Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

A general basis for quarter-power scaling in animals

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarterpower scaling can arise even when there is no underlying fractality. The canonical “fourth dimension” in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal “service volume” where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

The story of Temple Bar: creating Dublin's cultural quarter

The paper conceptualises and explores the links between cities, commerce, urbanism and cultural planning by drawing on Temple Bar in Dublin as an example of how, by linking these concepts to practice in real concrete situations urban life or urban culture can be created and/or revitalised. Temple Bar is Dublin's emerging cultural quarter, an experiment in urban revitalisation which is deliberately focused on culture and urbanism as ways of rediscovering the good city. It has attracted considerable interest from across Europe, and has secured EC funding to kick-start the process of renewal. The author was appointed by the Irish Government to prepare the area management and development strategy for Temple Bar in 1990. Wary of the dangers of property led regeneration, of the destructive impacts of sudden or cataclysmic change, the agencies in Temple Bar have deliberately adopted a strategic management approach to the area. This is referred to as 'urban stewardship', a process of looking after and respecting a place, and helping it to help itself. The paper explores whether there is a 'culture of cities' and whether it is possible to recreate an urban culture. Following Raymond Williams, an anthropological definition of culture is employed, "... a particular way of life, which expresses certain meaning and values not only in art and learning but also in institutional and ordinary behaviour". Rather than being simply an add-on to the serious concerns of economic development and the built environment, culture has both helped shape, and continues to develop in, the streets, spaces and buildings of the city.