Lack of Hyperbolicity in Asymptotic Erd\"os--Renyi Sparse Random Graphs

In this work we prove that the giant component of the Erd\"os--Renyi random graph $G(n,c/n)$ for c a constant greater than 1 (sparse regime), is not Gromov $\delta$-hyperbolic for any positive $\delta$ with probability tending to one as $n\to\infty$. As a corollary we provide an alternative proof that the giant component of $G(n,c/n)$ when c>1 has zero spectral gap almost surely as $n\to\infty$.Comment: Updated version with improved results and narrativ

Load Shifting in the Smart Grid: To Participate or Not?

Demand-side management (DSM) has emerged as an important smart grid feature that allows utility companies to maintain desirable grid loads. However, the success of DSM is contingent on active customer participation. Indeed, most existing DSM studies are based on game-theoretic models that assume customers will act rationally and will voluntarily participate in DSM. In contrast, in this paper, the impact of customers' subjective behavior on each other's DSM decisions is explicitly accounted for. In particular, a noncooperative game is formulated between grid customers in which each customer can decide on whether to participate in DSM or not. In this game, customers seek to minimize a cost function that reflects their total payment for electricity. Unlike classical game-theoretic DSM studies which assume that customers are rational in their decision-making, a novel approach is proposed, based on the framework of prospect theory (PT), to explicitly incorporate the impact of customer behavior on DSM decisions. To solve the proposed game under both conventional game theory and PT, a new algorithm based on fictitious player is proposed using which the game will reach an epsilon-mixed Nash equilibrium. Simulation results assess the impact of customer behavior on demand-side management. In particular, the overall participation level and grid load can depend significantly on the rationality level of the players and their risk aversion tendency.Comment: 9 pages, 7 figures, journal, accepte

Integrating Energy Storage into the Smart Grid: A Prospect Theoretic Approach

In this paper, the interactions and energy exchange decisions of a number of geographically distributed storage units are studied under decision-making involving end-users. In particular, a noncooperative game is formulated between customer-owned storage units where each storage unit's owner can decide on whether to charge or discharge energy with a given probability so as to maximize a utility that reflects the tradeoff between the monetary transactions from charging/discharging and the penalty from power regulation. Unlike existing game-theoretic works which assume that players make their decisions rationally and objectively, we use the new framework of prospect theory (PT) to explicitly incorporate the users' subjective perceptions of their expected utilities. For the two-player game, we show the existence of a proper mixed Nash equilibrium for both the standard game-theoretic case and the case with PT considerations. Simulation results show that incorporating user behavior via PT reveals several important insights into load management as well as economics of energy storage usage. For instance, the results show that deviations from conventional game theory, as predicted by PT, can lead to undesirable grid loads and revenues thus requiring the power company to revisit its pricing schemes and the customers to reassess their energy storage usage choices.Comment: 5 pages, 4 figures, conferenc

Biodegradable and compostable alternatives to conventional plastics

This article is available open access through the publisher’s website at the link below. Copyright @ 2009 The Royal Society.Packaging waste forms a significant part of municipal solid waste and has caused increasing environmental concerns, resulting in a strengthening of various regulations aimed at reducing the amounts generated. Among other materials, a wide range of oil-based polymers is currently used in packaging applications. These are virtually all non-biodegradable, and some are difficult to recycle or reuse due to being complex composites having varying levels of contamination. Recently, significant progress has been made in the development of biodegradable plastics, largely from renewable natural resources, to produce biodegradable materials with similar functionality to that of oil-based polymers. The expansion in these bio-based materials has several potential benefits for greenhouse gas balances and other environmental impacts over whole life cycles and in the use of renewable, rather than finite resources. It is intended that use of biodegradable materials will contribute to sustainability and reduction in the environmental impact associated with disposal of oil-based polymers. The diversity of biodegradable materials and their varying properties makes it difficult to make simple, generic assessments such as biodegradable products are all ‘good’ or petrochemical-based products are all ‘bad’. This paper discusses the potential impacts of biodegradable packaging materials and their waste management, particularly via composting. It presents the key issues that inform judgements of the benefits these materials have in relation to conventional, petrochemical-based counterparts. Specific examples are given from new research on biodegradability in simulated ‘home’ composting systems. It is the view of the authors that biodegradable packaging materials are most suitable for single-use disposable applications where the post-consumer waste can be locally composted.EPSR