All Outputs (25)

Efficient and Scalable Inverse Kinematics for Continuum Robots (2023)
Journal Article

With their flexible nature, continuum robots offer hyper-redundancy regarding their workspace; their backbone can take many shapes upon a single tip position and orientation. Deciphering which backbone shape to use under certain conditions is crucial... Read More about Efficient and Scalable Inverse Kinematics for Continuum Robots.

The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity (2023)
Journal Article

We study the dynamics of the non-local Lotka-Volterra system ut=Duuxx+u(1-φ - u-αv), vt=Dvvxx+v(1-φ - v-βu), where a star denotes the spatial convolution and the kernel φ is a top hat function. We initially focus on the case of small, equal diffusivi... Read More about The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity.

A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem (2023)
Journal Article

High demand for components with complex geometries at macro and micro levels drives the development of additive manufacturing (AM). However, the scientific basis for designing energy beam scanning strategies (e.g. beam scanning speed, beam path, beam... Read More about A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem.

The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics (2023)
Journal Article

In this paper, we consider the classical Riemann problem for a generalized Burgers equation, u t + h α ( x ) u u x = u x x , $$\begin{equation*} u_t + h_{\alpha }(x) u u_x = u_{xx}, \end{equation*}$$ with a spatially dependent, nonlinear sound speed,... Read More about The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics.

Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I. General theory and the near local limit (2022)
Journal Article

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

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

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

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.

Slow travelling wave solutions of the nonlocal Fisher-KPP equation (2020)
Journal Article

© 2020 IOP Publishing Ltd & London Mathematical Society. We study travelling wave solutions, u = U(x - ct), of the nonlocal Fisher- KPP equation in one spatial dimension, dimension, (Display equation presented), with D = 1 and c = 1, where = = u is... Read More about Slow travelling wave solutions of the nonlocal Fisher-KPP equation.

A dam-break driven by a moving source: a simple model for a powder snow avalanche (2019)
Journal Article

We study the two-dimensional, irrotational flow of an inviscid, incompressible fluid injected from a line source moving at constant speed along a horizontal boundary, into a second, immiscible, inviscid fluid of lower density. A semi-infinite, horizo... Read More about A dam-break driven by a moving source: a simple model for a powder snow avalanche.

Geometrical modelling of pulsed laser ablation of high performance metallic alloys (2019)
Journal Article

Modelling of Pulsed Laser Ablation (PLA) for the prediction of complex geometries has generally achieved limited success when aimed at large structures resulting from a high number of overlapped pulses, in particular for the ablation of metallic mate... Read More about Geometrical modelling of pulsed laser ablation of high performance metallic alloys.

On modelling of laser assisted machining: forward and inverse problems for heat placement control (2018)
Journal Article

Laser assisted machining (LAM) is one of the most efficient ways to improve the machinability of difficult-to-cut materials (e.g. Nickel-based superalloys). In the conventional LAM process, the laser beam is focused ahead of the cutting area at a fix... Read More about On modelling of laser assisted machining: forward and inverse problems for heat placement control.

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow (2018)
Journal Article

The free surface and flow field structure generated by the uniform acceleration (with dimensionless acceleration σ) of a rigid plate, inclined at an angle α ∈ (0, π/2) to the exterior horizontal, as it advances (σ > 0) or retreats (σ < 0) from an ini... Read More about The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow.

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 2. Well-posedness and stability of the principal flow (2018)
Journal Article

We consider the problem of a rigid plate, inclined at an angle α ∈ (0, π/2) to the horizontal, accelerating uniformly from rest into, or away from, a semi-infinite strip of inviscid, incompressible fluid under gravity. Following on from Gallagher et... Read More about The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 2. Well-posedness and stability of the principal flow.

Thick drops climbing uphill on an oscillating substrate (2018)
Journal Article

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by suffciently strong, vertical oscillations (Brunet, Eggers, and Deegan, Phys. Rev. Lett. 99, 2007). In this paper, we study a two dimensional, inviscid, ir... Read More about Thick drops climbing uphill on an oscillating substrate.

The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface (2017)
Journal Article

Investigation of the microstructure change due to phase transition in nanosecond pulsed laser processing of diamond (2017)
Journal Article

Experiments and theory are employed to investigate the thermal damage induced by infra-red nanosecond pulses in atmospheric air into a boron-doped diamond target. Micro-Raman spectroscopy, Transmission Electron Microscopy (TEM) analysis and surface t... Read More about Investigation of the microstructure change due to phase transition in nanosecond pulsed laser processing of diamond.

New models for energy beam machining enable accurate generation of freeforms (2017)
Journal Article

We demonstrate that, despite differences in their nature, many energy beam controlled-depth machining processes (e.g. waterjet, pulsed laser, focused ion beam) can be modelled using the same mathematical framework – a partial differential evolution e... Read More about New models for energy beam machining enable accurate generation of freeforms.

Waterjet and laser etching: the nonlinear inverse problem (2017)
Journal Article

In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional... Read More about Waterjet and laser etching: the nonlinear inverse problem.

A study of surface swelling caused by graphitisation during pulsed laser ablation of carbon allotrope with high content of sp ³ bounds (2017)
Journal Article

Experiments and theory are employed to investigate the laser ablation of boron doped diamond and tetrahedral amorphous carbon using nanosecond pulses. For a single pulse at low values of fluence, the laser induces a swelling of the surface due to gra... Read More about A study of surface swelling caused by graphitisation during pulsed laser ablation of carbon allotrope with high content of sp ³ bounds.