High Tc superconductors: The scaling of Tc with the number of bound holes associated with charge transfer neutralizing the multivalence cations

It is observed that for the known high-T(sub c) Cu-, Tl-, and Bi-based superconductors, T(sub c) scales consistently with the number of bound holes per unit cell which arise from charge transfer excitations of frequency approximately = 3 x 10(exp 13) that neutralized the multivalence cations into diamagnetic states. The resulting holes are established on the oxygens. Extrapolation of this empirical fit in the up-temperature direction suggests a T(sub c) of about 220-230 K at a value of 25 holes/unit cell (approximately the maximum that can be materials-engineered into a high-T(sub c) K2MnF4 or triple Perovskite structure). In the down-temperature direction, the extrapolation gives a T(sub c) in the vicinity of 235 K for the Y-Ba-Cu-O system as well as the known maximum temperature of 23 K for low-T(sub c) materials shown by Nb3Ge. The approach is also consistent with the experimental findings that only multivalence ions which are diamagnetic in their atomic state (Cu, Tl, Bi, Pb, and Sb) associate with high-T(sub c) compounds

A model for the formation of the active region corona driven by magnetic flux emergence

We present the first model that couples the formation of the corona of a solar active region to a model of the emergence of a sunspot pair. This allows us to study when, where, and why active region loops form, and how they evolve. We use a 3D radiation MHD simulation of the emergence of an active region through the upper convection zone and the photosphere as a lower boundary for a 3D MHD coronal model. The latter accounts for the braiding of the magnetic fieldlines, which induces currents in the corona heating up the plasma. We synthesize the coronal emission for a direct comparison to observations. Starting with a basically field-free atmosphere we follow the filling of the corona with magnetic field and plasma. Numerous individually identifiable hot coronal loops form, and reach temperatures well above 1 MK with densities comparable to observations. The footpoints of these loops are found where small patches of magnetic flux concentrations move into the sunspots. The loop formation is triggered by an increase of upwards-directed Poynting flux at their footpoints in the photosphere. In the synthesized EUV emission these loops develop within a few minutes. The first EUV loop appears as a thin tube, then rises and expands significantly in the horizontal direction. Later, the spatially inhomogeneous heat input leads to a fragmented system of multiple loops or strands in a growing envelope.Comment: 13 pages, 10 figures, accepted to publication in A&

Magnetic Jam in the Corona of the Sun

The outer solar atmosphere, the corona, contains plasma at temperatures of more than a million K, more than 100 times hotter that solar surface. How this gas is heated is a fundamental question tightly interwoven with the structure of the magnetic field in the upper atmosphere. Conducting numerical experiments based on magnetohydrodynamics we account for both the evolving three-dimensional structure of the atmosphere and the complex interaction of magnetic field and plasma. Together this defines the formation and evolution of coronal loops, the basic building block prominently seen in X-rays and extreme ultraviolet (EUV) images. The structures seen as coronal loops in the EUV can evolve quite differently from the magnetic field. While the magnetic field continuously expands as new magnetic flux emerges through the solar surface, the plasma gets heated on successively emerging fieldlines creating an EUV loop that remains roughly at the same place. For each snapshot the EUV images outline the magnetic field, but in contrast to the traditional view, the temporal evolution of the magnetic field and the EUV loops can be different. Through this we show that the thermal and the magnetic evolution in the outer atmosphere of a cool star has to be treated together, and cannot be simply separated as done mostly so far.Comment: Final version published online on 27 April 2015, Nature Physics 12 pages and 8 figure

Faulhaber's Theorem on Power Sums

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic