7 problems

Filtering is considered for approximations in the spherical harmonics method, and thermal radiative transfer is identified as another physically significant problem to which the fi…

Let $O_{N,5}$ be the optimized model with approximation order $N$ and entropy-approximation parameter $5$, optimized on the interval $[-5,5]$. Let $O_5(x)$ denote the corresponding…

Let $O_{2K+1}$ denote the optimized polynomial approximation model of degree $2K+1$, and let $\beta_{BS}$ denote the Boltzmann–Shannon entropy function. Fix an interval of the real…

A polarized radiative transfer equation is considered in a basis of the polarization plane, with the optical rotation term denoted by ${\mathcal{N}}$. A metriplectic formulation is…

Let $hat{x}inpartialmathcal{D}$ be a boundary point, let $n_{hat{x}}$ be the unit outer normal there, and introduce the rescaled normal coordinate … For $y\in[0,\infty)$, let…

Let the characteristic fields of the regularized reduced model be the fields corresponding to its characteristic speeds $\lambda^{(N)}_k$, with the fields corresponding to…

Diffusion-limit conjecture. In the small $\epsilon$ regime, the radiative transfer equation is asymptotically close to the diffusion equation above. The conjecture concerns the rig…