Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic symmetry

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics

TIR-based dynamic liquid-level and flow-rate sensing and its application on centrifugal microfluidic platforms

For the first time we present a technique for the spatio-temporally resolved localization of liquid-gas interfaces on centrifugal microfluidic platforms based on total internal reflection (TIR) at the channel wall. The simple setup consists of a line laser and a linear image sensor array mounted in a stationary instrument. Apart from identifying the presence of (usually unwanted) gas bubbles, the here described online meniscus detection allows to measure liquid volumes with a high precision of 1.9%. Additionally, flow rates and viscosities (range: 1-10.7 mPa s) can be sensed even during rotation at frequencies up to 30 Hz with a precision of 4.7% and 4.3%, respectively

Sol-Gel Derived Ferroelectric Nanoparticles Investigated by Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) was used to investigate the ferroelectric properties of sol-gel derived LiNbO$_3$ nanoparticles. To determine the degree of ferroelectricity we took large-area images and performed statistical image-analysis. The ferroelectric behavior of single nanoparticles was verified by poling experiments using the PFM tip. Finally we carried out simultaneous measurements of the in-plane and the out-of-plane piezoresponse of the nanoparticles, followed by measurements of the same area after rotation of the sample by 90$^{\circ}$ and 180$^{\circ}$. Such measurements basically allow to determine the direction of polarization of every single particle