The Applied Analysis & Modelling Division consists of three groups: Applied Analysis, Mesoscale & Continuum Modelling, and Molecular Modelling.
The main directions of the Applied Analysis team concern derivation of rigorous novel results for challenging stochastic, nonlinear and asymptotic problems, mainly the (a) Development of innovative stochastic dynamics for a rigorous mathematical study of the effects of thermal fluctuations, and modelling of motion by mean curvature with stochastic forcing based on Malliavin calculus. (b) Investigation and rigorous justification of the unified scattering transform for the initial/boundary value problem for several soliton equations as well as the rigorous study of WKB methods for non-self-adjoint Dirac operator with non-analytic data.
The Mesoscale and Continuum Modelling team focuses on challenging problems in nanoscience and mathematical geophysics, mainly in the modelling and simulation for the generation and control of optical beams, with applications in particle manipulation, filamentation, micromachining, and propagation in turbulent environments, in investigation of the valley degree of freedom in the dynamics of optical waves in photonic graphene and investigation of the interaction between multimodal behavior and nonlinearity in different systems which are important for nanotechnological applications, and in investigation of a variety of skyrmionic.
The Molecular Dynamics team is working on the development of novel mathematical and computational methods for the study of molecular systems/materials across multiple length and time scales, and combines these methods with statistical analysis and data mining approaches.
The Applied Analysis & Modelling Division consists of three groups: