Publications // Universität Oldenburg

The downloadable preprints may differ slightly from the published versions.

Preprints

[unpublished] bibtex | Dokument aufrufen
A. Meiners und H. Uecker, Helfrich cylinders -- instabilities, bifurcations and amplitude equations.
@unpublished{hcyl, author = {Meiners, A. and Uecker, H.}, title= {Helfrich cylinders -- instabilities, bifurcations and amplitude equations}, note = {Available at arXiv}, url="https://cloud.uol.de/s/ZTXtZoJiaJBKbCH", year = {2025} }

Published

[article] bibtex | Dokument aufrufen
F. Al Saadi, E. Knobloch, A. Meiners, und H. Uecker, "Breathers and mixed oscillatory states near a Turing–Hopf instability in a two–component reaction–diffusion system" Physica D: Nonlinear Phenomena, vol. 472, p. 134482. 2025.
doi: 10.1016/j.physd.2024.134482
@article{ALSAADI2025134482, title = {Breathers and mixed oscillatory states near a Turing–Hopf instability in a two–component reaction–diffusion system}, journal = {Physica D: Nonlinear Phenomena}, volume = {472}, pages = {134482}, year = {2025}, issn = {0167-2789}, doi = {https://doi.org/10.1016/j.physd.2024.134482}, url = {https://cloud.uol.de/s/t2fDjtmjrwze2ra}, author = {Fahad {Al Saadi} and Edgar Knobloch and Alexander Meiners and Hannes Uecker}, keywords = {Localized oscillatory states, Breathing, Mixed modes, Numerical bifurcation and continuation, Snaking, Isolas, Zipping-up}, abstract = {Numerical continuation is used to study the interaction between a finite wave number Turing instability and a zero wave number Hopf instability in a two-species reaction-diffusion model of a semiconductor device. The model admits two such codimension-two interactions, both with a subcritical Turing branch that is responsible for the presence of spatially localized Turing states. The Hopf branch may also be subcritical. We uncover a large variety of spatially extended and spatially localized states in the vicinity of these points and by varying a third parameter show how disconnected branches of time-periodic spatially localized states can be “zipped up” into snaking branches of time-periodic oscillations. These are of two types: a Turing state embedded in an oscillating background, and a breathing Turing state embedded in a non-oscillating background. Stable two-frequency states resembling a mixture of these two states are also identified. Our results are complemented by direct numerical simulations. The findings explain the origin of the large multiplicity of localized steady and oscillatory patterns arising from the Turing–Hopf interaction and shed light on the competition between them.} }
[article] bibtex | Dokument aufrufen
A. Meiners und H. Uecker, "Numerical Continuation and Bifurcation for Differential Geometric PDEs" Numerical Mathematics: Theory, Methods and Applications, vol. 17, iss. 3. 2024.
doi: 10.4208/nmtma.OA-2024-0005
@article{NMTMA-17-3, author = {Meiners, Alexander and Uecker, Hannes}, title = {Numerical Continuation and Bifurcation for Differential Geometric PDEs}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {3}, pages = {555--606}, abstract = {We describe some differential geometric bifurcation problems and their treatment in the Matlab continuation and bifurcation toolbox pde2path. The continuation steps consist in solving the PDEs for the normal displacement of an immersed surface $X ⊂\mathbb{R}^3,$ with bifurcation detection and possible subsequent branch switching. The examples include minimal surfaces such as Enneper’s surface and a Schwarz-P-family, some non-zero constant mean curvature surfaces such as liquid bridges, and some 4th order biomembrane models. In all of these we find interesting symmetry-breaking bifurcations. A few of these are (semi)analytically known and hence used as benchmarks. }, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0005}, url = {https://cloud.uol.de/s/FBYieM3nAFZp6CQ} }
[article] bibtex | Dokument aufrufen
A. Meiners und B. Vertman, "Spectral zeta function on discrete tori and Epstein-Riemann Hypothesis" Journal of Number Theory, vol. 244. 2023.
doi: 10.1016/j.jnt.2022.08.004
@article{MEINERS2023418, title = {Spectral zeta function on discrete tori and Epstein-Riemann Hypothesis}, journal = {Journal of Number Theory}, volume = {244}, pages = {418-461}, year = {2023}, issn = {0022-314X}, doi = {https://doi.org/10.1016/j.jnt.2022.08.004}, url = {https://www.sciencedirect.com/science/article/pii/S0022314X2200186X}, author = {Alexander Meiners and Boris Vertman}, keywords = {Epstein zeta function, Spectral zeta function, Epstein-Riemann Hypothesis}, abstract = {We consider the combinatorial Laplacian on a sequence of discrete tori which approximate the α-dimensional torus. In the special case α=1, Friedli and Karlsson derived an asymptotic expansion of the corresponding spectral zeta function in the critical strip, as the approximation parameter goes to infinity. There, the authors have also formulated a conjecture on this asymptotics, that is equivalent to the Riemann Hypothesis. In this paper, inspired by the work of Friedli and Karlsson, we prove that a similar asymptotic expansion holds for α=2. Similar argument applies to higher dimensions as well. A conjecture on this asymptotics gives an equivalent formulation of the Epstein-Riemann Hypothesis, if we replace the standard discrete Laplacian with the 9-point star discrete Laplacian.}

Tutorials

[misc] bibtex | Dokument aufrufen
A. Meiners und H. Uecker, Differential geometric bifurcation problems in pde2path -- algorithms and tutorial examples.
@misc{geomtut, author = {Meiners, A. and Uecker, H.}, TITLE = {Differential geometric bifurcation problems in pde2path -- algorithms and tutorial examples}, url= "https://cloud.uol.de/s/iMDai3idbz3TpPx", YEAR = {2023} }

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