A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

Improvement of an extension of a H?lder-type inequality

In this paper an extension of a H?lder-type inequality given in [C. E. M. Pearce and J. Pe?ari?, On an extension of H?lder??s inequality, Bull. Austral. Math. Soc., 51(1995), 453?C458] is improved using log-convexity. Furthermore, new Cauchy-type means are defined and their monotonicity property is proven.     

Schur-convexity and the Simpson formula

The main objective of this work is to give a necessary and sufficient condition for the function defined as the difference of the Simpson quadrature rule and the arithmetic integral mean to be Schur-convex.     

Analyticity of functions analytic on circles

Let Δ be the open unit disc in, let pbΔ, and let f be a continuous function on which extends holomorphically from each circle in centered at the origin and from each circle in which passes through p. Then f is holomorphic on Δ.     

On discrete and continuous wirtinger inequalities

We shall present several generalizations of discrete Wirtinger's inequality, and establish their continuous analogs.     

Means for Divided Differences and Exponential Convexity

In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.