Retrieving the refractive index of a sphere from the phase spectrum of its light-scattering profile

We studied the Fourier spectrum of the light-scattering profiles of single particles in the Rayleigh-Gans-Debye (RGD) and Wentzel–Kramers–Brillouin (WKB) approximations. In the case of a homogeneous sphere, we found the relationship between the key parameters of the spectrum (including its phase) and the sphere characteristics – both analytically and numerically in the framework of the approximations and the rigorous Lorentz–Mie theory, respectively. Based on these results, we have improved the existing spectral characterization method for spheres extending the applicability range to particles with a higher refractive index.

The Degree of Linear Polarization for Suspended Particle Fields from Diverse Natural Waters

The Degree of Linear Polarization (DoLP) for unperturbed particle fields in waters from six diverse regions around the globe was measured with the custom Multi-Angle Scattering Optical Tool (MASCOT). DoLP here is defined as the ratio of two elements of Mueller scattering matrix, i.e., -M12/M11. Field sites covered inland waters, coastal oceans and open oceans, including both ocean color Case I and II water types. The angular shape of the measured particulate DoLP was analyzed in detail for each field site and for the ensemble average. Three parameters used to quantitatively characterize DoLP shape were the symmetry with respect to 90°, peak magnitude, and peak angle of measured DoLP angular curve. Vertical profiles of particulate DoLP were analyzed with maximum recorded depth of 111 m. Converse to Rayleigh scatterers, we found measured particulate DoLPs were not symmetric with respect to 90°. On average, DoLP peaks were shifted slightly toward larger angles, with most falling between estimated values of 90° and 95°. All particulate DoLP peak magnitudes generally varied within [0.6, 0.9]. Lorenz-Mie (homogeneous sphere) light scattering theory was used to construct a new inversion for bulk particulate refractive index from a lookup table based on DoLP and spectral attenuation measurements. We compared the Mie-DoLP-based particulate refractive index retrieval with the backscattering-based model from (Twardowski et al., J. Geophys. Res., 2001, 106(C7), 14,129–14,142). Particulate refractive index retrieved with the two models were in some cases comparable. At two of the six field sites we saw good agreement between the two models, whereas at another two field sites we observed large discrepancies between the two models. Further investigation on the choice of the modeled particle shapes and compositions may improve this retrieval approach. Results are compatible with previous studies on DoLPs in natural waters and comprehensive observations are provided on the particulate DoLP angular shape, vertical profile and global distributions that are important for future vector radiative transfer simulations. This study is relevant to future PACE polarimeters and associated remote retrieval of oceanic particle composition using polarimetry.

The Use of Zero-Mass Particles in Analytical and Multi-body Dynamics: sphere rolling on an arbitrary surface

Zero-mass particles are, as a rule, never used in analytical dynamics, because they lead to singular mass matrices. However, recent advances in the development of the explicit equations of motion of constrained mechanical systems with singular mass matrices permit their use under certain circumstances. This paper shows that the use of such particles can be very efficacious in some problems in analytical dynamics that have resisted easy, general formulations, and in obtaining the equations of motion for complex multi-body systems. We explore the ease and simplicity that suitably used zero-mass particles can provide in formulating and simulating the equations of motion of a rigid, non-homogeneous sphere rolling under gravity, without slipping, on an arbitrarily prescribed surface. Computational results comparing the significant difference in the motion of a homogeneous sphere and a non-homogeneous sphere rolling down an asymmetric arbitrarily prescribed surface are obtained, along with measures of the accuracy of the computations. While the paper shows the usefulness of zero-mass particles applied to the classical problem of a rolling sphere, the development given is described in a general enough manner to be applicable to numerous other problems in analytical and multi-body dynamics that may have much greater complexity.

Synthesis of ZnO/ZnFe2O4 nanocomposites in organic-free media and their photocatalytic activity under natural sunlight

Nanocomposite ZnO/ZnFe2O4 photocatalysts with different proportions of ZnFe2O4 were synthesized in organic-free media using metal nitric as precursors. The ZnO phase with hexagonal wurtzite structure and low crystallinity of ZnFe2O4 was confirmed using XRD (X-Ray diffraction). Different morphologies of the nanocomposites were obtained ranging from rice grain-like with a porous surface to homogeneous sphere-like nanoparticles as shown in Scanning Electron Microscopy (SEM) and TEM Transmission Electron Microscopy (TEM) studies. Magnetic properties measured by Visible Sampler Magnetometer (VSM) showed diamagnetic and paramagnetic behavior for the nanocomposites. Analysis with Diffuse Reflectance Spectrophotometer (DRS) UV-vis showed an increase the composition of ferrite in composites increasing its ability to absorb visible light. Photocatalytic activities of ZnO/ZnFe2O4 nanocomposites on the degradation of Rhodamine B dye reached 95.6% after 3 h under natural sunlight suggesting their suitability for sunlight driven photocatalytic applications.

The Reflection Map and Infinitesimal Deformations of Sphere Mappings

The reflection map introduced by D’Angelo is applied to deduce simpler descriptions of nondegeneracy conditions for sphere maps and to the study of infinitesimal deformations of sphere maps. It is shown that the dimension of the space of infinitesimal deformations of a nondegenerate sphere map is bounded from above by the explicitly computed dimension of the space of infinitesimal deformations of the homogeneous sphere map. Moreover a characterization of the homogeneous sphere map in terms of infinitesimal deformations is provided.

Monoclinic sphere packings. III. Trivariant lattice complexes of P2/c and P21/c

All homogeneous sphere packings were derived that refer to the trivariant lattice complexes of monoclinic space-group types P2/c and P21/c. In total, sphere packings of 55 types have been found. The maximal inherent symmetry is monoclinic for 17 types while the other types comprise at least one sphere packing with cubic (four cases), hexagonal (six cases), tetragonal (eight cases) or orthorhombic (20 cases) symmetry.

Radio Continuum Spectra of Planetary Nebulae

Radio continuum emission of planetary nebulae is a rich source of information about their structure and physical parameters. Although radio emission is well studied, planetary nebulae show higher spectral indices than expected for homogeneous sphere. A few competing models exist in the literature to explain this discrepancy. We propose that it is related to non-spherical morphology of most of planetary nebulae.

Monoclinic sphere packings. II. Trivariant lattice complexes with mirror symmetry

All homogeneous sphere packings were derived that refer to the three trivariant monoclinic lattice complexes with mirror symmetry. In total, 29 types of sphere packings have been found. Only for three types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for 13 types, tetragonal for eight types, hexagonal for four types and cubic for one type.