All Outputs (4)

Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I. General theory and the near local limit (2022)
Journal Article
Billingham, J., & Needham, D. J. (2022). Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I. General theory and the near local limit. Nonlinearity, 35(12), 6098-6123. https://doi.org/10.1088/1361-6544/ac98ea

We study non-negative travelling wave solutions, u ≡ U (x − ct) with constant wavespeed c > 0, of the cubic nonlocal Fisher-KPP equation in one spatial dimension, namely, ∂u ∂t = ∂ 2 u ∂x 2 + u 2 1 − 1 λ ∞ −∞ ϕ y − x λ u (y, t) dy , for (x, t) ∈ R ×... Read More about Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I. General theory and the near local limit.

Slugging in horizontal channel flow (2022)
Journal Article
Giddings, J. A., Billingham, J., & Cox, S. M. (2022). Slugging in horizontal channel flow. IMA Journal of Applied Mathematics, 87(5), 906-933. https://doi.org/10.1093/imamat/hxac024

The stratified flow of gas-liquid mixtures is important in many industries, in particular oil and gas, where the formation of liquid slugs is usually undesirable. In this paper, we analyse the hydraulic model for turbulent, two-layer, gas-liquid flow... Read More about Slugging in horizontal channel flow.

On modelling coolant penetration into the microchannels at the tool-workpiece interface (2022)
Journal Article
Wei, W., Robles-Linares, J. A., Liao, Z., Wang, Z., Luna, G. G., Billingham, J., & Axinte, D. (2022). On modelling coolant penetration into the microchannels at the tool-workpiece interface. Journal of Manufacturing Processes, 84, 43-54. https://doi.org/10.1016/j.jmapro.2022.09.044

A network of microchannels is formed at the interface between the cutting tool and the workpiece during machining due to their rough surface structures. The penetration of coolant into these microchannels has a great effect on the machined surface qu... Read More about On modelling coolant penetration into the microchannels at the tool-workpiece interface.

Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model (2022)
Journal Article
Fadai, N. T., & Billingham, J. (2022). Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model. Journal of Physics A: Mathematical and Theoretical, 55(40), Article 405701. https://doi.org/10.1088/1751-8121/ac8ef5

We examine travelling wave solutions of the partial differential equation u_t = u_xx + u(1 − u * φ) on a moving domain x ≤ L(t), where u * φ is the spatial convolution of the population density with a kernel φ(y). We provide asymptotic approximations... Read More about Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model.