A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.