Related papers: Diffusion in stellar interiors: critical tests of …
Low-mass stars exhibit, at all stages of their evolution, the signatures of complex physical processes that require challenging modeling beyond standard stellar theory. In this review, we recall the most striking observational evidences…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Recently 3D hydrodynamical simulations of stellar surface convection have become feasible thanks to advances in computer technology and efficient numerical algorithms. Available observational diagnostics indicate that these models are…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Stellar space density analyses, once a very active area of astronomical research, involved transforming counts of stars to given limiting magnitudes in selected areas of the sky into graphs of the number of stars per cubic parsec as a…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
Diffusion of atoms and molecules is a key process for the chemical evolution in the star forming regions of the interstellar medium. Accurate data on the mobility of many important interstellar species is however often not available and…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We present…
A mayor problem that arises in the computation of stellar atmosphere models is the self consistent determination of the temperature distribution via the constraint of energy conservation. The energy balance includes the gains due to the…
It has long been understood that the light curve of a transiting planet constrains the density of its host star. That fact is routinely used to improve measurements of the stellar surface gravity and has been argued to be an independent…
The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to…
Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
We present here a method to study the distribution of electron density fluctuations in pulsar directions as well as to estimate pulsar distances. The method, based on a simple two-component model of the scattering medium discussed by Gwinn…
An implicit method for radiative transfer in SPH is described. The diffusion approximation is used, and the hydrodynamic calculations are performed by a fully three--dimensional SPH code. Instead of the energy equation of state for an ideal…
We come back to the analytical solution of the standard transfer problem in a stellar atmosphere. It consists in solving the radiative transfer equation in a homogeneous and isothermal plane-parallel atmosphere, with light scattering taken…
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse to fully resolve it. Recently, numerical solutions of…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…