Research Output per year

## 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

**. For further details, please visit my webpage at**

*Teaching*

### Research Group Contact Details

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

http://www.macs.hw.ac.uk/~ms713/transport.html

### 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 randomnes*s 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*.

### Keywords

- 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.

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## Selected Research Output 2009 2017

## 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. 3259-3277Research output: Contribution to journal › Article

## 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 journal › Article

## Homogenization of a catalyst layer model for periodically distributed pore geometries in PEM fuel cells

Schmuck, M. & Berg, P. 2013 In : Applied Mathematics Research eXpress. 2013, 1, p. 57-78 22 p.Research output: Contribution to journal › Article

## New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

Schmuck, M. Feb 2013 In : Journal of Mathematical Physics. 54, 2, 21 p., 021504Research output: Contribution to journal › Article

## 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., 244101Research output: Contribution to journal › Article

## 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 journal › Article

## 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 journal › Article

## Computational investigation of porous media phase field formulations: Microscopic, effective macroscopic, and Langevin equations

Ververis, A. & Schmuck, M. 1 Sep 2017 In : Journal of Computational Physics. 344, p. 485–498 14 p.Research output: Contribution to journal › Article