Nalan Antar

Weakly nonlinear waves in a prestressed thin elastic tube containing a viscous fluid

Abstract In this work, we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible viscous fluid. In order to include the geometrical and structural dispersion into analysis, the walls inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, is shown to be governed by the Korteweg–de Vries–Burgers (KdVB) equation. Due to dependence of coefficients of the governing equation on the initial deformation, the material and viscosity parameters, the profile of the travelling wave solution to the KdVB equation changes with these parameters. These variations are calculated numerically for some elastic materials and the effects of initial deformation and the viscosity parameter on the propagation characteristics are discussed.

The boundary layer approximation and nonlinear waves in elastic tubes

Abstract In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and approximate equations of an incompressible viscous fluid, the propagation of weakly nonlinear waves is examined. In order to include the geometrical and structural dispersion into analysis, the walls inertial and shear deformation are taken into account in determining the inner pressure-inner cross sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves, in the long-wave approximation, are shown to be governed by the Korteweg–de Vries (KdV) and the Korteweg–de Vries–Burgers (KdVB), depending on the balance between the nonlinearity, dispersion and/or dissipation. In the case of small viscosity (or large Reynolds number), the behaviour of viscous fluid is quite close to that ideal fluid and viscous effects are confined to a very thin layer near the boundary. In this case, using the boundary layer approximation we obtain the viscous-Korteweg–de Vries and viscous-Burgers equations.

Evolution equations for nonlinear waves in a tapered elastic tube filled with a viscous fluid

Abstract In this work, employing the reductive perturbation method and treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube, the propagation of weakly nonlinear waves is investigated in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, depending on the viscosity and perturbation parameters we obtained various evolution equations as the extended Korteweg–de Vries (KdV), extended KdV Burgers and extended perturbed KdV equations. Progressive wave solutions to these evolution equations are obtained and it is observed that the wave speeds increase with the distance for negative tapering while they decrease for positive tapering.

The Korteweg–de Vries–Burgers hierarchy in fluid-filled elastic tubes

Abstract In this work, contribution of higher order terms in modified reductive perturbation method is studied for the propagation of weakly nonlinear waves in fluid-filled elastic tubes. The basic set of equation of fluid and equation of tube is reduced to the Korteweg–de Vries–Burgers equation for the first order displacement component in the radial direction and a linear Korteweg–de Vries–Burgers inhomogeneous equation for the second order displacement component in the radial direction. Dynamical processes of the solitary waves have been numerically analyzed by solving the Korteweg–de Vries–Burgers equation for the first order and the linearized KdV–Burgers equation with an inhomogeneous equation for the second order using pseudo-spectral method.

Non-linear wave modulation in a prestressed fluid field thin elastic tube

In the present work, employing the non-linear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, the amplitude modulation of weakly non-linear waves is examined. Assuming the weakness of dispersive effects and utilizing the reductive perturbation technique, it is shown that the amplitude modulation of these waves is governed by a non-linear Schrodinger (NLS) equation. Some special solutions of the NLS equation are given and the modulational instability of the plane wave solution is discussed for some elastic materials and initial deformations.

Pulse shaping mechanism in mode-locked lasers

A pulse shaping mechanism applied to mode-locked lasers is proposed. By adding a linear (forcing) term in the power energy saturation model, we are able to control the resulting pulses in both energy and shape. In fact, this term also provides a focusing effect keeping most of the pulses energy confined within the width of the forcing. The appropriate condition for which mode-locking occurs is also derived and links the physical parameters of the system (gain, loss, filtering) to those of the pulse (amplitude, width, energy). Thus, given the desired pulse one only needs to fix the lasers parameters accordingly, so as to obey this condition, and mode-locking will occur.