| Summary: | Fungi generally exist as unicellular organisms (yeasts) or in a vegetative state in which a mycelium, i.e. an interconnected network of tubes (hyphae) is formed. The mycelium can operate over a very large range of scales (each hypha is only a few microns in diameter, yet mycelia can be kilometres across). Fungi are of fundamental importance to many natural processes: certain species have major roles in decomposition and nutrient cycling in the soil; some form vital links with plant roots allowing nutrient transfer. Other species are essential to industrial processes: citric acid production for use in soft drinks; brewing and baking; treatment of industrial effluent and ground toxins. Unfortunately, certain species can cause devastating damage to crops, serious disease in humans or can damage building materials. In this thesis we constructed new models for the development of fungal mycelia. At this scale, partial differential equations representing the interaction of biomass with the underlying substrate is the appropriate choice. Models are essentially based on those derived by Davidson and co workers (see e.g. Boswell et al.(2007)). These models are of a complex mathematical structure, comprising both parabolic and hyperbolic parts. Thus, their analytic and numerical properties are nontrivial. The objectives of this thesis are to: (i) obtain a solid understanding of the physiology of growth and function and the varying mathematical techniques used in model construction. (ii) revisit existing models to reinterpret the various model components in a simple form. (iii) construct models to compare the growth dynamics of different phenotype for new species to see if these "scale " appropriately.
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