Ayesha Sagheer is a PhD student in the Department of Engineering, King’s College London. Her doctoral research focuses on the mechanics of creases in thin sheets, investigating deformation, instability, and pattern formation in elastic materials.

She completed an MPhil in Mathematics at Capital University, graduating with a Gold Medal for achieving the highest grade in her cohort. Her academic background is rooted in applied mathematics, with research experience spanning fluid mechanics, neural networks, and analytical techniques for solving partial differential equations.

Research Interests

• Mechanics of creases and instabilities in thin sheets
• Solid mechanics and continuum modelling
• Fluid mechanics and Navier–Stokes analysis
• Deep learning for solving physical and PDE-based problems
• Analytical and computational techniques for physically meaningful partial differential equations

Ayesha Sagheer’s research focuses on understanding complex physical phenomena in solid and fluid systems through a combination of analytical and computational approaches.

She studies the mechanics of creases and instabilities in thin sheets, using mathematical modelling and finite element analysis to explore nonlinear behaviour in elastic materials. Her work also extends to fluid mechanics, applying Proper Orthogonal Decomposition to Navier–Stokes equations. She integrates deep learning techniques with classical methods to solve physically meaningful partial differential equations, bridging theoretical analysis and practical computation.

Her interests lie in the intersection of applied mathematics, solid mechanics, and computational physics, with a focus on developing methods that combine physical insight with predictive modelling.

Thesis Title

Proper Orthogonal Decomposition Analysis of Navier-Stokes Equations in Different Geometries 

Supervisor Team

First Supervisor: Dr Michael Gomez

Publications

• Neural network-based numerical analysis of some convection-diffusion-based initial boundary-value problems
• Analytical solution of Atangana-Baleanu fractional viscoelastic relaxation model – Laplacian approach