I am a final year PhD student under the supervision of Prof. Charlie Elliott and Dr. Björn Stinner. My office is B3.04 in the Zeeman Building and if you wish to contact me, my email is P.J.Herbert<at>warwick.ac.uk. My interests lie in PDE and their applications, especially biological applications. I am also particularly interested in numerical analysis in non-standard settings.
I graduated from Warwick in 2016 with an MMath, I did my project under the supervision of Prof. 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' applied to embedded groups of point particles by the membrane.
Second order splitting of a class of fourth order PDE with point constraints (with C. M. Elliott), in Mathematics of Computation.
Small deformations to spherical biomembranes (with C. M. Elliott and L. Hatcher), to appear in Advanced Studies in Pure Mathematics, Volume 85.
- 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
- Term 2: Supervisions for second year maths students, TA for MA3H0 Numerical Analysis and PDE's
- Term 1: Supervisions for first year math students, TA for MA4A2 Advanced PDEs
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
April 2019: Biological membranes with deformations induced by point particles, at BAMC 2019
May 2019: Biological membranes with deformations induced by point particles, at the MASDOC 2019 retreat
July 2019: A quadratic energy for a near tube biological membrane, FU Berlin Numerical Analysis of PDE biweekly meeting.
Non Research Activities
I am the Chair of the maths SGSLC (2018/2019,2019/2020) and chair of MASDOC SSLC. I was Secretary (2017/2018,2018/2019) for the MASDOC SSLC. I helped to organise the MASDOC 2019 retreat.