Related papers: An analytically iterative method for solving probl…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
The self-regulation of cosmic ray (CR) transport in the interstellar and intracluster media has long been viewed through the lenses of linear and quasilinear kinetic plasma physics. Such theories are believed to capture the essence of CR…
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…
We use the GALPROP code and the Advanced Composition Explorer (ACE) data to derive the cosmic ray (CR) isotopic composition at the sources. The composition is derived for two propagation models, diffusive reacceleration and plain diffusion.…
We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
Recent advances on gamma-ray observations from SuperNova Remnants and Molecular Clouds offer the possibility to study in detail the properties of the propagation of escaping Cosmic Rays (CR). However, a complete theory for CR transport…
We propose a new method to determine the dipole (and quadrupole) component of a distribution of cosmic ray arrival directions, which can be applied when there is partial sky coverage and/or inhomogeneous exposure. In its simplest version it…
Anisotropy is very important to understand cosmic ray (CR) source and interstellar environment. The theoretical explanation of cosmic rays anisotropy from experiments remains challenging and even puzzling for a long time. In this paper, by…
Cosmic rays (CR) propagate through the galactic scales down to the smaller scales at which stars form. CRs are close to energy equipartition with the other components of the interstellar medium and can provide a support against gravity if…
Galactic cosmic rays (CRs) inside the heliosphere are affected by solar modulation. To investigate this phenomenon and its underlying physical mechanisms, we have performed a data-driven analysis of the temporal dependence of the CR proton…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
The stability of the cosmic ray modified shock (CRMS) is studied by means of numerical simulations. Owing to the nonlinear feedback of cosmic-ray (CR) acceleration, a downstream state of the modified shock can no longer be uniquely…
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration…
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to…