Models of Earth's main magnetic field incorporating flux and radial vorticity constraints

We describe a new technique for implementing the constraints on magnetic fields arising from two hypotheses about the fluid core of the Earth, namely the frozen-flux hypothesis and the hypothesis that the core is in magnetostrophic force balance with negligible leakage of current into the mantle. These hypotheses lead to time-independence of the integrated flux through certain ‘null-flux patches' on the core surface, and to time-independence of their radial vorticity. Although the frozen-flux hypothesis has received attention before, constraining the radial vorticity has not previously been attempted. We describe a parametrization and an algorithm for preserving topology of radial magnetic fields at the core surface while allowing morphological changes. The parametrization is a spherical triangle tesselation of the core surface. Topology with respect to a reference model (based on data from the Oersted satellite) is preserved as models at different epochs are perturbed to optimize the fit to the data; the topology preservation is achieved by the imposition of inequality constraints on the model, and the optimization at each iteration is cast as a bounded value least-squares problem. For epochs 2000, 1980, 1945, 1915 and 1882 we are able to produce models of the core field which are consistent with flux and radial vorticity conservation, thus providing no observational evidence for the failure of the underlying assumptions. These models are a step towards the production of models which are optimal for the retrieval of frozen-flux velocity fields at the core surfac

Complexation of lanthanides, actinides and transition metal cations with a 6-(1,2,4-triazin-3-yl)-2,2’:6’,2’’-terpyridine ligand: implications for actinide(III) /lanthanide(III) partitioning

The quadridentate N-heterocyclic ligand 6-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2’:6’,2’’-terpyridine (CyMe4-hemi-BTBP) has been synthesized and its interactions with Am(III), U(VI), Ln(III) and some transition metal cations have been evaluated by X-ray crystallographic analysis, Am(III)/Eu(III) solvent extraction experiments, UV absorption spectrophotometry, NMR studies and ESI-MS. Structures of the 1:1 complexes with Eu(III), Ce(III) and the linear uranyl (UO22+) ion were obtained by X-ray crystallographic analysis, and showed similar coordination behavior to related BTBP complexes. In methanol, the stability constants of the Ln(III) complexes are slightly lower than those of the analogous quadridentate bis-triazine BTBP ligands, while the stability constant for the Yb(III) complex is higher. 1H NMR titrations and ESI-MS with lanthanide nitrates showed that the ligand forms only 1:1 complexes with Eu(III), Ce(III) and Yb(III), while both 1:1 and 1:2 complexes were formed with La(III) and Y(III) in acetonitrile. A mixture of isomeric chiral 2:2 helical complexes was formed with Cu(I), with a slight preference (1.4:1) for a single directional isomer. In contrast, a 1:1 complex was observed with the larger Ag(I) ion. The ligand was unable to extract Am(III) or Eu(III) from nitric acid solutions into 1-octanol, except in the presence of a synergist at low acidity. The results show that the presence of two outer 1,2,4-triazine rings is required for the efficient extraction and separation of An(III) from Ln(III) by quadridentate N-donor ligand

Shine bright or live long: substituent effects in [Cu(N^N)(P^P)]+-based light-emitting electrochemical cells where N^N is a 6-substituted 2,2'-bipyridine

We report [Cu(P^P)(N^N)][PF6] complexes with P^P = bis(2-(diphenylphosphino)phenyl)ether (POP) or 4,5-bis(diphenylphosphino)-9,9-dimethylxanthene (xantphos) and N^N = 6-methyl-2,2′-bipyridine (Mebpy), 6-ethyl-2,2′-bipyridine (Etbpy), 6,6′-dimethyl-2,2′-bipyridine (Me2bpy) or 6-phenyl-2,2′-bipyridine (Phbpy). The crystal structures of [Cu(POP)(Phbpy)][PF6]·Et2O, [Cu(POP)(Etbpy)][PF6]·Et2O, [Cu(xantphos)(Me2bpy)][PF6], [Cu(xantphos)(Mebpy)][PF6]·CH2Cl2·0.4Et2O, [Cu(xantphos)(Etbpy)][PF6]·CH2Cl2·1.5H2O and [Cu(xantphos)(Phbpy)][PF6] are described; each copper(I) centre is distorted tetrahedral. In the crystallographically determined structures, the N^N domain in [Cu(xantphos)(Phbpy)]+ and [Cu(POP)(Phbpy)]+ is rotated ∼180° with respect to its orientation in [Cu(xantphos)(Mebpy)]+, [Cu(POP)(Etbpy)]+ and [Cu(xantphos)(Etbpy)]+; in each complex containing xantphos, the xanthene ‘bowl’ retains the same conformation in the solid-state structures. The two conformers resulting from the 180° rotation of the N^N ligand were optimized at the B3LYP-D3/(6-31G**+LANL2DZ) level and are close in energy for each complex. Variable temperature NMR spectroscopy evidences the presence of two conformers of [Cu(xantphos)(Phbpy)]+ in solution which are related by inversion of the xanthene unit. The complexes exhibit MLCT absorption bands in the range 378 to 388 nm, and excitation into each MLCT band leads to yellow emissions. Photoluminescence quantum yields (PLQYs) increase from solution to thin-film and powder; the highest PLQYs are observed for powdered [Cu(xantphos)(Mebpy)][PF6] (34%), [Cu(xantphos)(Etbpy)][PF6] (37%) and [Cu(xantphos)(Me2bpy)][PF6] (37%) with lifetimes of 9.6–11 μs. Density functional theory calculations predict that the emitting triplet (T1) involves an electron transfer from the Cu–P^P environment to the N^N ligand and therefore shows a 3MLCT character. T1 is calculated to be ∼0.20 eV lower in energy than the first singlet excited state (S1). The [Cu(P^P)(N^N)][PF6] ionic transition-metal (iTMC) complexes were tested in light-emitting electrochemical cells (LECs). Turn-on times are fast, and the LEC with [Cu(xantphos)(Me2bpy)][PF6] achieves a maximum efficacy of 3.0 cd A−1 (luminance = 145 cd m−2) with a lifetime of 1 h; on going to the [Cu(xantphos)(Mebpy)][PF6]-based LEC, the lifetime exceeds 15 h but at the expense of the efficacy (1.9 cd A−1). The lifetimes of LECs containing [Cu(xantphos)(Etbpy)][PF6] and [Cu(POP)(Etbpy)][PF6] exceed 40 and 80 h respectively

Predictions for PP-wave string amplitudes from perturbative SYM

The role of general two-impurity multi-trace operators in the BMN correspondence is explored. Surprisingly, the anomalous dimensions of all two-impurity multi-trace BMN operators to order g_2^2\lambda' are completely determined in terms of single-trace anomalous dimensions. This is due to suppression of connected field theory diagrams in the BMN limit and this fact has important implications for some string theory processes on the PP-wave background. We also make gauge theory predictions for the matrix elements of the light-cone string field theory Hamiltonian in the two string-two string and one string-three string sectors.Comment: 46 pages, 12 figures. V3:typos correcte

Conformal boundary and geodesics for AdS5×S5AdS_5\times S^5 and the plane wave: Their approach in the Penrose limit

Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise, some typos correcte

Beta-functions in Yang-Mills Theory from Non-critical String

The renormalization group equations of the Yang-Mills theory are examined in the non-critical string theory according to the framework of the holography. Under a simple ansatz for the tachyon, we could find several interesting solutions which are classified by the value of the tachyon potential at the vacuum. We show two typical, asymptotic-free solutions which are different in their infrared behaviors. For both types of solutions, we could obtain quark-confinement potential from the Wilson-loop. The stability of the tachyon and the ZigZag symmetry are also discussed for these solutions.Comment: 16 pages, 5 figure

Non-Abelian BIonic Brane Intersections

We study "fuzzy funnel" solutions to the non-Abelian equations of motion of the D-string. Our funnel describes n^6/360 coincident D-strings ending on n^3/6 D7-branes, in terms of a fuzzy six-sphere which expands along the string. We also provide a dual description of this configuration in terms of the world volume theory of the D7-branes. Our work makes use of an interesting non-linear higher dimensional generalization of the instanton equations.Comment: 17 pages uses harvmac; v2: small typos corrected, refs adde

Yang-Mills theory from non-critical string

The correspondence of the non-critical string theory and the Yang-Mills theory is examined according to the recent Polyakov's proposal, and two possible solutions of the bulk equations are addressed near the fixed points of the pure Yang-Mills theory: (i) One solution asymptotically approaches to the AdS space at the ultraviolet limit where the conformally invariant field theory is realized. (ii) The second one approaches to the flat space in both the infrared and the ultraviolet limits. The area law of the Wilson-loop and the asymptotic freedom with logarithmic behaviour are seen in the respective limit.Comment: 17 pages, no figure, Late