ECCOMAS PhD Olympiads, Munich 2026
Mathematics for Materials Modelling group, EPFL, Lausanne, Switzerland
July 21, 2026
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Molecular Dynamics (MD) simulations act as a numerical microscope when experiments are unfeasible/unaffordable
Applications include drug design and materials discovery
Motion of atomic nuclei modelled with a stochastic process \(X\) on space \(\mathcal{X}\) of atomic configurations
Stationary distribution is the Gibbs measure \(\mu(\mathrm{d}x) = Z_\beta^{-1}\mathrm{e}^{-\beta V(x)}\,\mathrm{d}x\) for the potential energy \(V:\mathcal{X}\to\mathbb{R}\) and inverse temperature \(\beta = 1/(k_{\mathrm{B}}T)\)
Thermodynamic averages require samples under the Gibbs measure
Dynamical quantities (reaction rates, transport coefficients, autocorrelations…) require long unbiased trajectories, and are much harder to estimate
Main obstruction is metastability
Simulation step \(\approx 1\,\mathrm{fs}\), interesting kinetic events \(\gtrsim 1\,\mu\mathrm{s}\implies\) timescale problem