832 research outputs found
The combined effect of temperature and disorder on interlayer exchange coupling in magnetic multilayers
We study the combined effect of temperature and disorder in the spacer on the
interlayer exchange coupling. The temperature dependence is treated on ab
initio level. We employ the spin-polarized surface Green function technique
within the tight-binding linear muffin-tin orbital method and the Lloyd
formulation of the IEC. The integrals involving the Fermi-Dirac distribution
are calculated using an efficient method based on representation of integrands
by a sum of complex exponentials. Application is made to
Co/Cu_{100-x}M_x/Co(001) trilayers (M=Zn, Au, and Ni) with varying thicknesses
of the spacer.Comment: 5 pages, LaTeX, 1 figure. Submitted to Phil. Mag.
A statistical approach to persistent homology
Assume that a finite set of points is randomly sampled from a subspace of a
metric space. Recent advances in computational topology have provided several
approaches to recovering the geometric and topological properties of the
underlying space. In this paper we take a statistical approach to this problem.
We assume that the data is randomly sampled from an unknown probability
distribution. We define two filtered complexes with which we can calculate the
persistent homology of a probability distribution. Using statistical estimators
for samples from certain families of distributions, we show that we can recover
the persistent homology of the underlying distribution.Comment: 30 pages, 2 figures, minor changes, to appear in Homology, Homotopy
and Application
Evaluation of the optical conductivity tensor in terms of contour integrations
For the case of finite life-time broadening the standard Kubo-formula for the
optical conductivity tensor is rederived in terms of Green's functions by using
contour integrations, whereby finite temperatures are accounted for by using
the Fermi-Dirac distribution function. For zero life-time broadening, the
present formalism is related to expressions well-known in the literature.
Numerical aspects of how to calculate the corresponding contour integrals are
also outlined.Comment: 8 pages, Latex + 2 figure (Encapsulated Postscript
The narrowing of the US gender earnings gap, 1959 - 1999: a cohort-based analysis
Using Census and Current Population Survey data spanning 1959 through 1999, we assess the relative contributions of two factors to the decline in the gender wage gap: changes across cohorts in the relative slopes of men's and women's age-earnings profiles, versus changes in relative earnings levels at labor market entry. We find that changes in relative slopes account for about one-third of the narrowing of the gender wage gap over the past 40 years. Under quite general conditions, we argue that this provides an upper bound estimate of the contribution of changes in work experience and other post-school investments (PSIs) to the decline of the gender wage gap
Controlling Complexation Behavior of Early Lanthanides via the Subtle Interplay of their Lewis Acidity with the Chemical Stability of 5,5'-(Azobis)tetrazolide
Two novel nitrogen-rich lanthanide compounds of 5,5'-(azo bis)tetrazolide (ZT) were synthesized and structurally characterized. The dinuclear, isostructural compounds [Ce2(ZT)2CO3(H2O)12] · 4 H2O (1) and [Pr2(ZT)2CO3(H2O)12]·4H2O (2) were synthesized via two independent routes. Compound 1 was obtained after partial Lewis acidic decomposition of ZT by CeIV in aqueous solution of (NH4)2Ce(NO3)6 and Na2ZT. Compound 2 was obtained by crystallization from aqueous solutions of Pr(NO3)3, Na2ZT, and Na2CO3. By X-ray diffraction analysis at 200 K, it was found that the trivalent lanthanide cations are bridged by a bidentate carbonato ligand and each cation is further coordinated by six H2O ligands and one ZT ligand thus being ninefold coordinated
Hamilton and the square root of minus one
Quaternions, objects consisting of a scalar and a vector, sound like a mysterious concept from the past. In the nineteenth century, the theory of quaternions was praised as one of the most brilliant achievements in mathematical physics. The originator of this theory, Hamilton, surely one of the greatest scientists in that area, spent about 18 years in discussing all kinds of algebraic and geometric properties of quaternions. His research was communicated to the Philosophical Magazine in three series of papers comprising a total of 29 contributions. In this commentary, these three series of papers are revisited concentrating primarily on the algebraic properties of quaternions
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