Multiparameter mathematical models of the filtration problem of unstructured and structured fluids

The article is devoted to constructing a generalized mathematical model and the method of their solution of the process of filtration of fluids with various linear and nonlinear characteristics. The multiparameter model contains 13 mathematical models developed in due time by scientific research and included new mathematical models. The classification of these models is carried out in accordance with the laws of filtration, and they are confirmed by the results of numerical solutions. For unknown boundaries of disturbances, the application of the "shuttle" iteration method made it possible to reduce the number of iterations.

Topological Defect Arrays in Nematic Liquid Crystals Assisted by Polymeric Pillar Arrays: Effect of the Geometry of Pillars

Topological defects that spontaneously occur in condensed matter and structured fluids such as liquid crystals are useful for their elastic and optical properties, but often the applicability of defect arrays to optics and photonic devices relies on the regularity and tunability of the system. In our recent work [Adv. Opt. Mater. 8, 1900991 (2020)], we showed the formation of regular, reconfigurable, and scalable patterns by exploiting the elastic response of a defect array in liquid crystals in the presence of a polymeric pillar array. In this work, we experimentally investigate the role of size and shape of the pillars on the defect array. We find that the pillar size and geometry provide additional means to regulate the response time, the threshold voltage for the defects’ formation, and the spatial arrangement of the defects.