@article{21743,
  abstract     = {We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden–Weinstein structure. Our method integrates the Liouville 1-form of the Marsden–Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures.},
  author       = {Bauer, Martin and Ishida, Sadashige and Michor, Peter W.},
  issn         = {1432-1467},
  journal      = {Journal of Nonlinear Science},
  number       = {2},
  publisher    = {Springer Nature},
  title        = {{Symplectic structures on the space of space curves}},
  doi          = {10.1007/s00332-026-10266-8},
  volume       = {36},
  year         = {2026},
}

@article{14884,
  abstract     = {We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.},
  author       = {Davoli, Elisa and D’Elia, Lorenza and Ingmanns, Jonas},
  issn         = {1432-1467},
  journal      = {Journal of Nonlinear Science},
  number       = {2},
  publisher    = {Springer Nature},
  title        = {{Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions}},
  doi          = {10.1007/s00332-023-10005-3},
  volume       = {34},
  year         = {2024},
}

@article{10550,
  abstract     = {The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter.},
  author       = {Fellner, Klemens and Fischer, Julian L and Kniely, Michael and Tang, Bao Quoc},
  issn         = {1432-1467},
  journal      = {Journal of Nonlinear Science},
  publisher    = {Springer Nature},
  title        = {{Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion}},
  doi          = {10.1007/s00332-023-09926-w},
  volume       = {33},
  year         = {2023},
}