A Mathematical Representation of the Wheatley Heart Valve

Starting from a hand-drawn contour plot, this note develops a set of intersecting and contiguous circles whose perimeter, upon extending appropriately to three dimensions, can be seen to be a natural mathematical representation of the Wheatley heart valve

Numerical investigation of three dimensional viscoelastic free surface flows: impacting drop problem

This work presents a numerical investigation of three dimensional viscoelastic\ud free surface flows. In particular, using two different numerical methodologies, we have\ud simulated a typical free-surface benchmark flow problem: the impact of a viscoelastic\ud fluid droplet with a rigid boundary. The numerical method was recently proposed by\ud Figueiredo et al. [1] and has been implemented in a in-house viscoelastic flow solver. In\ud this methodology, a finite difference scheme is adopted combining the Marker-And-Cell\ud (MAC) method with a Front-Tracking strategy. In order to preserve mass conservation\ud properties for transient viscoelastic fluid flows, we have modified the methodology in [1]\ud to include an improvement on the MAC discretization of the velocity boundary conditions\ud at free-surfaces. The code is verified by solving the drop impact problem for a Newtonian\ud fluid. After this verification, we employ the Oldroyd-B model to assess the differences\ud between the methodologies, and compare our results with the ones in the literature.\ud Finally, a detailed study of the influence of the relevant rheological parameters of the\ud non-linear viscoelastic models (Giesekus and XPP) is reported, regarding the deformation\ud and spreading of the viscoelastic fluid drop after impacting on a rigid surface.FAPESP (processos nos. 2011/09194-7, 2013/07375-0)CNPq (processo no. 473589/2013-3)European Conference on Computational Mechanics, 5.\ud European Conference on Computational Fluid Dynamics, 6

Improved objective bayesian estimator for a PLP model hierarchically represented subject to competing risks under minimal repair regime

In this paper, we propose a hierarchical statistical model for a single repairable system subject to several failure modes (competing risks). The paper describes how complex engineered systems may be modelled hierarchically by use of Bayesian methods. It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes another one already presented in the literature and continues the study initiated by us in another published paper. Some properties of the new model are discussed. We conduct statistical inference under an objective Bayesian framework. A simulation study is carried out to investigate the efficiency of the proposed methods. Finally, our methodology is illustrated by two practical situations currently addressed in a project under development arising from a partnership between Petrobras and six research institutes

Numerical solutions of Cauchy integral equations and applications

This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis.Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.</p

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Não disponívelThe main objective of this work is the study and implementation of Predictor-Corrector procedures based on the Adams methods for Initial Value Problems. These methods are used with variable order and variable step size. Properties of convergence and stability concerning two different ways of changing the step size, namely: the variable step and interpolation techniques, are discussed. The computer implementation of these techniques through STEP/DE and GEAR codes is analysed,. Numerical examples results with comments which illustrate the behavior of the mentioned codes are presented

Numerical solutions of Cauchy integral equations and applications

This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis.Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.</p

Regularization of a mathematical model of the Wheatley heart valve

This note considers the mathematical model published in the Journal of Biomechanical Engineering by McKee et al. The model presented there suffers from the fact that there is a line discontinuity in the first derivative producing what appears to be a kink in each of the leaflets. This note is concerned with regularizing the shape of the valve while holding to Wheatley's essential idea