15 papers
Backward error analysis for matrix discretizations of 2-D Euler equations
Eugen Bronasco, Klas Modin
We introduce a formalism of Lie--Poisson reduction of Butcher series. The corresponding forest momentum map allows for describing backward error analysis of isospectral symplectic…
Madelung hydrodynamics and Poisson geometry of wave functions
Boris Khesin, Klas Modin
We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. We prove that for arbitrary oriented manifolds th…
Geometric shape matching for recovering protein conformations from single-particle Cryo-EM data
Erik Jansson, Jonathan Krook, Klas Modin +1
We address recovery of the three-dimensional backbone structure of single polypeptide proteins from single-particle cryo-electron microscopy (Cryo-SPA) data. Cryo-SPA produces nois…
Symplectic Isospectral Runge--Kutta Methods as Lie group methods
Paolo Cifani, Klas Modin, Cecilia Pagliantini +1
We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cot…
Arnold stability and rigidity in Zeitlin's model of hydrodynamics
Luca Melzi, Klas Modin
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behavi…
Structure-preserving long-time simulations of turbulence in magnetized ideal fluids
Klas Modin, Michael Roop
We address three two-dimensional magnetohydrodynamics models: reduced magnetohydrodynamics (RMHD), Hazeltine's model, and the Charney--Hasegawa--Mima (CHM) equation. These models a…