Staggered and extreme localization of electron states in fractal space

We present exact analytical results revealing the existence of a countable infinity of unusual single particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond shaped loops as the 'unit cells'. The family of localized states form clusters of increasing size, much in the sense of Aharonov-Bohm cages [J. Vidal et al., Phys. Rev. Lett. 81, 5888 (1998)], but now without a magnetic field. The length scale at which the localization effect for each of these states sets in can be uniquely predicted following a well defined prescription developed within the framework of real space renormalization group. The scheme allows an exact evaluation of the energy eigenvalue for every such state which is ensured to remain in the spectrum of the system even in the thermodynamic limit. In addition, we discuss the existence of a perfectly conducting state at the band center of this geometry and the influence of a uniform magnetic field threading each elementary plaquette of the lattice on its spectral properties. Of particular interest is the case of extreme localization of single particle states when the magnetic flux equals half the fundamental flux quantum.Comment: 9 pages, 8 figure

Dynamical phenomena in Fibonacci Semiconductor Superlattices

We present a detailed study of the dynamics of electronic wavepackets in Fibonacci semiconductor superlattices, both in flat band conditions and subject to homogeneous electric fields perpendicular to the layers. Coherent propagation of electrons is described by means of a scalar Hamiltonian using the effective-mass approximation. We have found that an initial Gaussian wavepacket is filtered selectively when passing through the superlattice. This means that only those components of the wavepacket whose wavenumber belong to allowed subminibands of the fractal-like energy spectrum can propagate over the entire superlattice. The Fourier pattern of the transmitted part of the wavepacket presents clear evidences of fractality reproducing those of the underlying energy spectrum. This phenomenon persists even in the presence of unintentional disorder due to growth imperfections. Finally, we have demonstrated that periodic coherent-field induced oscillations (Bloch oscillations), which we are able to observe in our simulations of periodic superlattices, are replaced in Fibonacci superlattices by more complex oscillations displaying quasiperiodic signatures, thus sheding more light onto the very peculiar nature of the electronic states in these systems.Comment: 7 pagex, RevTex, 5 Postscript figures. Physical Review B (in press

Exciton Optical Absorption in Self-Similar Aperiodic Lattices

Exciton optical absorption in self-similar aperiodic one-dimensional systems is considered, focusing our attention on Thue-Morse and Fibonacci lattices as canonical examples. The absorption line shape is evaluated by solving the microscopic equations of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values, according to the Thue-Morse or Fibonacci sequences. Results are compared to those obtained in random lattices with the same stechiometry and size. We find that aperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra which clearly differ from the case of random systems, indicating a most peculiar exciton dynamics. We successfully explain the obtained spectra in terms of the two-center problem. This allows us to establish the origin of all the absorption lines by considering the self-similar aperiodic lattices as composed of two-center blocks, within the same spirit of the renormalization group ideas.Comment: 16 pages in REVTeX 3.0. 2 figures on request to F. D-A ([email protected]

Fluorescence decay in aperiodic Frenkel lattices

We study motion and capture of excitons in self-similar linear systems in which interstitial traps are arranged according to an aperiodic sequence, focusing our attention on Fibonacci and Thue-Morse systems as canonical examples. The decay of the fluorescence intensity following a broadband pulse excitation is evaluated by solving the microscopic equations of motion of the Frenkel exciton problem. We find that the average decay is exponential and depends only on the concentration of traps and the trapping rate. In addition, we observe small-amplitude oscillations coming from the coupling between the low-lying mode and a few high-lying modes through the topology of the lattice. These oscillations are characteristic of each particular arrangement of traps and they are directly related to the Fourier transform of the underlying lattice. Our predictions can be then used to determine experimentally the ordering of traps.Comment: REVTeX 3.0 + 3PostScript Figures + epsf.sty (uuencoded). To appear in Physical Review

Energy spectra of quasiperiodic systems via information entropy

We study the relationship between the electronic spectrum structure and the configurational order of one-dimensional quasiperiodic systems. We take the Fibonacci case as an specific example, but the ideas outlined here may be useful to accurately describe the energy spectra of general quasiperiodic systems of technological interest. Our main result concerns the {\em minimization} of the information entropy as a characteristic feature associated to quasiperiodic arrangements. This feature is shown to be related to the ability of quasiperiodic systems to encode more information, in the Shannon sense, than periodic ones. In the conclusion we comment on interesting implications of these results on further developments on the issue of quasiperiodic order.Comment: REVTeX 3.0, 8 pages, 3 figures available on request from FD-A ([email protected]), Phys Rev E submitted, MA/UC3M/02/9

Construcción de esculturas de hormigón con elementos procedentes del reciclado

This paper shows the conceptual development, project, constructive and execution processes of a group of seven sculptures designed to act as containers of other art works carried out by the Spanish artist Jesús Soler. This sculptural group bases its message on the sustainability and the recycling of materials. Its fundamental boundary conditions are the capacity to be mounted and dismounted without any anchorage to the soil, durability and protection of the art work in front of meteorological agents. The sculptural group transmits by itself an environmental message. This paper describes the geometry and proportions, based on the “Le Corbusier Modulor” and the golden section, as well as all the constructive techniques applied for the correct design of each sculpture: formwork systems, concrete with recycled arid, corten steel frames, anchorages, etc. Finally the first assembly process of this itinerant sculptural work is described; it is mounted in the Parque del Retiro in the city of Madrid (Spain).Este trabajo recoge el desarrollo conceptual, de proyecto, construcción y de ejecución de un conjunto de siete esculturas disenadas para actuar como contenedores de otras obras de arte (17 cuadros) realizadas por el artista Jesús Soler. Este conjunto escultórico basa su mensaje en la sostenibidad y el reciclaje. Presenta, como condiciones de contorno fundamentales, la capacidad de ser montado y desmontado sin necesidad de anclar al terreno, durabilidad y protección de las obras frente a agentes meteorológicos y todo ello transmitiendo por sí mismas un mensaje medioambiental. Se describe en el documento la geometría y proporciones basadas en el “Modulor” de Le Corbusier y, por consiguiente, en la sección áurea, así como todas las técnicas constructivas aplicadas para el correcto diseno de cada obra: sistemas de encofrado, hormigones con áridos reciclados, marcos de acero corten, anclajes, etc. Finalmente se describe el primer proceso de montaje de esta obra itinerante, en el Parque del Retiro de Madrid

Fast block QR update in digital signal processing

[EN] The processing of digital sound signals often requires the computation of the QR factorization of a rectangular system matrix. However, sometimes, only a given (and probably small) part of the system matrix varies from the current sample to the next one. We exploit this fact to reuse some computations carried out to process the former sample in order to save execution time in the processing of the current sample. These savings can be critical for real-time applications running on low power consumption devices with high mobility. In addition, we propose a simple out-of-order task-parallel algorithm for the QR factorization using OpenMP that exploits the multicore capability of modern processors. Furthermore, in the presence of a Graphics Processing Unit (GPU) in the system, our algorithm is able to off-load some tasks to the GPU to accelerate the computation on these hardware devices.This work was supported by the Spanish Ministry of Economy and Competitiveness under MINECO and FEDER projects TEC2015-67387-C4-1-R and TIN2014-53495-R; and the Generalitat Valenciana PROMETEOII/2014/003Alventosa, FJ.; Alonso-Jordá, P.; Vidal Maciá, AM.; Piñero, G.; Quintana-Ortí, ES. (2019). Fast block QR update in digital signal processing. The Journal of Supercomputing. 75(3):1051-1064. https://doi.org/10.1007/s11227-018-2298-5S10511064753Augonnet C, Thibault S, Namyst R (2010) StarPU: a runtime system for scheduling tasks over accelerator-based multicore machines. Research Report RR-7240, INRIAButtari A, Langou J, Kurzak J, Dongarra J (2008) Parallel tiled QR factorization for multicore architectures. Concurr Comput Pract Exp 20(13):1573–1590Buttari A, Langou J, Kurzak J, Dongarra J (2009) A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Comput 35(1):38–53Chan E, Quintana-Ortí ES, Quintana-Ortí G, van de Geijn R (2007) Supermatrix out-of-order scheduling of matrix operations for smp and multi-core architectures. In: Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA ’07. ACM, New York, pp 116–125Chan E, Van Zee FG, Quintana-Ortí ES, Quintana-Ortí G, De Van Geijn R (2007) Satisfying your dependencies with supermatrix. In: Proceedings—2007 IEEE International Conference on Cluster Computing, CLUSTER 2007. pp 91–99Chan E, Van Zee FG, Bientinesi P, Quintana-Ortí ES, Quintana-Ortí G, van de Geijn RA (2008) Supermatrix: a multithreaded runtime scheduling system for algorithms-by-blocks. In: Chatterjee S, Scott ML (eds) PPOPP. ACM, New york, pp 123–132Golub GH, Van Loan CF (2013) Matrix computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, BaltimoreGunter BC, van de Geijn RA (2005) Parallel out-of-core computation and updating the QR factorization. ACM Trans Math Softw 31(1):60–78Joffrain T, Quintana-Ortí ES, van de Geijn RA (2004) Rapid development of high-performance out-of-core solvers. In: Applied Parallel Computing, State of the Art in Scientific Computing, 7th International Workshop, PARA 2004, Lyngby, Denmark, June 20–23, 2004, revised selected papers. pp 413–422NVIDIA. The cuBLAS library. http://docs.nvidia.com/cuda/cublas . Accessed May 2017Openblas. http://www.openblas.net . Accessed May 2017Quintana-Ortí G, Quintana-Ortí ES, Van De Geijn RA, Van Zee FG, Chan E (2009) Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Trans Math Softw 36(3):14:1–14:26The OmpSs Programming Model. https://pm.bsc.es/ompss . Accessed May 2017Wende F, Steinke T, Cordes F (2014) Multi-threaded kernel offloading to gpgpu using hyper-q on kepler architecture. Technical Report 14-19, ZIB, Takustr.7, 14195 Berli