Neutron diffraction study of crystal structure and antiferromagnetic ordering in the heavy fermion compound CePd2Al3

Nuclear and magnetic structures of an annealed polycrystalline sample of the heavy-fermion compound CePd₂Al₃ prepared by arc-melting were investigated by neutron powder diffraction. The chemical structure corresponds well to the ordered hexagonal PrNi₂Al₃-type structure. The antiferromagnetic structure of CePd₂Al₃ with an ordered magnetic moment _Ce=0.47(2) _B at saturation is remarkably similar to that in the heavy fermion superconductor UPd₂Al₃. The additional incommensurate magnetic structures reported previously both for UPd₂Al₃ and CePd₂Al₃ are not observed in the present sample of CePd₂Al₃. At 1.4 K the magnetoresistivity of CePd₂Al₃ measured up to 14 T indicates only one field-induced phase transition at 3.0 T.     

On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain

Summary The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parametera and the numberN of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, ifa is varied proportional to 1/N with an exponent 0<<1, then the approximate eigenvalue converges faster than any finite power of 1/N asN. Some numerical examles are given.