I am a current student in the Mathsys II CDT studying for a PhD in Mathematics of Real-World Systems. My research interests span mathematical models that involve hybrid and multi-scale dynamics, stochastic processes, numerical integration, epidemiology and fluids mechanics. To be honest, any topic that invokes the use of a mathematical model is of interest to me!
More specifically, my PhD project, supervised by Dr. Massimiliano Tamborrino, is focused on the development and improvement of time-parallel numerical integration algorithms. These algorithms have the potential to provide numerical speed up for a wide range of problems involving time-dependent ODEs/PDEs in areas from climate modelling to space weather. Our focus is on developing new algorithms that incorporate probabilistic techniques. In the long term, our goal is to apply these algorithms, thus provide speed up, for the simulation of nuclear magnetic fusion, in collaboration with our external partners Dr. Debasmita Samaddar and Dr. Lynton Appel at UKAEA.
MSc Individual Project (2020) - Hats and pancakes in the sky: high-speed droplet dynamics
- A first incursion into the development of models to predict droplet deformation and trajectory in the face of an incoming aerofoil using high resolution direct numerical simulations (DNS) in Basilisk.
- Supervised by Dr. Radu Cimpeanu and Dr. Ed Brambley.
[Deformation of a half-droplet interface at successive times t = 250, 300 and 350 as the flow field accelerates from the right hand side. Simulations were calculated on an adaptive mesh solver in Basilisk. ]
MSc Research Group Project (2020) - Stochastic parareal: an application of probabilistic methods to time-parallelisation
- An investigation into whether stochastic methods could be incorporated into the parareal algorithm in order to extract further parallel speed-up when integrating systems of ODEs.
- Supervised by Dr. Massimiliano Tamborrino, Dr. Debasmita Samaddar and Dr. Lynton Appel.
- Fellow group members: Yijie Zhou, Haoran Ni, Jimmy McKendrick and Jack Bara.
MSc Individual Project (2019) - Spin-down in the absence of reflected waves
- Main aims were to reproduce the results from the Physics of Fluids paper Spin-up and spin-down in a half cone: a pathological situation or not? using much simpler analytical and computational techniques and to identify any markedly different/contradictory results.
- Supervised by Prof. Edward Johnson at University College London.
[A numerical simulation of mass transport streamlines (of an inviscid fluid) building up in the south western corner of the half cone geometry following a spin-down of the fluid.]
Summer Research Project (2017) - Hybrid methods for simulating reaction-diffusion systems
- Ten week internship researching and developing a novel hybrid 'blending' algorithm to combine stochastic simulation algorithms (SSAs) with deterministic partial differential equations (PDEs) in order to simulate reaction-diffusion processes more efficiently.
- Supervised by Dr. Christian Yates, University of Bath.
[Hybrid blending method where particles in a one dimensional domain are tracked in compartments in and whilst simultaneously tracked at their exact positions in and .
PhD in Mathematics for Real-World Systems, University of Warwick (2020-Present) - Working on it...
MSc in Mathematics for Real-World Systems, University of Warwick (2019-20) - Graduated with Distinction
MSc in Mathematical Modelling, University College London (2018-19) - Graduated with Distinction
BSc in Mathematics with Industrial Placement, University of Bath (2013-17) - Graduated with Upper Second Class Honours
Senior Graduate Teaching Assistant , University of Warwick (2020-Present)
- TA for MA250 Introduction to PDEs providing support classes and marking assignments. Also provide assignment/class test marking for CS260 Algorithms.
Mathematics Tutor, Kings College London (2020-Present)
- Leading of practical and seminar sessions (virtually) for third year undergraduates in numerical methods for differentiation and integration in Python. Also lead tutorials for the first year dynamical systems module.
Webmaster, Warwick SIAM-IMA Student Chapter (2020-Present)
- In charge of organising online aspects of the Warwick SIAM Student Chapter.
Interdisciplinary article on complexity science (2020) - PDF
- Article written for an interdisciplinary module discussing whether increased complexity in scientific models leads to less informative results.
UK Mathematics Trust Volunteer (2017-Present)
- Roles have included student mentoring/tutoring for UKMT competitions, BMO marking and annual Maths Miniatures competition judging.
kamran dot pentland at warwick dot ac dot uk
Office D1.13, Zeeman Building
- Playing football for Maths SFC at Warwick.
- Very much into classic cinema and TV as well as fantasy novels.
- Scuba diving (in warmer climates!)
- Snowboarding (in colder climates!)