Analysis of nonlinear spatio-temporal partial differential equations : applications to host-parasite systems and bubble growth

• Main Author: Bradley, Aoibhinn Maire
• Format: Doctoral or Postdoctoral Thesis
• Language: unknown
• Published: 2014
• Subjects: mountain hare
• Online Access: https://doi.org/10.48730/enb7-ka29; https://stax.strath.ac.uk/concern/theses/9z902z85m

The mountain hare population currently appears to be under threat in Scotland. The natural population cycles exhibited by this species are thought to be, at least in part, due to its infestation by a parasitic worm. We seek to gain an understanding of these population dynamics through a mathematical model of this system and so determine whether low population levels observed in the field are a natural trough associated with this cycling, or whether they point to a more serious decline in overall population densities. A generic result, that can be used to predict the presence of periodic travelling waves (PTWs) in a spatially heterogeneous system, is reported. This result is applicable to any two population host-parasite system with a supercritical Hopf bifurcation in the reaction kinetics. Application of this result to two examples of well studied host-parasite systems, namely the mountain hare and the red grouse systems, predicts and illustrates, for the first time, the existence of PTWs as solutions for these reaction advection diffusion schemes. One method for designing bone scaffolds involves the acoustic irradiation of a reacting polymer foam resulting in a final sample with graded porosity. The work in this thesis represents the first attempt to derive a mathematical model, for this empirical method, in order to inform the experimental design and tailor the porosity profile of samples. We isolate and study the direct effect of the acoustic pressure amplitude as well as its indirect effect on the reaction rate. We demonstrate that the direct effect of the acoustic pressure amplitude is negligible due to a high degree of attenuation by the sample. The indirect effect, on reaction rate, is significant and the standing wave is shown to produce a heterogeneous bubble size distribution. Several suggestions for further work are made. The mountain hare population currently appears to be under threat in Scotland. The natural population cycles exhibited by this species are thought to be, at least in part, due to ...