These are active and growing areas of research in the UK. In molecular dynamics, physicists and chemists traditionally focused on algorithmic aspects and the force fields. With increased computer power, multi-scale and quantum aspects are becoming more relevant. The mathematical formulation of adaptive strategies leads to interesting problems involving nonlinear partial differential equations and probability theory. Real systems considered in physics and material science can be often analysed in terms of models with interacting particles. These include a range of systems from those with classically interacting particles playing a role in nonlinear elasticity including crack propagation, rupture of polymers, and phase transitions and critical phenomena to those where quantum effects are dominant. Interacting particle systems are used as models of discrete stochastic dynamics that provide the mathematical underpinnings of agent based modelling of complex phenomena in biology, economics, and other sciences. This leads to challenging mathematical problems requiring probabilistic and analytic approaches [A, P] with the aid of numerical analysis [C]. It includes the study of efficient algorithms, large scale behaviour, continuum and various scaling limits involving the rigorous derivation of PDEs, multi-scale stochastic processes and renormalization descriptions, effective approximations like super-adiabatic representation for chemical quantum systems, various stochastic processes, gradient fields used in the study of phase coexistence and nonlinear elasticity and interacting Brownian bridges and interacting random permutations used in the study of Bose-Einstein condensation.