189 citations · 385 across the 18 of their papers we have counts for
20 papers
A metriplectic formulation of polarized radiative transfer
Vincent Bosboom, Michael Kraus, Matthias Schlottbom
We present a metriplectic formulation of the radiative transfer equation with polarization and varying refractive index and show that this formulation automatically satisfies the f…
Control of Parasitism in Variational Integrators for Degenerate Lagrangian Systems
Farrukh Shehzad, Yousaf Habib, Michael Kraus +1
This paper deals with the control of parasitism in variational integrators for degenerate Lagrangian systems by writing them as general linear methods. This enables us to calculate…
Symplectic model reduction methods for the Vlasov equation
Tomasz M. Tyranowski, Michael Kraus
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solvin…
A discrete Nambu bracket for 2D extended Magnetohydrodynamics
D. A. Kaltsas, M. Kraus, G. N. Throumoulopoulos
In this note we propose a trilinear bracket formulation for the Hamiltonian extended Magnetohydrodynamics (XMHD) model with homogeneous mass density. The corresponding two-dimensio…
Variational integrators for stochastic dissipative Hamiltonian systems
Michael Kraus, Tomasz M. Tyranowski
Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which…
Energy-, momentum-, density-, and positivity-preserving spatio-temporal discretizations for the nonlinear Landau collision operator with exact H-theorems
Eero Hirvijoki, Joshua W. Burby, Michael Kraus
This paper explores energy-, momentum-, density-, and positivity-preserving spatio-temporal discretizations for the nonlinear Landau collision operator. We discuss two approaches,…
Variational Integrators for Inertial Magnetohydrodynamics
Michael Kraus
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonica…
Metriplectic particle-in-cell integrators for the Landau collision operator
Eero Hirvijoki, Michael Kraus, Joshua W. Burby
In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structu…
Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
C. Leland Ellison, John M. Finn, Joshua W. Burby +3
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets…
Projected Variational Integrators for Degenerate Lagrangian Systems
Michael Kraus
We propose and compare several projection methods applied to variational integrators for degenerate Lagrangian systems, whose Lagrangian is of the form $L = \vartheta(q) \cdot \dot…
Metriplectic Integrators for the Landau Collision Operator
Michael Kraus, Eero Hirvijoki
We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metri…
Variational Integrators for Ideal Magnetohydrodynamics
Michael Kraus, Omar Maj
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discre…
GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
Michael Kraus, Katharina Kormann, Philip J. Morrison +1
We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive…
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Michal Kraus
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilb…
Variational Integrators for Reduced Magnetohydrodynamics
Michael Kraus, Emanuele Tassi, Daniela Grasso
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian…
Variational Integrators for Nonvariational Partial Differential Equations
Michael Kraus, Omar Maj
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as w…
On the equivalence between coarse and uniform embeddability of quasi-Banach spaces into a Hilbert space
Michal Kraus
We give a direct proof of the fact that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it uniformly embeds into a Hilbert space.
Variational Integrators in Plasma Physics
Michael Kraus
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesi…
Coarse and uniform embeddings between Orlicz sequence spaces
Michal Kraus
We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is…
Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory
H. -G. Döbereiner, E. Evans, M. Kraus +2
Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes…