PROPAGATION OF HARMONIC WAVES IN AN INITIALLY STRESSED THIN ELASTIC TUBE FILLED WITH AN INVISCID FLUID

1996 ◽  
Vol 20 (1) ◽  
pp. 1-15
Author(s):  
Hilmi Demiray ◽  
Sadik Dost
Keyword(s):  
Harmonic Wave ◽  
Relevant Literature ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Governing Equations ◽  
Field Equations ◽  
Initial Field ◽  
Human Artery ◽  
Special Cases ◽  
Mean Pressure

This article presents a theoretical analysis for the wave propagation in a thin walled prestressed elastic tube filled with an inviscid fluid. Considering the blood flow in human artery and its physiological conditions, the tube is assumed to be initially subjected to a mean pressure Pi and the axial stretch λ2. The governing equations of the tube and the fluid are obtained by adding a small incremental disturbance on this initial field. In the formulation, the interaction between the blood and its container is taken into account. A harmonic wave type of solution is sought for the field equations, and the associated dispersion relation is obtained by using appropriate boundary conditions. Some special cases as well as a general case are thoroughly discussed and the results of the present formulation is compared with those of the relevant literature.

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

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 Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

Mathematical aspects of trapping modes in the theory of surface waves

1987 ◽  
Vol 183 ◽  
pp. 421-437 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Bound States ◽  
Constant Width ◽  
Minimum Energy ◽  
Horizontal Cylinder ◽  
Linear Operators ◽  
Inviscid Fluid ◽  
Infinite Length ◽  
Horizontal Canal ◽  
Special Cases ◽  
Characteristic Modes

A horizontal canal of infinite length and of constant width and depth contains inviscid fluid under gravity. The fluid is bounded internally by a submerged horizontal cylinder which extends right across the canal and has its generators normal to the sidewalls. Suppose that the fluid is set in motion by a surface pressure varying across the canal, then some of the energy is radiated to infinity while some of the energy is trapped in characteristic modes (bound states) near the cylinder. The existence of trapping modes in special cases was shown by Stokes (1846) and Ursell (1951); a general treatment, given by Jones (1953), is based on the theory of elliptic partial differential equations in unbounded domains. In the present paper a much simpler treatment is given which uses only the theory of bounded symmetric linear operators together with Kelvin's minimum-energy theorem of classical hydrodynamics.

Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

1969 ◽  
Vol 36 (4) ◽  
pp. 757-762 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Structural Analysis ◽  
Legendre Polynomials ◽  
Direct Reduction ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Higher Order ◽  
Governing Equations ◽  
Field Equations ◽  
Displacement Boundary ◽  
Polynomial Expansions

Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

On uniqueness in dynamic poroelasticity

1963 ◽  
Vol 53 (4) ◽  
pp. 783-788 ◽  
Author(s):  
H. Deresiewicz ◽  
R. Skalak
Keyword(s):  
Porous Media ◽  
Liquid Medium ◽  
Uniqueness Theorem ◽  
Dissimilar Materials ◽  
Elastic Solid ◽  
Porous Solid ◽  
Uniqueness Of Solution ◽  
Biot’S Theory ◽  
Field Equations ◽  
Special Cases

Abstract Conditions are derived sufficient for uniqueness of solution of the field equations of Biot's theory of liquid-filled porous media, particular attention being paid to continuity requirements at an interface between two such dissimilar materials. It is found that at an interface two distinct sets of conditions will satisfy the demands of the mathematical uniqueness theorem, one of them being discarded on physical grounds. The permissible set is then discussed in relation to a number of possible models of the structure of a pair of elements in contact. The special cases of an impermeable elastic solid or a liquid medium in contact with a saturated porous solid are also examined.

PROPAGATION OF WEAKLY NONLINEAR WAVES IN A FLUID-FILLED THIN ELASTIC TUBE

1999 ◽  
Vol 23 (2) ◽  
pp. 253-265
Author(s):  
H. Demiray
Keyword(s):  
Nonlinear Waves ◽  
Vries Equation ◽  
Perturbation Technique ◽  
Fluid Pressure ◽  
Static Field ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
De Vries ◽  
Weakly Nonlinear Waves

In this work, we study the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions under which the arteries function, the tube is assumed to be subjected to a uniform pressure P0 and a constant axial stretch ratio λz. In the course of blood flow in arteries, it is assumed that a finite time dependent radial displacement is superimposed on this static field but, due to axial tethering, the effect of axial displacement is neglected. The governing nonlinear equation for the radial motion of the tube under the effect of fluid pressure is obtained. Using the exact nonlinear equations of an incompressible inviscid fluid and the reductive perturbation technique, the propagation of weakly nonlinear waves in a fluid-filled thin elastic tube is investigated in the longwave approximation. The governing equation for this special case is obtained as the Korteweg-de-Vries equation. It is shown that, contrary to the result of previous works on the same subject, in the present work, even for Mooney-Rivlin material, it is possible to obtain the nonlinear Korteweg-de-Vries equation.

Vascular impedance analysis in dog lung with detailed morphometric and elasticity data

1994 ◽  
Vol 77 (2) ◽  
pp. 706-717 ◽  
Author(s):  
R. Z. Gan ◽  
R. T. Yen
Keyword(s):  
Pulsatile Flow ◽  
Input Impedance ◽  
Characteristic Impedance ◽  
Main Pulmonary Artery ◽  
Impedance Analysis ◽  
Elastic Tube ◽  
Vascular Impedance ◽  
Mean Pressure ◽  
Vascular Obstruction ◽  
Arteries And Veins

On the basis of experimentally measured morphometric and elasticity data and model-derived mean pressure-flow conditions, we attempt a theoretical modeling of pulsatile flow in the whole lung. In the model we use the "elastic tube" for arteries and veins, and the vascular impedance in arteries and veins follows Womersley's theory and electric analogue. We employ the “sheet-flow” theory to describe the flow in the capillaries and to obtain the microvascular impedance matrix. The characteristic impedance of each order along the vascular tree, the input impedance at the capillary entrance and exit, and the pulmonary arterial input impedance at the main pulmonary artery are computed under certain physiological conditions. Using the pulsatile flow model, we investigate the effects of arterial vascular obstruction on pulmonary vascular impedance. The model-derived data are compared with the available experimental results in the literature.

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