Kondo Temperature in Multilevel Quantum Dots

We develop a general method to evaluate the Kondo temperature in a multilevel quantum dot that is weakly coupled to conducting leads. Our theory reveals that the Kondo temperature is strongly enhanced when the intradot energy-level spacing is comparable to or smaller than the charging energy. We propose an experiment to test our result, which consists of measuring the size-dependence of the Kondo temperature.Comment: 4 pages, 1 figure and supplementary material. Revised and improved version, to appear in Phys. Rev. Let

The Dirac particle on central backgrounds and the anti-de Sitter oscillator

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.Comment: 16 pages, Late

On the computation of the term w21z2zˉw_{21}z^2\bar{z} of the series defining the center manifold for a scalar delay differential equation

In computing the third order terms of the series of powers of the center manifold at an equilibrium point of a scalar delay differential equation, with a single constant delay $r>0,$ some problems occur at the term $w_{21}z^2\bar{z}.$ More precisely, in order to determine the values at 0, respectively $-r$ of the function $w_{21}(\,.\,),$ an algebraic system of equations must be solved. We show that the two equations are dependent, hence the system has an infinity of solutions. Then we show how we can overcome this lack of uniqueness and provide a formula for $w_{21}(0).$Comment: Presented at the Conference on Applied and Industrial Mathematics- CAIM 2011, Iasi, Romania, 22-25 September, 2011. Preprin

Approximative analytical solutions of the Dirac equation in Schwarzschild spacetime

Approximative analytic solutions of the Dirac equation in the geometry of Schwarzschild black holes are derived obtaining information about the discrete energy levels and the asymptotic behavior of the energy eigenspinors.Comment: 8 page

GraphX: Unifying Data-Parallel and Graph-Parallel Analytics

From social networks to language modeling, the growing scale and importance of graph data has driven the development of numerous new graph-parallel systems (e.g., Pregel, GraphLab). By restricting the computation that can be expressed and introducing new techniques to partition and distribute the graph, these systems can efficiently execute iterative graph algorithms orders of magnitude faster than more general data-parallel systems. However, the same restrictions that enable the performance gains also make it difficult to express many of the important stages in a typical graph-analytics pipeline: constructing the graph, modifying its structure, or expressing computation that spans multiple graphs. As a consequence, existing graph analytics pipelines compose graph-parallel and data-parallel systems using external storage systems, leading to extensive data movement and complicated programming model. To address these challenges we introduce GraphX, a distributed graph computation framework that unifies graph-parallel and data-parallel computation. GraphX provides a small, core set of graph-parallel operators expressive enough to implement the Pregel and PowerGraph abstractions, yet simple enough to be cast in relational algebra. GraphX uses a collection of query optimization techniques such as automatic join rewrites to efficiently implement these graph-parallel operators. We evaluate GraphX on real-world graphs and workloads and demonstrate that GraphX achieves comparable performance as specialized graph computation systems, while outperforming them in end-to-end graph pipelines. Moreover, GraphX achieves a balance between expressiveness, performance, and ease of use

Geometric models of (d+1)-dimensional relativistic rotating oscillators

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.Comment: 7 pages, Late

A framework for design engineering education in a global context

This paper presents a framework for teaching design engineering in a global context using innovative technologies to enable distributed teams to work together effectively across international and cultural boundaries. The DIDET Framework represents the findings of a 5-year project conducted by the University of Strathclyde, Stanford University and Olin College which enhanced student learning opportunities by enabling them to partake in global, team based design engineering projects, directly experiencing different cultural contexts and accessing a variety of digital information sources via a range of innovative technology. The use of innovative technology enabled the formalization of design knowledge within international student teams as did the methods that were developed for students to store, share and reuse information. Coaching methods were used by teaching staff to support distributed teams and evaluation work on relevant classes was carried out regularly to allow ongoing improvement of learning and teaching and show improvements in student learning. Major findings of the 5 year project include the requirement to overcome technological, pedagogical and cultural issues for successful eLearning implementations. The DIDET Framework encapsulates all the conclusions relating to design engineering in a global context. Each of the principles for effective distributed design learning is shown along with relevant findings and suggested metrics. The findings detailed in the paper were reached through a series of interventions in design engineering education at the collaborating institutions. Evaluation was carried out on an ongoing basis and fed back into project development, both on the pedagogical and the technological approaches