differential equationstwo level atomone dimensional medium/ A0560 Transport processes: theory A9710 Stellar characteristicsThe equations of radiative transfer and of statistical equilibrium of a two-level atom are solved by means of differential and integral equations for a one-dimensional medium. The ...
On a family of differential ap- proximations of the radiative transfer equation. Journal of Mathematical Chem- istry, 50(4):689-702, 2012.W. Han, J. Eichholz, and G. Wang. On a family of differential approximations of the radiative transfer equation. Journal of Mathematical Chemistry, 50:...
Fig. 4: Radiative transfer theory of a 3D graphene network. a The theory of radiative transfer can be used to describe a disordered medium with reflective boundaries and bulk absorption and scattering processes (left). For a graphene 3D network, the former contribution is zero, while the absorp...
It taught me a lot about differential equations and numerical methods, and a bit about computers, which, at that time would require entire buildings for something less powerful than what we now have in a laptop. We developed fragments of the code on teletypes: simple keyboards connected to a...
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought to bear. One powerful and useful way to do this is the...
This leads to a purely differential equation for the net radiative flux. The spectral properties appear in the formulation in two functions, which are introduced by the approximation and which depend on the reference state of the gas. These functions are found by analytical matching procedures, ...
The truncation of this infinite system is the moment closure problem. Many types of closures have been presented in the literature. In this note, we demonstrate that optimal prediction, an approach originally developed to approximate the mean solution of systems of nonlinear ordinary differential ...
This chapter will introduce the particle swarm optimization (PSO) algorithm giving an overview of it. In order to formally present the mathematical formulation of PSO algorithm, the classical version will be used, that is, the inertial version; meanwhile
The fundamental assumptions are as follows: ① the effects of longitudinal heat transfer and radiative heat transfer are ignored; ② the fluid flow and heat transfer inside the wellbore are steady; and ③ the heat transfer in the formation outside cement sheath is unsteady. The differential ...
Differential, time-averaged gas phase absorbance spectra along the beam path can then be inferred following the DIAL principle. The fast rise time of the pulse combined with a high frequency data acquisition enables a spatial resolution in the order of 1 cm. First, we establish the theoretical ...