Network Density of States

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of associated differential operators. But the translation from spectral geometry to spectral graph theory has largely focused on results involving only a few extreme eigenvalues and their associated eigenvalues. Unlike in geometry, the study of graphs through the overall distribution of eigenvalues - the spectral density - is largely limited to simple random graph models. The interior of the spectrum of real-world graphs remains largely unexplored, difficult to compute and to interpret. In this paper, we delve into the heart of spectral densities of real-world graphs. We borrow tools developed in condensed matter physics, and add novel adaptations to handle the spectral signatures of common graph motifs. The resulting methods are highly efficient, as we illustrate by computing spectral densities for graphs with over a billion edges on a single compute node. Beyond providing visually compelling fingerprints of graphs, we show how the estimation of spectral densities facilitates the computation of many common centrality measures, and use spectral densities to estimate meaningful information about graph structure that cannot be inferred from the extremal eigenpairs alone.Comment: 10 pages, 7 figure

An ultrahigh-vacuum cryostat for simultaneous scanning tunneling microscopy and magneto-transport measurements down to 400mK

We present the design and calibration measurements of a scanning tunneling microscope setup in a 3He ultrahigh-vacuum cryostat operating at 400 mK with a hold time of 10 days. With 2.70 m in height and 4.70 m free space needed for assembly, the cryostat fits in a one-story lab building. The microscope features optical access, an xy table, in situ tip and sample exchange, and enough contacts to facilitate atomic force microscopy in tuning fork operation and simultaneous magneto-transport measurements on the sample. Hence, it enables scanning tunneling spectroscopy on microstructured samples which are tuned into preselected transport regimes. A superconducting magnet provides a perpendicular field of up to 14 T. The vertical noise of the scanning tunneling microscope amounts to 1 pmrms within a 700 Hz bandwidth. Tunneling spectroscopy using one superconducting electrode revealed an energy resolution of 120 mueV. Data on tip-sample Josephson contacts yield an even smaller feature size of 60 mueV, implying that the system operates close to the physical noise limit.Comment: 12 pages, 11 figure

The Use of a Complexity Model to Facilitate in the Selection of a Fuel Cell Assembly Sequence

Various tools and methods exists for arriving at an optimised assembly sequence with most using a soft computing approach. However, these methods have issues including susceptibly to early convergence and high computational time. The typical objectives for these methods are to minimise the number of assembly change directions, orientation changes or the number of tool changes. This research proposes an alternative approach whereby an assembly sequence is measured based on its complexity. The complexity value is generated using design for assembly metrics and coupled with considerations for product performance, component precedence and material handling challenges to arrive at a sequence solution which is likely to be closest to the optimum for cost and product quality. The case presented in this study is of the assembly of a single proton exchange membrane fuel cell. This research demonstrates a practical approach for determining assembly sequence using data and tools that are used and available in the wider industry. Further work includes automating the sequence generation process and extending the work by considering additional factors such as ergonomics

A Framework for Automatically Realizing Assembly Sequence Changes in a Virtual Manufacturing Environment

© 2016 The Authors. Global market pressures and the rapid evolution of technologies and materials force manufacturers to constantly design, develop and produce new and varied products to maintain a competitive edge. Although virtual design and engineering tools have been key to supporting this fast rate of change, there remains a lack of seamless integration between and within tools across the domains of product, process, and resource design-especially to accommodate change. This research examines how changes to designs within these three domains can be captured and evaluated within a component based engineering tool (vueOne, developed by the Automation Systems Group at the University of Warwick). This paper describes how and where data within these tools can be mapped to quickly evaluate change (where typically a tedious process of data entry is required) decreasing lead times and cost and increasing productivity. The approach is tested on a sub-assembly of a hydrogen fuel cell, where an assembly system is modelled and changes are made to the sequence which is translated through to control logic. Although full implementation has not yet been realized, the concept has the potential to radically change the way changes are made and the approach can be extended to supporting other change types provided the appropriate rules and mapping

Hydrogen Fuel Cell Pick and Place Assembly Systems: Heuristic Evaluation of Reconfigurability and Suitability

Proton Exchange Membrane Fuel Cells (PEMFCs) offer numerous advantages over combustion technology but they remain economically uncompetitive except for in niche applications. A portion of this cost is attributed to a lack of assembly expertise and the associated risks. To solve this problem, this research investigates the assembly systems that do exist for this product and systematically decomposes them into their constituent components to evaluate reconfigurability and suitability to product. A novel method and set of criteria are used for evaluation taking inspiration from heuristic approaches for evaluating manufacturing system complexity. It is proposed that this can be used as a support tool at the design stage to meet the needs of the product while having the capability to accept potential design changes and variants for products beyond the case study presented in this work. It is hoped this work develops a new means to support in the design of reconfigurable systems and form the foundation for fuel cell assembly best practice, allowing this technology to reduce in cost and find its way into a commercial space

Symmetry of bound and antibound states in the semiclassical limit

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h. This simple result was inspired by a numerical experiment and we describe the numerical scheme for an efficient computation of resonances in one dimension

The Importance of Correlations and Fluctuations on the Initial Source Eccentricity in High-Energy Nucleus-Nucleus Collisions

In this paper, we investigate various ways of defining the initial source eccentricity using the Monte Carlo Glauber (MCG) approach. In particular, we examine the participant eccentricity, which quantifies the eccentricity of the initial source shape by the major axes of the ellipse formed by the interaction points of the participating nucleons. We show that reasonable variation of the density parameters in the Glauber calculation, as well as variations in how matter production is modeled, do not significantly modify the already established behavior of the participant eccentricity as a function of collision centrality. Focusing on event-by-event fluctuations and correlations of the distributions of participating nucleons we demonstrate that, depending on the achieved event-plane resolution, fluctuations in the elliptic flow magnitude $v_2$ lead to most measurements being sensitive to the root-mean-square, rather than the mean of the $v_2$ distribution. Neglecting correlations among participants, we derive analytical expressions for the participant eccentricity cumulants as a function of the number of participating nucleons, \Npart,keeping non-negligible contributions up to \ordof{1/\Npart^3}. We find that the derived expressions yield the same results as obtained from mixed-event MCG calculations which remove the correlations stemming from the nuclear collision process. Most importantly, we conclude from the comparison with MCG calculations that the fourth order participant eccentricity cumulant does not approach the spatial anisotropy obtained assuming a smooth nuclear matter distribution. In particular, for the Cu+Cu system, these quantities deviate from each other by almost a factor of two over a wide range in centrality.Comment: 18 pages, 10 figures, submitted to PR