The Angular Momentum Operator in the Dirac Equation

The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard cartesian (fixed) frame and the second one is the diagonal (rotating) frame. After separating variables in the Dirac equation in spherical coordinates, and solving the corresponding eingenvalues equations associated with the angular operators, we obtain that the spinor solution in the rotating frame can be expressed in terms of Jacobi polynomials, and it is related to the standard spherical harmonics, which are the basis solution of the angular momentum in the Cartesian tetrad, by a similarity transformation.Comment: 13 pages,CPT-94/P.3027,late

Application of remote sensing to state and regional problems

The use of remote sensing techniques to help the state of Mississippi recognize and solve its environmental, resource, and socio-economic problems through inventory, analysis, and monitoring is suggested

Magnetocaloric effect in Gd/W thin film heterostructures

In an effort to understand the impact of nanostructuring on the magnetocaloric effect, we have grown and studied gadolinium in MgO/W(50 $\textrm{\AA}$)/[Gd(400 $\textrm{\AA}$)/W(50 $\textrm{\AA}$)]$_8$ heterostructures. The entropy change associated with the second order magnetic phase transition was determined from the isothermal magnetization for numerous temperatures and the appropriate Maxwell relation. The entropy change peaks at a temperature of 284 K with a value of approximately 3.4 J/kg-K for a 0-30 kOe field change; the full width at half max of the entropy change peak is about 70 K, which is significantly wider than that of bulk Gd under similar conditions. The relative cooling power of this nanoscale system is about 240 J/kg, somewhat lower than that of bulk Gd (410 J/kg). An iterative Kovel-Fisher method was used to determine the critical exponents governing the phase transition to be $\beta=0.51$, and $\gamma=1.75$. Along with a suppressed Curie temperature relative to the bulk, the fact that the convergent value of $\gamma$ is that predicted by the 2-D Ising model may suggest that finite size effects play an important role in this system. Together, these observations suggest that nanostructuring may be a promising route to tailoring the magnetocaloric response of materials

Cohomology of toric line bundles via simplicial Alexander duality

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original algorithm but also a speed-up version of it. Our proof is independent from (in fact appeared earlier on the arXiv than) the proof by H. Roschy and T. Rahn (arXiv:1006.2392), and has several advantages such as being shorter and cleaner and can also settle the additional conjecture on "Serre duality for Betti numbers" which was raised but unresolved in arXiv:1006.2392.Comment: 9 pages. Theorem 1.1 and Corollary 1.2 improved; Abstract and Introduction modified; References updated. To appear in Journal of Mathematical Physic

Giant Antiferromagnetically Coupled Moments in a Molecule-Based Magnet with Interpenetrating Lattices

The molecule-based magnet [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] contains two weakly-coupled, interpenetrating sublattices in a body-centered cubic structure. Although the field-dependent magnetization indicates a metamagnetic transition from an antiferromagnet to a paramagnet, the hysteresis loop also exhibits a substantial magnetic remanance and coercive field uncharacteristic of a typical metamagnet. We demonstrate that this material behaves like two giant moments with a weak antiferromagnetic coupling and a large energy barrier between the orientations of each moment. Because the sublattice moments only weakly depend on field in the transition region, the magnetic correlation length can be directly estimated from the magnetization.Comment: 3 figure

Electrochemical Energy Storage Subsystems Study, Volume 2

The effects on life cycle costs (LCC) of major design and performance technology parameters for multi kW LEO and GEO energy storage subsystems using NiCd and NiH2 batteries and fuel cell/electrolysis cell devices were examined. Design, performance and LCC dynamic models are developed based on mission and system/subsystem requirements and existing or derived physical and cost data relationships. The models are exercised to define baseline designs and costs. Then the major design and performance parameters are each varied to determine their influence on LCC around the baseline values

A Modified Version of the Waxman Algorithm

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices

Extended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method

We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than previous.Comment: 9 page