Dimensionality of Local Minimizers of the Interaction Energy

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.Comment: 27 page

Nonlocal interactions by repulsive-attractive potentials: radial ins/stability

In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and attract each other in the long range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. We point out the the conditions of radial ins/stability are sharp.Comment: 42 pages, 7 figure

Los catálogos de material y la historia de la educación matemática

El trabajo que se presenta se enmarca en una línea de investigación en auge desde finales del siglo XX: el estudio del patrimonio material e inmaterial de las instituciones educativas y, dentro de ella, la cultura material de la escuela, y, en particular, los materiales escolares (Viñao, 2002; Del Pozo, 2006). Esos materiales eran construidos y comercializados por diversas casas comerciales que los publicitaron mediante la edición de catálogos dedicados total o parcialmente al material escolar (Martínez, Moreno y Sebastián, 2013). Por tanto, los catálogos de material escolar son una fuente importante para conocer qué materiales había en las aulas en un determinado periodo y la función que tenían dichos materiales en los procesos de enseñanza y aprendizaje

Managing knowledge in the context of sustainable construction

The 21st century has been a growing awareness of the importance of the sustainability agenda. Moreover for construction, it has become increasingly important as clients are pushing for a more sustainable product to complement their organisations’ own strategic plans. Sustainable development can be defined as development that meets the needs of the present without compromising the ability of future generations to meet their needs. Sustainable construction is therefore seen as the application of sustainable practices to the activities of the construction sector. One of the key factors in making construction projects more sustainable is overcoming the obstacles of capturing and managing the knowledge required by project teams to effect such change. Managing this knowledge is key to the construction industry because of the unique characteristics of its projects, i.e. multi-disciplinary teams, dynamic participation of team members, heavy reliance on previous experiences/heuristics, the one-off nature of the projects, tight schedules, limited budget, etc. Initiatives within the industry and academic research are developing mechanisms and tools for managing knowledge in construction firms and projects. Such work has so far addressed the issues of capturing, storing, and transferring knowledge

Retrieval of three-dimensional wind fields from Doppler radar data using an efficient two-step approach

In this work, we describe an efficient approach for wind retrieval from dual Doppler radar data. The approach produces a gridded field that not only satisfies the observations, but also satisfies the anelastic mass continuity equation. <br><br> The method is based on the so-called three-dimensional variational approach to the retrieval of wind fields from radar data. The novelty consists in separating the task into steps that reduce the amount of data processed by the global minimization algorithm, while keeping the most relevant information from the radar observations. The method is flexible enough to incorporate observations from several radars, accommodate complex sampling geometries, and readily include dropsonde or sounding observations in the analysis. <br><br> We demonstrate the usefulness of our method by analyzing a real case with data collected during the TPARC/TCS-08 field campaign

An exceptionally well-preserved skeleton of Thomashuxleya externa (Mammalia, Notoungulata), from the Eocene of Patagonia, Argentina

We describe one of the oldest notoungulate skeletons with associated craniodental and postcranial elements: Thomashuxleya externa (Isotemnidae) from Cañadón Vaca in Patagonia, Argentina (Vacan subage of the Casamayoran SALMA, middle Eocene). We provide body mass estimates given by different elements of the skeleton, describe the bone histology, and study its phylogenetic position. We note differences in the scapulae, humerii, ulnae, and radii of the new specimen in comparison with other specimens previously referred to this taxon. We estimate a body mass of 84 ± 24.2 kg, showing that notoungulates had acquired a large body mass by the middle Eocene. Bone histology shows that the new specimen was skeletally mature. The new material supports the placement of Thomashuxleya as an early, divergent member of Toxodontia. Among placentals, our phylogenetic analysis of a combined DNA, collagen, and morphology matrix favor only a limited number of possible phylogenetic relationships, but cannot yet arbitrate between potential affinities with Afrotheria or Laurasiatheria. With no constraint, maximum parsimony supports Thomashuxleya and Carodnia with Afrotheria. With Notoungulata and Litopterna constrained as monophyletic (including Macrauchenia and Toxodon known for collagens), these clades are reconstructed on the stem to Euungulata (i.e., Perissodactyla and Artiodactyla). Unconstrained, Bayesian analysis weakly supports the possibility that Thomashuxleya is a stem xenarthran; with Notoungulata and Litopterna constrained as monophyletic, the two clades are recovered as sister to Perissodactyla. Anatomical data sampled thus far for Thomashuxleya, combined with collagen amino acids for Pleistocene meridiungulates, substantially limit the number of possible affinities for endemic South American species among mammals, although ambiguity still remains

Quantum simulation of the Anderson Hamiltonian with an array of coupled nanoresonators: delocalization and thermalization effects

The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.Comment: Replaced with new improved version. To appear in EPJ Q