Publications and Talks
Publications and Talks
Julian Braun and Thomas Hudson. On the linearised force balance condition in the analysis of atomistic dislocation models. arXiv:2609.39642
Matthew Harrison, Thomas Hudson, Mohaddeseh Mousavi Nezhad, Monica Riva and Alberto Guadagnini. Propagation of variance across spatially averaged Gaussian and generalized sub-Gaussian random fields. Proc. R. Soc. A 482 (2026), 20250585
Thomas Hudson, Akaraphon Jantaraphum and Patrick van Meurs. Simulations of dislocation dynamics on an atomic lattice: the effect of collision rules. arXiv:2605.30682
Thomas Rocke, Thomas Hudson, Richard Beanland and James Kermode. Accurate and Efficient Interatomic Potentials for Dislocations in InP. arXiv:2604.20515
Joseph Duque Lopez, Sergei Dudarev, James Kermode and Thomas Hudson. Bridging Atomistic and Continuum Descriptions of Nanoscale Dislocation Loops in Tungsten. Phys. Rev. Materials 10 (2026), 095402
Thomas Hudson, Xingjie Helen Li and Sarah Murphy. Numerical Stability Revisited: A Family of Benchmark Problems for the Analysis of Explicit Stochastic Differential Equation Integrators. ESAIM M2AN 60 (2026), no. 4, 1741-1768
Thomas Hudson, Matthaeus Ragg. Existence and uniqueness for the fractional advection-diffusion equation. arXiv:2501.14972
Thomas Hudson, Filip Rindler and Joshua Rydell. A quantitative model for the Frank-Read dislocation source based on pinned mean curvature flow. Proc. R. Soc. A 481 (2025), 20240740
Geraldine Anis, Thomas Hudson and Peter Brommer. Dislocation dynamics in Ni-based superalloys: Parameterising dislocation trajectories from atomistic simulations. Phys. Rev. Materials 8 (2024), no. 12, 123604
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.
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 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
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.
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.
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.
Nicodemo di Pasquale, Thomas Hudson and Matteo Icardi. Systematic derivation of hybrid coarse-grained models. Phys. Rev. E 99 (2019) 013303.
Thomas Hudson. An existence result for Discrete Dislocation Dynamics in three dimensions. arXiv:1806.00304.
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 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.
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.
A digital copy of my doctoral thesis, Stability and Regularity of Defects in Crystalline Solids, may be found here.
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.