Publications and Talks
A list of my publications can be found below.
Articles (in approximate reverse chronological order)
Geraldine Anis, Thomas Hudson and Peter Brommer. Dislocation dynamics in Ni-based superalloys: Parameterising dislocation trajectories from atomistic simulations. arXiv:2310.01239
Thomas Hudson and Xingjie Li. Dynamical properties of coarse-grained linear SDEs. SIAM MMS 22 (2024), no. 1, 406-435
Soumendu Bagchi et al. White Paper: “New Mathematics for the Exascale: Applications to Materials Science”. Available for download here.
Thomas Hudson and Filip Rindler. Elasto-plastic evolution of single crystals driven by dislocation flow. Math. Models Methods Appl. Sci. 32 (2022), no. 5, 851-910
Julian Braun, Thomas Hudson and Christoph Ortner. Asymptotic expansion of the elastic far-field of a crystalline defect. Arch. Ration. Mech. Anal. 245 (2022), 1437-1490
Nicodemo di Pasquale, Thomas Hudson, Matteo Icardi, Lorenzo Rovigatti and Marco Spinaci. A systematic analysis of the memory term in coarse-grained models: the case of the Markovian approximation. EJAM 34 (2023), no. 2, 326-345
Thomas Hudson, Patrick van Meurs and Mark Peletier. Atomistic origins of continuum dislocation dynamics. Math. Models Methods Appl. Sci. 30 (2020), no. 13, 2557-2618.
Maciej Buze, Thomas Hudson and Christoph Ortner. Analysis of cell size effects in atomistic crack propagation. ESAIM M2AN, 54 (2020), no. 6, 1821-1847.
Thomas Hudson and Xingjie Helen Li. Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism. SIAM MMS, 18 (2020), no. 2, 1113-1135.
Maciej Buze, Thomas Hudson and Christoph Ortner. Analysis of an atomistic model for anti-plane fracture. Math. Models Methods Appl. Sci. 29 (2019) no. 13, 2469-2521.
Thomas Hudson. An existence result for Discrete Dislocation Dynamics in three dimensions. arXiv:1806.00304.
Nicodemo di Pasquale, Thomas Hudson and Matteo Icardi. Systematic derivation of hybrid coarse-grained models. Phys. Rev. E 99 (2019) 013303.
Thomas Hudson, Frédéric Legoll and Tony Lelièvre. Stochastic homogenization for a scalar viscoelastic model exhibiting stress–strain hysteresis. ESAIM M2AN, 54 (2020), no. 3, 879-928.
Thomas Hudson and Marco Morandotti. Properties of screw dislocation dynamics: time estimates on boundary and interior collisions. SIAM J. Appl. Math. 77 (2017) no. 5, 1678-1705.
Cameron Hall, Thomas Hudson and Patrick van Meurs. Asymptotic analysis of boundary layers in a repulsive particle system. Acta Appl. Math. 153 (2018) no. 1, 1-54.
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 (2015) no. 1, 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. Math. Model. Numer. Anal. 46 (2012) no. 1, 81-110.
Doctoral thesis
A digital copy of my doctoral thesis, Stability and Regularity of Defects in Crystalline Solids, may be found here.
Recorded talks
A video of a research talk which I gave at IPAM in April 2023 can be found here.
A video of an online talk on my research which I gave at Compensated Compactness and Applications to Materials Science, a workshop held at BIRS in April 2023 can be found here.
A tutorial talk on Multiscale Methods for Materials Science which I gave as part of the long programme New Mathematics for the Exascale: Applications to Materials Science at IPAM, UCLA in March 2023 can be found here.
A video of a talk on my research on dislocation dynamics which I gave at Mathematical design of new materials - strategies and algorithms for the design of alloys and metamaterials, a workshop held at the ICMS in March 2019 can be found here.
A video of a talk on my research which I made at Analysis of Dislocation Models for Crystal Defects, a workshop held at the Casa Matemática Oaxaca in June 2017 can be found here.