A discrete bidirectional reflectance model in remote sensing

A numerical scheme is devised to develop a discrete bidirectional reflectance model. A pseudospectral method is utilized with which the discrete solution of the radiative transfer equation is made part of this development. To produce discrete bidirectional reflectance values, a set of algebraic equations is solved. Illustrative examples are given to demonstrate the performance of the developed model.     

Tau method approximation for radiative transfer problems in a slab medium

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.     

A low-dimensional conjugacy for elliptic equations and symmetry breaking on rotated domains

A topological conjugacy is established between certain elliptic PDEs with one unbounded time direction and a simple second-order differential equation, admitting the dynamics of such PDEs to be examined on a two-dimensional submanifold. By this means, periodic solutions can be obtained to elliptic equations as perturbations of those that are independent of time.     

Thieno[3,4‐b]pyrazines and Its Extended Analogs: Important Buildings Blocks for Conjugated Materials

This review describes the synthesis and characterization of thieno[3,4‐b]pyrazines and its extended fused‐ring analogs as important building blocks for the production of low‐band gap conjugated materials.     

Photophysics and Rotational Dynamics of a Hydrophilic Molecule in a Room Temperature Ionic Liquid

We have studied the photophysics and rotational diffusion of hydrophilic solute 7‐(N, N′‐diethylamino)coumarin‐3‐carboxylic acid (7‐DCCA) in a room temperature ionic liquid methyltrioctylammonium bis(trifluoromethylsulfonyl) imide ([N₁₈₈₈][NTf₂]). Comparison of activation energies of viscous flow and nonradiative decay shows that the photophysical properties of 7‐DCCA are not guided by the bulk viscosity of the medium but are dependent on the specific solute solvent interaction and structural heterogeneity of the medium. The rotational relaxation behaviour of 7‐DCCA in [N₁₈₈₈][NTf₂] shows significant deviation from the Stokes Einstein Debye hydrodynamic model of rotational diffusion. This is indicative of the influence of specific solute solvent interaction on the rotational relaxation behaviour of 7‐DCCA. Comparison of activation energy of rotational relaxation with activation energy of viscous flow clearly reinforces our assumption that the structural heterogeneity of the medium and specific solute solvent interaction plays a dominant role on the rotational diffusion instead of bulk viscosity.     

Tris(4‐bromophenyl)aminium hexachloridoantimonate (`Magic Blue'): a strong oxidant with low inner‐sphere reorganization

Both the radical cation tris(4‐bromophenyl)aminium hexachloridoantimonate (`Magic Blue'), (C₁₈H₁₂Br₃N)[SbCl₆], (I), and neutral tris(4‐bromophenyl)amine, C₁₈H₁₂Br₃N, (II), show extremely similar three‐bladed propeller structures with planar N atoms. Key geometric features, such as the C—N bond distances and the angles between the planes of the aryl groups and the central NC₃ plane, are identical within experimental uncertainty in the two structures. This contrasts with the significant structural changes observed on oxidation of more electron‐rich triarylamines, where resonance contributes to the stabilization of the radical cation, and suggests that, in general, more strongly oxidizing triarylaminium cations will have lower inner‐sphere reorganization energies than their lower‐potential analogues.