Search results for "computational"
showing 10 items of 5884 documents
In Silico Shear and Intramural Stresses are Linked to Aortic Valve Morphology in Dilated Ascending Aorta
2017
Objective/Background: The development of ascending aortic dilatation in patients with bicuspid aortic valve (BAV) is highly variable, and this makes surgical decision strategies particularly challenging. The purpose of this study was to identify new predictors, other than the well established aortic size, that may help to stratify the risk of aortic dilatation in BAV patients.Methods: Using fluid-structure interaction analysis, both haemodynamic and structural parameters exerted on the ascending aortic wall of patients with either BAV ( n = 21) or tricuspid aortic valve (TAV; n = 13) with comparable age and aortic diameter (42.7 +/- 5.3 mm for BAV and 45.4 +/- 10.0 mm for TAV) were compared…
Statistical shape analysis of ascending thoracic aortic aneurysm: Correlation between shape and biomechanical descriptors
2020
An ascending thoracic aortic aneurysm (ATAA) is a heterogeneous disease showing different patterns of aortic dilatation and valve morphologies, each with distinct clinical course. This study aimed to explore the aortic morphology and the associations between shape and function in a population of ATAA, while further assessing novel risk models of aortic surgery not based on aortic size. Shape variability of n = 106 patients with ATAA and different valve morphologies (i.e., bicuspid versus tricuspid aortic valve) was estimated by statistical shape analysis (SSA) to compute a mean aortic shape and its deformation. Once the computational atlas was built, principal component analysis (PCA) allow…
Comparison and multiresolution analysis of irregular meshes with appearance attributes
2004
We present in this dissertation a method to compare and to analyse irregular meshes with appearance attributes. First, we propose a mesh comparison method using a new attribute deviation metric. Considered meshes contain geometric and appearance attributes (e.g. color, texture,temperature). The proposed deviation assessment allows the computation of local attribute differences between two meshes. We present an application of this method to mesh simplification algorithm quality assessment.Then we propose two multiresolution analysis schemes for irregular meshes with appearance attributes. First, a mesh is decomposed in a discret number of levels of detail. We introduce a surface geometry rel…
Simple connections between generalized hypergeometric series and dilogarithms
1997
AbstractConnections between generalized hypergeometric series and dilogarithms are investigated. Some simple relations of an Appell's function and dilogarithms are found.
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams
2000
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.
New indefinite integrals from a method using Riccati equations
2018
ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...
Energy dissipative solutions to the Kobayashi-Warren-Carter system
2017
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\Gamma$-convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions togethe…
The Euler–Lagrange equation for the Anisotropic least gradient problem
2016
Abstract In this paper we find the Euler–Lagrange equation for the anisotropic least gradient problem inf { ∫ Ω ϕ ( x , D u ) : u ∈ B V ( Ω ) , u | ∂ Ω = f } being ϕ a metric integrand and f ∈ L 1 ( ∂ Ω ) . We also characterize the functions of ϕ -least gradient as those whose boundary of the level set is ϕ -area minimizing in Ω .
Indefinite integrals of products of special functions
2016
ABSTRACTA method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of the method are presented, which applies directly to functions which obey homogeneous differential equations. However, functions which obey inhomogeneous equations can be incorporated into the products and examples are given of integrals involving products of Bessel functions combined with Lommel, Anger and Weber functions. Many new integrals are derived for a selection of special functions, including Bessel functions, associated Legendre functions, and elliptic integrals. A number of integrals o…
More indefinite integrals from Riccati equations
2019
ABSTRACTTwo new methods for obtaining indefinite integrals of a special function using Riccati equations are presented. One method uses quadratic fragments of the Riccati equation, the solutions of...