Microstructured optical fibres (MOFs) are a new type of optical fibres that possess a wide range of optical properties and many advantages over common optical fibres. Those are provided by unique structures defined by a pattern of periodic or quasi-periodic arrangement of air holes that run through the fibre length. In recent years, MOFs have opened up new possibilities in the field of optics and photonics, enabling the development of advanced devices and novel optical systems for different applications. The key application areas of PCFs vary from telecommunications and high-power energy transmission to quantum optics and sensing. The stack-and-draw method is a standard manufacturing technique for MOFs, where a preform is first manually created and then drawn in a high-tech furnace into a fibre with the required final dimensions and position of the air holes. Since in the manufacturing process experimenters can control only a few parameters, mathematical models and numerical simulations of the drawing process are highly requested. They not only allow to deepen the understanding of physical phenomena occurring during the drawing process, but they also accurately predict the final cross-section shape and size of the fibre. In this manuscript, we assume thermal equilibrium between the furnace and the fibre and propose a functional form of the fibre temperature distribution. We utilise it with asymptotic mass, momentum, and evolution equations for free surfaces already available in the literature to describe the process of fibre drawing. By doing so, the complex heat exchange problem between the fibre and the furnace need not be solved. The numerical results of the whole asymptotic model overall agree well with experimental data available in the literature, both for the case of annular capillaries and for the case of holey fibres.

The flow field around a straight chain of multiple slip spherical particles rotating steadily in an incompressible Newtonian fluid about their line of centers is analyzed at low Reynolds numbers. The particles may vary in radius, slip coefficient, and angular velocity, and they are permitted to be unevenly spaced. Through the use of a boundary collocation method, the Stokes equation governing the fluid flow is solved semi-analytically. The interaction effects among the particles are found to be noteworthy under appropriate conditions. For the rotation of two spheres, our collocation results for their hydrodynamic torques are in good agreement with the analytical asymptotic solution in the literature obtained by using a method of twin multipole expansions. For the rotation of three spheres, the particle interaction effect indicates that the existence of the third particle can influence the torques exerted on the other two particles noticeably. The interaction effect is stronger on the smaller or less slippery particles than on the larger or more slippery ones. Torque results for the rotation of chains of many particles visibly show the shielding effect among the particles.

Propagation of electromagnetic (EM) waves inside and on the surface of the human body is the subject of active research in area of biomedical applications. This research area is the basis for wireless monitoring of biological object parameters and characteristics. Much attention has been paid to radio-frequency identification systems, which are intended for biomedical applications. Solutions to the following problems are crucial to achieve the stated goals in the area of wireless monitoring: EM wave propagation inside regular and multilayer biological media, through the interface between different media, and on-body surface wave propagation. The biological object monitoring is based on a consideration of the followingprocesses: a) propagation of the EM wave in a biological medium considered as the dielectric with a high dielectric permittivity and substantial conductivity; b) penetration of the EM wave through the biological medium–air interface (wave reflection and refraction); c) propagation of the EM wave in a multi-layer biological medium; d) propagation of the EM wave along the plane or curved surface of biological objects.