arXiv subjects

M. Rasmussen

Publications and source records attributed to M. Rasmussen.

3 recordsLinked to original sources

arXiv2023

Smooth Persistence of Attractors for Set-Valued Dynamical Systems: A Boundary Map Approach

We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical propagation of uncertainty. In order to tackle the inherent difficulties associated to the multi-valued structure of such dynamical systems, we introduce a single-valued map, the so-called boundary map, which is a contactomorphism of the unit-tangent bundle of the state space, with the following characteristic property: boundaries of attractors of the set-valued dynamical system correspond in a unique way to invariant Legendrian manifolds of this map. We show how the underlying contact geometry guarantees the smooth persistence of such attractors under perturbations of the set-valued dynamical system, provided that the associated boundary map is normally hyperbolic at the unit normal bundle of the boundary.

math.DS↗

arXiv2022

An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks

Reacting astrophysical flows can be challenging to model because of the difficulty in accurately coupling hydrodynamics and reactions. This can be particularly acute during explosive burning or at high temperatures where nuclear statistical equilibrium is established. We develop a new approach based on the ideas of spectral deferred corrections (SDC) coupling of explicit hydrodynamics and stiff reaction sources as an alternative to operator splitting that is simpler than the more comprehensive SDC approach we demonstrated previously. We apply the new method to a double detonation problem with a moderately-sized astrophysical nuclear reaction network and explore the timestep size and reaction network tolerances to show that the simplified-SDC approach provides improved coupling with decreased computational expense compared to traditional Strang operator splitting. This is all done in the framework of the Castro hydrodynamics code, and all algorithm implementations are freely available.

astro-ph.IM↗

arXiv2018

Ion Impact Induced Ultrafast Electron Dynamics in Correlated Materials and Finite Graphene Clusters

Strongly correlated systems of fermions have an interesting phase diagram arising from the Hubbard gap. Excitation across the gap leads to the formation of doubly occupied lattice sites (doublons). This state offers interesting electronic and optical properties. Moreover, when the system is driven out of equilibrium interesting collective dynamics may arise that are related to the spatial propagation of doublons. Here, a novel mechanism that was recently proposed by us [Balzer \textit{et al.}, submitted for publication] is verified by exact diagonalization and nonequilibrium Green functions (NEGF) simulations---fermionic doublon creation by the impact of energetic ions. We report the formation of a nonequilibrium steady state with homogeneous doublon distribution. A physically intuitive picture is given in terms of an analytical model for a two-site system where the doublon formation is explained in terms of a two-fold passage of an avoided crossing (Landau-Zener picture). The effect should be particularly important for strongly correlated finite systems, such as graphene nanoribbons, and directly observable with fermionic atoms in optical lattices. We demonstrate that doublon formation and propagation in correlated lattice systems can be accurately simulated with NEGF. In addition to two-time results we present single-time results within the generalized Kadanoff-Baym ansatz (GKBA) with Hartree-Fock propagators (HF-GKBA), and we present systematic improvements that use correlated propagators (correlated GKBA).

cond-mat.str-el↗