Discrete-Time Conserved Quantities for Damped Oscillators

Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.

Protestantism, Spectacle, Motherhood and Vice: Dublin's New Pleasure Gardens

In 1748, Bartholomew Mosse, a curious combination of surgeon, obstetrician and entertainment impresario, established a pleasure garden on the northern fringes of Dublin. Ostensibly designed to fund the construction of a maternity hospital to be located adjacently, Mosse’s New Pleasure Gardens became one of the premier leisure resorts in Dublin. This was to have a profound effect on the city’s urban form. Within a few years the gardens became an epicentre of speculative development as the upper classes jostled to build their houses in the vicinity. Meanwhile, the creation nearby of Sackville Mall, a wide and generous strolling ground, established a whole section of the city dedicated to haute spectacle, display and leisure. Like other pleasure gardens in the British Isles, Mosse’s venture introduced new, commodified forms of entertainment. In the colonial context of eighteenth-century Ireland, however, ‘a land only recently won and insecurely held’ (Foster, 1988) by the Protestant Anglo-Irish settler class, the production of culture and spectacle was perhaps more significant than elsewhere. Indeed, the form of Mosse’s gardens echoed the private city gardens of a key figure in the Anglo-Irish aristocracy, while the hospital itself was constructed in a style of a Palladian country house, symbol of colonial presence in the countryside. However, like other pleasure gardens, the mix of music and alcohol, the heterogeneous crowd culled from across social and gender boundaries, and a landscape punctuated with secluded corners, meant that it also acquired a dubious reputation as a haunt of louche and illicit behaviours. The curious juxtaposition between a maternity hospital and pleasure garden, therefore, begins to assume other, hitherto hidden complexities. These are borne out by a closer examination of the architecture of the hospital, the shape of its landscape and the records of its patrons and patients.