Related papers: Formal Solutions for Polarized Radiative Transfer.…
The use of polarimetric techniques is nowadays widespread among solar and stellar astronomers. However, notwithstanding the recommandations that have often been made about the publication of polarimetric results in the astronomical…
Partial Differential Equations (PDEs) describe several problems relevant to many fields of applied sciences, and their discrete counterparts typically involve the solution of sparse linear systems. In this context, we focus on the analysis…
We present two new accurate and efficient method to compute the formal solution of the polarized radiative transfer equation. In this work, the source function and the absorption matrix are approximated using quadratic and cubic Bezier…
Modern investigations of magnetic chemically peculiar stars reveal a variety of complex processes in their atmospheres. Realistic spectrum synthesis modelling of these objects has to take into account anomalous chemical composition, strong…
Stokes inversion codes are crucial in returning properties of the solar atmosphere, such as temperature and magnetic field strength. However, the success of such algorithms to return reliable values can be hindered by the presence of…
We introduce an integral equation formulation of the surface Stokes equations, constructed using two-dimensional Stokeslets. The resulting integral equations are Fredholm integral equations of the second kind and can be discretized to high…
The shapes of Stokes profiles contain much information about the atmospheric conditions that produced them. However, a variety of different atmospheric structures can produce very similar profiles. Thus, it is important for proper…
To explain the linear polarization observed in spatially resolved structures in the solar atmosphere, the solution of polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries is essential. For strong resonance…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
Inversion techniques applied to the radiative transfer equation for polarized light are capable of inferring the physical parameters in the solar atmosphere (temperature $T$, magnetic field ${\bf B}$, and line-of-sight velocity $v_{\rm…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
We present a general radiative transfer model which allows the Zeeman diagnostics of complex and unresolved solar magnetic fields. Present modeling techniques still rely to a large extent on a-priori assumptions about the geometry of the…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
A statistical model is used to determine how stochastic fluctuations in the intensities of orthogonal polarization modes contribute to the modulation and depolarization of pulsar radio emission. General expressions for the distributions of…
Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code…
Aims:We introduce analytical response functions and their main properties as an important diagnostic tool that help understand Stokes profile formation physics and the meaning of well-known behaviors of standard inversion codes of the…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…