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The impact of electrode resistance on the biogalvanic characterisation technique (2016)
Journal Article
Chandler, J., Head, D., Hubbard, M. E., Neville, A., Jayne, D., & Culmer, P. (2016). The impact of electrode resistance on the biogalvanic characterisation technique. Physiological Measurement, 38(2), https://doi.org/10.1088/1361-6579/38/2/101

Measurement of a tissue-specific electrical resistance may offer a discriminatory metric for evaluation of tissue health during cancer surgery. With a move toward minimally-invasive procedures, applicable contact sensing modalities must be scalable,... Read More about The impact of electrode resistance on the biogalvanic characterisation technique.

A multiscale analysis of drug transport and response for a multiphase tumor model (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (in press). A multiscale analysis of drug transport and response for a multiphase tumor model. European Journal of Applied Mathematics, https://doi.org/10.1017/S0956792516000413

In this article we consider the spatial homogenization of a multi- phase model for avascular tumour growth and response to chemother- apeutic treatment. The key contribution of this work is the derivation of a system of homogenized partial differenti... Read More about A multiscale analysis of drug transport and response for a multiphase tumor model.

Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth (2016)
Journal Article
Collis, J., Hubbard, M. E., & O'Dea, R. D. (2016). Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309, https://doi.org/10.1016/j.cma.2016.06.015

In this work we consider the discretization of a recently formulated (Collis et al., [22]) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element sch... Read More about Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth.

An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations (2016)
Journal Article
Yang, F., Goodyer, C. E., Hubbard, M. E., & Jimack, P. K. (2017). An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations. Advances in Engineering Software, 103, https://doi.org/10.1016/j.advengsoft.2016.06.003

This paper describes a new software tool that has been developed for the efficient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Specifically, the software is designed to provide optimal computat... Read More about An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations.

Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane (2016)
Journal Article
Sivapuratharasu, M., Hibberd, S., Hubbard, M. E., & Power, H. (2016). Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane. Physica D: Nonlinear Phenomena, 325, 86-97. https://doi.org/10.1016/j.physd.2016.03.008

This study provides an extended approach to the mathematical simulation of thin-film flow on a flat inclined plane relevant to flows subject to high surface shear. Motivated by modelling thin-film structures within an industrial context, wave structu... Read More about Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane.