1,653 research outputs found

    U-Pb geochronology of the El Jadida rhyolite and relation to possible Lower Cambrian recycling (Coastal block, Moroccan Meseta).

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    The El Jadida (Mazagan) dome, whose existence was reported as early as 1934 by Yovanovitch and Freys, constitutes one of the first outcrops of the Moroccan Meseta where the Precambrian (PIII?)-Paleozoic (Lower Cambrian?) boundary was established (Gigout, 1951; Cornée et al., 1984). Since then, it is listed as one of the few locations where the basement of the Moroccan Variscan belt can be observed (Hoepffner et al.. 2005; Michard et al., 2010).Despite, the absence of geochronological and biostratigraphic precise data to constrain the time interval recorded here, there are stratigraphic similarities that allow a correlation with the Ediacaran-Cambrian geological record of Anti-Atlas belt (Cornée et al., 1984). In this study, we developed a petrographic, geochemical and U-Pb geochronological study using zircon extracted from: (i) the El Jadida rhyolite with the aim of characterizing the magma source and estimate the age of crystallization; (ii) a microbreccia sampled at the base of the El Jadida Dolomitic Formation for determining provenance

    Spectral characteristics for a spherically confined -1/r + br^2 potential

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    We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential V(r)V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure

    Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors

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    We determine the specific heat amplitude ratio near a mm-axial Lifshitz point and show its universal character. Using a recent renormalization group picture along with new field-theoretical ϵL\epsilon_{L}-expansion techniques, we established this amplitude ratio at one-loop order. We estimate the numerical value of this amplitude ratio for m=1m=1 and d=3d=3. The result is in very good agreement with its experimental measurement on the magnetic material MnPMnP. It is shown that in the limit m→0m \to 0 it trivially reduces to the Ising-like amplitude ratio.Comment: 8 pages, RevTex, accepted as a Brief Report in Physical Review

    Solvable Systems of Linear Differential Equations

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    The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

    Bulk and Boundary Critical Behavior at Lifshitz Points

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    Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard Ï•4\phi^4 model. Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of the 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior at mm-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of the mm modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian's boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.Comment: Invited contribution to STATPHYS 22, to be published in the Proceedings of the 22nd International Conference on Statistical Physics (STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP), 4--9 July 2004, Bangalore, Indi

    Variational analysis for a generalized spiked harmonic oscillator

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    A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

    Anomalous dimensions and phase transitions in superconductors

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    The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the η\eta exponent is a consequence of a special singular behavior in momentum space. The negative sign of η\eta comes from the divergence of the critical correlation function at finite distances. This behavior implies the existence of a Lifshitz point in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential ηA=4−d\eta_A=4-d has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling σ(ω)∼ξz−2\sigma(\omega)\sim\xi^{z-2}. The prediction z≈3.7z\approx 3.7 is obtained from existing Monte Carlo data.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR
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