A Classical Construction for the Digital Fundamental Group

A version of topology's fundamental group is developed for digital images in dimension at most 3 in [7] and [8]. In the latter paper, it is shown that such a digital image X , k 3, has a continuous analog C(X) Rk such that X has digital fundamental group isomorphic to 1(C(X)). However, the construction of the digital fundamental group in [7] and [8] does not greatly resemble the classical construction of the fundamental group of a topological space. In the current paper, we show how classical methods of algebraic topology may be used to construct the digital fundamental group. We construct the digital fundamental group based on the notions of digitally continuous functions presented in [10] and digital homotopy [3]. Our methods are very similar to those of [6], which uses different notions of digital topology. We show that the resulting theory of digital fundamental groups is related to that of [7] and [8] in that it yields isomorphic fundamental groups for the digital images considered in the latter papers (for certain connectedness types).     

Life cycle sustainability assessment of electricity options for the UK

The UK electricity mix will change significantly in the future. This provides an opportunity to consider the full life cycle sustainability of the options currently considered as most suitable for the UK: gas, nuclear, offshore wind and photovoltaics (PV). In an attempt to identify the most sustainable options and inform policy, this paper applies a sustainability assessment framework developed previously by the authors to compare these electricity options. To put discussion in context, coal is also considered as a significant contributor to the current electricity supply. Each option is assessed and compared in terms of its economic, environmental and social implications, using a range of sustainability indicators. The results show that no one technology is superior and that certain trade‐offs must be made. For example, nuclear and offshore wind power have the lowest life cycle environmental impacts, except for freshwater ecotoxicity for which gas is the best option; coal and gas are the cheapest options (£74 and 66/MWh, respectively, at 10% discount), but both have high global warming potential (1072 and 379 g CO₂ eq./kWh); PV has relatively low global warming potential (88 g CO₂ eq./kWh) but high cost (£302/MWh), as well as high ozone layer and resource depletion. Nuclear, wind and PV increase some aspects of energy security: in the case of nuclear, this is due to inherent fuel storage capabilities (energy density 290 million times that of natural gas), whereas wind and PV decrease fossil fuel import requirements by up to 0.2 toe/MWh. However, all three options require additional installed capacity for grid management. Nuclear also poses complex risk and intergenerational questions such as the creation of 10.16 m³/TWh of nuclear waste for long‐term geological storage. Copyright © 2012 John Wiley & Sons, Ltd.     

An analysis of caprolactam polymerization

A versatile model for ε-caprolactam polymerization is presented. A deterministic, mathematical basis for obtaining the most probable distribution of molecular weights in batch polymerization is developed. Continuous polycaproamide production has been modeled and shown to give othe than most probable distribution in many cases. The effect of adding monofunctional agents has been investigated. Results of some preliminary studies toward determining the optimal reactor configuration are presented.     

Rapid evaluation of alkali-silica reactivity of aggregates using a nonlinear resonance spectroscopy technique

A new nonlinear acoustic technique — Nonlinear Impact Resonance Acoustic Spectroscopy (NIRAS) — is developed and used to characterize the alkali-reactivity of different aggregates. Cementitious materials such as mortar and concrete exhibit a hysteretic and nonlinear elastic behavior in their constitutive relations. This hysteretic nonlinearity is associated with interfacial debonding between the different constituents, and it changes with the progress of damage such as that induced by the alkali-silica reaction (ASR). One of the consequences of the hysteretic nonlinear property of these materials is the decrease in resonance frequencies, with increased excitation amplitude. This shift in the resonance frequency as a function of the material nonlinearity parameter can be used to directly characterize the damage state of the material. This research tracks the variation of the nonlinearity parameter during a standard accelerated mortar bar test (AMBT) to assess the potential for alkali-reactivity of aggregates. The results show that the NIRAS technique is more sensitive than conventional linear acoustic methods and is capable of accurately characterizing the reactivity of the aggregates examined. Furthermore, the results show advantages over standard expansion measurements for differentiating various aggregates having similar levels of reactivity, particularly at early test ages. These changes in the nonlinearity parameter are benchmarked against results from a petrographic analysis. Thus, the proposed NIRAS is a promising technique for the rapid identification of alkali-reactive aggregates.