Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation
Cusimano, Nicole (2015) Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation. PhD thesis, Queensland University of Technology.
This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.
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|Item Type:||QUT Thesis (PhD)|
|Supervisor:||Burrage, Pamela & Burrage, Kevin|
|Keywords:||non-local operators in space, fractional Laplacian, reflecting boundary conditions, heterogeneous media, computational biology, computational electrophysiology|
|Divisions:||Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Institution:||Queensland University of Technology|
|Deposited On:||29 Jun 2015 00:16|
|Last Modified:||09 Dec 2015 01:47|
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