scholarly journals Modulation of nonlinear waves in a fluid-filled elastic tube with stenosis

2004 ◽  
Vol 2004 (60) ◽  
pp. 3205-3218 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Amplitude Modulation ◽  
Nonlinear Waves ◽  
Variable Coefficient ◽  
Composite System ◽  
Harmonic Wave ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Reductive Perturbation ◽  
Thin Walled

Treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation is obtained as the variable-coefficient nonlinear Schrödinger equation. It is observed that the speed of the harmonic wave increases with distance from the center of stenosis.

Nonlinear Wave Modulation in a Fluid-Filled Elastic Tube with Stenosis

2008 ◽  
Vol 63 (1-2) ◽  
pp. 24-34 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Variable Coefficient ◽  
Wave Speed ◽  
Harmonic Wave ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Axial Distance ◽  
Nls Equation ◽  
Wave Speeds ◽  
Straight Lines

In the present work, treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation was obtained as the variable coefficient nonlinear Schr¨odinger (NLS) equation. By setting the stenosis function equal to zero, we observed that this variable coefficient NLS equation reduces to the conventional NLS equation. After introducing a new dependent variable and a set of new independent coordinates, we reduced the evolution equation to the conventional NLS equation. By seeking a progressive wave type of solution to this evolution equation we observed, that the wave trajectories are not straight lines anymore; they are rather some curves in the (ξ ,τ ) plane. It was further observed that the wave speeds for both enveloping and harmonic waves are variable, and the speed of the enveloping wave increases with increasing axial distance, whereas the speed of the harmonic wave decreases with increasing axial coordinates. The numerical calculations indicated that the speed of the harmonic wave decreases with increasing time parameter, but the sensitivity of wave speed to this parameter is quite weak.

Interactions of Nonlinear Waves in Fluid-Filled Elastic Tubes

2007 ◽  
Vol 62 (1-2) ◽  
pp. 21-28
Author(s):  
Hilmi Demiray
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Elastic Tube ◽  
Wave Number ◽  
Inviscid Fluid ◽  
Leading Order ◽  
Elastic Tubes ◽  
Longwave Approximation ◽  
Thin Walled ◽  
Analytical Phase

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k3), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.

scholarly journals Propagation of Nonlinear Pressure Waves in Blood

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
A. Elgarayhi ◽  
E. K. El-Shewy ◽  
Abeer A. Mahmoud ◽  
Ali A. Elhakem
Keyword(s):  
Vries Equation ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Pressure Waves ◽  
Weakly Nonlinear ◽  
Flow Problems ◽  
Inner Radius ◽  
Reductive Perturbation ◽  
Conditions Of Stability

The propagation of weakly nonlinear pressure waves in a fluid-filled elastic tube has been investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude. The effect of the final inner radius of the tube on the basic properties of the soliton wave was discussed. Moreover, the conditions of stability and the soliton existence via the potential and the corresponding phase portrait were computed. The applicability of the present investigation to flow problems in arteries is discussed.

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

2006 ◽  
Vol 61 (12) ◽  
pp. 641-651
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Wave Speed ◽  
Kdv Equation ◽  
Order Term ◽  
Perturbation Expansion ◽  
Reductive Perturbation Method ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
Elastic Tubes

Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid, we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term, which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation, and it is observed that the wave speed is variable, which results from the stenosis. We study the variation of the wave speed with the distance parameter τ for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However, sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small.

scholarly journals Modulation of Electron-Acoustic Waves in a Plasma with Vortex Electron Distribution

2015 ◽  
Vol 16 (2) ◽  
pp. 61-66 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Evolution Equation ◽  
Acoustic Waves ◽  
Harmonic Wave ◽  
Fractional Power ◽  
Reductive Perturbation Method ◽  
Field Equations ◽  
Nls Equation ◽  
Electron Acoustic Waves ◽  
Electron Acoustic ◽  
Trapped Vortex

AbstractIn the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrödinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.

One-dimensional shock turbulence in a compressible fluid

1974 ◽  
Vol 65 (3) ◽  
pp. 581-601 ◽  
Author(s):  
Tomomasa Tatsumi ◽  
Hiroshi Tokunaga
Keyword(s):  
Compressible Fluid ◽  
Nonlinear Waves ◽  
Burgers Equation ◽  
Reductive Perturbation Method ◽  
One Dimensional ◽  
Expansion Waves ◽  
Burgers Turbulence ◽  
Reductive Perturbation ◽  
Equation Of Heat Conduction ◽  
Contact Surfaces

The interactions of weak nonlinear disturbances in a compressible fluid including shocks, expansion waves and contact surfaces are investigated by making use of the reductive perturbation method. It is found that the nonlinear waves belonging to different families of characteristics behave almost independently of each other, while those belonging to the same family are governed by either the Burgers equation or the equation of heat conduction. Thus the statistical properties of one-dimensional shock turbulence in a compressible fluid are reduced to those of the solutions of the Burgers equation. In particular, the law of energy decay of shock turbulence is shown to be identical to that of Burgers turbulence.

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