Stable splitting of bivariate spline spaces by Bernstein-Bézier methods

We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains

Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

What is the true charge transfer gap in parent insulating cuprates?

A large body of experimental data point towards a charge transfer instability of parent insulating cuprates to be their unique property. We argue that the true charge transfer gap in these compounds is as small as 0.4-0.5\,eV rather than 1.5-2.0\,eV as usually derived from the optical gap measurements. In fact we deal with a competition of the conventional (3d$^9$) ground state and a charge transfer (CT) state with formation of electron-hole dimers which evolves under doping to an unconventional bosonic system. Our conjecture does provide an unified standpoint on the main experimental findings for parent cuprates including linear and nonlinear optical, Raman, photoemission, photoabsorption, and transport properties anyhow related with the CT excitations. In addition we suggest a scenario for the evolution of the CuO$_2$ planes in the CT unstable cuprates under a nonisovalent doping.Comment: 13 pages, 5 figures, submitted to PR

Triaxial projected shell model approach

The projected shell model analysis is carried out using the triaxial Nilsson+BCS basis. It is demonstrated that, for an accurate description of the moments of inertia in the transitional region, it is necessary to take the triaxiality into account and perform the three-dimensional angular-momentum projection from the triaxial Nilsson+BCS intrinsic wavefunction.Comment: 9 pages, 2 figure

Local RBF approximation for scattered data fitting with bivariate splines

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given

Internal stresses in steel plate generated by shape memory alloy inserts

Neutron strain scanning was employed to investigate the internal stress fields in steel plate coupons with embedded prestrained superelastic NiTi shape memory alloy inserts. Strain fields in steel were evaluated at T = 21 °C and 130 °C on virgin coupons as well as on mechanically and thermally fatigued coupons. Internal stress fields were evaluated by direct calculation of principal stress components from the experimentally measured lattice strains as well as by employing an inverse finite element modeling approach. It is shown that if the NiTi inserts are embedded into the elastic steel matrix following a carefully designed technological procedure, the internal stress fields vary with temperature in a reproducible and predictable way. It is estimated that this mechanism of internal stress generation can be safely applied in the temperature range from −20 °C to 150 °C and is relatively resistant to thermal and mechanical fatigue. The predictability and fatigue endurance of the mechanism are of essential importance for the development of future smart metal matrix composites or smart structures with embedded shape memory alloy components