Mathematical simulation of the stress-strain state of the winding of a closed magnetic system

Mathematical modeling of the stress-strain state of the winding of a closed magnetic system was carried out, which consists in the development of a three-dimensional geometric model of the helical winding and the determination of the values of the characteristics of the magnetic system, which are best from the point of view of meeting the requirements of the technical task of the designed object.Проведено математичне моделювання напружено-деформованого стану обмотки замкнутої магнітної системи, котре полягає в розробці тривимірної геометричної моделі гвинтової обмотки та визначенні значень характеристик магнітної системи, найкращих з точки зору задоволення вимог технічного завдання проектованого об’єкта

Determination of volume, shape and refractive index of individual blood platelets

Light scattering patterns (LSP) of blood platelets were theoretically and experimentally analyzed. We used spicular spheroids as a model for the platelets with pseudopodia. The discrete dipole approximation was employed to simulate light scattering from an individual spicular spheroid constructed from a homogeneous oblate spheroid and 14 rectilinear parallelepipeds rising from the cell centre. These parallelepipeds have a weak effect on the LSP over the measured angular range. Therefore, a homogeneous oblate spheroid was taken as a simplified optical model for platelets. Using the T-matrix method, we computed the LSP over a range of volumes, aspect ratios and refractive indices. Measured LSPs of individual platelets were compared one by one with the theoretical set and the best fit was taken to characterize the measured platelets, resulting in distributions of volume, aspect ratio and refractive index.Comment: 10 pages, 6 figure

Absorption and scattering properties of arbitrarily shaped particles in the Rayleigh domain: A rapid computational method and a theoretical foundation for the statistical approach

We provide a theoretical foundation for the statistical approach for computing the absorption properties of particles in the Rayleigh domain. We present a general method based on the Discrete Dipole Approximation (DDA) to compute the absorption and scattering properties of particles in the Rayleigh domain. The method allows to separate the geometrical aspects of a particle from its material properties. Doing the computation of the optical properties of a particle once, provides them for any set of refractive indices, wavelengths and orientations. This allows for fast computations of e.g. absorption spectra of arbitrarily shaped particles. Other practical applications of the method are in the interpretation of atmospheric and radar measurements as well as computations of the scattering matrix of small particles as a function of the scattering angle. In the statistical approach, the optical properties of irregularly shaped particles are represented by the average properties of an ensemble of particles with simple shapes. We show that the absorption cross section of an ensemble of arbitrarily shaped particles with arbitrary orientations can always be uniquely represented by the average absorption cross section of an ensemble of spheroidal particles with the same composition and fixed orientation. This proves for the first time that the statistical approach is generally viable in the Rayleigh domain.Comment: Accepted for publication in JQSR