Newest published article in Computational Materials Science (January 2019) on

• Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality with highlights such as ``a concise account of Variational and systematic Non-equilibrium Thermodynamic formulations'', ``a promising Novel Theoretical-Computational Tool for the systematic and reliable effective description of multiphase flow in porous media and a wide range of applications'', ``Universality of Coarsening Rates which are independent of geometries of perforations''.
  A summary/graphical abstract is available here.

June 25-27, 2018: EPSRC funded Workshop on

• Complex Heterogeneous Systems taking place at Heriot-Watt University, Edinburgh.
  The preliminary programme can be downoaded here.

New group members:

• Alexandre Simon Exchange Research Student from France
  
  Project on Machine Learning
  in Summer 2018.

• Jonathan Meyer ETP funded Research Student
  
  Industrial Project on Energy
  in 2018.

• Dr. Selcuk Atalay started to work on the EPSRC funded project
  
  Transport and Reactions in Complex Heterogeneous Multiphase Systems
  in July 2017.

• Ms. Jeta Molla will start her PhD project associated with the EPSRC fundend project
  
  Transport and Reactions in Complex Heterogeneous Multiphase Systems,
  in October 2017.

Most recent research results:

• Rigorous and computational advances on the evolution of interfaces:
  M. Schmuck, G.A. Pavliotis, and S. Kalliadasis, Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality, arXiv:1804:09228, accepted in Comp. Mater. Sci. (2018).
• Computational VALIDATION of upscaled/homogenized phase field equations and UNIVERSALITY in periodic porous media:
  A. Ververis & M. Schmuck Computational investigation of porous media phase field formulations: microscopic, effective macroscopic, and Langevin equations, Journal of Computational Physics, 344:485-498 (2017).
• Effective composite cathode formulation accounting for phase transforming intercalation hosts:
  Schmuck, M., Upscaling of solid-electrolyte composite intercalation cathodes for energy storage systems: Homogenized composite cathode equations, Applied Mathematics Research eXpress, 2017(2):402-430 (2017).
• Error estimastes/convergence rates for the porous media approximation of phase field equations:
  Schmuck, M. & Kalliadasis, S., Rate of convergence of general phase field equations in strongly heterogeneous media towards their homogenized limit: error estimates for upscaled phase field equations, SIAM Journal on Applied Mathematics, 77(4):1471-1492 (2017).

Available PhD projects:

• Look at Analysis & Probability and Applied & Computational Mathematics for the following projects:
  
  
  (1) From Photosynthesis to Solar Cells: investigating new theoretical and computational directions
  
  
  (2) Modelling, Analysis, and Numerics for Stochastic Multiscale Systems
  
  
  (3) Quantum inspired mathematical formulation for decision-making: computing and algorithms

Previous highlights:

• IMA online first
  On the appearance of randomness in deterministic equations: Evolutionary renormalization and maximum entropy principles
  With a talk at APS-DFD conference!


• Published in Nonlinearity
  New immiscible flow equations in porous media
           An effective/upscaled/homogenized macroscopic Stokes-Cahn-Hilliard formulation:
           Mathematical analysis and first computations with talk at APS-DFD conference!


• On the role of randomness in deterministic PDEs with dissipation:
  A systematic framework for Stochastic Mode Reduction and Uncertainty Quantification.


• How the microscale can induce new transport characteristics:
  New transport mechanism for dilute electrolytes!
      How the microscale and material properties define macroscopic transport characteristics.