arXiv subjects

Rainer Grauer

Publications and source records attributed to Rainer Grauer.

At least 19 recordsLinked to original sources

arXiv2026

Intermittency from instanton calculus at the transition to turbulence and fusion rules

Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a semi-analytical method that yields high-order structure function exponents by combining instanton calculus, fusion rule predictions, and low-order statistical inputs from direct numerical simulations (DNS). We use instanton predictions, calibrated by DNS, to evaluate high velocity gradient (VG) moments at the onset of intermittency, and then infer scaling exponents in fully developed turbulence via fusion rules. We show that the method captures the crossover at $\mathrm{Re}_λ\approx 1$ in the VG moment scaling, highlight the necessity of including fluctuations around instantons, and discuss future extensions.

physics.flu-dyn↗

arXiv2026

A Comparison of Active Flux Methods for the Vlasov-Poisson System

Active Flux is a third-order accurate, fairly novel finite volume method for hyperbolic conservation laws that is becoming increasingly popular. It evolves additional nodal degrees of freedom (DOF) located on cell interfaces and shared by neighboring cells. The numerical fluxes are then computed from these DOFs. A crucial component of Active Flux methods is the evolution operator of the point values, which enables the natural use of semi-Lagrangian ideas and makes Active Flux an attractive candidate for a grid-based approach to the Vlasov equation. Here, we compare two recently proposed Active Flux methods for the 1D1V Vlasov-Poisson system: a split-step method and an unsplit method.

math.NA↗

arXiv2026

An asymptotic-preserving five-moment two-species plasma model coupled to an external magnetohydrodynamic solver

Accurately modeling collisionless space plasmas requires capturing small-scale kinetic effects while keeping global-scale simulations computationally tractable. Traditional multiscale approaches often rely on localized magnetohydrodynamics (MHD)-particle-in-cell (PIC) coupling or dynamic model hierarchies. In this work, we extend an established, adaptive multi-model hierarchy spanning from fully kinetic Vlasov descriptions to fluid models by introducing an asymptotic-preserving (AP) strategy that couples a two-species, five-moment fluid description with an ideal MHD solver. This coupling is the final critical step toward enabling efficient global simulations because the kinetic-scale physics in nonideal regions is entirely handled by finer models in the hierarchy. Kinetic descriptions natively solve Maxwell's equations and thus capture fast plasma waves, oscillations, and light waves, which are absent in the MHD dynamics. To address this difference without sacrificing computational efficiency, our AP framework seamlessly projects these fast dynamics onto the slow MHD dynamics, ensuring rigorous consistency at the model interfaces. We detail the AP two-fluid formulation, the variable-coupling interface, and its integration into external frameworks. Finally, we demonstrate the validity and robustness of the fully coupled framework, from kinetics to ideal MHD, through magnetic reconnection simulations.

physics.plasm-ph↗

arXiv2025

Modelling cosmic-ray transport: magnetised versus unmagnetised motion in astrophysical magnetic turbulence

Cosmic-ray transport in turbulent astrophysical environments remains a multifaceted problem and, despite decades of study, the impact of complex magnetic field geometry -- evident in simulations and observations -- has only recently received more focussed attention. To understand how ensemble-averaged transport behaviour emerges from the intricate interactions between cosmic rays and structured magnetic turbulence, we run test-particle experiments in snapshots of a strongly turbulent magnetohydrodynamics simulation. We characterise particle-turbulence interactions via the gyro radii of particles and their experienced field-line curvatures, which reveals two distinct transport modes: magnetised motion, where particles are tightly bound to strong coherent flux tubes and undergo large-scale mirroring; and unmagnetised motion, characterised by chaotic scattering through weak and highly tangled regions of the magnetic field. We formulate an effective stochastic process for each mode: compound subdiffusion with long mean free paths for magnetised motion, and a Langevin process with short mean free paths for unmagnetised motion. A combined stochastic walker that alternates between these two modes accurately reproduces the mean squared displacements observed in the test-particle data. Our results emphasise the critical role of coherent magnetic structures in comprehensively understanding cosmic-ray transport and lay a foundation for developing a theory of geometry-mediated transport.

physics.plasm-ph↗

arXiv2025

Anisotropic Cosmic Ray Transport in strong MHD Turbulence due to Magnetic Mirroring and Resonant Curvature Scattering

The transport of cosmic rays through turbulent astrophysical plasmas still constitutes an open problem. Building on recent progress, we study the combined effect of magnetic mirroring and resonant curvature scattering on parallel and perpendicular transport. We conduct test-particle simulations in snapshots of an anisotropic magnetohydrodynamics simulation with $δB/B_0\sim 1$ and record magnetic moment variation and field line curvature around pitch-angle reversals. We find for strongly magnetized particles that (i) pitch-angle reversals may occur either in coherent regions of the field with small variation of the magnetic moment via magnetic mirroring or in chaotic regions of the field with strong variation of the magnetic moment via resonant curvature scattering; (ii) parallel transport can be modeled as a Lévy walk with a truncated power-law distribution based on pitch-angle reversal times; and (iii) perpendicular transport is enhanced by resonant curvature scattering in synergy with chaotic field line separation and diminished by magnetic mirroring due to confinement in locally ordered field line bundles. While magnetic mirroring constitutes the bulk of reversal events, resonant curvature scattering additionally acts on trajectories that fall in the loss cones of typical mirroring structures and thus provides the cut-off for the reversal time distribution. Our results, which highlight the role of the magnetic field line geometry in cosmic-ray transport processes, are consistent with energy-independent diffusion coefficients. We conclude by considering how energy-dependent observations could arise from an intermittently inhomogeneous interstellar medium.

astro-ph.HE↗

arXiv2025

Synthetic Turbulence via an Instanton Gas Approximation

Sampling synthetic turbulent fields as a computationally tractable surrogate for direct numerical simulations (DNS) is an important practical problem in various applications, and allows to test our physical understanding of the main features of real turbulent flows. Reproducing higher-order Eulerian correlation functions, as well as Lagrangian particle statistics, requires an accurate representation of coherent structures of the flow in the synthetic turbulent fields. To this end, we propose in this paper a systematic coherent-structure based method for sampling synthetic random fields, based on a superposition of instanton configurations - an instanton gas - from the field-theoretic formulation of turbulence. We discuss sampling strategies for ensembles of instantons, both with and without interactions and including Gaussian fluctuations around them. The resulting Eulerian and Lagrangian statistics are evaluated numerically and compared against DNS results, as well as Gaussian and log-normal cascade models that lack coherent structures. The instanton gas approach is illustrated via the example of one-dimensional Burgers turbulence throughout this paper, and we show that already a canonical ensemble of non-interacting instantons without fluctuations reproduces DNS statistics very well. Finally, we outline extensions of the method to higher dimensions, in particular to magnetohydrodynamic turbulence for future applications to cosmic ray propagation.

physics.flu-dyn↗

arXiv2025

Optimal Landau-type closure parameters for two-fluid simulations of plasma turbulence at kinetic scales

Two fluid simulations using local Landau-fluid closures derived from linear theory provide an efficient computational framework for plasma modelling, since they bridge the gap between computationally intensive kinetic simulations and fluid descriptions. Their accuracy in representing kinetic effects depends critically on the validity of the linear approximation used in the derivation: the plasma should not be too far from local thermodynamic equilibrium, LTE. However, many of the problems where these models are of particular interest (such as plasma turbulence and instabilities) are in fact quite far from LTE. The question then arises, if kinetic scale processes are still sufficiently well captured outside of the theoretical regime of applicability of the closure. In this paper, we show that two fluid simulations with Landau fluid closures can effectively reproduce the energy spectra obtained with fully kinetic Vlasov simulations, used as references, as long as the local closure parameter is appropriately chosen. Our findings validate the usage of two fluid simulations with Landau-fluid closure as a possible alternative to fully kinetic simulations of turbulence, in cases where being able to simulate extremely large domains is of particular interest.

physics.plasm-ph↗

arXiv2025

The role of magnetic boundaries in kinematic and self-consistent magnetohydrodynamic simulations of precession-driven dynamo action in a closed cylinder

We numerically examine dynamo action generated by a flow of an electrically conducting fluid in a precessing cylindrical cavity. We compare a simplified kinematic approach based on the solution of the magnetic induction equation with a prescribed velocity field with the results from a self-consistent three-dimensional simulation of the complete set of magnetohydrodynamic equations. In all cases, we observe a minimum for the onset of dynamo action in a transitional regime, within which the hydrodynamic flow undergoes a change from a large-scale to a more small-scale, turbulent behaviour. However, significant differences in the absolute values for the critical magnetic Reynolds number occur depending on the physical properties of the external layers surrounding the flow active domain. The strong influence of the electromagnetic properties of outer layers with the large variation of the critical magnetic Reynolds number can be related to the existence of two different branches with dynamo action. In contrast to the kinematic models, the nonlinear MHD simulations reveal a small scale dynamo solution with the magnetic energy remaining significantly smaller than the kinetic energy of the flow. In irregular intervals, we observe dynamo bursts with a local concentration of the magnetic field, resulting in a global increase of the magnetic energy by a factor of 3 to 5. However, diffusion of the local patches caused by strong local shear is too rapid, causing these features to exist for only a short period so that their dynamical impact on the dynamo remains small.

physics.flu-dyn↗

arXiv2025

Generation of cosmic ray trajectories by a Diffusion Model trained on test particles in 3D magnetohydrodynamic turbulence

Models for the transport of high energy charged particles through strong magnetic turbulence play a key role in space and astrophysical studies, such as describing the propagation of solar energetic particles and high energy cosmic rays. Inspired by the recent advances in high-performance machine learning techniques, we investigate the application of generative diffusion models to synthesizing test particle trajectories obtained from a turbulent magnetohydrodynamics simulation. We consider velocity increment, spatial transport and curvature statistics, and find excellent agreement with the baseline trajectories for fixed particle energies. Additionally, we consider two synthetic turbulence models for comparison. Finally, challenges towards an application-ready transport model based on our approach are discussed.

physics.flu-dyn↗

arXiv2024

A split-step Active Flux method for the Vlasov-Poisson system

Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the respective interface to evolve the cell-average in a conservative way. In this paper, we apply the method to the Vlasov-Poisson system describing the time evolution of the time-dependent distribution function of a collisionless plasma. In particular, we consider the evaluation of the flux integrals in higher dimensions. We propose a dimensional splitting and three types of formulations of the flux integral: a one-dimensional reconstruction of second order, a third-order reconstruction based on information along each dimension, and a third-order reconstruction based on a discrepancy formulation of the Active Flux method. Numerical results in 1D1V phase-space compare the properties of the various methods.

math.NA↗

arXiv2024

Towards Synthetic Magnetic Turbulence with Coherent Structures

Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic turbulence. We present a novel method, featuring coherent structures, conditional structure function scaling and fieldline curvature statistics comparable to magnetohydrodynamic turbulence. Enhanced transport of charged particles is investigated as well. This method presents significant progress towards physically faithful synthetic turbulence.

physics.space-ph↗

arXiv2024

Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation

Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme fluctuations on the statistics of the energy dissipation rate. While the contribution of the instanton alone is insufficient, we obtain excellent agreement with direct simulations when including Gaussian fluctuations and the corresponding zero mode. Fluctuations are crucial to obtain the correct scaling when quasi-singular events govern the turbulence statistics.

physics.flu-dyn↗

arXiv2023

The muphyII Code: Multiphysics Plasma Simulation on Large HPC Systems

Collsionless astrophysical and space plasmas cover regions that typically display a separation of scales that exceeds any code's capabilities. To help address this problem, the muphyII code utilizes a hierarchy of models with different inherent scales, unified in an adaptive framework that allows stand-alone use of models as well as a model-based dynamic and adaptive domain decomposition. This requires ensuring excellent conservation properties, careful treatment of inner-domain model boundaries for model coupling, and robust time stepping algorithms, especially with the use of electron subcycling. This multi-physics approach is implemented in the muphyII code, tested on different scenarios of space plasma reconnection and evaluated against space probe data and higher-fidelity simulation results from literature. Adaptive model refinement is highlighted in particular, and a hybrid model with kinetic ions, pressure-tensor fluid electrons, and Maxwell fields is appraised.

physics.comp-ph↗

arXiv2023

Geometrical Formulation of Hybrid Kinetic and Gyrokinetic Hamiltonian Field Theory for Astrophysical and Laboratory Plasmas

In the present work, a consistent Lagrangian model that encapsulates fully kinetic ions and gyrokinetic electrons for solar wind electromagnetic turbulence is formulated. Using a consistent method, where both electrons and protons are treated with the same mathematical formalism, we derive and implement a model in which high frequency waves and kinetic electrons effects are described in a computationally cost-efficient way. To that aim, higher order Lie-transform perturbation methods applied to Hamiltonian formulation of guiding center motion are used in order to describe the dynamics of particles and fields. Furthermore, the use of a Hamiltonian formulation allow us to introduce an abelian and gauge invariant electromagnetic field theory for the closure of the system.

physics.plasm-ph↗

arXiv2022

Symmetries and zero modes in sample path large deviations

Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati differential equations along the large deviation minimizers or instantons, either forward or backward in time. Previous works in this direction often rely on the existence of isolated minimizers with positive definite second variation. By adopting techniques from field theory and explicitly evaluating the large deviation prefactors as functional determinant ratios using Forman's theorem, we extend the approach to general systems where degenerate submanifolds of minimizers exist. The key technique for this is a boundary-type regularization of the second variation operator. This extension is particularly relevant if the system possesses continuous symmetries that are broken by the instantons. We find that removing the vanishing eigenvalues associated with the zero modes is possible within the Riccati formulation and amounts to modifying the initial or final conditions and evaluation of the Riccati matrices. We apply our results in multiple examples including a dynamical phase transition for the average surface height in short-time large deviations of the one-dimensional Kardar-Parisi-Zhang equation with flat initial profile.

cond-mat.stat-mech↗

arXiv2022

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a 1 + 1-dimensional field u(t, ξ), where each Gaussian component uξ(t) is synthesized with identical underlying noise but different covariance function Cξ(t,s) parameterized by a log-normally distributed parameter ξ. Due to the Gaussianity of each component uξ(t), we can exploit standard sampling alogrithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u(t) is then initialized by assigning each point in time t a ξ(t) and therefore a specific value from u(t, ξ), where the time-dependent parameter ξ(t) follows a log-normal process with a large correlation time scale compared to the correlation time of u(t, ξ). We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.

physics.data-an↗

arXiv2022

Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations

We investigate the spatio-temporal structure of the most likely configurations realising extremely high vorticity or strain in the stochastically forced 3D incompressible Navier-Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realising an extreme constraint as solution of a large optimisation problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-rotating vortex rings. We additionally observe that the most likely configurations for vorticity and strain spontaneously break their rotational symmetry for extremely high observable values. Instanton calculus and large deviation theory allow us to show that these maximum likelihood realisations determine the tail probabilities of the observed quantities. In particular, we are able to demonstrate that artificially enforcing rotational symmetry for large strain configurations leads to a severe underestimate of their probability, as it is dominated in likelihood by an exponentially more likely symmetry broken vortex-sheet configuration.

physics.flu-dyn↗

arXiv2022

A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations

Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic plasma configurations. However, a reduction of the high computational cost that is inherent to fully kinetic simulations would be desirable, especially at high velocity space resolutions. For this purpose, low-rank approximations can be employed. The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astrophysical and fusion plasmas. In this paper we present a new parallel low-rank solver for the full six-dimensional electromagnetic Vlasov-Maxwell equations with a compression of the particle distribution function in velocity space. Special attention is paid to mass conservation and Gauss's law. The low-rank Vlasov solver is applied to standard benchmark problems of plasma turbulence and magnetic reconnection and compared to the full grid method. It yields accurate results at significantly reduced computational cost.

physics.plasm-ph↗