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.     

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.