Professor JOHN KING's Outputs (79)

Modelling the influence of vitamin D and probiotics on inflammation and the intestinal microbiota in older adults (2025)
Journal Article
Franks, S., Dunster, J., Carding, S., Lord, J., Hewison, M., Calder, P., & King, J. (in press). Modelling the influence of vitamin D and probiotics on inflammation and the intestinal microbiota in older adults. Scientific Reports. https://www.nature.com/srep/

The relationship between the intestinal microbiota and human health during ageing is an area of increasing interest due to increasing health challenges experienced by ageing populations. This paper develops a mathematical model describing the age-rel... Read More about Modelling the influence of vitamin D and probiotics on inflammation and the intestinal microbiota in older adults.

Nonlinear Systems of PDEs Admitting Infinite‐Dimensional Lie Algebras and Their Connection With Ricci Flows. II: The Two‐Dimensional Space Case (2025)
Journal Article
Cherniha, R., & King, J. R. (2025). Nonlinear Systems of PDEs Admitting Infinite‐Dimensional Lie Algebras and Their Connection With Ricci Flows. II: The Two‐Dimensional Space Case. Studies in Applied Mathematics, 155(4), e70120. https://doi.org/10.1111/sapm.70120

Motivated by previous results in special cases associated with Ricci flows, all possible two-components evolutions systems of (1+2)-dimensional second-order partial differential equations (PDEs) admitting an infinite-dimensional Lie algebra are const... Read More about Nonlinear Systems of PDEs Admitting Infinite‐Dimensional Lie Algebras and Their Connection With Ricci Flows. II: The Two‐Dimensional Space Case.

Conservation laws that depend on functions and PDE reduction: Extending Noether 1 ½ (2025)
Journal Article
Hydon, P. E., & King, J. R. (2025). Conservation laws that depend on functions and PDE reduction: Extending Noether 1 ½. European Journal of Applied Mathematics, 1-18. https://doi.org/10.1017/s0956792525100090

This paper develops methods for simplifying systems of partial differential equations (PDEs) that have families of conservation laws which depend on arbitrary functions of the independent or dependent variables. Cases are identified in which such met... Read More about Conservation laws that depend on functions and PDE reduction: Extending Noether 1 ½.

Touchdown-singularity formation and criticality in the thin-film equation (2025)
Journal Article
King, J. R., & Bowen, M. (2025). Touchdown-singularity formation and criticality in the thin-film equation. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 383(2296), 20230375. https://doi.org/10.1098/rsta.2023.0375

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.

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), 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.

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. C. (2024). Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation. Nonlinearity, 37(10), 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.

Nonlinear systems of PDEs admitting infinite‐dimensional Lie algebras and their connection with Ricci flows (2024)
Journal Article
Cherniha, R., & King, J. R. (2024). Nonlinear systems of PDEs admitting infinite‐dimensional Lie algebras and their connection with Ricci flows. Studies in Applied Mathematics, 153(3), e12737. https://doi.org/10.1111/sapm.12737

A wide class of two‐component evolution systems is constructed admitting an infinite‐dimensional Lie algebra. Some examples of such systems that are relevant to reaction–diffusion systems with cross‐diffusion are highlighted. It is shown that a nonli... Read More about Nonlinear systems of PDEs admitting infinite‐dimensional Lie algebras and their connection with Ricci flows.

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. W., 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, 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. D., 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), 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.

FUTURE MACHINE: Making Myths & Designing Technology for a Responsible Future: Making Myths and Entanglement: Community engagement at the edge of participatory design and user experience (2023)
Presentation / Conference Contribution
Jacobs, R., Spence, J., Abbott, F., Chamberlain, A., Heim, W., Yemaoua Dayo, A., Kemp, D., Benford, S., Price, D., Shackford, R., Robson, J., Locke, C., & King, J. (Eds.). (2023). FUTURE MACHINE: Making Myths & Designing Technology for a Responsible Future: Making Myths and Entanglement: Community engagement at the edge of participatory design and user experience [Edited Proceedings]. Mindtrek '23: 26th International Academic Mindtrek Conference, Tampere, Finland. https://doi.org/10.1145/3616961.3616979

This paper explores the unique methods and strategies employed by a team of artists, in collaboration with engineers, programmers, a climate scientist, researchers and members of the public, who have come together to create the Future Machine, with t... Read More about FUTURE MACHINE: Making Myths & Designing Technology for a Responsible Future: Making Myths and Entanglement: Community engagement at the edge of participatory design and user experience.

Electrochemical transport modelling and open-source simulation of pore-scale solid–liquid systems (2023)
Journal Article
Barnett, R., Municchi, F., King, J., & Icardi, M. (2023). Electrochemical transport modelling and open-source simulation of pore-scale solid–liquid systems. Engineering with Computers, 39(6), 4129-4152. https://doi.org/10.1007/s00366-023-01828-5

The modelling of electrokinetic flows is a critical aspect spanning many industrial applications and research fields. This has introduced great demand in flexible numerical solvers to describe these flows. The underlying phenomena are microscopic, no... Read More about Electrochemical transport modelling and open-source simulation of pore-scale solid–liquid systems.

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, 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. R., & Weideman, J. A. C. (2023). Blow up in a periodic semilinear heat equation. Physica D: Nonlinear Phenomena, 446, 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.

Cauchy-Dirichlet problems for the porous medium equation (2022)
Journal Article
Bowen, M., King, J. R., & Witelski, T. P. (2023). Cauchy-Dirichlet problems for the porous medium equation. Discrete and Continuous Dynamical Systems - Series A, 43(3&4), 1143-1174. https://doi.org/10.3934/dcds.2022182

We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on inter... Read More about Cauchy-Dirichlet problems for the porous medium equation.

Metabolic modeling-based drug repurposing in Glioblastoma (2022)
Journal Article
Tomi-Andrino, C., Pandele, A., Winzer, K., King, J., Rahman, R., & Kim, D.-H. (2022). Metabolic modeling-based drug repurposing in Glioblastoma. Scientific Reports, 12, 11189. https://doi.org/10.1038/s41598-022-14721-w

The manifestation of intra- and inter-tumor heterogeneity hinders the development of ubiquitous cancer treatments, thus requiring a tailored therapy for each cancer type. Specifically, the reprogramming of cellular metabolism has been identified as a... Read More about Metabolic modeling-based drug repurposing in Glioblastoma.

A genome-scale metabolic model of Cupriavidus necator H16 integrated with TraDIS and transcriptomic data reveals metabolic insights for biotechnological applications (2022)
Journal Article
Pearcy, N., Garavaglia, M., Millat, T., Gilbert, J. P., Song, Y., Hartman, H., Woods, C., Tomi-Andrino, C., Bommareddy, R. R., Cho, B. K., Fell, D. A., Poolman, M., King, J. R., Winzer, K., Twycross, J., & Minton, N. P. (2022). A genome-scale metabolic model of Cupriavidus necator H16 integrated with TraDIS and transcriptomic data reveals metabolic insights for biotechnological applications. PLoS Computational Biology, 18(5), e1010106. https://doi.org/10.1371/journal.pcbi.1010106

Exploiting biological processes to recycle renewable carbon into high value platform chemicals provides a sustainable and greener alternative to current reliance on petrochemicals. In this regard Cupriavidus necator H16 represents a particularly prom... Read More about A genome-scale metabolic model of Cupriavidus necator H16 integrated with TraDIS and transcriptomic data reveals metabolic insights for biotechnological applications.

Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching (2022)
Book Chapter
Pinel, G. D., Horder, J. L., King, J. R., McIntyre, A., Mongan, N. P., López, G. G., & Benest, A. V. (2022). Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching. In A. V. Benest (Ed.), Angiogenesis: Methods and Protocol (pp. 369-426). Springer. https://doi.org/10.1007/978-1-0716-2059-5_29

RNA-seq is a common approach used to explore gene expression data between experimental conditions or cell types and ultimately leads to information that can shed light on the biological processes involved and inform further hypotheses. While the prot... Read More about Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching.