Practical Application of the Probabilistic‐Statistical Model of the Suspension Separation in Hydrocyclones

An effective practical approach that allows not only a significant reduction in the scope of practical experiments in the course of studying suspension separation processes in hydrocyclones, but also makes it possible to assess the intensity of random components of the processes and define the interrelation between such components and hydrodynamics of flows in a hydrocyclone is presented. Within the frames of the developed probabilistic‐statistical model of suspension separation in hydrocyclones on the basis of statistical self‐similarity properties, a relationship was found between determined and random components of the processes. This allowed transitioning from three‐parameter probability density functions for suspension particles in hydrocyclones to two‐parameter functions; thus significantly improving the efficiency of practical application of the developed model.     

Asymptotic Properties of a Probabilistic‐Statistical Model of Particle Classification in Hydrocyclones

The peculiarities of practical implementation of a probabilistic‐statistical model for a hydrodynamic stage of particle classification process of liquid‐solid polydisperse systems in cylinder‐conic hydrocyclones of small size have been investigated. Within reasonable assumptions, stationary solutions of the Fokker‐Planck‐Kolmogorov kinetic equation were obtained for the considered separation process. In order to describe changes in characteristics of suspension separation in hydrocyclones it was proposed to use stationary distributions, which parameters depend not only on hydraulic and dynamic features of flows inside an apparatus, but also are determined by relative magnitudes of the impact of particle classification and centrifugal forces in comparison with the intensity of random perturbations.     

Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.     

Exploiting the bioactive properties of essential oils and their potential applications in food industry

Food Science and Biotechnology - Fruits are an abundant source of minerals and nutrients. High nutritional value and easy-to-consume property have increased its demand. In a way to fulfil this...