This PhD project at the University of Bristol's School of Physics focuses on the critical behaviour in active matter, specifically investigating whether the critical point of motility-induced phase separation (MIPS) aligns with known equilibrium universality classes or represents a new form of non-equilibrium criticality. The research will employ large-scale GPU simulations of active Brownian, run-and-tumble, and lattice-gas models, combined with finite-size scaling analyses such as Binder-cumulant crossings, compressibility peaks, and correlation-length estimates from structure factors. These methods will be used to map phase boundaries and extract critical exponents, leveraging the university's ISAMBARD 3 supercomputer and BlueCrystal Phase 5 HPC cluster for high-performance computation. The project aims to resolve the universality of MIPS, a fundamental and timely question in statistical and non-equilibrium physics, with potential applications in designing and controlling active materials, soft robotics, and microfluidic platforms. The research group is led by Prof. Nigel Wilding, with additional expertise from Prof. Francesco Turci, Dr. Simon Hanna, and Prof. T. Liverpool. The successful candidate will join a vibrant graduate research community, benefit from comprehensive induction and skills training, and have access to a supportive environment for career development. Funding covers full tuition and a stipend for home students, with a limited number of fully-funded places for outstanding international candidates. Applicants should have a strong background in physics or a related field, and meet the university's English language requirements. The application deadline is 19 January 2026. For further information, contact Prof. Nigel Wilding or the Bristol Physics Graduate School.

This PhD project at the University of Bristol's School of Physics focuses on developing machine learning approaches to simulate active matter in new statistical ensembles. The research aims to overcome the limitations of traditional fixed-(N, V, Pe) simulations by creating machine-learned 'reservoir moves' for grand-canonical–style simulations. The project will leverage symmetry-aware graph neural networks, diffusion models, and policy models trained on canonical trajectories to enable smart particle insertions, deletions, and activity updates that preserve key structural and flow statistics. Validation will involve reproducing one- and two-body observables, mapping MIPS binodals, and exploring wetting/drying and critical scaling, with systematic benchmarking against standard molecular dynamics, Monte Carlo, and heuristic methods. Large-scale computations will utilize the ISAMBARD AI supercomputer and BlueCrystal Phase 5 HPC cluster. The research is timely, addressing the challenge of accessing phase coexistence, interfacial phenomena, and critical behavior in active systems, which are currently constrained by ensemble limitations. Success will provide a general-purpose toolkit for nonequilibrium ensembles, advancing understanding and design in soft materials, biological collectives, and microfluidic active suspensions. The project is supervised by Professor Nigel Wilding (lead), Dr. F. Turci, and Dr. S. Hanna, all experts in theoretical and computational physics. The Physics Graduate School at Bristol offers a vibrant, diverse community, comprehensive induction, targeted skills training, and strong support for career development. Scholarships are available for home students (covering UKRI-rate stipend, tuition, and training), with a limited number of fully-funded places for outstanding international candidates. Applicants should have a strong background in physics or a related field, with at least a UK upper second-class honours degree or equivalent, and meet English language requirements. Applications require a CV, personal statement, and transcripts, and should be submitted via the University of Bristol's online system, specifying 'Bristol Physics Research Scholarships' as the funding source. The deadline for applications is 19 January 2026. The School of Physics is committed to diversity and equality, encouraging applications from under-represented groups.