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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 2: 237-258. doi: 10.3934/mbe.2010.7.237
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Morphological spatial patterns in a reaction diffusion model for metal growth

  • 1.
    Dipartimento di Ingegneria dell’Innovazione, Università del Salento - Lecce, via per Monteroni, I-73100 Lecce
  • 2.
    Dipartimento di Scienze Motorie e della Salute, Università di Cassino, Campus Folcara, Loc. S.Angelo, I-03043 Cassino
  • 3.
    Dipartimento di Matematica, Università del Salento - Lecce, via per Arnesano, I-73100 Lecce
  • Received: 01 May 2009 Accepted: 29 June 2018 Published: 01 April 2010

  • MSC : 35K57, 62P30, 65M.

  • In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate - within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability and selection of solutions are also provided. By the numerical approximation of the equations, simulations are presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd alloys.

    Citation: Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. Morphological spatial patterns in a reaction diffusion model for metal growth[J]. Mathematical Biosciences and Engineering, 2010, 7(2): 237-258. doi: 10.3934/mbe.2010.7.237

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  • In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate - within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space analysis is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability and selection of solutions are also provided. By the numerical approximation of the equations, simulations are presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd alloys.


  • This article has been cited by:

    1. Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura, Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation, 2013, 17, 1432-8488, 467, 10.1007/s10008-012-1945-7
    2. Ivonne Sgura, Amos S. Lawless, Benedetto Bozzini, Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation, 2019, 27, 1741-5977, 618, 10.1080/17415977.2018.1490278
    3. DEBORAH LACITIGNOLA, BENEDETTO BOZZINI, IVONNE SGURA, Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay, 2015, 26, 0956-7925, 143, 10.1017/S0956792514000370
    4. Alessandra Gianoncelli, Ivonne Sgura, Patrizia Bocchetta, Deborah Lacitignola, Benedetto Bozzini, High-lateral resolution X-ray fluorescence microspectroscopy and dynamic mathematical modelling as tools for the study of electrodeposited electrocatalysts, 2015, 44, 00498246, 263, 10.1002/xrs.2617
    5. Benedetto Bozzini, Deborah Lacitignola, Claudio Mele, Ivonne Sgura, Coupling of Morphology and Chemistry Leads to Morphogenesis in Electrochemical Metal Growth: A Review of the Reaction-Diffusion Approach, 2012, 0167-8019, 10.1007/s10440-012-9725-z
    6. B Bozzini, M Amati, L Gregoratti, D Lacitignola, I Sgura, I Krastev, Ts Dobrovolska, Intermetallics as key to spiral formation in In–Co electrodeposition. A study based on photoelectron microspectroscopy, mathematical modelling and numerical approximations, 2015, 48, 0022-3727, 395502, 10.1088/0022-3727/48/39/395502
    7. B. Bozzini, G. Gambino, D. Lacitignola, S. Lupo, M. Sammartino, I. Sgura, Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth, 2015, 70, 08981221, 1948, 10.1016/j.camwa.2015.08.019
    8. Olga A. Shilova, Fractals, morphogenesis and triply periodic minimal surfaces in sol–gel-derived thin films, 2020, 95, 0928-0707, 599, 10.1007/s10971-020-05279-y
    9. Benedetto Bozzini, Alessandra Gianoncelli, George Kourousias, Marco Boniardi, Andrea Casaroli, Simone Dal Zilio, Rafaqat Hussain, Majid Kazemian Abyaneh, Maya Kiskinova, Claudio Mele, Sandra Tedeschi, Gian Pietro De Gaudenzi, The role of chromium in the corrosion performance of cobalt- and cobalt-nickel based hardmetal binders: A study centred on X-ray absorption microspectroscopy, 2020, 92, 02634368, 105320, 10.1016/j.ijrmhm.2020.105320
    10. Maria R. Pinto, Gabriel F. Costa, Eduardo G. Machado, Raphael Nagao, Self‐Organization in Electrochemical Synthesis as a Methodology towards New Materials, 2020, 7, 2196-0216, 2979, 10.1002/celc.202000065
    11. Ivonne Sgura, Benedetto Bozzini, Deborah Lacitignola, Numerical approximation of Turing patterns in electrodeposition by ADI methods, 2012, 236, 03770427, 4132, 10.1016/j.cam.2012.03.013
    12. Deborah Lacitignola, Benedetto Bozzini, Ivonne Sgura, Spatio-Temporal Organization in a Morphochemical Electrodeposition Model: Analysis and Numerical Simulation of Spiral Waves, 2014, 132, 0167-8019, 377, 10.1007/s10440-014-9910-3
    13. Benedetto Bozzini, Ivonne Sgura, Deborah Lacitignola, Claudio Mele, Mariapia Marchitto, Antonio Ciliberto, Prediction of Morphological Properties of Smart-Coatings for Cr Replacement, Based on Mathematical Modelling, 2010, 138, 1662-8985, 93, 10.4028/www.scientific.net/AMR.138.93
    14. Ivonne Sgura, Benedetto Bozzini, XRF map identification problems based on a PDE electrodeposition model, 2017, 50, 0022-3727, 154002, 10.1088/1361-6463/aa5a1f
    15. Ankit Singh, Vikas Maurya, Manoj K. Rajpoot, New two-derivative implicit-explicit Runge-Kutta methods for stiff reaction-diffusion systems, 2022, 471, 00219991, 111610, 10.1016/j.jcp.2022.111610
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    17. Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura, Frequency as the Greenest Additive for Metal Plating: Mathematical and Experimental Study of Forcing Voltage Effects on Electrochemical Growth Dynamics, 2011, 6, 14523981, 4553, 10.1016/S1452-3981(23)18348-9
    18. Ioannis K. Chatzipaschalis, Ioannis Tompris, Konstantinos Rallis, Theodoros Panagiotis Chatzinikolaou, Iosif-Angelos Fyrigos, Michail-Antisthenis Tsompanas, Andrew Adamatzky, Phil Ayres, Antonio Rubio, Georgios Ch. Sirakoulis, 2024, Chapter 22, 978-3-031-71551-8, 265, 10.1007/978-3-031-71552-5_22
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