Publications by authors named "Klemens Fellner"

4 Publications

  • Page 1 of 1

Uniform convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and the limiting Shockley-Read-Hall model.

J Elliptic Parabol Equ 2020 7;6(2):529-598. Epub 2020 May 7.

Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria.

In this paper, we establish convergence to equilibrium for a drift-diffusion-recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy-entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.
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http://dx.doi.org/10.1007/s41808-020-00068-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7659445PMC
May 2020

A bi-monomeric, nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics.

J Theor Biol 2019 11 13;480:241-261. Epub 2019 Aug 13.

INRA, UR892, Virologie Immunologie Moléculaires, Jouy-en-Josas 78350, France. Electronic address:

In this article, in order to understand the appearance of oscillations observed in protein aggregation experiments, we propose, motivate and analyse mathematically the differential system describing the kinetics of the following reactions: [Formula: see text] with n finite or infinite. This system may be viewed as a variant of the seminal Becker-Döring system, and is capable of displaying sustained though damped oscillations.
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http://dx.doi.org/10.1016/j.jtbi.2019.08.007DOI Listing
November 2019

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

Appl Anal 2016 4;95(12):2661-2682. Epub 2015 Nov 4.

Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, 8010Graz, Austria.

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.
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http://dx.doi.org/10.1080/00036811.2015.1105962DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5894435PMC
November 2015

Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling.

Phys Rev E Stat Nonlin Soft Matter Phys 2012 Apr 17;85(4 Pt 1):041912. Epub 2012 Apr 17.

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.

Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations.
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http://dx.doi.org/10.1103/PhysRevE.85.041912DOI Listing
April 2012
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