?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Fractional+models+in+space+for+diffusive+processes+in+heterogeneous+media+with+applications+in+cell+motility+and+electrical+signal+propagation&rft.creator=Cusimano%2C+Nicole&rft.subject=non-local+operators+in+space&rft.subject=fractional+Laplacian&rft.subject=reflecting+boundary+conditions&rft.subject=heterogeneous+media&rft.subject=computational+biology&rft.subject=computational+electrophysiology&rft.description=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%2C+offering+new+insights+into+the+relationships+between+structure+and+function.+In+particular%2C+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.&rft.publisher=Queensland+University+of+Technology&rft.date=2015&rft.type=Thesis&rft.format=application%2Fpdf&rft.relation=https%3A%2F%2Feprints.qut.edu.au%2F84092%2F1%2FNicole_Cusimano_Thesis.pdf&rft.rights=free_to_read&rft.relation=Cusimano%2C+Nicole+(2015)+Fractional+models+in+space+for+diffusive+processes+in+heterogeneous+media+with+applications+in+cell+motility+and+electrical+signal+propagation.+PhD+thesis%2C+Queensland+University+of+Technology.&rft.id_number=https%3A%2F%2Feprints.qut.edu.au%2F84092%2F&rft.identifier=Science+%26+Engineering+Faculty%3B+School+of+Mathematical+Sciences