An analysis is presented of parametric instability in a finite-length rotating cylinder subject to periodic axial compression by small sinusoidal oscillations of one of its ends (the ‘piston’). The instability is due to resonant interactions between inertialwave (Kelvin) modes of the cylinder and the oscillatory compression and is resisted by viscosity, acting both through thin boundary layers ...

We consider the inverse scattering problem of determining the shape and the material properties of a thin dielectric infinite cylinder having an open arc as cross section from knowledge of the TM-polarized scattered electromagnetic field at a fixed frequency. We investigate two reconstruction approaches, namely the linear sampling method and the reciprocity gap functional method, using far fiel...

The phase behavior of the system of parallel rigid triblock copolymers is examined using the second virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel partic...

Abstract. We consider the inverse scattering problem of determining the shape and the material properties of a thin dielectric infinite cylinder having an open arc as cross section from a knowledge of the TM-polarized scattered electromagnetic field at a fixed frequency. We investigate two reconstruction approaches, namely the linear sampling method and the reciprocity gap functional method, us...

We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. The parameters involved determine a rich variety of qualitatively different flows. We obtain sufficient conditions for finite speed of support propagatio...

We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate an iterative spectral algorithm for computing these steady states. Fin...

Certain high power laser applications require thin homogeneous laser lines. In this paper we describe the concept, fabrication and characterization of a 1-D diffuser that generates such a line. The device is based on an array of concave cylinder lenses with a statistically distributed width and a fix radius of curvature. The fabrication is based on isotropic wet etching of fused silica. Measure...

A method is presented to investigate diffraction of an electromagnetic plane wave by an infinitely thin infinitely conducting circular cylinder with longitudinal slots. It is based on the use of the combined boundary conditions method that consists on expressing the continuity of the tangential components of both the electric and the magnetic fields in a single equation. This method proves to b...