Current affiliation: Warwick Mathematics Institute, University of Warwick
Funded by:
The Leverhulme Trust

Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL

Office: D2.03

Phone: +44 (0)24 761 51345
Email: t.hudson.1 (usual symbol)

Career and education
  • 2010 - 2014: DPhil in Mathematics at OxPDE, Mathematical Institute, University of Oxford.
    • Thesis title: Stability and Regularity of Defects in Crystalline Solids.
    • Supervised by Christoph Ortner.
    • Funded by 4-year full studentship.
  • 2006-2010: MMath in Mathematics, Merton College and Mathematical Institute, University of Oxford.
    • Classification: First class.

Editorial Activities

Principal research interests and expertise

My research focuses on questions relating to the mathematics of solid materials, and principally on crystals. Crystals are made up of atoms laid out in a regular repeating pattern, and include most metals at room temperature and pressure.

I am particularly interested in modelling defects and microstructure of these materials, i.e. the behaviour of small-scale phenomena which affect material properties of crystals on much larger scales. Defects are known to play an important role in the behaviour of plastic (or irreversible) deformation of crystals, and ultimately govern their failure. Deriving and improving predictive models for the evolution of microstructure therefore has important potential consequences for engineering applications.

Some research topics I have worked on in the past include:

  • Micromechanics of materials:
    • Crystalline defects, especially dislocations and their evolution
    • Thermodynamics limits: linking microscopic and macroscopic properties of solids
    • Metastability and temperature-driven evolution of defects
  • Asymptotic methods in the Calculus of Variations, PDE and Stochastic Analysis:
    • Gamma-convergence techniques
    • Stochastic Homogenization
    • Large Deviations Theory


People I have worked with during my career include:

Publications and other media

Publications available online:

  • Thomas Hudson and Marco Morandotti. Properties of screw dislocation dynamics: time estimates on boundary and interior collisions. arXiv:1703.02474. Accepted for publication in SIAM Journal of Applied Mathematics.
  • Cameron Hall, Thomas Hudson and Patrick van Meurs. Asymptotic analysis of boundary layers in a repulsive particle system. arXiv:1609.03236. Accepted for publication in Acta Appl. Math.
  • Thomas Hudson. Upscaling a model for the thermally-driven motion of screw dislocations. Arch. Ration. Mech. Anal, 224 (2017) no. 1, 291-352.
  • Thomas Hudson and Christoph Ortner. Analysis of stable screw dislocation configurations in an anti-plane lattice model. SIAM J. Math. Anal. 47-1 (2015), 291-320.
  • Thomas Hudson and Christoph Ortner. Existence and stability of a screw dislocation under anti-plane deformation. Arch. Ration. Mech. Anal, 213 (2014) no. 3, 887-929.
  • Thomas Hudson. Gamma-expansion for a 1D Confined Lennard-Jones model with point defect. Netw. Heterog. Media, 8 (2013) no. 2, 501-527.
  • Thomas Hudson and Christoph Ortner. On the stability of Bravais lattices and their Cauchy-Born approximations. M2AN Math. Model. Numer. Anal., 46:81-110, 2012.
Publications in preparation:

  • Thomas Hudson, Frédéric Legoll and Tony Lelièvre. Stochastic homogenization for a scalar viscoelastic model exhibiting stress–strain hysteresis.
  • Thomas Hudson, Mark Peletier and Patrick van Meurs. Atomistic origins of dislocation dynamics at finite temperature.
  • Nicodemo di Pasquale, Thomas Hudson and Matteo Icardi. On the derivation of hybrid coarse-grained/atomistic models.
Doctoral thesis:

  • A digital copy of my doctoral thesis, entitled "Stability and Regularity of Defects in Crystalline Solids", may be found here.

Other media

  • A video of a research presentation I made at the workshop "Analysis of Dislocation Models for Crystal Defects" at the Casa Matemática Oaxaca in June 2017 can be found here.