Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

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Abstract

We focus on the morphochemical reaction-diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerical simulations. We show the occurrence of spatial pattern propagation and derive the Ginzburg-Landau equation describing the envelope of the traveling wavefront.
Lingua originaleEnglish
pagine (da-a)1948-1969
Numero di pagine22
RivistaDefault journal
Volume70
Stato di pubblicazionePublished - 2015

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Turing Patterns
Nonlinear analysis
Nonlinear Analysis
Metals
Turing Instability
Traveling Wavefronts
Amplitude Equations
Reaction-diffusion Model
Multiple Scales
Stable Solution
Ginzburg-Landau Equation
Spatial Pattern
Bifurcation Analysis
Wavefronts
Normal Form
Envelope
Governing equation
Branch
Bifurcation
Propagation

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cita questo

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title = "Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth",
abstract = "We focus on the morphochemical reaction-diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerical simulations. We show the occurrence of spatial pattern propagation and derive the Ginzburg-Landau equation describing the envelope of the traveling wavefront.",
keywords = "Bifurcation analysis, Computational Mathematics, Computational Theory and Mathematics, Modeling and Simulation, Morphochemical electrodeposition, Pattern formation, Reaction-diffusion, Turing instability",
author = "Gaetana Gambino and Salvatore Lupo and Sammartino, {Marco Maria Luigi} and Lacitignola and Sgura and Bozzini",
year = "2015",
language = "English",
volume = "70",
pages = "1948--1969",
journal = "Default journal",

}

TY - JOUR

T1 - Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

AU - Gambino, Gaetana

AU - Lupo, Salvatore

AU - Sammartino, Marco Maria Luigi

AU - Lacitignola, null

AU - Sgura, null

AU - Bozzini, null

PY - 2015

Y1 - 2015

N2 - We focus on the morphochemical reaction-diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerical simulations. We show the occurrence of spatial pattern propagation and derive the Ginzburg-Landau equation describing the envelope of the traveling wavefront.

AB - We focus on the morphochemical reaction-diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerical simulations. We show the occurrence of spatial pattern propagation and derive the Ginzburg-Landau equation describing the envelope of the traveling wavefront.

KW - Bifurcation analysis

KW - Computational Mathematics

KW - Computational Theory and Mathematics

KW - Modeling and Simulation

KW - Morphochemical electrodeposition

KW - Pattern formation

KW - Reaction-diffusion

KW - Turing instability

UR - http://hdl.handle.net/10447/162170

M3 - Article

VL - 70

SP - 1948

EP - 1969

JO - Default journal

JF - Default journal

ER -