Related papers: Second Order Closures for the Radiative Transfer E…
In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy…
Cosmological simulations of reionization often treat radiative transfer by solving for the monopole and dipoles of the intensity field and by making ansatz for the quadrupole moments to close the system of equations. We investigate the…
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric…
A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40 (where it was…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
Using the renormalization group approach, we consider the $O(N)\otimes O(M)$ model in four and more dimensions. We find that independently on $N$ and $M$, for $N\geq M\geq 2$, a transition can be of both the first and second order. In…
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 study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and…
In this note, we show that there exist solutions of the Muskat problem which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime. This proves existence of…
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
This is our fourth work in the series on machine learning (ML) moment closure models for the radiative transfer equation (RTE). In the first three papers of this series, we considered the RTE in slab geometry in 1D1V (i.e. one dimension in…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
Carefully accounting for neutrino transport is an essential component of many astrophysical studies. Solving the full transport equation is too expensive for most realistic applications, especially those involving multiple spatial…
The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science and planetology. In the presence of…
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This…
In the paper we have developed a theory of stability preserving structural transformations of systems of second-order ordinary differential equations (ODEs), i.e., the transformations which preserve the property of Lyapunov stability. The…
Closure seems to be something rheologists would prefer to avoid. Here, the story of closure is told in such a way that one should enduringly forget any improper undertone of "uncontrolled approximation" or "necessary evil" which might…
This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a…