All Outputs (53)

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), 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.

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, 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.

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, Article 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.

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 (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.

Free boundary problems for Stokes flow, with applications to the growth of biological tissues (2021)
Journal Article
King, J., & Venkataraman, C. (2021). Free boundary problems for Stokes flow, with applications to the growth of biological tissues. Interfaces and Free Boundaries, 23(4), 433–458. https://doi.org/10.4171/IFB/459

We formulate, analyse and numerically simulate what are arguably the two simplest Stokes-flow free boundary problems relevant to tissue growth, extending the classical Stokes free boundary problem by incorporating (i) a volumetric source (the nutrien... Read More about Free boundary problems for Stokes flow, with applications to the growth of biological tissues.

Solutions with snaking singularities for the fast diffusion equation (2021)
Journal Article
Fila, M., King, J. R., Takahashi, J., & Yanagida, E. (2021). Solutions with snaking singularities for the fast diffusion equation. Transactions of the American Mathematical Society, 374(12), 8775-8792. https://doi.org/10.1090/tran/8479

We construct solutions of the fast diffusion equation, which exist for all t ∈ R and are singular on the set γ(t) := is(s);-∞ < s ≤ ct, c > 0, where ∈ C3(R;Rn), n ≥ 2. We also give a precise description of the behavior of the solutions near γ (t). Read More about Solutions with snaking singularities for the fast diffusion equation.

Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: nonstandard scaling (2021)
Journal Article
King, J. R., Köry, J., & Ptashnyk, M. (2021). Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: nonstandard scaling. SIAM Journal on Applied Mathematics, 81(4), 1361-1388. https://doi.org/10.1137/19M1309626

In this paper we undertake a multiscale analysis of nutrient uptake by plant roots by considering different scale relations between the radius of root hairs and the distance between them. We combine the method of formal asymptotic expansions and rigo... Read More about Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: nonstandard scaling.

Time dependent asymptotic analysis of the gene regulatory network of the AcrAB-TolC efflux pump system in gram-negative bacteria (2021)
Journal Article
Youlden, G. H., Ricci, V., Wang-Kan, X., Piddock, L. J., Jabbari, S., & King, J. R. (2021). Time dependent asymptotic analysis of the gene regulatory network of the AcrAB-TolC efflux pump system in gram-negative bacteria. Journal of Mathematical Biology, 82, Article 31. https://doi.org/10.1007/s00285-021-01576-4

Efflux pumps are a mechanism of intrinsic and evolved resistance in bacteria. If an efflux pump can expel an antibiotic so that its concentration within the cell is below a killing threshold the bacteria are resistant to the antibiotic. Efflux pumps... Read More about Time dependent asymptotic analysis of the gene regulatory network of the AcrAB-TolC efflux pump system in gram-negative bacteria.

A Model to Investigate the Impact of Farm Practice on Antimicrobial Resistance in UK Dairy Farms (2021)
Journal Article
Lanyon, C. W., King, J. R., Stekel, D. J., & Gomes, R. L. (2021). A Model to Investigate the Impact of Farm Practice on Antimicrobial Resistance in UK Dairy Farms. Bulletin of Mathematical Biology, 83(4), Article 36. https://doi.org/10.1007/s11538-021-00865-9

© 2021, The Author(s). The ecological and human health impact of antibiotic use and the related antimicrobial resistance (AMR) in animal husbandry is poorly understood. In many countries, there has been considerable pressure to reduce overall antibio... Read More about A Model to Investigate the Impact of Farm Practice on Antimicrobial Resistance in UK Dairy Farms.

Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations (2021)
Journal Article
Keeler, J., Blyth, M., & King, J. (2021). Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations. Nonlinearity, 34(1), 532-561. https://doi.org/10.1088/1361-6544/abb18f

Solutions u(x) to the class of inhomogeneous nonlinear ordinary differential equations taking the form u + u 2 = αf (x) for parameter α are studied. The problem is defined on the x line with decay of both the solution u(x) and the imposed forcing f (... Read More about Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations.

Type II singularities on complete non-compact Yamabe flow (2020)
Journal Article
Choi, B., Daskalopoulos, P., & King, J. (2021). Type II singularities on complete non-compact Yamabe flow. Journal für die reine und angewandte Mathematik, 2021(772), 83-119. https://doi.org/10.1515/crelle-2020-0032

This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact confor-mally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the max... Read More about Type II singularities on complete non-compact Yamabe flow.

Type II Singularities on complete non-compact Yamabe flow (2020)
Journal Article
Choi, B., Daskalopoulos, P., & King, J. (2021). Type II Singularities on complete non-compact Yamabe flow. Journal für die reine und angewandte Mathematik, 2021(772), 83-119. https://doi.org/10.1515/crelle-2020-0032

This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact confor-mally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the max... Read More about Type II Singularities on complete non-compact Yamabe flow.

A Systematic Upscaling of Nonlinear Chemical Uptake Within a Biofilm (2020)
Journal Article
Dalwadi, M. P., & King, J. R. (2020). A Systematic Upscaling of Nonlinear Chemical Uptake Within a Biofilm. SIAM Journal on Applied Mathematics, 80(4), 1723-1750. https://doi.org/10.1137/19m130220x

When modelling transport of a chemical species to a colony of bacteria in a biofilm, it is computationally expensive 4 to treat each bacterium even as a point sink, let alone to capture the finite nature of each bacterium. Instead, models tend to 5 t... Read More about A Systematic Upscaling of Nonlinear Chemical Uptake Within a Biofilm.