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Nayef Shkeir

I am currently a first year PhD student in Mathematics of Real-World Systems at the MathSys II CDT. My main interests are in stochastic systems, rare-event quantification and deep learning with applications in fluid and atmospheric dynamics, turbulent plasma, financial systems and any other fun problems.

PhD Outline:

Title : Rare-events in turbulent fluid flow (for now)

Supervisor : Dr. Tobias Grafke (Mathematics), University of Warwick

The PhD has a focus on developing and building up on current statistical theory with modelling the occurrence and stability of large-scale structures in fluids. We analyse stability of large structures in spatially extended stochastic systems with large time-scale separation. Concretely, we are looking at planetary atmospheres and plasma flows, where large zonal jets are stable structures driven by fast turbulent fluctuations.

We apply methods from stochastic averaging and homogenization to large scale flows in order to describe both the expected mean behaviour of large-scale structures on a turbulent background, as well as typical fluctuations and rare excitations away from typical states.

In collaboration with MetOffice UK and the Courant Institute of Mathematical Sciences, NYU (Eric Vanden-Eijnden).


MSc Project - Meta-stability in atmospheric jets (Paper)


Supervisor - Dr. Tobias Grafke (Mathematics), University of Warwick

Atmospheric flows on rotating planets are prone to form jets that are surprisingly stable in time. This behaviour can be predicted by simulating the planet’s atmosphere numerically. In certain parameter regimes,
the underlying dynamical system has multiple locally stable solutions, corresponding to atmosphere configurations with different numbers of jets. This project explores novel tools such as stochastic averaging to efficiently compute meta-stable states.

Vorticity field evolution showing the formation of a stable 4 jet configuration and eddy shearing.

MSc Research Study Group - Using Generative Adversarial Networks to create multi-channel images of cells undergoing macropinocytosis (Paper)


Supervisor - Prof. Till Bretschneider (Computer Science), University of Warwick

We studied the relationship of multi-channel protein distributions within cells through the application of a 2D and 3D conditional generative adversarial network (pix2pix), where a target protein distribution is learned from a reference protein.

4th Year Project - Designing and modelling a sensorially appealing vortex


Supervisor - Dr. Petr Denissenko (Engineering), University of Warwick

  • The aim was to design a vortex dominated flow for Anish Kapoor's art installation 'Descension' and computationally simulate the flow.
  • The simulations (VOF-LES) were carried out in an opensource C++ toolbox (OpenFOAM) and compared to experimental data.
  • 3D surface wave mathematical models were also developed based on vortex models (Rankine and Lamb-Oseen).

A simulation of a free surface in a cylinder partially filled with water with a propeller rotating at 250 rpm.



SPAAM (Statistics, Probability, Analysis and Applied Mathematics) seminar series


PhD in Mathematics of Real-World Systems, University of Warwick, 2020-

MSc in Mathematics of Real-World Systems, University of Warwick, 2019-2020

MEng in Mechanical Engineering, University of Warwick, 2015-2019


  • 2020/2021 - TA for Matrix Analysis & Algorithms (MA398, third-year maths module)



Office :

Zeeman Building,
University of Warwick,

External Links