Non-Commutative Tools for Topological Insulators

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have non-trivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.Comment: Final version (some arguments were corrected

The Laplace-Beltrami operator on surfaces with axial symmetry

A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.Comment: 13 pages, 11 figure

The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields

The non-commutative theory of charge transport in mesoscopic aperiodic systems under magnetic fields, developed by Bellissard, Shulz-Baldes and collaborators in the 90's, is complemented with a practical numerical implementation. The scheme, which is developed within a $C^*$-algebraic framework, enable efficient evaluations of the non-commutative Kubo formula, with errors that vanish exponentially fast in the thermodynamic limit. Applications to a model of a 2-dimensional Quantum spin-Hall insulator are given. The conductivity tensor is mapped as function of Fermi level, disorder strength and temperature and the phase diagram in the plane of Fermi level and disorder strength is quantitatively derived from the transport simulations. Simulations at finite magnetic field strength are also presented.Comment: 10 figure

Fostering energy-awareness in simulations behind scientific workflow management systems

© 2014 IEEE.Scientific workflow management systems face a new challenge in the era of cloud computing. The past availability of rich information regarding the state of the used infrastructures is gone. Thus, organising virtual infrastructures so that they not only support the workflow being executed, but also optimise for several service level objectives (e.g., Maximum energy consumption limit, cost, reliability, availability) become dependent on good infrastructure modelling and prediction techniques. While simulators have been successfully used in the past to aid research on such workflow management systems, the currently available cloud related simulation toolkits suffer form several issues (e.g., Scalability, narrow scope) that hinder their applicability. To address this need, this paper introduces techniques for unifying two existing simulation toolkits by first analysing the problems with the current simulators, and then by illustrating the problems faced by workflow systems through the example of the ASKALON environment. Finally, we show how the unification of the selected simulators improve on the the discussed problems

Fostering energy-awareness in scientific cloud users

© 2014 IEEE.Academic cloud infrastructures are constructed and maintained so they minimally constrain their users. Since they are free and do not limit usage patterns, academics developed such behavior that jeopardizes fair and flexible resource provisioning. For efficiency, related work either explicitly limits user access to resources, or introduces automatic rationing techniques. Surprisingly, the root cause (i.e., the user behavior) is disregarded by these approaches. This paper compares academic cloud user behavior to its commercial equivalent. We deduce, that academics should behave like commercial cloud users to relieve resource provisioning. To encourage this behavior, we propose an architectural extension to academic infrastructure clouds. We evaluate our extension via a simulation using real life academic resource request traces. We show a potential resource usage reduction while maintaining the unlimited nature of academic clouds

An architecture to stimulate behavioral development of academic cloud users

Academic cloud infrastructures are constructed and maintained so they minimally constrain their users. Since they are free and do not limit usage patterns, academics developed such behavior that jeopardizes fair and flexible resource provisioning. For efficiency, related work either explicitly limits user access to resources, or introduce automatic rationing techniques. Surprisingly, the root cause (i.e., the user behavior) is disregarded by these approaches. This article compares academic cloud user behavior to its commercial equivalent. We deduce, that academics should behave like commercial cloud users to relieve resource provisioning. To encourage commercial like behavior, we propose an architectural extension to existing academic infrastructure clouds. First, every user's energy consumption and efficiency is monitored. Then, energy efficiency based leader boards are used to ignite competition between academics and reveal their worst practices. Leader boards are not sufficient to completely change user behavior. Thus, we introduce engaging options that encourage academics to delay resource requests and prefer resources more suitable for the infrastructure's internal provisioning. Finally, we evaluate our extensions via a simulation using real life academic resource request traces. We show a potential resource utilization reduction (by the factor of at most 2.6) while maintaining the unlimited nature of academic clouds. © 2014 Elsevier Inc