10.1007/s11249-016-0780-x

Weitere Artikel der Ausgabe 3/2016

Transition Between Mixed Lubrication and Elastohydrodynamic Lubrication with Randomly Rough Surfaces

  • Original Paper

Investigation on Material Response to Ultrahigh Velocity Impact on Ceramics by Micro Particle

  • Original Paper

Solid/Self-Lubrication Mechanisms of an Additively Manufactured Ni–Ti–C Metal Matrix Composite

  • Original Paper

Reply to Comment on “Calculated Trajectories of Curling Stones Under Asymmetrical Friction: Validation of Published Models”

  • Reply to Comment

Effect of 2D Boron Nitride Nanoplate Additive on Tribological Properties of Natural Oils

  • Original Paper

The Tribofilm Formation of ZDDP Under Reciprocating Pure Sliding Conditions

  • Open Access
  • Original Paper

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise