Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Solution oriented partnerships - A new business model for integrating global-production efficiencies with sustainability

A business model for integrating global-production efficiencies with sustainability is discussed. Two trends that emulate some of the aspects of the wealthy are the increasing willingness of many to pay extra for customization such as clothes, of kitchens and the increasing acceptance of purchasing a service as a product substitute. Two final trends that are also based in the attitudes of people is an increased awareness of the value of local culture and an increased concern with issues of sustainability. The results show that the goal congruence between for-profit and not-for-profit organizations puts emphasis on value and belief of the organization.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.

Solution-phase exfoliation of graphite for ultrafast photonics

We exfoliate graphite in both aqueous and non-aqueous environments through mild sonication followed by centrifugation. The dispersions are enriched with monolayers. We mix them with polymers, followed by slow evaporation to produce optical quality composites. Nonlinear optical measurements show similar to 5% saturable absorption. The composites are then integrated into fiber laser cavities to generate 630 fs pulses at 1.56 mu m. This shows the viability of solution phase processing for graphene based photonic devices. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Buyer-supplier partnerships during product design and development in the global automotive sector: Who invests, in what and when?

This paper explores the concept of partnerships between buyers and suppliers in the global automotive sector during product design and development. Partnerships are often the goal in a shift away from adversarial arms-length relationships. The objective of this research is to provide empirical evidence to explain the levels of mutual investment expected and achieved in partnerships from both buyer and supplier perspectives. During this research, 25 employees from 12 global supplier organisations who were in partnership with a specific vehicle manufacturer (VM) were interviewed. Twelve employees from this VM were also interviewed. The research showed the differences between partnerships and non-partnerships and the disparities in the expectations of investment from each partner. For suppliers and buyers to get the most out of partnerships, clear expectations and investments needed over time should be understood and agreed early in the relationship. © 2009 Elsevier B.V.All rights reserved.

On Solving Non-Standard H-/H2/H-Infinity Fault Detection Problems

We discuss solvability issues of H_-/H_2/infinity optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standard H_-/H_2/infinity optimization problem for which we discuss possible solution approaches. Using an appropriate definition of the H- index, we provide a complete solution of this problem in the case of H2-norm. Furthermore, we discuss the solvability issues in the case of H-infinity-norm.

On solving non-standard ℍ -/ℍ 2/∞ fault detection problems

We discuss solvability issues of ℍ -/ℍ 2/∞ optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standard ℍ -/ ℍ 2/∞ optimization problem for which we discuss possible solution approaches. Using an appropriate definition of the ℍ -- index, we provide a complete solution of this problem in the case of ℍ 2-norm. Furthermore, we discuss the solvability issues in the case of ℍ ∞-norm. © 2011 IEEE.

A probabilistic energy model for non-domestic building sectors applied to analysis of school buildings in greater London

The diversity of non-domestic buildings at urban scale poses a number of difficulties to develop models for large scale analysis of the stock. This research proposes a probabilistic, engineering-based, bottom-up model to address these issues. In a recent study we classified London's non-domestic buildings based on the service they provide, such as offices, retail premise, and schools, and proposed the creation of one probabilistic representational model per building type. This paper investigates techniques for the development of such models. The representational model is a statistical surrogate of a dynamic energy simulation (ES) model. We first identify the main parameters affecting energy consumption in a particular building sector/type by using sampling-based global sensitivity analysis methods, and then generate statistical surrogate models of the dynamic ES model within the dominant model parameters. Given a sample of actual energy consumption for that sector, we use the surrogate model to infer the distribution of model parameters by inverse analysis. The inferred distributions of input parameters are able to quantify the relative benefits of alternative energy saving measures on an entire building sector with requisite quantification of uncertainties. Secondary school buildings are used for illustrating the application of this probabilistic method. © 2012 Elsevier B.V. All rights reserved.

Non-reflective boundary conditions for non-uniform mean velocity inlet and outlet flows

The numerical solution of problems in unbounded physical space requires a truncation of the computational domain to a reasonable size. As a result, the conditions on the artificial boundaries are generally unknown. Assumptions like constant pressure or velocities are only valid in the far field and lead to spurious reflections if applied on the boundaries of the truncated domain. A number of attempts have been made over the past decades to design conditions that prevent such reflections. One approach is based on characteristics. The standard analysis assumes a spatially uniform mean flow field but this is often impractical. In the present paper we show how to extend the formulation to the more general case of a non-uniform mean velocity field. A number of test cases are provided and our results compare favourably with other boundary conditions. In principle the present approach can be extended to include non-uniformities in all variables.

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.