Modulated pressure waves in large elastic tubes

G. R. Mefire Yone, C. B. Tabi, A. Mohamadou, H. P. Ekobena Fouda, T. C. Kofané

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

Modulational instability is the direct way for the emergence of wave patterns and localized structures in nonlinear systems. We show in this work that it can be explored in the framework of blood flow models. The whole modified Navier-Stokes equations are reduced to a difference-differential amplitude equation. The modulational instability criterion is therefore derived from the latter, and unstable patterns occurrence is discussed on the basis of the nonlinear parameter model of the vessel. It is found that the critical amplitude is an increasing function of α, whereas the region of instability expands. The subsequent modulated pressure waves are obtained through numerical simulations, in agreement with our analytical expectations. Different classes of modulated pressure waves are obtained, and their close relationship with Mayer waves is discussed.

Original languageEnglish
Article number033128
JournalChaos
Volume23
Issue number3
DOIs
Publication statusPublished - Jul 8 2013

Fingerprint

Elastic Tubes
elastic waves
tubes
Modulational Instability
blood flow
Difference-differential Equations
nonlinear systems
Localized Structures
Navier-Stokes equation
Amplitude Equations
vessels
Increasing Functions
Modified Equations
Blood Flow
occurrences
Vessel
Navier Stokes equations
Expand
Nonlinear systems
Navier-Stokes Equations

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Mefire Yone, G. R., Tabi, C. B., Mohamadou, A., Ekobena Fouda, H. P., & Kofané, T. C. (2013). Modulated pressure waves in large elastic tubes. Chaos, 23(3), [033128]. https://doi.org/10.1063/1.4819480
Mefire Yone, G. R. ; Tabi, C. B. ; Mohamadou, A. ; Ekobena Fouda, H. P. ; Kofané, T. C. / Modulated pressure waves in large elastic tubes. In: Chaos. 2013 ; Vol. 23, No. 3.
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Mefire Yone, GR, Tabi, CB, Mohamadou, A, Ekobena Fouda, HP & Kofané, TC 2013, 'Modulated pressure waves in large elastic tubes', Chaos, vol. 23, no. 3, 033128. https://doi.org/10.1063/1.4819480

Modulated pressure waves in large elastic tubes. / Mefire Yone, G. R.; Tabi, C. B.; Mohamadou, A.; Ekobena Fouda, H. P.; Kofané, T. C.

In: Chaos, Vol. 23, No. 3, 033128, 08.07.2013.

Research output: Contribution to journalArticle

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T1 - Modulated pressure waves in large elastic tubes

AU - Mefire Yone, G. R.

AU - Tabi, C. B.

AU - Mohamadou, A.

AU - Ekobena Fouda, H. P.

AU - Kofané, T. C.

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AB - Modulational instability is the direct way for the emergence of wave patterns and localized structures in nonlinear systems. We show in this work that it can be explored in the framework of blood flow models. The whole modified Navier-Stokes equations are reduced to a difference-differential amplitude equation. The modulational instability criterion is therefore derived from the latter, and unstable patterns occurrence is discussed on the basis of the nonlinear parameter model of the vessel. It is found that the critical amplitude is an increasing function of α, whereas the region of instability expands. The subsequent modulated pressure waves are obtained through numerical simulations, in agreement with our analytical expectations. Different classes of modulated pressure waves are obtained, and their close relationship with Mayer waves is discussed.

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Mefire Yone GR, Tabi CB, Mohamadou A, Ekobena Fouda HP, Kofané TC. Modulated pressure waves in large elastic tubes. Chaos. 2013 Jul 8;23(3). 033128. https://doi.org/10.1063/1.4819480