Ferromagnetism and temperature-dependent Electronic Structure of hcp Gadolinium

We use a combination of a many-body model analysis with an ab initio band structure calculation to derive the temperature dependent electronic quasiparticle structure of the rare-earth metal Gadolinium. As a local-moment system Gd is properly represented by the ferromagnetic (multiband) Kondo-lattice model (s-f (d-f) model). The single-particle part of the model-Hamiltonian is taken from an augmented spherical wave (ASW) band calculation. The proposed method avoids the double counting of relevant interactions by exploiting an exact limiting case of the model and takes into account the correct symmetry of atomic orbitals. The a priori only weakly correlated 5d conduction bands get via interband exchange coupling to the localized 4f levels a distinct temperature dependence which explains by a Rudermann-Kittel-Kasuya-Yosida (RKKY) -type mechanism the ferromagnetism of Gd. We get a self-consistently derived Curie temperature of 294.1 K and a T=0-moment of 7.71 $\mu_{\rm B}$, surprisingly close to the experimental values. The striking induced temperature-dependence of the 5d conduction bands explains respective photoemission data. The only parameter of the theory (interband exchange coupling J) is uniquely fixed by the band calculation.Comment: 12 pages, 9 figure

Minimal proper non-IRUP instances of the one-dimensional Cutting Stock Problem

We consider the well-known one dimensional cutting stock problem (1CSP). Based on the pattern structure of the classical ILP formulation of Gilmore and Gomory, we can decompose the infinite set of 1CSP instances, with a fixed demand n, into a finite number of equivalence classes. We show up a strong relation to weighted simple games. Studying the integer round-up property we computationally show that all 1CSP instances with $n\le 9$ are proper IRUP, while we give examples of a proper non-IRUP instances with $n=10$. A gap larger than 1 occurs for $n=11$. The worst known gap is raised from 1.003 to 1.0625. The used algorithmic approaches are based on exhaustive enumeration and integer linear programming. Additionally we give some theoretical bounds showing that all 1CSP instances with some specific parameters have the proper IRUP.Comment: 14 pages, 2 figures, 2 table

Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider such corrections and present a calculation of the four-loop light-by-light-type corrections where the external photon couples to a closed electron or muon loop. We perform an asymptotic expansion in the ratio of electron and muon mass and reduce the resulting integrals to master integrals which we evaluate using analytical and numerical methods. We confirm the results present in the literature which are based on different computational methods.Comment: 16 page

Microstructural characterization of AISI 431 martensitic stainless steel laser-deposited coatings

High cooling rates during laser cladding of stainless steels may alter the microstructure and phase constitution of the claddings and consequently change their functional properties. In this research, solidification structures and solid state phase transformation products in single and multi layer AISI 431 martensitic stainless steel coatings deposited by laser cladding at different processing speeds are investigated by optical microscopy, Scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), orientation imaging microscopy (OIM), ternary phase diagram, Schaeffler and TTT diagrams. The results of this study show how partitionless solidification and higher solidification rates alter the microstructure and phase constitution of martensitic stainless steel laser deposited coatings. In addition, it is shown that while different cladding speeds have no effect on austenite–martensite orientation relationship in the coatings, increasing the cladding speed has resulted in a reduction of hardness in deposited coatings which is in contrast to the common idea about obtaining higher hardness values at higher cladding speeds.

Feedback control of unstable cellular solidification fronts

We present a numerical and experimental study of feedback control of unstable cellular patterns in directional solidification (DS). The sample, a dilute binary alloy, solidifies in a 2D geometry under a control scheme which applies local heating close to the cell tips which protrude ahead of the other. For the experiments, we use a real-time image processing algorithm to track cell tips, coupled with a movable laser spot array device, to heat locally. We show, numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable, and the spacing becomes uniform through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Precision measurement of the branching ratio in the 6P3/2 decay of BaII with a single trapped ion

We present a measurement of the branching ratios from the 6P3/2 state of BaII into all dipoleallowed decay channels (6S1/2, 5D3/2 and 5D5/2). Measurements were performed on single 138Ba+ ions in a linear Paul trap with a frequency-doubled mode-locked Ti:Sapphire laser resonant with the 6S1/2->6P3/2 transition at 455 nm by detection of electron shelving into the dark 5D5/2 state. By driving a pi Rabi rotation with a single femtosecond pulse, a absolute measurement of the branching ratio to 5D5/2 state was performed. Combined with a measurement of the relative decay rates into 5D3/2 and 5D5/2 states performed with long trains of highly attenuated 455 nm pulses, it allowed the extraction of the absolute ratios of the other two decays. Relative strengths normalized to unity are found to be 0.756+/-0.046, 0.0290+/-0.0015 and 0.215+/-0.0064 for 6S1/2, 5D3/2 and 5D5/2 respectively. This approximately constitutes a threefold improvement over the best previous measurements and is a sufficient level of precision to compare to calculated values for dipole matrix elements.Comment: 6 pages, 5 figures, 1 tabl