A Look Inside the Lighthill Source Term

Abstract We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfvén waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.

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Stationary Non-equilibrium Solutions for Coagulation Systems

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-021-01623-w ◽

2021 ◽

Vol 240 (2) ◽

pp. 809-875

Author(s):

Marina A. Ferreira ◽

Jani Lukkarinen ◽

Alessia Nota ◽

Juan J. L. Velázquez

Keyword(s):

Power Law ◽

Source Term ◽

Continuous Model ◽

Stationary Solutions ◽

Weight Functions ◽

Equilibrium Solutions ◽

Coagulation Rate ◽

Diffusion Limited Aggregation ◽

Coagulation Equations ◽

Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

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Validity of the source term for the Fukushima Dai-ichi Nuclear Power Station accident estimated using local-scale atmospheric dispersion simulations to reproduce the large-scale atmospheric dispersion of 137Cs

Journal of Environmental Radioactivity ◽

10.1016/j.jenvrad.2021.106704 ◽

2021 ◽

Vol 237 ◽

pp. 106704

Author(s):

Masanao Kadowaki ◽

Akiko Furuno ◽

Haruyasu Nagai ◽

Hideyuki Kawamura ◽

Hiroaki Terada ◽

...

Keyword(s):

Nuclear Power Station ◽

Nuclear Power ◽

Large Scale ◽

Source Term ◽

Atmospheric Dispersion ◽

Local Scale ◽

Power Station

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A compact exact law for compressible isothermal Hall magnetohydrodynamic turbulence

Journal of Plasma Physics ◽

10.1017/s0022377821000374 ◽

2021 ◽

Vol 87 (2) ◽

Author(s):

Renaud Ferrand ◽

Sébastien Galtier ◽

Fouad Sahraoui

Keyword(s):

Source Term ◽

Reynolds Numbers ◽

Space Plasmas ◽

Order Structure ◽

Magnetohydrodynamic Turbulence ◽

Statistical Homogeneity ◽

Background Magnetic Field ◽

Taylor Hypothesis ◽

Spacecraft Data

Using mixed second-order structure functions, a compact exact law is derived for isothermal compressible Hall magnetohydrodynamic turbulence with the assumptions of statistical homogeneity, time stationarity and infinite kinetic/magnetic Reynolds numbers. The resulting law is written as the sum of a Yaglom-like flux term, with an overall expression strongly reminiscent of the incompressible law, and a pure compressible source. Being mainly a function of the increments, the compact law is Galilean invariant but is dependent on the background magnetic field if one is present. Only the magnetohydrodynamic source term requires multi-spacecraft data to be estimated whereas the other components, which include those introduced by the Hall term, can be fully computed with single-spacecraft data using the Taylor hypothesis. These properties make this compact law more appropriate for analysing both numerical simulations and in situ data gathered in space plasmas, in particular when only single-spacecraft data are available.

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