The Applied Mathematics group contributes to research on a wide range of topics in Continuum Mechanics, Mathematical Biology, Nonlinear Systems, Numerical Analysis and Scientific Computing.

The Applied Mathematics Group is recognised for world leading and internationally excellent research and has active collaborations with researchers from industry, healthcare, and other areas of science and engineering. The group provides opportunities for postgraduate research across many areas of Applied Mathematics. Many PhD projects arise from engineering applications and involve collaborations with academic and industrial partners.

Continuum Mechanics is a traditionally strong research field within the School. Active research is pursued in the areas of bubble dynamics, biological and physiological fluid mechanics, dynamic wetting, flow in porous media, dynamics of liquid jets and drops, flows with phase transitions, fuel cells and many more. This research involves mathematical modelling, mathematical analysis of models and the underlying physical phenomena, as well as development of novel computational tools.

Research activities in Mathematical Biology range from applications in healthcare (antimicrobial resistance, cancer, epilepsy, microsurgical robots and infertility for example) and climate change (response of plants to increasing carbon dioxide levels), through fundamental biology (left-right symmetry-breaking in early embryo development; the role of anisotropy in tissue growth) and ecology (complexity of ecosystems and food webs), to novel mathematical and computational methods (meshfree computations for viscous flow, spitting schemes for stochastic differential equations). This research has close links to a range of stakeholders, in particular, the Centre for Systems Modelling and Quantitative Biomedicine, Institute for Microbiology and Infection, Healthcare Technology Institute, and Birmingham Institute for Forestry Research.

Research in the broad area of Nonlinear Systems combines the development of fundamental mathematical theory and methodology for solving reaction-diffusion systems, inverse problems and dynamical systems with contribution to a wide range of engineering and industrial applications. The application areas include nonlinear waves in river flows, oil pipeline flows, free surface flows and jets, chemical reactions and hydrogen fuel cell models.

Research in Numerical Analysis and Scientific Computing covers a wide range of areas related to the design, analysis and implementation of robust and accurate numerical algorithms for solving mathematical problems coming from real-life applications. The areas of particular focus and expertise include numerical methods for partial differential and boundary integral equations, adaptive algorithms, numerical linear algebra, approximation theory, numerical methods for uncertainty quantification, algorithms for large-scale problems, and research software development.

Researchers and PhD students have access to powerful computing resources and facilities, including the University High Performance Computing cluster BlueBEAR and large-data storage facility (BEAR Research Data Store).

Training of PhD students is provided through individual supervision of research as well as by taking relevant taught modules and attending advanced research seminars and conferences.

Why study Applied Mathematics PhD at Birmingham?
The School of Mathematics has a strong research culture, with researchers of international stature in each of its main specialisms.
The University of Birmingham is one of the prestigious Russell group research-intensive Universities in the UK. The School of Mathematics attracts gifted graduate students from across the world.
The School collaborates widely with multiple disciplines, including Biological and Medical Sciences, Chemical Engineering and within industry. In particular, Birmingham is an emerging centre for multidisciplinary Biological Systems Science research, and is in a unique position, being adjacent to one of the largest super-hospitals in Europe, catering for a highly diverse population.
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