Lucia Scardia

Lucia Scardia is an Associate Professor in the Department of Mathematics at Heriot-Watt University (Edinburgh EH14 4AS). Her research focuses on calculus of variations, partial differential equations, homogenisation (deterministic and stochastic), and harmonic analysis, with applications in material science including plasticity, dislocations, non-local aggregation problems, nonlinear elasticity, and fracture theories.

Research Focus

Primary research domains include:

• Variational methods for PDEs and homogenisation
• Mathematical modeling of dislocations and plasticity
• Stochastic analysis of material defects
• Nonlocal interaction problems and fracture mechanics
• Anisotropic energy minimization

Publication Trends

Recent publications (2019-2025) demonstrate strong focus on: Homogenisation techniques in stochastic/perforated domains; variational analysis of anisotropic/nonlocal energies; explicit minimisers for Coulomb/Riesz interactions; free-discontinuity problems; and mathematical descriptions of dislocation patterns. Work consistently employs Gamma-convergence and variational methods.

Student Supervision & Grants

Supervised 18+ students including PhD candidate Xavier Pellet (2015-2019) and numerous Bachelor/Master projects on variational methods, dislocations, and PDEs. Major grants include:

• EPSRC EP/V00204X/1: Mathematical Theory of polycrystalline materials (£576,848, 2021-2024)
• EPSRC EP/V008897/1: Generalised Solutions of Nonlinear PDEs (£35,960, 2021-2024)
• EPSRC First Grant EP/N035631/1: Dislocation Patterns beyond equilibrium (£95,699, 2016)

Academic Leadership

Organizes major conferences including 'Optimal Transport and Calculus of Variations' (ICMS 2023) and 'Polycrystals: Microstructure and Plasticity' (ICMS 2022). Co-founder of the 'One World PDE seminar' (2021-present).