Numerical simulation of the electromagnetic wave reflection from 2D random semi-infinite strongly scattering media

Light scattering in disordered media plays an important role in various areas of applied science from biophysics to astronomy. In this paper we study two approaches to calculate scattering properties of semi-infinite densely packed media with high contrast and wavelength scale inhomogeneities by combining the Fourier Modal Method and the super-cell approach. Our work reveals capabilities to attain ensemble averaged solutions for the Maxwell's equations in complex media, and demonstrated numerical convergence supports the consistency of the considered approaches.Comment: 10 pages, 7 figure

Mathematical simulation of a profile cutter as a surface of revolution

Various types of cutters (spherical, toroidal, etc.) are used in surface processing of parts of a transmission mechanism. The cost of a special profile tool is somewhat higher than that of such cutters. But the increase in the cost of the tool is compensated by a significant reduction in the time of processing parts. The present paper deals with a mathematical model of a profile cutter surface (as a surface of revolution) for processing parts of a cylindrical transmission gear with an eccentrically cycloidal gearing (EC-gearing). A computer program for determining radii of the cutter's circular cross sections for a given set of axial displacements was created

The mathematical model of the chevron-arch gearing transmitter

The teeth of herringbone transmission wheels are obtained by docking two helical wheels with an opposite arrangement of teeth, which can solve the problem of the axial force. The mathematical model of coupling chevron teeth of the driving wheel in the area of their docking using the arch tooth fragment is developed. The conjugacy area surface of the driven wheel chevron teeth is obtained as the envelope of the surfaces family formed by the arched tooth during the process of the parts motion

Generation of nearly pure and highly directional magnetic light in fluorescence of rare earth ions

We discover regimes for promoting decay rates of magnetic light due to magnetic dipole (MD) transitions of trivalent rare earth ions located inside or near dielectric homogeneous spheres by as much as three orders of magnitude. A number of configurations involving sphere parameters and a rare earth emitter radial position are determined at which the branching ratio of MD transition is approaching its limit value of unity, signifying that transitions from a given parent level (e.g., $^5$D$_0$ level of Eu$^{3+}$) are entirely dominated by the MD transition. Dimensionless directivity of MD emission, radiative decay rates, and fluorescence of magnetic light can be enhanced by the the factor exceeding $25$, $10^3$, and $10^4$, respectively.Comment: article: 32 pages, 7 figures; supplementary materials: 8 page