A comparison of numerical and analytical radiative-transfer solutions for plane albedo of natural waters

Several numerical and analytical solutions of the radiative transfer equation (RTE) were compared for plane albedo in a problem of solar light reflection by sea water. The study incorporated the simplest case—a semi-infinite one-dimensional plane—parallel absorbing and scattering homogeneous layer illuminated by a monodirectional light beam. Inelastic processes (such as Raman scattering and fluorescence), polarization and air-water surface refraction-reflection effects, were not considered. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Calculations were performed using parameters across all possible ranges (single-scattering albedo ω₀ and refracted solar zenith angle θ₁), but with a special emphasis on natural waters. All computations were made for two scattering phase functions, which included an almost isotropic Rayleigh phase function and strongly anisotropic double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations, which represent the extreme cases of ω₀→0 and ω₀→1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation developed earlier, resulted in a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.     

Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?^{n+ 1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?^{n+ 1}) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?^{n+ 1, 1}). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.     

Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.     

Phase Diagrams of Semicrystalline Polymer–Crystalline Substances: Polyolefins–1,2,4,5-Tetrachlorobenzene

The full phase diagrams of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and isotactic polypropylene (i-PP) mixtures with 1,2,4,5-tetrachlorobenzene (TeCB), including the solubility curve of TeCB in a solid polymer, were constructed by an optical method. The diagrams contain a eutectic point that corresponds to the situation when the crystallization of TeCB out of its solution in a polyolefin is accompanied by the crystallization of monomer units of the macromolecules. As a result, the polymer acquires a gel structure with crystallites as crosslinks and amorphous regions saturated with TeCB. It is demonstrated that the eutectic point position on the phase diagram can be used for ranking polymers with respect to their thermodynamic affinity to a solvent. For the studied systems, the affinity to TeCB was decreased in the order i-PP, HDPE, and LDPE. Direct experimental evidence was obtained that TeCB crystals can be dissolved in a solid polymer via a vapor phase mechanism, which leads to the polymer amorphization.     

The study of phase,microstructure, and magnetocaloric properties in LaFe11.6*xSi1.4B0.1 alloys

The effect of Fe on the phase and magnetocaloric property of LaFe_11.6*xSi_1.4B_0.1 alloys with x = 1.0–1.4 have been studied. The results show that the excess of Fe will make the α-Fe phases increase, but the easy corrosion LaFeSi phase reduces in LaFe_11.6*xSi_1.4B_0.1 alloys. All LaFe_11.6*xSi_1.4B_0.1 alloys keep the first-order magnetic phase transition. The saturation magnetizations of LaFe_11.6*xSi_1.4B_0.1 alloys with x > 1 are much higher than LaFe_11.6Si_1.4B_0.1 alloy under 2T magnetic field. This results in the maximum isothermal magnetic entropy changes, and the relative cooling power of LaFe_11.6*xSi_1.4B_0.1 alloys is bigger than for LaFe_11.6Si_1.4B_0.1 alloys.     

Influence of surface and bulk layers on the crossover features for interaction parameters of a ferroelectric thin film

The phase diagram of a ferroelectric thin film is studied by using the usual mean-field approximation. The crossover features, from the ferroelectric-dominant phase diagram to the paraelectric-dominant phase diagram, for the physical parameters of the thin film are discussed. Special attention is devoted to the investigation of surface and bulk layers, and how to influence the crossover values of exchange interactions and transverse fields.     

Study on optical characterization of TGB and reentrant smectic-A phases in binary mixture of two liquid crystals

In this work, our investigation is to study the optical and thermal properties of the binary mixture of cholesteric and nematic compounds, namely, cholesteryl nonanoate and p-methoxybenzylidene-p-ethylaniline, which exhibits a very interesting liquid crystalline twisted grain boundary (TGB) phase and reentrant smectic-A phase. The chiral liquid crystalline TGB phases and reentrant smectic-A phases have been observed at different concentrations and at different temperatures. The existence of TGB and reentrant smectic-A phases is confirmed by differential scanning calorimetry and optical microscopic studies. The variation of optical anisotropy has been discussed. The helical pitch of the cholesteric phase has also been discussed.