I am a second year PhD (third year MASDOC) student under the supervision of Professor Charlie Elliott and Björn Stinner. My office is B3.04 and if you wish to contact me, my email is P<dot>J<dot>Herbert@warwick.ac.uk. My interests lie in surface PDE and their applications, especially in biological applications alongside the respective numerical analysis and methods for solving the discrete equations. Another topic which interests me is non-uniqueness of solutions and how they may be interpreted.
I graduated in 2016 from Warwick with an MMath, I did my project under the supervision of Professor James Robinson discussing the stationary Navier-Stokes equations.
For my MASDOC MSc project I studied the shape of biomembranes with embedded proteins using a linearisation Cahnam-Helfrich energy for both the sphere and in the case of a plane, extending the work of A Variational Approach to Particles in Lipid Membranes using the tools of Small deformations of Helfrich energy minimising surfaces with applications to biomembranes.
My current research is around the topic of point particles embedded in these biological membranes along with a so called second order splitting method. Details of the second order splitting can be found in the paper of Elliott, Fritz and Hobbs Second order splitting for a class of fourth order equations. We are also studying the 'forcing' associated to the movement of embedded groups of point particles.
- Supervisions for first year maths students
- Supervisions for first year non-maths students
- Term 1: Supervisions for second year maths students, TA for MA250 Introduction to PDE
- Term 2: Supervisions for second year maths students, TA for MA3B8 Complex Analysis
- Term1: Supervisions for second year maths students, TA for MA3G7 Functional Analysis I and C++ part of MA913 Scientific ComputingMA913 Scientific Computing
October 2017: Particles in Biomembranes, at the Warwick Post Graduate Seminar
December 2017: Particles in Biomembranes, at WIMP Autumn meeting (Warwick)
April 2018: Particles in Biomembranes, at CDT Joint Colloquium (Oxford)
April 2018: Particles in Biomembranes, at the MASDOC 2018 retreat
October 2018: An introduction to surface PDEs and surface finite elements at the Warwick Post Graduate Seminar
Non Academic Activities
I am the Chair of the maths SGSLC (2018/2019) and Secretary (2017/2018,2018/2019) for the MASDOC SSLC.