Outputs (57)

Smoothing of the higher-order stokes phenomenon (2025)
Journal Article
Howls, C. J., King, J. R., Nemes, G., & Olde Daalhuis, A. B. (2025). Smoothing of the higher-order stokes phenomenon. Studies in Applied Mathematics, 154(2), Article e70008. https://doi.org/10.1111/sapm.70008

For over a century, the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. In 1989, Berry demonstrated it is possible to smooth this discontinuity in broad classes of problems with the prefa... Read More about Smoothing of the higher-order stokes phenomenon.

Touchdown-singularity formation and criticality in the thin-film equation (2024)
Journal Article
King, J. R., & Bowen, M. (in press). Touchdown-singularity formation and criticality in the thin-film equation. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences,

The thin-film equation, ht = −(h n hxxx)x, is significant physically in the description of surface-tension-driven flows of thin films of viscous liquids and has served an important role mathematically in elucidating the properties and challenges of h... Read More about Touchdown-singularity formation and criticality in the thin-film equation.

Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response (2024)
Journal Article
Franks, S. J., Dunster, J. L., Carding, S. R., Lord, J. M., Hewison, M., Calder, P. C., & King, J. R. (2024). Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response. Mathematical Medicine and Biology, 41(4), 304-345. https://doi.org/10.1093/imammb/dqae017

The intestinal microbiota play a critical role in human health and disease, maintaining metabolic and immune/inflammatory health, synthesizing essential vitamins and amino acids and maintaining intestinal barrier integrity. The aim of this paper is t... Read More about Modelling the influence of vitamin D and probiotic supplementation on the microbiome and immune response.

Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation (2024)
Journal Article
Fasondini, M., King, J. R., & Weideman, J. A. (2024). Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation. Nonlinearity, 37(10), Article 105005. https://doi.org/10.1088/1361-6544/ad700b

Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is on tracking the dynamics of the singularities in the complexified spac... Read More about Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation.

Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain (2024)
Journal Article
Franks, S. J., Gowler, P. R., Dunster, J. L., Turnbull, J., Gohir, S. A., Kelly, A., Valdes, A. M., King, J. R., Barrett, D. A., Chapman, V., & Preston, S. (2024). Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain. Mathematical Biosciences, 374, Article 109228. https://doi.org/10.1016/j.mbs.2024.109228

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid... Read More about Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain.

Mathematical models of coagulation—are we there yet? (2024)
Journal Article
Owen, M. J., Wright, J. R., Tuddenham, E. G., King, J. R., Goodall, A. H., & Dunster, J. L. (2024). Mathematical models of coagulation—are we there yet?. Journal of Thrombosis and Haemostasis, 22(6), 1689-1703. https://doi.org/10.1016/j.jtha.2024.03.009

Background
Mathematical models of coagulation have been developed to mirror thrombin generation in plasma, with the aim of investigating how variation in coagulation factor levels regulates hemostasis. However, current models vary in the reactions t... Read More about Mathematical models of coagulation—are we there yet?.

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport (2023)
Journal Article
Bellows, S., Janes, G., Avitabile, D., King, J. R., Bishopp, A., & Farcot, E. (2023). Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport. PLoS Computational Biology, 19(11), Article e1011646. https://doi.org/10.1371/journal.pcbi.1011646

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling... Read More about Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties (2023)
Journal Article
King, J. R., Richardson, G. W., & Foster, J. M. (2023). Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties. European Journal of Applied Mathematics, 34(5), 1099-1132. https://doi.org/10.1017/S0956792523000098

The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. T... Read More about Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties.

Burgers’ equation in the complex plane (2023)
Journal Article
VandenHeuvel, D. J., Lustri, C. J., King, J. R., Turner, I. W., & McCue, S. W. (2023). Burgers’ equation in the complex plane. Physica D: Nonlinear Phenomena, 448, Article 133686. https://doi.org/10.1016/j.physd.2023.133686

Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers' equation in the... Read More about Burgers’ equation in the complex plane.

Blow up in a periodic semilinear heat equation (2023)
Journal Article
Fasondini, M., King, J., & Weideman, J. (2023). Blow up in a periodic semilinear heat equation. Physica D: Nonlinear Phenomena, 446, Article 133660. https://doi.org/10.1016/j.physd.2023.133660

Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel res... Read More about Blow up in a periodic semilinear heat equation.