Mathematical relationships between representations of structure in linear interconnected dynamical systems

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relationships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. © 2011 AACC American Automatic Control Council.

Buyer-supplier relationships in a servitized environment: An examination with Cannon and Perreault's framework

Purpose: The purpose of this study is to examine a buyer's adoption of servitization and the associated implications for the relationships with its suppliers. Design/methodology/approach: The authors use the case study approach to examine the tripartite relationship between a manufacturing company and two of its two suppliers. The paper explores the perspectives of employees on multiple organisational levels, and collects evidence on both sides of a relationship. The authors use template analysis utilising Cannon and Perreault's relationship connectors framework to analyse the data. Findings: There are overarching implications of servitization adoption for buyer-supplier relationships. The implications are notable in all five relationship connectors. Parties expected more open exchange of information, operational linkages were strengthened and changes in the structural arrangements of relationships were witnessed. Legal contracts are complemented by relational norms. The authors also observed a departure away from a win-lose mentality and increased levels of supplier adaptation to support the buyer's provision of integrated solutions. Research limitations/implications: The findings are confined to this tripartite relationship and to an extent are context specific. Practical implications: The study unveils buyer-supplier relationships in a servitized context and provides managers with a better understanding of some of the potential implications that the adoption of a servitization strategy may have for managing buyer-supplier relationships. Originality/value: This is the first empirical study that explores the implications of servitization on buyer-supplier relationships. It advances the understanding of the implications that the adoption of servitization has on the manner in which two parties interrelate and conduct commercial exchange. © Emerald Group Publishing Limited.

Transient ventilation dynamics induced by heat sources of unequal strength

We examine theoretically the transient displacement flow and density stratification that develops within a ventilated box after two localized floor-level heat sources of unequal strengths are activated. The heat input is represented by two non-interacting turbulent axisymmetric plumes of constant buoyancy fluxes B1 and B2 > B1. The box connects to an unbounded quiescent external environment of uniform density via openings at the top and base. A theoretical model is developed to predict the time evolution of the dimensionless depths λj and mean buoyancies δj of the 'intermediate' (j = 1) and 'top' (j = 2) layers leading to steady state. The flow behaviour is classified in terms of a stratification parameter S, a dimensionless measure of the relative forcing strengths of the two buoyant layers that drive the flow. We find that dδ1/dτ α 1/λ1 and dδ2/dτ α 1/λ2, where τ is a dimensionless time. When S 1, the intermediate layer is shallow (small λ1), whereas the top layer is relatively deep (large λ2) and, in this limit, δ1 and δ2 evolve on two characteristically different time scales. This produces a time lag and gives rise to a 'thermal overshoot', during which δ1 exceeds its steady value and attains a maximum during the transients; a flow feature we refer to, in the context of a ventilated room, as 'localized overheating'. For a given source strength ratio ψ = B1/B2, we show that thermal overshoots are realized for dimensionless opening areas A < Aoh and are strongly dependent on the time history of the flow. We establish the region of {A, ψ} space where rapid development of δ1 results in δ1 > δ2, giving rise to a bulk overturning of the buoyant layers. Finally, some implications of these results, specifically to the ventilation of a room, are discussed. © Cambridge University Press 2013.