MURMURS AND NOISE CAUSED BY ARTERIAL NARROWING – THEORY AND CLINICAL PRACTICE

2006 ◽  
Vol 06 (04) ◽  
pp. L415-L425 ◽  
Author(s):  
MARTIN BIER ◽  
ORVILLE W. DAY ◽  
DAVID W. PRAVICA
Keyword(s):  
Clinical Trial ◽  
Duplex Ultrasound ◽  
Type Equation ◽  
Decay Rates ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Small Clinical Trial ◽  
Complex Eigenvalues ◽  
Flow Through ◽  
Sound Spectrum

Arterial narrowing can cause an audible whirling in the blood flow. We propose diagnosing such narrowing by simply recording that sound and analyzing its spectrum. We show how the Navier-Stokes equation for flow through a narrowing can be turned into a Schrödinger type equation. The complex eigenvalues of the latter equation give the frequencies and decay rates of the vortices present in the whirling pattern. Our diagnosis is based on understanding the relation between features in the sound spectrum and the severity of the narrowing. Today the most commonly used method of diagnosis is duplex ultrasound. In a small clinical trial our method appears to be as good as duplex ultrasound.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

scholarly journals Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guochun Wu ◽  
Han Wang ◽  
Yinghui Zhang
Keyword(s):  
Electric Field ◽  
Decay Rates ◽  
Navier Stokes ◽  
Optimal Time ◽  
Poisson System ◽  
Navier Stokes Equation ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
The Cauchy Problem ◽  
Time Decay Rates

<p style='text-indent:20px;'>We are concerned with the Cauchy problem of the 3D compressible Navier–Stokes–Poisson system. Compared to the previous related works, the main purpose of this paper is two–fold: First, we prove the optimal decay rates of the higher spatial derivatives of the solution. Second, we investigate the influences of the electric field on the qualitative behaviors of solution. More precisely, we show that the density and high frequency part of the momentum of the compressible Navier–Stokes–Poisson system have the same <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> decay rates as the compressible Navier–Stokes equation and heat equation, but the <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> decay rate of the momentum is slower due to the effect of the electric field.</p>

scholarly journals An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Aziz Fri
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Type Equation ◽  
Reaction Diffusion ◽  
Growth Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
New Framework

The aim of this paper is to extend the usual framework of PDE with Au=-div ax,u,∇u to include a large class of cases with Au=∑β≤α-1βDβAβx,u,∇u,…,∇αu, whose coefficient Aβ satisfies conditions (including growth conditions) which guarantee the solvability of the problem Au=f. This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation.

TRANSITION TO TURBULENCE FROM PLANE COUETTE FLOW

2015 ◽  
Vol 57 (2) ◽  
pp. 89-113 ◽  
Author(s):  
L. K. FORBES
Keyword(s):  
Couette Flow ◽  
Applied Mathematics ◽  
Fluid Flows ◽  
Type Equation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Unstable Flow ◽  
Navier Stokes Equation ◽  
Fluid Turbulence ◽  
Sommerfeld Equation

Modelling fluid turbulence is perhaps one of the hardest problems in Applied Mathematics. In a recent paper, the author argued that the classical Navier–Stokes equation is not sufficient to describe the transition to turbulence, but that a Reiner–Rivlin type equation is needed instead. This is explored here for the simplest of all viscous fluid flows, the Couette flow, which is a simple shear between two moving plates. It is found that at high wavenumbers, the transition to unstable flow at the critical Reynolds number is characterized by a large number of eigenvalues of the Orr–Sommerfeld equation moving into the unstable zone essentially simultaneously. This would generate high-dimensional chaos almost immediately, and is a suggested mechanism for the transition to turbulence. Stability zones are illustrated for the flow, and a simple asymptotic solution confirms some of the features of these numerical results.

Transient Electroosmotic Flow in Slit Microchannel Containing Salt-Free Medium

2009 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Surface Charge Density ◽  
Electroosmotic Flow ◽  
Theoretical Study ◽  
Capillary Tube ◽  
Navier Stokes ◽  
Free Medium ◽  
Navier Stokes Equation ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

A theoretical study on the transient electroosmotic flow through a slit microchannel containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electroosmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electroosmotic flow is detailed. The general behavior of electroosmotic flow in a planar slit is similar to that in a capillary tube; however, the rate of evolution of the flow in a tube with time is faster by a factor of about 2.4 than that in a slit with its width equal to the tube diameter.

Numerical and Experimental Study of Pressure Drop Reduction in a Power Plant Stack

2004 ◽  
Author(s):  
Murthy Lakshmiraju ◽  
Jie Cui ◽  
Stephen Idem ◽  
Sastry Munukutla
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Power Plants ◽  
Experimental Studies ◽  
Maximum Flow ◽  
Scale Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Through

As governmental regulations on the emission of the power industry became more restrictive, many power plants operating today experience severe problems. The fans that handle the flow through the stack, that were originally designed to handle a certain maximum flow rate, are now required to handle even higher flow rates due to the introduction of emission control devices. In this study, computational fluid dynamics (CFD) and experimental studies have been carried out on the scale model of a stack to identify means for pressure drop reduction. The CFD model was constructed using the commercial software CFX-5.6. The model solves the Reynolds averaged Navier-Stokes equation with Shear-Stress turbulence model (SST) and the CFD results are validated by data taken from the scale model. Baffles of different orientation have been installed in the stack under different flow conditions. Both numerical and experimental results confirm that adding baffles can reduce the pressure drop in a stack significantly. Thus, with minimum effort, power plants can keep running the stacks at a higher flow rate.

scholarly journals Numerical Simulation of Nonlinear Pulsatile Newtonian Blood Flow through a Multiple Stenosed Artery

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Satyasaran Changdar ◽  
Soumen De
Keyword(s):  
Blood Flow ◽  
Flow Model ◽  
Cylindrical Tube ◽  
Navier Stokes ◽  
Normal Functioning ◽  
Arterial Segment ◽  
Navier Stokes Equation ◽  
Stenosed Artery ◽  
Incompressible Newtonian Fluid ◽  
Flow Through

An appropriate nonlinear blood flow model under the influence of periodic body acceleration through a multiple stenosed artery is investigated with the help of finite difference method. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier-Stokes equation. The nonlinear equation is solved numerically with the proper boundary conditions and pressure gradient that arise from the normal functioning of the heart. Results are discussed in comparison with the existing models.

An Actively Controlled Micromixer

1999 ◽  
Author(s):  
Marion Volpert ◽  
Carl D. Meinhart ◽  
Igor Mezic ◽  
Mohammed Dahleh
Keyword(s):  
Stokes Equation ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Mixing Efficiency ◽  
Navier Stokes Equation ◽  
Two Fluids ◽  
Flow Through ◽  
Flow Configurations ◽  
Active Mixing

Abstract An active mixing strategy has been developed to enhance mixing of two fluids through a microchannel. Mixing is enhanced when the flow through the main channel of the mixer is perturbed by three sets of secondary flow channels. Numerical solutions of the flow through the mixer are calculated by simulating the full Navier-Stokes equation, the Stokes equation, and a simple analytical model based upon the superposition of elementary velocity profiles. The analytical model agrees qualitatively with Navier-Stokes and Stokes solutions for Reynolds numbers, Re = 5. A mixing coefficient is developed to quantitatively evaluate mixing efficiency for various flow configurations. The results indicate enhanced mixing for two possible flow configurations.

scholarly journals The Riccati Equation and the Hidden Parameter &Variable

2021 ◽  
Author(s):  
Ji-Xiang Zhao
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Riccati Equation ◽  
Stokes Equation ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Elementary Quadrature ◽  
Linear Odes ◽  
Hidden Parameter

Abstract Using suitable function transformation in combination with a specific Riccati-type equation solvable, general solution of the Riccati equation in the form of elementary quadrature is given. In the process of solving the Riccati equation, the hidden parameter and variable are discovered. This indicates that hidden parameter & variable exist in all differential equations associated with the Riccati equation, such as the second-order linear ODEs, the Schrödinger equation and the Navier–Stokes equation.

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