Synthesis of positive-real functions with low-complexity series-parallel networks

The purpose of this paper is to continue to develop the recently introduced concept of a regular positive-real function and its application to the classification of low-complexity two-terminal networks. This paper studies five- and six-element series-parallel networks with three reactive elements and presents a complete characterisation and graphical representation of the realisability conditions for these networks. The results are motivated by an approach to passive mechanical control which makes use of the inerter device. ©2009 IEEE.

Measurement of liquid film thickness by optical fluorescence and its application to an oscillating piston positive displacement flowmeter

The movement of the circular piston in an oscillating piston positive displacement flowmeter is important in understanding the operation of the flowmeter, and the leakage of liquid past the piston plays a key role in the performance of the meter. The clearances between the piston and the chamber are small, typically less than 60 νm. In order to measure this film thickness a fluorescent dye was added to the water passing through the meter, which was illuminated with UV light. Visible light images were captured with a digital camera and analysed to give a measure of the film thickness with an uncertainty of less than 7%. It is known that this method lacks precision unless careful calibration is undertaken. Methods to achieve this are discussed in the paper. The grey level values for a range of film thicknesses were calibrated in situ with six dye concentrations to select the most appropriate one for the range of liquid film thickness. Data obtained for the oscillating piston flowmeter demonstrate the value of the fluorescence technique. The method is useful, inexpensive and straightforward and can be extended to other applications where measurement of liquid film thickness is required. © 2011 IOP Publishing Ltd.

One style does not fit all

The different types of outsourcing and the management requirements for each of them are discussed. An outsourcing has a high strategic importance to the buying company when it is aligned with the organization's long term strategies and when its results are either positive or negative. Functional outsourcings are characterized by both low strategic importance and financial impact, and the products/services that fall in this category belong to support activities which are highly standardized. Leverage outsourcings are those that have a low strategic importance, but high financial impact to the outsourcer, and they concentrate on operational aspects, leaving strategic issues.

Unified modelling in support of organization design and change

The aim of this research is to provide a unified modelling-based method to help with the evaluation of organization design and change decisions. Relevant literature regarding model-driven organization design and change is described. This helps identify the requirements for a new modelling methodology. Such a methodology is developed and described. The three phases of the developed method include the following. First, the use of CIMOSA-based multi-perspective enterprise modelling to understand and capture the most enduring characteristics of process-oriented organizations and externalize various types of requirement knowledge about any target organization. Second, the use of causal loop diagrams to identify dynamic causal impacts and effects related to the issues and constraints on the organization under study. Third, the use of simulation modelling to quantify the effects of each issue in terms of organizational performance. The design and case study application of a unified modelling method based on CIMOSA (computer integrated manufacturing open systems architecture) enterprise modelling, causal loop diagrams, and simulation modelling, is explored to illustrate its potential to support systematic organization design and change. Further application of the proposed methodology in various company and industry sectors, especially in manufacturing sectors, would be helpful to illustrate complementary uses and relative benefits and drawbacks of the methodology in different types of organization. The proposed unified modelling-based method provides a systematic way of enabling key aspects of organization design and change. The case company, its relevant data, and developed models help to explore and validate the proposed method. The application of CIMOSA-based unified modelling method and integrated application of these three modelling techniques within a single solution space constitutes an advance on previous best practice. Also, the purpose and application domain of the proposed method offers an addition to knowledge. © IMechE 2009.

Self-similar organization of arrays of individual carbon nanotubes and carbon nanotube micropillars

It is well-known that carbon nanotube (CNT) growth from a dense arrangement of catalyst nanoparticles creates a vertically aligned CNT forest. CNT forests offer attractive anisotropic mechanical, thermal, and electrical properties, and their anisotropic structure is enabled by the self-organization of a large number of CNTs. This process is governed by individual CNT diameter, spacing, and the CNT-to-CNT interaction. However, little information is known about the self-organization of CNTs within a forest. Insight into the self-organization is, however, essential for tailoring the properties of the CNT forests for applications such as electrical interconnects, thermal interfaces, dry adhesives and energy storage. We demonstrate that arrays of CNT micropillars having micron-scale diameters organize in a similar manner as individual CNTs within a forest. For example, as previously demonstrated for individual CNTs within a forest, entanglement of small-diameter CNT micropillars during the initial stage of growth creates a film of entwined pillars. This layer enables coordinated subsequent growth of the pillars in the vertical direction, in a case where isolated pillars would not grow in a self-supporting fashion. Finally, we provide a detailed overview of the self-organization as a function of the diameter, length and spacing of the CNT pillars. This study, which is applicable to many one-dimensional nanostructured films, demonstrates guidelines for tailoring the self-organization which can enable control of the collective mechanical, electrical and interfacial properties of the films. © 2009 Elsevier B.V. All rights reserved.

Positive Correlations in Tunneling through coupled Quantum Dots

Due to the Fermi-Dirac statistics of electrons the temporal correlations of tunneling events in a double barrier setup are typically negative. Here, we investigate the shot noise behavior of a system of two capacitively coupled quantum dot states by means of a Master equation model. In an asymmetric setup positive correlations in the tunneling current can arise due to the bunching of tunneling events. The underlying mechanism will be discussed in detail in terms of the current-current correlation function and the frequency-dependent Fano factor.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.