Morphological spatial patterns in a reaction diffusion model for metal growth

doi:10.3934/mbe.2010.7.237

Mathematical Biosciences and Engineering, 2010, 7(2): 237-258. doi: 10.3934/mbe.2010.7.237. 35K57, 62P30, 65M.

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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

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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.

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Keywords: Turing instability; pattern formation; electrodeposition; numerical simulations.

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

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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, Journal of Solid State Electrochemistry, 2013, 17, 2, 467, 10.1007/s10008-012-1945-7
2. Ivonne Sgura, Benedetto Bozzini, Deborah Lacitignola, Numerical approximation of Turing patterns in electrodeposition by ADI methods, Journal of Computational and Applied Mathematics, 2012, 236, 16, 4132, 10.1016/j.cam.2012.03.013
3. DEBORAH LACITIGNOLA, BENEDETTO BOZZINI, IVONNE SGURA, Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay, European Journal of Applied Mathematics, 2015, 26, 02, 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, X-Ray Spectrometry, 2015, 44, 4, 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, Acta Applicandae Mathematicae, 2012, 10.1007/s10440-012-9725-z
6. Deborah Lacitignola, Benedetto Bozzini, Ivonne Sgura, Spatio-Temporal Organization in a Morphochemical Electrodeposition Model: Analysis and Numerical Simulation of Spiral Waves, Acta Applicandae Mathematicae, 2014, 132, 1, 377, 10.1007/s10440-014-9910-3
7. 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, Journal of Physics D: Applied Physics, 2015, 48, 39, 395502, 10.1088/0022-3727/48/39/395502
8. 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, Computers & Mathematics with Applications, 2015, 70, 8, 1948, 10.1016/j.camwa.2015.08.019
9. Ivonne Sgura, Benedetto Bozzini, XRF map identification problems based on a PDE electrodeposition model, Journal of Physics D: Applied Physics, 2017, 50, 15, 154002, 10.1088/1361-6463/aa5a1f
10. Ivonne Sgura, Amos S. Lawless, Benedetto Bozzini, Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation, Inverse Problems in Science and Engineering, 2018, 1, 10.1080/17415977.2018.1490278
11. 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, Advanced Materials Research, 2010, 138, 93, 10.4028/www.scientific.net/AMR.138.93

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