The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave

In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function $Z(\vec{x},t)$. It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology.Comment: 9 pages, 5 figure

Thorium-doping induced superconductivity up to 56 K in Gd1-xThxFeAsO

Following the discovery of superconductivity in an iron-based arsenide LaO1-xFxFeAs with a superconducting transition temperature (Tc) of 26 K[1], Tc was pushed up surprisingly to above 40 K by either applying pressure[2] or replacing La with Sm[3], Ce[4], Nd[5] and Pr[6]. The maximum Tc has climbed to 55 K, observed in SmO1-xFxFeAs[7, 8] and SmFeAsO1-x[9]. The value of Tc was found to increase with decreasing lattice parameters in LnFeAsO1-xFx (Ln stands for the lanthanide elements) at an apparently optimal doping level. However, the F- doping in GdFeAsO is particularly difficult[10,11] due to the lattice mismatch between the Gd2O2 layers and Fe2As2 layers. Here we report observation of superconductivity with Tc as high as 56 K by the Th4+ substitution for Gd3+ in GdFeAsO. The incorporation of relatively large Th4+ ions relaxes the lattice mismatch, hence induces the high temperature superconductivity.Comment: 4 pages, 3 figure

Wilson Fermions on a Randomly Triangulated Manifold

A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2-d, on an arbitrary orientable manifold without boundary. It can be easily converted into a computer code. The equivalence, on a sphere, of Majorana fermions and Ising spins in 2-d is rederived. The method can, in principle, be extended to higher dimensions.Comment: 18 pages, latex, 6 eps figures, fig2 corrected, Comment added in the conclusion sectio

Superconductivity in heavily boron-doped silicon carbide

The discoveries of superconductivity in heavily boron-doped diamond (C:B) in 2004 and silicon (Si:B) in 2006 renew the interest in the superconducting state of semiconductors. Charge-carrier doping of wide-gap semiconductors leads to a metallic phase from which upon further doping superconductivity can emerge. Recently, we discovered superconductivity in a closely related system: heavily-boron doped silicon carbide (SiC:B). The sample used for that study consists of cubic and hexagonal SiC phase fractions and hence this lead to the question which of them participates in the superconductivity. Here we focus on a sample which mainly consists of hexagonal SiC without any indication for the cubic modification by means of x-ray diffraction, resistivity, and ac susceptibility.Comment: 9 pages, 5 figure

Topological Aspect of Knotted Vortex Filaments in Excitable Media

Scroll waves exist ubiquitously in three-dimensional excitable media. It's rotation center can be regarded as a topological object called vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and even linked and knotted. In this letter, we give a rigorous topological description of knotted vortex filaments. By using the $\phi$-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments and use this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.Comment: 4 pages, no figures, Accepted by Chin. Phys. Let

Inference of mixed information in Formal Concept Analysis

Negative information can be considered twofold: by means of a negation operator or by capturing the absence of information. In this second approach, a new framework have to be developed: from the syntax to the semantics, including the management of such generalized knowledge representation. In this work we traverse all these issues in the framework of formal concept analysis, introducing a new set of inference rules to manage mixed (positive and negative) attributes.TIN2014-59471-P of the Science and Innovation Ministry of Spain, co-funded by the European Regional Development Fund (ERDF). UNIVERSIDAD DE MÁLAGA. Campus de Excelencia Internacional Andalucía Tech

Possibility of Unconventional Pairing Due to Coulomb Interaction in Fe-Based Pnictide Superconductors: Perturbative Analysis of Multi-Band Hubbard Models

Possibility of unconventional pairing due to Coulomb interaction in iron-pnictide superconductors is studied by applying a perturbative approach to realistic 2- and 5-band Hubbard models. The linearized Eliashberg equation is solved by expanding the effective pairing interaction perturbatively up to third order in the on-site Coulomb integrals. The numerical results for the 5-band model suggest that the eigenvalues of the Eliashberg equation are sufficiently large to explain the actual high Tc for realistic values of Coulomb interaction and the most probable pairing state is spin-singlet s-wave without any nodes just on the Fermi surfaces, although the superconducting order parameter changes its sign between the small Fermi pockets. On the other hand the 2-band model is quite insufficient to explain the actual high Tc.Comment: 2 pages, 3 figures. Proceedings of the Intl. Symposium on Fe-Oxypnictide Superconductors (Tokyo, 28-29th June 2008