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.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Product intelligence in industrial control: Theory and practice

This paper explores the evolving industrial control paradigm of product intelligence. The approach seeks to give a customer greater control over the processing of an order - by integrating technologies which allow for greater tracking of the order and methodologies which allow the customer [via the order] to dynamically influence the way the order is produced, stored or transported. The paper examines developments from four distinct perspectives: conceptual developments, theoretical issues, practical deployment and business opportunities. In each area, existing work is reviewed and open challenges for research are identified. The paper concludes by identifying four key obstacles to be overcome in order to successfully deploy product intelligence in an industrial application. © 2013 Elsevier Ltd. All rights reserved.

A conceptual client-designer framework: Inspiring the development of inclusive design interactive techniques

The adoption of inclusive design approach into design practice is compatible to the needs of an ageing society. However, tools and methods that promote inclusivity during new product development are scarcely used in industry. This paper is part of a research project that investigates ways to accommodate inclusive design into the design process in industrial context. The present paper is based on the finds from the observations and interviews with industrial designers and interviews with stakeholders. The outcomes from the study supported a better understanding of the client-designer dynamic as well as the stages in the design process where information related to inclusive design could be introduced. The findings were essential to inspire the development of an inclusive design interactive technique to be used by clients and designers. © 2013 Springer-Verlag Berlin Heidelberg.

Drop speeds from drop-on-demand ink-jet print heads

Measured drop speeds from a range of industrial drop-on-demand (DoD) ink-jet print head designs scale with the predictions of very simple physical models and results of numerical simulations. The main drop/jet speeds at a specified stand-off depend on fluid properties, nozzle exit diameter, and print head drive amplitude for fixed waveform timescales. Drop speeds from the Xaar, Spectra Dimatix, and MicroFab DoD print heads tested with (i) Newtonian, (ii) weakly elastic, and (iii) highly shear-thinning fluids all show a characteristic linear rise with drive voltage (setting) above an apparent threshold drive voltage. Jetting, simple modeling approaches, and numerical simulations of Newtonian fluids over the typical DoD printing range of surface tensions and viscosities were studied to determine how this threshold drive value and the slope of the characteristic linear rise depend on these fluid properties and nozzle exit area. The final speed is inversely proportional to the nozzle exit area, as expected from volume conservation. These results should assist specialist users in the development and optimization of DoD applications and print head design. For a given density, the drive threshold is determined primarily by viscosity, and the constant of proportionality k linking speed with drive above a drive threshold becomes independent of viscosity and surface tension for more viscous DoD fluid jetting. © 2013 Society for Imaging Science and Technology.

Scaling of transitionally-rough flow structures in DNSes of channels with riblets up to Reτ=550

The linear, drag-reducing effect of vanishingly small riblets breaks down once their size is in the transitionally-rough regime. We have previously reported that this breakdown is caused by the additional Reynolds stresses produced by the appearance of elongated spanwise rollers just above the riblet surface. These rollers are related with the Kelvin--Helmholtz instability of free shear layers, and to similar structures appearing over other rough and porous surfaces. However, because of the limited Reτ=180 in our previous DNSes, it could not be determined whether those structures scaled in inner or outer units. Furthermore, it is questionable if results in the transitionally-rough regime at Reτ=180 can be extrapolated to configurations of practical interest. At such small Reynolds numbers, roughness of transitional size can perturb a large portion of the boundary layer, which is not the case in most industrial and atmospheric applications. To clarify these issues we have conducted a set of DNSes at Reτ=550. Our results indicate that the spanwise rollers scale in wall units, and support the validity of the extrapolation to configurations of practical interest.

Understanding and navigating industrial emergence

Industrial emergence is a broad and complex domain, with relevant perspectives ranging in scale from the individual entrepreneur and firm with the business decisions and actions they make to the policies of nations and global patterns of industrialisation. The research described in this article has adopted a holistic approach, based on structured mapping methods, in an attempt to depict and understand the dynamics and patterns of industrial emergence across a broad spectrum from early scientific discovery to large-scale industrialisation. The breadth of scope and application has enabled a framework and set of four tools to be developed that have wide applicability. The utility of the approaches has been demonstrated through case studies and trials in a diverse range of industrial contexts. The adoption of such a broad scope also presents substantial challenges and limitations, with these providing an opportunity for further research. © IMechE 2013.

Initial investigation into the use of GGBS-MgO in soil stabilisation

Portland cement (PC) is the most widely used binder for ground improvement. However, there are significant environmental impacts associated with its production in terms of high energy consumption and CO2 emissions. Hence, the use of industrial by-products materials or new low-carbon footprint alternative cements has been encouraged. Ground granulated blastfurnace slag (GGBS), a by-product of the steel industry, has been successfully used for such an application, usually activated with an alkali such as lime or PC. In this study the use of MgO as a novel activator for GGBS in ground improvement of soft soils is addressed and its performance was compared to the above two conventional activators as well as PC alone. The GGBS:activator ratio used in this study was 9:1. A range of tests was performed at three curing periods (7, 28 and 90 days), including unconfined compressive strength (UCS), permeability and microstructure analysis. The results show that the MgO performed as the most efficient activator yielding the highest strength and the lowest permeability indicating a very high stabilisation efficiency of the system. © 2012 American Society of Civil Engineers.

Award Winner in the Young Investigator Category, 2014 Society for Biomaterials Annual Meeting and Exposition, Denver, Colorado, April 16-19, 2014: Periodically perforated core-shell collagen biomaterials balance cell infiltration, bioactivity, and mechanical properties.

Orthopedic tissue engineering requires biomaterials with robust mechanics as well as adequate porosity and permeability to support cell motility, proliferation, and new extracellular matrix (ECM) synthesis. While collagen-glycosaminoglycan (CG) scaffolds have been developed for a range of tissue engineering applications, they exhibit poor mechanical properties. Building on previous work in our lab that described composite CG biomaterials containing a porous scaffold core and nonporous CG membrane shell inspired by mechanically efficient core-shell composites in nature, this study explores an approach to improve cellular infiltration and metabolic health within these core-shell composites. We use indentation analyses to demonstrate that CG membranes, while less permeable than porous CG scaffolds, show similar permeability to dense materials such as small intestine submucosa (SIS). We also describe a simple method to fabricate CG membranes with organized arrays of microscale perforations. We demonstrate that perforated membranes support improved tenocyte migration into CG scaffolds, and that migration is enhanced by platelet-derived growth factor BB-mediated chemotaxis. CG core-shell composites fabricated with perforated membranes display scaffold-membrane integration with significantly improved tensile properties compared to scaffolds without membrane shells. Finally, we show that perforated membrane-scaffold composites support sustained tenocyte metabolic activity as well as improved cell infiltration and reduced expression of hypoxia-inducible factor 1α compared to composites with nonperforated membranes. These results will guide the design of improved biomaterials for tendon repair that are mechanically competent while also supporting infiltration of exogenous cells and other extrinsic mediators of wound healing.

An exploration of risk management in global industrial investment

This article explores risk management in global industrial investment by identifying linkages and gaps between theories and practices. It identifies opportunities for further development of the field. Three related bodies of literature have been reviewed: risk management, global manufacturing and investment. The review suggests that risk management in global manufacturing is overlooked in the literature; that existing theoretical risk management processes are not well developed in the global manufacturing context and that the investment literature applies mainly to financial risk assessment rather than investment risk management structures. Further, there appears to be a serious lack of systematic industrial risk management in investment decision making. This article highlights the opportunities to deploy current good practices more effectively as well as the need to develop more robust theories of industrial investment risk management. The approach adopted to investigate this multidisciplinary topic included a historical review of literature to understand the diverse background of theoretical development. A case study research approach was adopted to collect data, involving four global manufacturing companies and one risk management advisory company to observe the patterns and rationale of current practices. Supporting arguments from secondary data sources reinforced the findings. The research focuses risk management in global industrial investment. It links theories with practice to understand the existing knowledge gap and proposes key research themes for further research. © 2013 Macmillan Publishers Ltd. 1460-3799 Risk Management.

Adapting data processing to compare model and experiment accurately: A discrete element model and magnetic resonance measurements of a 3d cylindrical fluidized bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid. © 2013 American Chemical Society.