@misc{Reich1994,
  author    = {Reich, Sebastian},
  title     = {Momentum conserving symplectic integrators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-16824},
  year      = {1994},
  abstract  = {In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).},
  language  = {en}
}
@misc{Reich1995,
  author    = {Reich, Sebastian},
  title     = {On the local qualitative behavior of differential-algebraic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46739},
  year      = {1995},
  abstract  = {A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field.},
  language  = {en}
}
@misc{Reich1991,
  author    = {Reich, Sebastian},
  title     = {On an existence and uniqueness theory for nonlinear differential-algebraic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46706},
  year      = {1991},
  abstract  = {An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example.},
  language  = {en}
}
@misc{AcevedoFallahReichetal.2017,
  author    = {Acevedo, Walter and Fallah, Bijan and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {627},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41874},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-418743},
  pages     = {545 -- 557},
  year      = {2017},
  abstract  = {Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts.},
  language  = {en}
}