Related papers: Diffusion in stellar interiors: critical tests of …
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and…
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…
We present here results of stellar evolution calculations that include the latest advances in radiative opacities and neutrino cooling, and discuss on the basis of these models how the internal stellar structure responds to mass-loss from…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The…
We present a numerical algorithm for the incorporation of the active cosmic ray transport, into the ZEUS-3D magnetohydrodynamical code. The cosmic ray transport is described by the diffusion-advection equation. The applied form of the…
Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely-hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We reveal the microscopic self-diffusion process of compact tri-interstitials in silicon using a combination of molecular dynamics and nudged elastic band methods. We find that the compact tri-interstitial moves by a collective…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Context: Internal chemical mixing in intermediate- and high-mass stars represents an immense uncertainty in stellar evolution models.In addition to extending the main-sequence lifetime, chemical mixing also appreciably increases the mass of…
Double-diffusive convection refers to mixing where the effects of thermal and composition gradients compete to determine the stability of a fluid. In addition to the familiar fast convective instability, such fluids exhibit the slow, direct…
In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…