Temporal changes in the environmental conditions upon which life depend are ubiquitous in nature, acting at every level of organisation from cells to ecosystems. Although the actions themselves are often poorly understood, they strongly depend on the temporal and hierarchical (organisational) scales at which they are measured; ecosystems are relatively stable through time while their species composition may undergo vast changes. Likewise any hierarchical level may be relatively stable in the short-term, but undergo vast long-term changes. This thesis aims to better understand the importance of these scales for mediating the impact of environmental variability on ecological systems. / The approach used herein employs both mathematical models and empirical data which represent food webs responding to environmental variability at different hierarchical scales. Within each of these representative food webs, the influence of environmental variability on the stability of the food web is determined using an approach which accounts for the effects of temporal scale. This thesis demonstrates that the stability of simple model food webs (high hierarchical scale) is tightly linked to environmental variability and the temporal scales at which these changes occur dictate which species in the model are most affected. At lower scales of organisation, empirical data indicate that environmental variability generally has a lesser impact on stability and that only certain temporal scales are responsible for this trend. At these temporal scales some species respond differently to environmental variability, negative changes in one species (or group) are offset by positive changes in another - a process known as compensation. These results highlight the importance of both temporal and hierarchical scale in mediating the response of food webs to environmental variability. Ultimately, they will serve to better understand how models and experiments should scale-up from low to high hierarchical and temporal scales.

Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 177-191).

Thesis (Ph.D.)--University of Washington. / Bibliography: l. [202]-208.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv., 2007. / Härtill 5 uppsatser.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Ph.D. in Marine Environmental Science. Includes bibliographical references. Also available in electronic version.

Diss. (sammanfattning) Umeå : Univ., 2004. / Härtill 4 uppsatser.

Thesis (Ph. D.)--University of Canterbury, 2008. / Typescript (photocopy). Includes bibliographical references (leaves 120-142). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [67]-75).