All Outputs (6)

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.

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.

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.

An asymptotic analysis of the malonyl-CoA route to 3-hydroxypropionic acid in genetically engineered microbes (2020)
Journal Article
Dalwadi, M. P., & King, J. R. (2020). An asymptotic analysis of the malonyl-CoA route to 3-hydroxypropionic acid in genetically engineered microbes. Bulletin of Mathematical Biology, 82, Article 36. https://doi.org/10.1007/s11538-020-00714-1

There has been recent interest in creating an efficient microbial production route for 3-hydroxypropionic acid, an important platform chemical. We develop and solve a mathematical model for the time-dependent metabolite concentrations in the malonyl-... Read More about An asymptotic analysis of the malonyl-CoA route to 3-hydroxypropionic acid in genetically engineered microbes.

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., Campilho, A., King, J. R., & 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.

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.