37 citations · 104 across the 11 of their papers we have counts for
12 papers
Basic and extendable framework for effective charge transport in electrochemical systems
Jeta Molla, Markus Schmuck
We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (c…
Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality
M. Schmuck, G. A. Pavliotis, S. Kalliadasis
We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic form…
Rate of Convergence of General Phase Field Equations towards their Homogenized Limit
M. Schmuck, S. Kalliadasis
Over the last few decades, phase-field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g. geometric PDEs and mean curvature flow,…
Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit
Markus Schmuck, Grigorios A. Pavliotis, Serafim Kalliadasis
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium conf…
New and general framework for adsorption processes on dynamic interfaces
Markus Schmuck, Serafim Kalliadasis
We introduce a new and general continuum thermodynamic framework for the mathematical analysis and computation of adsorption on dynamic interfaces. To the best of our knowledge, th…
A new stochastic mode reduction strategy for dissipative systems
M. Schmuck, M. Pradas, S. Kalliadasis +1
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximu…
Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media
Markus Schmuck, Marc Pradas, Gregorios A. Pavliotis +1
Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the…
New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials
Markus Schmuck
We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we…
Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains
Markus Schmuck, Marc Pradas, Greg A. Pavliotis +1
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well p…
Homogenization of a catalyst layer model for periodically distributed pore geometries in PEM fuel cells
Markus Schmuck, Peter Berg
We formally derive an effective catalyst layer model comprising the reduction of oxygen for periodically distributed pore geometries. By assumption, the pores are completely filled…
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
Markus Schmuck, Martin Z. Bazant
Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion w…
A New Mode Reduction Strategy for the Generalized Kuramoto-Sivashinsky Equation
M. Schmuck, M. Pradas, G. A. Pavliotis +1
Consider the generalized Kuramoto-Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front p…