Study of the relationships between materials and their radiative properties: Application to natural fibers for the spectral wavelengths range 0.25–2.5 μm

Measurements were made of the reflectance and transmittance of wool and cotton, natural and dyed, using an integrating sphere spectrophotometer.     

Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation

In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker–Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant–Friedrichs–Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker–Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numerical approximations of the solution of the relativistic heat equation for a set of examples in one and two dimensions including continuous initial data that develops jump discontinuities in finite time. We perform the numerical experiments through a class of explicit high order accurate conservative and stable numerical schemes and a semi-implicit nonlinear Crank–Nicolson type scheme.     

On an Integrable System of q-Difference Equations Satisfied by the Universal Characters: Its Lax Formalism and an Application to q-Painlevé Equations

The universal character is a generalization of the Schur function attached to a pair of partitions. We study an integrable system of q-difference equations satisfied by the universal characters, which is an extension of the q-KP hierarchy and is called the lattice q-UC hierarchy. We describe the lattice q-UC hierarchy as a compatibility condition of its associated linear system (Lax formalism) and explore an application to the q-Painlevé equations via similarity reduction. In particular a higher order analogue of the q-Painlevé VI equation is presented.     

Application of the transmission line matrix method for outdoor sound propagation modelling – Part 1: Model presentation and evaluation

The present paper deals with an original time-domain approach applied to outdoor sound propagation under meteorological effects. The transmission line matrix method, based on the Huygens’ principle, had already been validated over impedant grounds and complex topography. The presented formulation proposes to take into account meteorological effects (wind speed and temperature) through the relative sound speed. The necessary wavefront direction is determined through the calculation of the averaged intensity vector direction. A good agreement is found between simulations of both the transmission line matrix and parabolic equation methods. A relevant use of the method is shown in the framework of environmental acoustics and initial applications are proposed in Part 2.     

Franck--Condon factors and r-Centroids for the A 1∑+u-X1∑+g Band System of 107,109Ag2: Comparison of the Observed and Calculated Absorption Band Strengths

Franck-Condon factors and r-centrolds for the, A^1 ∑^＋ u-X^1∑^＋ 9 band system of ^107,109Ag2 are computed using Morse and Rydberg-Klein-Rees potentials for both lower and upper electronic states. The differences between the two sets of results are typically in the third decimal place for transitions involving vibrational levels with ν＇ and ν＂ up to about 15. Somewhat larger deviations appear for higher vibrational levels, but both sets of results follow the same pattern, which is to match well with the relative absorption band strength distribution in our experimental spectrum. The relative absorption band strengths are calculated by assuming that the electronic transition moment has only a weak dependence on the internuclear distance r. Good agreement between our measured and calculated absorption band strength ratios is found, which provides an excellent test of the calculated Franck- Condon factors and relative absorption band strengths. The r-centrold value for the （ν＇ = 0, ν＂ = 0） band is found to be approximately equal to the average value of r＇ and r＇＇e , indicating that the potentials of both states are not significantly aaharmonic around their minimum regions.