Topological SLAM using a graph-matching based method on omnidirectional images

Comunicación presentada en el XI Workshop of Physical Agents, Valencia, 9-10 septiembre 2010.

Colossal anisotropy in diluted magnetic topological insulators

We consider dilute magnetic doping in the surface of a three dimensional topological insulator where a two dimensional Dirac electron gas resides. We find that exchange coupling between magnetic atoms and the Dirac electrons has a strong and peculiar effect on both. First, the exchange-induced single ion magnetic anisotropy is very large and favors off-plane orientation. In the case of a ferromagnetically ordered phase, we find a colossal magnetic anisotropy energy, of the order of the critical temperature. Second, a persistent electronic current circulates around the magnetic atom and, in the case of a ferromagnetic phase, around the edges of the surface.

Exponential decay of spin-spin correlation between distant defect states produced by contour hydrogenation of polycyclic aromatic hydrocarbon molecules

The first few low-lying spin states of alternant polycyclic aromatic hydrocarbon (PAH) molecules of several shapes showing defect states induced by contour hydrogenation have been studied both by ab initio methods and by a precise numerical solution of Pariser-Parr-Pople (PPP) interacting model. In accordance with Lieb's theorem, the ground state shows a spin multiplicity equal to one for balanced molecules, and it gets larger values for imbalanced molecules (that is, when the number of π electrons on both subsets is not equal). Furthermore, we find a systematic decrease of the singlet-triplet splitting as a function of the distance between defects, regardless of whether the ground state is singlet or triplet. For example, a splitting smaller than 0.001 eV is obtained for a medium size C46H28 PAH molecule (di-hydrogenated [11]phenacene) showing a singlet ground state. We conclude that π electrons unbound by lattice defects tend to remain localized and unpaired even when long-range Coulomb interaction is taken into account. Therefore they show a biradical character (polyradical character for more than two defects) and should be studied as two or more local doublets. The implications for electron transport are potentially important since these unpaired electrons can trap traveling electrons or simply flip their spin at a very small energy cost.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.

Gibbs Energy of Mixing Function: Topological Analysis in Azeotropic Systems

ESAT 2014. 27th European Symposium on Applied Thermodynamics, Eindhoven University of Technology, July 6-9, 2014.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.