Characteristics of First-Order Vortex Lattice Melting: Jumps in Entropy and Magnetization

We derive expressions for the jumps in entropy and magnetization characterizing the first-order melting transition of a flux line lattice. In our analysis we account for the temperature dependence of the Landau parameters and make use of the proper shape of the melting line as determined by the relative importance of electromagnetic and Josephson interactions. The results agree well with experiments on anisotropic Y$_1$Ba$_2$Cu$_3$O$_{7-\delta}$ and layered Bi$_2$Sr$_2$Ca$_1$Cu$_2$O$_8$ materials and reaffirm the validity of the London model.Comment: 4 pages. We have restructured the paper to emphasize that in the London scaling regime (appropriate for YBCO) our results are essentially exact. We have also emphasized that a major controversy over the relevance of the London model to describe VL melting has been settled by this wor

A new broken U(1)-symmetry in extreme type-II superconductors

A phase transition within the molten phase of the Abrikosov vortex system without disorder in extreme type-II superconductors is found via large-scale Monte-Carlo simulations. It involves breaking a U(1)-symmetry, and has a zero-field counterpart, unlike vortex lattice melting. Its hallmark is the loss of number-conservation of connected vortex paths threading the entire system {\it in any direction}, driving the vortex line tension to zero. This tension plays the role of a generalized ``stiffness'' of the vortex liquid, and serves as a probe of the loss of order at the transition, where a weak specific heat anomaly is found.Comment: 5 pages, 3 figure

A Review of Progress Towards Simulation of Arc Quenching in Lightning Protection Devices Based on Multi Chamber Systems

Two distinct modes of follow current suppression were observed in multi-chamber systems (MCS) under lightning overvoltage: Zero Quenching (ZQ) and Impulse Quenching (IQ). Sufficiently lower erosion of electrodes and evaporation of discharge chamber walls makes the IQ more preferable as a mechanism of arc quenching. Since experimental search for best MCS design is both difficult and expensive numerical modeling is considered as a prospective method for geometry optimization. Several steps were made towards development of efficient arc model. This article highlights most important results of arc quenching simulation and current status of arc model development

Genetic Variation at Nuclear Loci Fails to Distinguish Two Morphologically Distinct Species of Aquilegia

Aquilegia formosa and pubescens are two closely related species belonging to the columbine genus. Despite their morphological and ecological differences, previous studies have revealed a large degree of intercompatibility, as well as little sequence divergence between these two taxa [1], [2]. We compared the inter- and intraspecific patterns of variation for 9 nuclear loci, and found that the two species were practically indistinguishable at the level of DNA sequence polymorphism, indicating either very recent speciation or continued gene flow. As a comparison, we also analyzed variation at two loci across 30 other Aquilegia taxa; this revealed slightly more differentiation among taxa, which seemed best explained by geographic distance. By contrast, we found no evidence for isolation by distance on a more local geographic scale. We conclude that the extremely low levels of genetic differentiation between A. formosa and A.pubescens at neutral loci will facilitate future genome-wide scans for speciation genes

Flux melting in BSCCO: Incorporating both electromagnetic and Josephson couplings

Multilevel Monte Carlo simulations of a BSCCO system are carried out including both Josephson as well as electromagnetic couplings for a range of anisotropies. A first order melting transition of the flux lattice is seen on increasing the temperature and/or the magnetic field. The phase diagram for BSCCO is obtained for different values of the anisotropy parameter $\gamma$. The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev. Lett. {\bf 75}, 1166 (1995)] is obtained for $\gamma\approx 250$ provided one assumes a temperature dependence $\lambda^2(0)/\lambda^2(T)=1-t$ of the penetration depth with $t=T/T_c$. Assuming a dependence $\lambda^2(0)/\lambda^2(T)=1-t^2$ the best fit is obtained for $\gamma\approx 450$. For finite anisotropy the data is shown to collapse on a straight line when plotted in dimensionless units which shows that the melting transition can be satisfied with a single Lindemann parameter whose value is about 0.3. A different scaling applies to the $\gamma=\infty$ case. The energy jump is measured across the transition and for large values of $\gamma$ it is found to increase with increasing anisotropy and to decrease with increasing magnetic field. For infinite anisotropy we see a 2D behavior of flux droplets with a transition taking place at a temperature independent of the magnetic field. We also show that for smaller values of anisotropy it is reasonable to replace the electromagnetic coupling with an in-plane interaction represented by a Bessel function of the second kind ($K_0$), thus justifying our claim in a previous paper.Comment: 12 figures, revtex

Universal properties for linelike melting of the vortex lattice

Using numerical results obtained within two models describing vortex matter (interacting elastic lines (Bose model) and uniformly frustrated XY-model) we establish universal properties of the melting transition within the linelike regime. These properties, which are captured correctly by both models, include the scaling of the melting temperature with anisotropy and magnetic field, the effective line tension of vortices in the liquid regime, the latent heat, the entropy jump per entanglement length, and relative jump of Josephson energy at the transition as compared to the latent heat. The universal properties can serve as experimental fingerprints of the linelike regime of melting. Comparison of the models allows us to establish boundaries of the linelike regime in temperature and magnetic field.Comment: Revtex, 12 pages, 2 EPS figure

Flux-line entanglement as the mechanism of melting transition in high-temperature superconductors in a magnetic field

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-T_c superconductors in ${\bf B}\parallel {\bf \hat{c}}$ is clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature T_m, while no sharp change can be found in the number and size distribution of vortex loops around T_m. Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of physical quantities are consistent with the above mechanism of the FLL melting. The Lindemann number is also evaluated without any phenomenological arguments.Comment: 10 pages, 5 Postscript figures, RevTeX; changed content and figures, Phys. Rev. B Rapid Commun. in pres

Nucleation of Stable Superconductivity in YBCO-Films

By means of the linear dynamic conductivity, inductively measured on epitaxial films between 30mHz and 30 MHz, the transition line $T_g (B)$ to generic superconductivity is studied in fields between B=0 and 19T. It follows closely the melting line $T_m (B)$ described recently in terms of a blowout of thermal vortex loops in clean materials. The critical exponents of the correlation length and time near $T_g (B)$, however, seem to be dominated by some intrinsic disorder. Columnar defects produced by heavy-ion irradiation up to field-equivalent-doses of $B_{\phi} = 10T$ lead to a disappointing reduction of $T_g (B \to 0)$ while for $B>B_{\phi}$ the generic line of the pristine film is recovered. These novel results are also discussed in terms of a loop-driven destruction of generic superconductivity.Comment: 11 pages including 7 EPS figures, accepted for publication in the Proceedings of the Spring Meeting of the German Physical Society, Muenster 1999,Festkoerperprobleme/Advances in Solid State Physics 199

Abrikosov vortex escape from a columnar defect as a topological electronic transition in vortex core

We study microscopic scenario of vortex escape from a columnar defect under the influence of a transport current. For defect radii smaller than the superconducting coherence length the depinning process is shown to be a consequence of two subsequent topological electronic transitions in a trapped vortex core. The first transition at a critical current $j_L$ is associated with the opening of Fermi surface segments corresponding to the creation of a vortex--antivortex pair bound to the defect. The second transition at a certain current $j_d > j_L$ is caused by merging of different Fermi surface segments, which accompanies the formation of a freely moving vortex.Comment: 5 pages, 4 figure

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.Comment: 38 pages, Appeared in RECOMB 201