Tranter
Construction of Weakly-Nonlinear Solutions Respecting the Apparent Zero-Mass Contradiction.Further analysis could be performed on the behaviour of the solutions to the system in a layered waveguide incorporating delamination. This will then be generalised to a given number of layers. A weakly-nonlinear solution will be constructed to this system of equations, with different regimes as instructed by the analysis of the dispersion curves. The first case will consider a three-layered waveguide and analysis of the dispersion curves will instruct the study of this system. The aim of this project is to study the initial-value problem describing wave propagation in a single section of a layered waveguide, for three or more layers. Solutions to these equations have been found, but the problem for three or more layers is more complicated. For a two-layered bar with a soft bonding layer, a system of coupled Boussinesq equations are derived. The type of bonding material between the layers determines the system of equations that arise. The propagation of nonlinear waves in a layered elastic waveguide can be described by Boussinesq-type equations. Initial-value Problem for a System of Boussinesq-type Equations.If you are interested in applying for a MRes or PhD in any of the areas above, please e-mail Dr Tranter for further information, as well as the NTU Doctoral School website. Weakly-nonlinear solutions to nonlinear partial differential equations.Diffuse-interface models for droplet motion.Pseudospectral and finite-difference techniques for partial differential equations.Localised and periodic nonlinear wave propagation in layered waveguides.Specifically Dr Tranter research is in the following areas: This lies within the Imaging, Materials and Engineering Research Centre and the Computation and Simulation research area within the department.
He continues to work on the propagation of nonlinear waves, such as solitons, in layered waveguides with a particular focus on the detection of finite delaminations within the structure, as well as continuing his research on droplet motion.ĭr Tranter has been Placement Manager in the Department of Mathematics and Physics since August 2020, responsible for undergraduate placements and summer internships, including Mathematics Undergraduate Research Studentships (MURS).ĭr Tranter's research interests are in nonlinear waves, fluid dynamics, mathematical modelling and numerical analysis. In 2019 Dr Tranter started work as a Lecturer in Applied Mathematics at Nottingham Trent University, his current role.
This model was used to simulate the effect of rain droplets on a solar panel. He then continued to work at Loughborough University on the modelling of droplets rolling down an incline plane, with either smooth or rough topography, using the diffuse-interface Cahn-Hilliard-Navier-Stokes model. Dr Tranter completed his PhD at Loughborough University in 2018, modelling the propagation of nonlinear waves in layered waveguides.