Bicubic b-spline surface approximation of invariant tori

Abstract

The invariant torus of a coupled system of Van der Pol oscillators is approximated using bicubic B-splines. The paper considers the case of strong nonlinear coupling. In particular, the shapes of invariant torii for the Van der Pol coupling parameter λ are computed in the range [0.1, 2.0]. Comparisons are given with results obtained by the MATLAB differential equation solver ode45. Very good normed residual errors of the determining equations for the approximate tori for the cases λ = 0.1, 0.6 are shown. At the upper limit of λ = 2.0 memory errors occured during the optimization phase for solving the determining equations so that full optimization for some knot sets was not achieved, but a visual comparison of the resulting invariant torus figure showed a close similarity to the solution using ode45.

In Vitro Evaluation of the Acetabular Cup Primary Stability by Impact Analysis

“…Cementless ACs are impacted into the acetabulum through a press-fitting procedure, which leads to the mechanical stability of this implant through the prestressed state of bone tissue [1,2], It has been recommended to keep the micromotions at the boneimplant interface below a threshold comprised between approxi mately 100 and 200 pm [3], in order to avoid the formation of fibrous tissue at the bone-implant interface and to favor osseointegration phenomena [4][5][6][7][8]. Micromotion at the microscopic scale as well as excessive stresses at the bone-implant interface may lead to aseptic loosening which is one of the most common causes of implant surgical failure.…”