Research in Applied Mathematics

Introduction

The research of the Applied Mathematics Group is broadly focused around the computational modelling and analysis of a wide range of dynamical systems from molecular to ecological scales. The diversity of applications and coherence of methodology promotes multifaceted interactions and fruitful collaboration within the group.

Through the activities of the  Centre for Mathematical Modelling (MMC), which provides the backbone for interdisciplinary research at the University of Leicester, the group is making substantial contributions in other areas of science by initiating interdisciplinary interaction and collaborations with top national and international centres of excellence as well as with researchers in other departments within the Science Faculty.

Research Overview

The research within Applied Mathematics can be broadly grouped in the following topics:

• Numerical Analysis and Scientific Computing (Cangiani, Davidchack, Georgoulis, Gorban, Kawai, Levesley, Tretyakov)
  Research interests of the group include areas such as  the numerical solution of partial differential equations, computational fluid dynamics, molecular dynamics simulation, approximation theory and stochastic numerics.
  

• Applied Dynamics and Computation  (Davidchack, Gorban, Tretyakov, Tyukin)
  Research interests of the group include areas such as molecular dynamics simulation, free energy methods for interfacial systems, numerical methods for dynamical systems, stochastic dynamics, physical and chemical kinetics, adaptive control of nonlinear dynamical systems.
  
• Fluid Modelling (Brilliantov, Garrett, Gorban, Levesley)
  Research interests of the group include in areas such as the the Lattice Boltzmann method for simulating fluid flow at high Reynolds' number, boundary layer stability theory for rotating bodies, the mathematical and computational modelling of a new class of fluid: granular gases.

• Mathematical Biology (Brilliantov, Cangiani, Gorban, Petrovskii, Morozov, Tyukin)
  The group employs a range of mathematical methods in modelling biological systems, including data mining, PDEs and control theory. Different applications include: analysis of bacterial DNA, pattern formation and biological invasion, modelling of prion diseases, motion perception.

• Mathematical Risk Theory and Finance (Grechuk, Levendorskii, Tretyakov)
  The group is engaged with research in risk measures, mathematical risk theory, and numerical methods for effective computation of financial quantities.