Research

My research interests span a number of fields, although historically my work has been across

  • optimisation
  • calculus of variations
  • machine learning
  • mathematical physics
  • material science
  • operations research
  • dynamical systems

Academic #

A polycrystalline microstructure showcasing a tessellation of grains, each with its own orientation, separated by grain boundaries - the mechanics behind the formation of which was the primary focus of my PhD.

PhD The Read-Shockley Law: A Discrete Dislocation Approach
We study low-angle grain boundaries as arrays of discrete dislocations (via the Ariza-Ortiz model) and derive the Read-Shockley law from an atomistic description, characterising the energy of optimal grain boundaries as a function of misorientation angle.

MSc On Discrete Dislocations & the Development of an Integral Representation for the Elastic Energy in the Continuum Limit
We study the Ariza-Ortiz model of crystalline materials and derive the elastic energy of a triangular lattice in the presence of two infinite walls of edge dislocation dipoles, and show that the energy satisfies the well known Read-Shockley law in the small angle limit.

MMath Equilibrium Measures for Nonlocal and Anisotropic Logarithmic Energies
We derive the equilibrium configurations of ensembles of particles interacting via logarithmic non-local and non-isotropic interaction potentials under the presence of a quadratic confinement.

UG Research Thermal Convection in Non-Newtonian Fluids.
We study Rayleigh-Bénard instability in thin layers of non-Newtonian (shear-thinning) fluids using perturbation theory and weakly nonlinear analysis. We derive a cubic-quintic Ginzburg-Landau equation to describe perturbation amplitude near the onset of instability and identify regions of Eckhaus and oscillatory instability.

Industrial #

Roles #

Research Fellow in Algorithmic Optimisation SmallSpark Space Systems & University of Southampton
Researched, developed and maintained optimisation software for the design of aerospace structures.

Mathematics Consultant DSTL & Nucleolus Software
Developed a trajectory-optimisation framework for routing UAV fleets to targets while minimising detection by adversarial electromagnetic sensors, maximising their localisation error, and accommodating coordinated jamming. This work led to the publication of Trajectory Optimisation of UAVs in the Electromagnetic Environment in Optimization and Engineering (2024).

Patents #

Design of an Aerodynamic Component Using Surrogate Modeling WO2024094979A1 · SmallSpark Space Systems Ltd (2024)
A computer-implemented method for aerodynamic design using surrogate modelling. A CFD solver evaluates designs parameterised by variable inputs; a surrogate is fitted to the resulting data and optimised to identify Pareto-optimal candidates. Iterative CFD refinement updates the surrogate until convergence, minimising expensive simulations while handling multiple conflicting objectives and constraints.

Reports #

Determining the Conductance of Networks Created by Randomly Dispersed Cylinders
Report for Peratech as part of the 165th European Study Group with Industry. Modelled a composite material as a packing of randomly oriented non-intersecting cylinders in 3D, generating a weighted network from inter-cylinder distances and estimating its effective conductance.

Improving the Resolution of 3D Microscopy Images
Report as part of the Graduate Modelling Camp at the University of Cambridge.

Escape the Sensors
Report for DSTL and PA Consulting as part of the Mathematical Challenges in the Electromagnetic Environment group, Isaac Newton Institute on developing a trajectory-optimisation framework for routing UAV fleets to targets while minimising detection by adversarial electromagnetic sensors

Measuring the Effect of Position Uncertainty in Swarms of Drones
Report for DSTL as part of the 162nd European Study Group with Industry.

Publications, Reports, & White Papers #

[1]
A. Atayev, “The Read–Shockley law: Discrete dislocation approach,” PhD thesis, University of Warwick, 2023. Available: https://wrap.warwick.ac.uk/id/eprint/190432/
[2]
A. Atayev, J. Fliege, and A. Zemkoho, “Trajectory optimisation of UAVs in the electromagnetic environment,” Optimization and Engineering, 2024, doi: 10.1007/s11081-024-09893-5.
[3]
S. Appella et al., “Determining the conductance of networks created by randomly dispersed cylinders,” Mathematics in Industry Reports, 2021, doi: 10.33774/miir-2021-3pqt1-v2.
[4]
A. Atayev et al., “Improving the resolution of 3D microscopy images,” Graduate Modelling Camp, University of Cambridge, 2021.
[5]
A. Atayev et al., “Escape the sensors,” Mathematical Challenges in the Electromagnetic Environment, Isaac Newton Institute, 2021. Available: https://warwick.ac.uk/fac/sci/masdoc/people/studentpages/students2018/atayev/escape_the_sensor___challenge_two.pdf
[6]
D. Allwright et al., “Measuring the effect of position uncertainty in swarms of drones,” 162nd European Study Group with Industry, University of Leeds, 2020.
[7]
A. Atayev, “On discrete dislocations and the development of an integral representation for the elastic energy in the continuum limit,” Master’s thesis, University of Warwick, 2019. doi: 10.5281/zenodo.19656378.
[8]
A. Atayev, “Equilibrium measures for nonlocal and anisotropic logarithmic energies,” Master’s thesis, University of Bath, 2018. doi: 10.5281/zenodo.19656270.