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The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N2, which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N2, are grossly hidden by compensation, when integration is carried out to get the molecular properties.

Based on the features of diurnal variation of ice surface albedo in the Lake Ulansuhai, the relationship between solar elevation angle and geographic coordinates and Julian days, together with normalized time, to express the diurnal variations of the ice albedo. Linear combinations of four probability density distribution functions with exponential forms, including Laplace, Gauss, Gumbel, and Cauchy equations, were used to simulate the diurnal variations in observed ice albedo from sunrise to sunset with solar elevation angle more than 5°. The results reveals that the Laplace combined statistical model is the best fit to the observations. It can not only clearly show the double-peak distribution in the diurnal variation in ice surface albedo when the elevation angle is greater than 5°, but also express the U-type distribution between the two peaks as the elevation angle is more than 15°. This model has advantages of simple form in expression and clear physical meaning. The length parameter is close to half day, and the peak location is associated with the time of sunrise, and the asymmetry of the two peaks can be also shown. It provides a solid foundation for the parameterization schemes on the diurnal variations in lake ice surface albedo in different regions. © 2020 by Journal of Lake Sciences.

In this work, we consider the perturbed Radhakrishnan-Kundu-Lakshmanan equation (RKL) which is the higher order nonlinear Schrodinger equation with cubic nonlinear terms in Kerr law. This equation is used to model propagation of solitons through an optical fiber. The multi-waves, interactions and Peregrine-like rational solutions of this equation are investigated with the aid of logarithmic transformation and symbolic computation without using Hirota bilinear forms By selecting appropriate values of the parameter, three dimensional plots are drawn to obtained solitons. Moreover, physical meanings of the solutions obtained were also presented.