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Moving boundary problems for quasi-steady conduction limited melting (2019)
Journal Article
Morrow, L. C., King, J. R., Moroney, T. J., & Mccue, S. (2019). Moving boundary problems for quasi-steady conduction limited melting. SIAM Journal on Applied Mathematics, 79(5), 2107-2131. https://doi.org/10.1137/18M123445X

The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan 5 problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that 6 the crystal melts completely, extending previous results that hold for a... Read More about Moving boundary problems for quasi-steady conduction limited melting.

A core mechanism for specifying root vascular pattern can replicate the anatomical variation seen in diverse plant species (2019)
Journal Article
Mellor, N., Vaughan-Hirsch, J., Kümpers, B. M., Help-Rinta-Rahko, H., Miyashima, S., Pekka Mähönen, A., …Bishopp, A. (2019). A core mechanism for specifying root vascular pattern can replicate the anatomical variation seen in diverse plant species. Development, 146(6), Article dev172411. https://doi.org/10.1242/dev.172411

Pattern formation is typically controlled through the interaction between molecular signals within a given tissue. During early embryonic development, roots of the model plant Arabidopsis thaliana have a radially symmetric pattern, but a heterogeneou... Read More about A core mechanism for specifying root vascular pattern can replicate the anatomical variation seen in diverse plant species.

A tractable mathematical model for tissue growth (2019)
Journal Article
Eyles, J., King, J. R., & Styles, V. (2019). A tractable mathematical model for tissue growth. Interfaces and Free Boundaries, 21(4), 463-493. https://doi.org/10.4171/IFB/428

© European Mathematical Society 2019 Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model t... Read More about A tractable mathematical model for tissue growth.

The structure of a dewetting rim with strong slip: the long-time evolution (2018)
Journal Article
Evans, P., King, J., & Münch, A. (2018). The structure of a dewetting rim with strong slip: the long-time evolution. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 16(3), 1365-1391. https://doi.org/10.1137/15M1051221

When a thin viscous film dewets from a solid substrate, the liquid forms a characteristic rim near the contact line as the contact line retracts. The shape of the rim and also the retraction rate vary strongly with the amount of slip that occurs at t... Read More about The structure of a dewetting rim with strong slip: the long-time evolution.

Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption (2018)
Journal Article
Foster, J., Gysbers, P., King, J., & Pelinovsky, D. (2018). Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity, 31(10), 4621-4648. https://doi.org/10.1088/1361-6544/aad30b

Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bif... Read More about Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption.

Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model (2018)
Journal Article
Cherniha, R., Davydovych, V., & King, J. R. (2018). Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model. Symmetry, 10(5), Article 171. https://doi.org/10.3390/sym10050171

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the oth... Read More about Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model.

Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity (2018)
Journal Article
Bokes, P., & King, J. R. (in press). Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity. Mathematical Medicine and Biology, https://doi.org/10.1093/imammb/dqy003

Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former i... Read More about Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity.

Finite indentation of highly curved elastic shells (2018)
Journal Article
Pearce, S. P., King, J. R., Steinbrecher, T., Leubner-Metzger, G., Everitt, N. M., & Holdsworth, M. J. (2018). Finite indentation of highly curved elastic shells. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2209), https://doi.org/10.1098/rspa.2017.0482

Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst measuring the app... Read More about Finite indentation of highly curved elastic shells.

New type I ancient compact solutions of the Yamabe flow (2017)
Journal Article
Daskalopoulos, P., del Pino, M., King, J., & Sesum, N. (2017). New type I ancient compact solutions of the Yamabe flow. Mathematical Research Letters, 24(6), 1667-1691. https://doi.org/10.4310/MRL.2017.v24.n6.a5

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancien... Read More about New type I ancient compact solutions of the Yamabe flow.

Stress-dependent local oxidation of silicon (2017)
Journal Article
Evans, J. D., & King, J. R. (2017). Stress-dependent local oxidation of silicon. SIAM Journal on Applied Mathematics, 77(6), 2012-2039. https://doi.org/10.1137/16M1060613

The two-dimensional isolation oxidation of silicon is considered for stress-dependent reaction and diffusion coefficients. The influence of such parameters is investigated numerically and asymptotically in the bird's beak problem and for curved geome... Read More about Stress-dependent local oxidation of silicon.

Theoretical approaches to understanding root vascular patterning: a consensus between recent models (2016)
Journal Article
Mellor, N., Adibi, M., El-Showk, S., De Rybel, B., King, J., Mähönen, A. P., …Bishopp, A. (in press). Theoretical approaches to understanding root vascular patterning: a consensus between recent models. Journal of Experimental Botany, https://doi.org/10.1093/jxb/erw410

The root vascular tissues provide an excellent system for studying organ patterning, as the specification of these tissues signals a transition from radial symmetry to bisymmetric patterns. The patterning process is controlled by the combined action... Read More about Theoretical approaches to understanding root vascular patterning: a consensus between recent models.

Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis (2016)
Journal Article
Ferguson, A., Pearce, S., Band, L. R., Yang, C., Ferjentsikova, I., King, J., …Wilson, Z. A. (in press). Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis. New Phytologist, 213, https://doi.org/10.1111/nph.14200

Viable pollen is essential for plant reproduction and crop yield. Its production requires coordinated expression at specific stages during anther development, involving early meiosis-associated events and late pollen wall formation. The ABORTED MICRO... Read More about Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis.

Hybrid vertex-midline modelling of elongated plant organs (2016)
Journal Article
Fozard, J. A., Bennett, M. J., King, J. R., & Jensen, O. E. (2016). Hybrid vertex-midline modelling of elongated plant organs. Interface Focus, 6(5), Article 20160043. https://doi.org/10.1098/rsfs.2016.0043

We describe a method for the simulation of the growth of elongated plant organs, such as seedling roots. By combining a midline representation of the organ on a tissue scale and a vertex-based representation on the cell scale, we obtain a multiscale... Read More about Hybrid vertex-midline modelling of elongated plant organs.

Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis (2016)
Journal Article
Mellor, N. L., Band, L. R., Pěnčík, A., Novak, O., Rashed, A., Holman, T., …Owen, M. R. (2016). Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis. Proceedings of the National Academy of Sciences, 113(39), 11022-11027. https://doi.org/10.1073/pnas.1604458113

Auxin is a key hormone regulating plant growth and development. We combine experiments and mathematical modeling to reveal how auxin levels are maintained via feedback regulation of genes encoding key metabolic enzymes. We describe how regulation of... Read More about Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis.

The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans (2016)
Journal Article
Pearson, T., Wattis, J. A., King, J., McDonald, I., & Mazzatti, D. (in press). The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans. Bulletin of Mathematical Biology, 78(6), https://doi.org/10.1007/s11538-016-0181-1

Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for... Read More about The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans.

A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana (2016)
Journal Article
Muraro, D., Larrieu, A., Lucas, M., Chopard, J., Byrne, H. M., Godin, C., & King, J. R. (in press). A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana. Journal of Theoretical Biology, 404, https://doi.org/10.1016/j.jtbi.2016.04.036

The growth of the root of Arabidopsis thaliana is sustained by the meristem, a region of cell proliferation and differentiation which is located in the root apex and generates cells which move shootwards, expanding rapidly to cause root growth. The b... Read More about A multi-scale model of the interplay between cell signalling and hormone transport in specifying the root meristem of Arabidopsis thaliana.

Asymptotic analysis of a doubly nonlinear diffusion equation (2015)
Journal Article
King, J. R. (2016). Asymptotic analysis of a doubly nonlinear diffusion equation. Nonlinear Analysis: Theory, Methods and Applications, 138, https://doi.org/10.1016/j.na.2015.12.003

investigate the doubly nonlinear diffusion equation ∂u/∂t=1/n ∇.(u^m│∇u│^n-1) ∇u) and the same equation expressed in terms of a `pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that... Read More about Asymptotic analysis of a doubly nonlinear diffusion equation.

Pushed and pulled fronts in a discrete reaction-diffusion equation (2015)
Journal Article
King, J. R., & O'Dea, R. D. (2015). Pushed and pulled fronts in a discrete reaction-diffusion equation. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-015-9829-3

We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction-diffusion equation on a one-dimensional integer lattice. The dependence of the wavespeed on the coupling strength µ between lattice poi... Read More about Pushed and pulled fronts in a discrete reaction-diffusion equation.