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Personal profile

Roles & Responsibilities

I am an Associate Professor at the Maxwell Institute for Mathematical Sciences

and the Department of Mathematics at Heriot-Watt University.

My responsibilities include Research and Teaching. For further details, please visit my webpage at




Research Group Contact Details

For recent news and information about current project supported by EPSRC and the group, please look at the following link:




Research interests

- Complex Heterogeneous Multiphase Systems (CHMSs):  Applying physical/variational and thermodynamic principles together with mathematical analysis for the reliable and systematic description of complex processes in real world/applications such as fuel cells, batteries, supercapacitors, desalination devices, solar cells, biofilm formation in porous and strongly heterogeneous environments, fluid and multiphase flow in porous media, and social and economic interactions such as opinion dynamics, growth, and energy.

- Partial Differential Equations (PDEs): Using the tools from calculus of variations and functional analysis for the better understanding and justification of physical formulations in CMSs. Studying dynamics by extending gradient flow formulations towards more realistic evolution of physical systems. This often involves the reformulation of problems in a relaxed sense such as weak or distributional formulations. Obtaining effective formulations by asymptotic analysis such as homogenisation theory and renormalisation group theory.

- Numerical Analysis and Computational Science: Developing efficient and reliable numerical schemes for CMSs by proving convergence, rigorously establish physical properties of discrete solutions and the subsequent validation by computational experiments. Of general interest is also the development of computational schemes for high-dimensional problems.

- Thermodynamics, Stochastics, Information, Randomness, and Random Media: Studying and analysing nonequilibrium thermodynamic systems for consistency. Investigating the appearance of randomness in seemingly deterministic physical systems which generally appear as PDE + Noise formulations. Another important topic is the reliable and systematic description of Random Media using statistical data, the theory of stochastic processes, and geometry.


  • QC Physics
  • Fluid Dynamics
  • Materials
  • dynamic of structures
  • QD Chemistry
  • Reactions
  • Surface chemistry
  • Electrochemistry
  • QA75 Electronic computers. Computer science
  • Numerical Methods
  • Partial Differential Equations
  • Stochastics

Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

macroscopic equations Physics & Astronomy
Upscaling Mathematics
formulations Physics & Astronomy
porosity Physics & Astronomy
Phase-field Equations Mathematics
Porous Media Mathematics
free energy Physics & Astronomy
porous medium Earth & Environmental Sciences

Co Author Network Recent external collaboration on country level. Dive into details by clicking on the dots.

Selected Research Output 2009 2019

  • 20 Article
  • 1 Conference contribution

Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media

Schmuck, M., Pradas, M., Pavliotis, G. & Kalliadasis, S., Dec 2013, In : Nonlinearity. 26, 12, p. 3259-3277

Research output: Contribution to journalArticle

Analysis of the Navier–Stokes–Nernst–Planck–Poisson system

Schmuck, M., Jun 2009, In : Mathematical Models and Methods in Applied Sciences. 19, 06, p. 993-1014 22 p.

Research output: Contribution to journalArticle

Fuel cells

New stochastic mode reduction strategy for dissipative systems

Schmuck, M., Pradas, M., Kalliadasis, S. & Pavliotis, G. A., 2013, In : Physical Review Letters. 110, 24, 5 p., 244101

Research output: Contribution to journalArticle

Homogenization of the Poisson-Nernst-Planck equations for ion transport in charged porous media

Schmuck, M. & Bazant, M. Z., 2015, In : SIAM Journal on Applied Mathematics. 75, 3, p. 1369-1401 33 p.

Research output: Contribution to journalArticle

Open Access
Ion Transport
Porous Media
Porous materials

Rate of convergence of general phase field equations in strongly heterogeneous media towards their homogenized limit

Schmuck, M. & Kalliadasis, S., 24 Aug 2017, In : SIAM Journal on Applied Mathematics. 77, 4, p. 1471-1492 22 p.

Research output: Contribution to journalArticle

Open Access
Phase-field Equations
Heterogeneous Media
Fourth Order
Rate of Convergence
Interfacial Flow
thermal noise