神马福利影片

Biography

I'm an Assistant Professor in the Warwick Centre for Predictive Modelling. My academic career started as a PhD student at and from 2011 to 2015, under the co-supervision of and . After a short postdoc and teaching position at , I then moved to in August 2017 after winning an EPSRC postdoctoral research fellowship. I was also a visiting scientist at (Paris) from September 2017 to October 2018, and won a Max Planck Institute research fellowship to visit the in Dresden in April 2018.

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Research

My broad research field is computational statistical physics, where I specialise in:

• Emergent electrostatics, slow mixing (eg, broken symmetry) and correlated dynamics in systems that experience the Berezinskii-Kosterlitz-Thouless phase transition, eg, certain planar magnets, superfluids and superconductors.
• Molecular simulation in soft-matter physics, with a focus on electrostatics, high precision and numerical stability.
• Monte Carlo sampling algorithms in statistical physics and Bayesian computational statistics, with a particular interest in piecewise deterministic Markov processes such as event-chain Monte Carlo.

My key 馃攽 scientific achievements split between these three interconnected specialisms:

Planar materials

• Discovered . This resolved the paradox of symmetry breaking being observed in many BKT experiments in spite of a predicted absence of spontaneous symmetry breaking. Examples include . The result provides a model for directional mixing (or memory) timescales in a wide array of experimental systems.
• Defined the above new concept — — which encompasses both spontaneous symmetry breaking and the experimental anomalies.
• Discovered in the 2D lattice-field Coulomb liquid (with and ). This was cited as a possible explanation for at the superconducting transition in the LSCO film and proved to induce the above general symmetry breaking.
• Developed the grand-canonical analogue of the and showed its equivalence to of planar magnets (see Section II and Appendix B of ). We then鈥�
• 鈥�presented an — a more realistic model of planar magnets, superfluids and superconductors — which mapped the topological nonergodicity to the ergodic exclusion of global phase twists in the magnetic spins / condensate wavefunction.
• . This elucidated fully the intimate connection between the topological order and broken U(1) symmetry at the BKT transition.

Molecular simulation and event-chain Monte Carlo

• Designed for numerically stable all-atom molecular Coulomb simulations in soft matter (with , and ). This is the only molecular simulation algorithm that mixes (equilibrates from a random initial configuration) Coulomb-based models in O(N log(N)) computations, where N is the number of particles. It also achieves machine precision and is the basis of鈥�
• 鈥�our mediator-based Python-C application , which we set out in detail with .

• Event-chain Monte Carlo is a piecewise deterministic Markov process (PDMP). PDMPs mix at least as fast (typically much faster) than the diffusive dynamics of Metropolis Monte Carlo, and also guarantee numerical stability, unlike molecular-dynamics simulations. therefore holds much promise for the simulation of electrically charged Coulomb systems.

Sampling algorithms and interface with Bayesian computational statistics

• Presented an , but in the language of statistics and machine learning (with statistician ). We took a particular interest in phase transitions and event-chain Monte Carlo, presenting the latter in the language of PDMPs in Bayesian computation. This project used and to simulate the models presented. We are now using our framework to explore correlated dynamics at phase transitions across statistical science — as we identified analogies with the emergent planar Coulomb liquid described above.
• Designed for high-stability simulation of probability models in Bayesian computation (with statisticians and Gareth Roberts — see section 5.2 of for details). By slowing down the Newtonian dynamics in high-gradient regions of probability space, this new simulation algorithm circumvents the numerical instabilities of Hamiltonian Monte Carlo when applied to light-tailed probability distributions. It also achieves machine precision and is the basis of our Python application .

Teaching

My teaching focuses on the new MSc course Predictive Modelling and Scientific Computing, where I am co-lecturer of and supervisor/examiner of both group and individual projects. In 2023-24, I also provided a guest lecture on advanced simulation algorithms for .

I also provide weekly maths support to my first-year tutees and am co-lecturer for the third-year module .

Selected publications

Projects and grants

Software packages

Vacancies

I have a HetSys PhD project advertised for 2026-27 entry. The project will develop advanced Monte Carlo simulation algorithms for simulating models of glasses and complex materials, with longer term applications ranging from optical fibres to novel pharmaceutical formulations.

Informal enquiries to michael DOT faulkner AT warwick DOT ac DOT uk are welcome.