Maria Bruna
Royal Society University Research Fellow
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Research
My research seeks to understand the behaviour of complex systems consisting of many interacting components. These systems appear in many different situations in biology and engineering, such as a population of cancer cells, or contaminant particles going through a filter. I work on developing and analysing mathematical and computational methods to represent these systems. In particular, I am interested in methods that can capture phenomena at multiple scales and explain how individual-level mechanisms (such as the interactions between particles) affect the population-level behaviour:
- Stochastic models of diffusion for finite-size particles
- Homogenisation of ordered and disordered porous media
- Cross-diffusion systems
- Models for segregation in heterogeneous systems
Publications
(2022).
Macroscopic behaviour in a two-species exclusion process via the method of matched asymptotics.
Preprint.
(2021).
Coarse graining of a Fokker--Planck equation with excluded volume effects preserving the gradient flow structure.
EJAM.
(2019).
The role of a strong confining potential in a nonlinear Fokker--Planck equation.
Nonlin. Anal..
(2019).
The influence of porous-medium microstructure on filtration.
J. Fluid Mech..
(2018).
Asymptotic gradient flow structures of a nonlinear Fokker-Planck equation.
Preprint.
(2018).
Stability estimates for systems with small cross-diffusion.
ESAIM: M2AN.
(2018).
Reactions, diffusion, and volume exclusion in a conserved system of interacting particles.
Phys. Rev. E.
(2017).
Cross-Diffusion Systems with Excluded Volume Effects and Asymptotic Gradient Flows.
J. Nonlinear Sci..
(2017).
Diffusion of particles with short-range interactions.
SIAM J. Appl. Math.
(2015).
Diffusion in Spatially Varying Porous Media.
SIAM J. Appl. Math..
(2014).
Diffusion of Finite-Size Particles in Confined Geometries.
Bull. Math. Biol..
(2012).
Diffusion of multiple species with excluded-volume effects.
J. Chem. Phys..
Contact
- bruna@maths.cam.ac.uk
- Office G1.10, Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences, Cambridge, CB3 0WA