Improved strategies for variational calculations for helium

The aim of this work is to apply trial functions constructed from Hylleraas functions with three independent sets of nonlinear scale factors to variational calculations for helium and helium-like ions. The ground state and low-lying Rydberg energy levels of these ions have been calculated to several orders of magnitude greater accuracy than previous work in this area while using an equal, or in most cases, a reduced number of basis functions. Each of the three sectors of the basis set is found to describe a different scale of coordinate space corresponding to the asymptotic, intermediate, and close-ranged distances between particles. The incorporation of the third, close-ranged sector, allows the basis set to better model complex correlation effects between the nucleus and the two electrons in the atomic three-body problem. Optimization of the basis set parameters is achieved through standard variational techniques and the validity of the wave functions near the electron-nucleus and electron-electron coalescence points is tested using the Kato cusp conditions. The tripled basis set is also applied to the 1/ Z perturbation expansion as a case study. A multiple-precision package, MPFUN90 written by David H. Bailey, was used to alleviate numerical instabilities which arose for certain states.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .N57. Source: Masters Abstracts International, Volume: 43-01, page: 0225. Adviser: G. W. F. Drake. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Exchange stiffness in ultrathin perpendicularly-magnetized CoFeB layers determined using spin wave spectroscopy

We measure the frequencies of spin waves in nm-thick perpendicularly magnetized FeCoB systems, and model the frequencies to deduce the exchange stiffness of this material in the ultrathin limit. For this, we embody the layers in magnetic tunnel junctions patterned into circular nanopillars of diameters ranging from 100 to 300 nm and we use magneto-resistance to determine which rf-current frequencies are efficient in populating the spin wave modes. Micromagnetic calculations indicate that the ultrathin nature of the layer and the large wave vectors used ensure that the spin wave frequencies are predominantly determined by the exchange stiffness, such that the number of modes in a given frequency window can be used to estimate the exchange. For 1 nm layers the experimental data are consistent with an exchange stiffness A= 20 pJ/m, which is slightly lower that its bulk counterpart. The thickness dependence of the exchange stiffness has strong implications for the numerous situations that involve ultrathin films hosting strong magnetization gradients, and the micromagnetic description thereof.Comment: 5 pages, 4 figures, submitted to PR

Fredholm conditions for invariant operators: finite abelian groups and boundary value problems

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth, compact, manifold $M$ without boundary and let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical, pseudodifferential operator acting between sections of two $\Gamma$-equivariant vector bundles $E_0$ and $E_1$. Let $\alpha$ be an irreducible representation of the group $\Gamma$. Then $P$ induces by restriction a map $\pi_\alpha(P) : H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ between the $\alpha$-isotypical components of the corresponding Sobolev spaces of sections. We study in this paper conditions on the map $\pi_\alpha(P)$ to be Fredholm. It turns out that the discrete and non-discrete cases are quite different. Additionally, the discrete abelian case, which provides some of the most interesting applications, presents some special features and is much easier than the general case. We thus concentrate in this paper on the case when $\Gamma$ is finite abelian. We prove then that the restriction $\pi_\alpha(P)$ is Fredholm if, and only if, $P$ is "$\alpha$-elliptic", a condition defined in terms of the principal symbol of $P$. If $P$ is elliptic, then $P$ is also $\alpha$-elliptic, but the converse is not true in general. However, if $\Gamma$ acts freely on a dense open subset of $M$, then $P$ is $\alpha$-elliptic for the given fixed $\alpha$ if, and only if, it is elliptic. The proofs are based on the study of the structure of the algebra $\psi^{m}(M; E)^\Gamma$ of classical, $\Gamma$-invariant pseudodifferential operators acting on sections of the vector bundle $E \to M$ and of the structure of its restrictions to the isotypical components of $\Gamma$. These structures are described in terms of the isotropy groups of the action of the group $\Gamma$ on $E \to M$

On the relevance of large scale pulsed-laser deposition: Evidence of structural heterogeneities in ZnO thin films

Pulsed-laser deposition is known as a well-suited method for growing thin films of oxide compounds presenting a wide range of functional properties. A limitation of this method for industrial process is the very anisotropic expansion dynamics of the plasma plume, which induces difficulties to grow on large scale films with homogeneous thickness and composition. The specific aspect of the crystalline or orientation uniformity has not been investigated, despite its important role on oxide films properties. In this work, the crystalline parameters and the texture of zinc oxide films are studied as a function of position with respect to the central axis of the plasma plume. We demonstrate the existence of large non-uniformities in the films. The stoichiometry, the lattice parameter, and the distribution of crystallites orientations drastically depend on the position with respect to the plume axis, i.e., on the oblique incidence of the ablated species. The origin of these non-uniformities, in particular, the unexpected tilted orientation of the ZnO c-axis may be attributed to the combined effects of the oblique incidence and of the ratio between oxygen and zinc fluxes reaching the surface of the growing film

Ground-state energies for helium, H-, and Ps-

Nonrelativistic energy and other properties of He, H- and Ps- were discussed using a triple basis set in Hylleraas coordinates. The stability and efficiency of the computational method was compared with the quasirandom method. Results showed that the triple basis set in Hylleraas coordinates is capable of exceeding the accuracy of calculations for three-body system based on quasirandom Monte Carlo methods

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds

Mass customization of teaching and learning in organizations

In search of methods that improve the efficiency of teaching and training in organizations, several authors point out that mass customization (MC) is a principle that covers individual needs of knowledge and skills and, at the same time, limits the development costs of customized training to those of mass training. MC is proven and established in the economic sector, and shows high potential for continuing education, too. The paper explores this potential and proposes a multidisciplinary, pragmatic approach to teaching and training in organizations. The first section of the paper formulates four design principles of MC deduced from an examination of economics literature. The second section presents amit™, a frame for mass customized training, designed according to the principles presented in the first section. The evaluation results encourage the further development and use of mass customized training in continuing education, and offer suggestions for future research