The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

Brandenburg, Axel; Johansen, Anders; Bourdin, Philippe-A.; Dobler, Wolfgang; Lyra, Wladimir; Rheinhardt, M.; Bingert, Sven; Haugen, Nils Erland L.; Mee, Antony J.; Gent, Frederick A.; Babkovskaia, Natalia; Yang, Chao‐Chin; Heinemann, T.; Dintrans, B.; Mitra, Dhrubaditya; Candelaresi, Simon; Warnecke, Jörn; Käpylä, Petri J.; Schreiber, Andreas; Chatterjee, Piyali; Käpylä, Maarit J.; Li, Xiangyu; Krüger, Jonas; Aarnes, Jørgen R.; Sarson, Graeme R.; Oishi, Jeffrey S.; Schober, Jennifer; Plasson, Raphaël; Sandín, C.; Karchniwy, Ewa; Rodrigues, Luiz Felippe S.; Hubbard, Alexander; Gómez, Gutiérrez; Snodin, A. P.; Losada, I. R.; Pekkilä, Johannes; Qian, Chengeng

doi:10.21105/joss.02807

Cited by 116 publications

(35 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[68,75] for details and Ref. [53] for the implementation in the Pencil Code [60]. The EM stress components in physical space are assembled as…”

Section: Em-sourced Gws In the Early Universementioning

confidence: 99%

“…The source code used for the simulations of this study, the Pencil Code, is freely available [60]. The simulation data are also available at Ref.…”

Section: Data Availabilitymentioning

confidence: 99%

“…There have been recent analytical works on nonhelical and helical magnetogeneses during the reheating era [57,58], which circumvent known difficulties such as the backreaction and strong coupling problems [59]. Numerical simulations of GWs from these magnetogeneses have also been performed [55,56] using the Pencil Code [60].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Leading-order nonlinear gravitational waves from reheating magnetogeneses

He,

Pol,

Brandenburg

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, ∆EGW, in terms of EM energy EEM as ∆EGW = (pEEM/k * ) 3 , where k * is the characteristic wave number, p = 0.84 and 0.88 are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while p = 0.45 is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as |∆PGW/PGW| = rEEM/k * and find r = 1.2 × 10 −1 , 7.2 × 10 −4 , and 3.2 × 10 −2 for the helical cases with reheating temperatures Tr = 300 TeV, 8 GeV, and 120 MeV, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed.

show abstract

“…[68,75] for details and Ref. [53] for the implementation in the Pencil Code [60]. The EM stress components in physical space are assembled as…”

Section: Em-sourced Gws In the Early Universementioning

confidence: 99%

“…The source code used for the simulations of this study, the Pencil Code, is freely available [60]. The simulation data are also available at Ref.…”

Section: Data Availabilitymentioning

confidence: 99%

See 1 more Smart Citation

Leading-order nonlinear gravitational waves from reheating magnetogeneses

He,

Pol,

Brandenburg

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We use the Pencil Code [53] to solve equations ( 1)-( 4) in a three-dimensional periodic domain of size L 3 = (2π) 3 with a resolution of up to 672 3 . This code employs a thirdorder accurate time-stepping method [54] and sixth-order explicit finite differences in space [55,56].…”

Section: F Numerical Setupmentioning

confidence: 99%

Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential

Schober,

Rogachevskii,

Brandenburg

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential µ5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of µ5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of µ5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before saturation occurs, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic α effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of µ5 develops a universal k −1 scaling independently of its initial shape, while the magnetic energy spectrum approaches a k −3 scaling.

show abstract

“…Meanwhile, significant progress has been made in the numerical solution of relic GWs from turbulent sources [21][22][23][24][25]. A useful tool is the Pencil Code, a massively parallel public domain code developed by the community of users for a broad range of applications [26]. It comes with a GW solver, where the modification to the dispersive GWs is straightforward.…”

Section: Introductionmentioning

confidence: 99%

Tensor spectrum of turbulence-sourced gravitational waves as a constraint on graviton mass

He,

Brandenburg,

Sinha

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a generic dispersive massive gravity theory and numerically study its resulting modified energy and strain spectra of gravitational waves (GWs) sourced by (i) fully developed turbulence during the electroweak phase transition (EWPT); and (ii) forced hydromagnetic turbulence during the QCD phase transition (QCDPT). The GW spectra are then computed in both the spatial and temporal Fourier domains. We find, from the spatial spectra, that the slope modifications are independent of the eddy size at QCDPT, and, from the temporal spectra, that the modifications are pronounced in the nHz-10nHz range -the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) -for a graviton mass m g in the range 2.2 × 10 −23 eV/c 2 m g 7.4 × 10 −22 eV/c 2 .

show abstract

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

Cited by 116 publications

References 44 publications

Leading-order nonlinear gravitational waves from reheating magnetogeneses

Leading-order nonlinear gravitational waves from reheating magnetogeneses

Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential

Tensor spectrum of turbulence-sourced gravitational waves as a constraint on graviton mass

Contact Info

Product

Resources

About