3 resultados para vectorial analytic solution

em QUB Research Portal - Research Directory and Institutional Repository for Queen's University Belfast


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The prediction and management of ecosystem responses to global environmental change would profit from a clearer understanding of the mechanisms determining the structure and dynamics of ecological communities. The analytic theory presented here develops a causally closed picture for the mechanisms controlling community and population size structure, in particular community size spectra, and their dynamic responses to perturbations, with emphasis on marine ecosystems. Important implications are summarised in non-technical form. These include the identification of three different responses of community size spectra to size-specific pressures (of which one is the classical trophic cascade), an explanation for the observed slow recovery of fish communities from exploitation, and clarification of the mechanism controlling predation mortality rates. The theory builds on a community model that describes trophic interactions among size-structured populations and explicitly represents the full life cycles of species. An approximate time-dependent analytic solution of the model is obtained by coarse graining over maturation body sizes to obtain a simple description of the model steady state, linearising near the steady state, and then eliminating intraspecific size structure by means of the quasi-neutral approximation. The result is a convolution equation for trophic interactions among species of different maturation body sizes, which is solved analytically using a novel technique based on a multiscale expansion.

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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.