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.     

The flow due to a rough rotating disk

Von Kármáns problem of a rotating disk in an infinite viscous fluid is extended to the case where the disk surface admits partial slip. The nonlinear similarity equations are integrated accurately for the full range of slip coefficients. The effects of slip are discussed. An existence proof is also given.     

A sharp condition for existence of an inertial manifold

It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel's theorem for Banach valued functions are used.     

Norm continuity and stability for a functional differential equation in Hilbert space

A functional differential equation in Hilbert space with initial data on [−h,0] is considered. An unbounded operator A and a square integrable weight function are acting in the distributed delay term. For a not necessarily continuous weight function the norm continuity of the associated solution semigroup is established at every t>h. In the case that the spectrum of A is real and negative, the asymptotic stability of the solution is obtained.     

Analysis of the Thermal Stability of Very Thin Surface Layers of Corrosion Inhibitors by Time-of-Flight Secondary Ion Mass Spectrometry

The powerful nature of the secondary ion mass spectrometry (SIMS) technique was explored in order to analyse very thin surface layers that were self-assembled on steel material from acidic solution. These surface layers are adsorbed corrosion inhibitors. The SIMS technique proved useful to characterise the molecular structure and homogeneity of thin surface layers in the nanometre range of specific analytes on the metallic substrate. Using SIMS, the thermal stability of these layers was further investigated and the desorption energy at a certain temperature was determined, where special attention was devoted to the method’s static limit. In order to compare, and for certain cases emphasise, the benefits gained by using SIMS in such surface analysis compared with the X-ray photoelectron spectroscopy (XPS) method, the same samples were also analysed by means of the latter. XPS is usually considered to be the most powerful analytical tool in surface analysis studies, but, as shown herein, it has certain limitations compared to SIMS. Finally, the surface topography was investigated by employing atomic force microscopy (AFM) in order to carry out a comprehensive surface analysis.

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Transglobal Evidentialism-Reliabilism

We propose an approach to epistemic justification that incorporates elements of both reliabilism and evidentialism, while also transforming these elements in significant ways. After briefly describing and motivating the non-standard version of reliabilism that Henderson and Horgan call “transglobal” reliabilism, we harness some of Henderson and Horgan’s conceptual machinery to provide a non-reliabilist account of propositional justification (i.e., evidential support). We then invoke this account, together with the notion of a transglobally reliable belief-forming process, to give an account of doxastic justification.

Instability of fully developed mixed convection with viscous dissipation in a vertical porous channel

Flow driven by an externally imposed pressure gradient in a vertical porous channel is analysed. The combined effects of viscous dissipation and thermal buoyancy are taken into account. These effects yield a basic mixed convection regime given by dual flow branches. Duality of flow emerges for a given vertical pressure gradient. In the case of downward pressure gradient, i.e. upward mean flow, dual solutions coincide when the intensity of the downward pressure gradient attains a maximum. Above this maximum no stationary and parallel flow solution exists. A nonlinear stability analysis of the dual solution branches is carried out limited to parallel flow perturbations. This analysis is sufficient to prove that one of the dual solution branches is unstable. The evolution in time of a solution in the unstable branch is also studied by a direct numerical solution of the governing equation.