Weakly Nonlinear Waves in Elastic Tubes Filled with a Layered Fluid

Demı́ray, Hilmi

doi:10.1515/ijnsns.2002.3.2.89

Cited by 3 publications

(3 citation statements)

References 17 publications

(18 reference statements)

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“…at vanishing viscosity. Such a behaviour is permissible for the blood near the walls of large arteries [18]. Then, the solution (59) implies propagation of solitary waves, where the wave amplitude is a constant.…”

Section: Analytical Solution For the Nonlinear Evolution Equation: Ap...mentioning

confidence: 99%

“…But, because of the significant complexity of fluid-solid structure models under consideration of the wall anisotropy, in the most works the vessel wall is assumed to be isotropic. Moreover, taking into account also the wall thickness-vessel radius (diameter) ratio, the arteries are treated as straight incompressible, thick viscoelastic [15], [16] or elastic tubes [17], as well as thin elastic [18]- [20] or viscoelastic tubes [21], [22]. Usually the arteries are modelled by circularly cylindrical long tubes with a constant cross-section.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On nonlinear waves of the blood flow through arteries

Nikolova,

Jordanov,

Vitanov

2017

Preprint

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We discuss propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm). The processes in the injured artery are modelled by equations for the motion of the wall of the artery and by equation for the motion of the fluid (the blood). For the case when long-wave approximation holds the model equations are reduced to a version of the perturbed Korteweg-deVries equation. Exact travelling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is discussed from the point of view of arterial mechanics.

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Section: Analytical Solution For the Nonlinear Evolution Equation: Ap...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On nonlinear waves of the blood flow through arteries

Nikolova,

Jordanov,

Vitanov

2017

Preprint

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“…The forces that direct the blood flow are gravity and pressure gradient force, while the hindering forces are shear forces resulting from viscosity and turbulence [5,7]. The wall thickness to vessel radius (diameter) ratio due to arteries, are considered flat incompressible, thick viscoelastic [5,8,9] or elastic tubes [10], as well as thin elastic [5,[11][12][13] or viscoelastic tubes [5,14,15]. Therefore, these features show obvious nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Simulation studies on hemodynamic models for blood flow

İzgi

2024

International Journal of Mathematics and Computer in Engineering

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One of the important fluid flows is blood flow seen in hemodynamics, which is a vital process and carries many ingredients from one place to another in the interior of the body. Blood is a special suspension; it is a non-Newtonian fluid as the blood flow cannot be compressed due to the imbalance in strain force and velocity. The blood flow is modelled by various equations which are based on fundamental equations such as Korteweg-De Vries (KdV) equation, nonlinear Schrödinger type equations. Our aim in this study is that the solitary solutions of the blood flow models are obtained in explicit form via Bernoulli method which is one of the ansatz-based methods. The results will be an important role in improving the models and they will support the theoretical basis and diagnose some blood diseases.

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