Overcritical state in superconducting round wires sheathed by iron

Magnetic measurements carried out on MgB_2 superconducting round wires have shown that the critical current density J_c(B_a) in wires sheathed by iron can be significantly higher than that in the same bare (unsheathed) wires over a wide applied magnetic field B_a range. The magnetic behavior is, however, strongly dependent on the magnetic history of the sheathed wires, as well as on the wire orientation with respect to the direction of the applied field. The behavior observed can be explained by magnetic interaction between the soft magnetic sheath and superconducting core, which can result in a redistribution of supercurrents in the flux filled superconductor. A phenomenological model explaining the observed behavior is proposed.Comment: 9 pages, 7 figure

Comments on the Entanglement Entropy on Fuzzy Spaces

We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using $1/N$ like expansion when only the near boundary degrees of freedom are incorporated. Numerical and qualitative evidences for the validity of near boundary approximation are finally given .Comment: 14 pages, 2 figure

The qq-log-convexity of Domb's polynomials

In this paper, we prove the $q$-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of $\pi$. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the $q$-log-convexity of Narayana polynomials of type $B$ and a criterion for determining $q$-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

Properties of superconducting MgB_2 wires: "in-situ" versus "ex-situ" reaction technique

We have fabricated a series of iron-sheathed superconducting wires prepared by the powder-in-tube technique from (MgB_2)_{1-x}:(Mg+2B)_x initial powder mixtures taken with different proportions, so that x varies from 0 to 1. It turned out that "ex-situ" prepared wire (x = 0) has considerable disadvantages compared to all the other wires in which "in-situ" assisted (0 < x < 1) or pure "in-situ" (x = 1) preparation was used due to weaker inter-grain connectivity. As a result, higher critical current densities J_c were measured over the entire range of applied magnetic fields B_a for all the samples with x > 0. Pinning of vortices in MgB_2 wires is shown to be due to grain boundaries. J_c(B_a) behavior is governed by an interplay between the transparency of grain boundaries and the amount of "pinning" grain boundaries. Differences between thermo-magnetic flux-jump instabilities in the samples and a possible threat to practical applications are also discussed.Comment: To be published in Supercond. Sci. Technol. (2003), in pres

On the qq-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture