Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling. (c) 1999 American Institute of Physics.     

Synthesis and characterization of a polyaniline-modified SnO<Subscript>2</Subscript> nanocomposite

Polyaniline-modified tin oxide and tin oxide nanoparticles were synthesized using a solution route technique. The obtained pristine products were characterized with X-ray diffraction, thermogravimetric analysis, scanning electron microscopy, and optical absorption spectroscopy. Thermogravimetric analysis results showed that the polyaniline-modified SnO₂ nanoparticles exhibit higher thermal stability than the SnO₂ nanoparticles. Scanning electron microscopy analysis on the as-synthesized powders showed spherical particle in the range of 50–100 nm.     

Microswimmers – From Single Particle Motion to Collective Behavior

Locomotion of autonomous microswimmers is a fascinating field at the cutting edge of science. It combines the biophysics of self-propulsion via motor proteins, artificial propulsion mechanisms, swimming strategies at low Reynolds numbers, the hydrodynamic interaction of swimmers, and the collective motion and synchronisation of large numbers of agents. The articles of this Special Issue are based on the lecture notes of an international summer school, which was organized by the DFG Priority Programme 1726 “Microswimmers – From Single Particle Motion to Collective Behaviour” in the fall of 2015. The minireviews provide a broad overview of the field, covering both elementary and advanced material, as well as selected areas from current research.     

Vibrational dynamics of fullerene molecules adsorbed on metal surfaces studied with synchrotron infrared radiation

Infrared (IR) spectroscopy of chemisorbed C₆₀ on Ag (111), Au (110) and Cu (100) reveals that a non-IR-active mode becomes active upon adsorption, and that its frequency shifts proportionally with the charge transferred from the metal to the molecule by about 5 cm^-1 per electron. The temperature dependence of the frequency and the width of this IR feature have also been followed for C₆₀/Cu (100) and were found to agree well with a weak anharmonic coupling (dephasing) to a low-frequency mode, which we suggest to be the frustrated translational mode of the adsorbed molecules. Additionally, the adsorption is accompanied by a broadband reflectance change, which is interpreted as due to the scattering of conduction electrons of the metal surface by the adsorbate. The reflectance change allows determination of the friction coefficient of the C₆₀ molecules, which results in rather small values (∼2×10⁹ s^-1 for Ag and Au, and ∼1.6×10⁹ s^-1for Cu), consistent with a marked metallic character of the adsorbed molecules. Pre-dosing of alkali atoms onto the metal substrates drastically changes the IR spectra recorded during subsequent C₆₀ deposition: anti-absorption bands, as well as an increase of the broadband reflectance, occur and are interpreted as due to strong electron–phonon coupling with induced surface states. Received: 6 June 2001 / Accepted: 23 October 2001 / Published online: 3 April 2002     

Surface and interface properties of thin pentacene and parylene layers

To improve Organic Thin Film Transistor (OTFT) properties we study OTFT semiconductor/dielectric interfacial properties via examination of the gate dielectric using thin Parylene C layer. Structural and morphology properties of pentacene layers deposited on parylene layer and SiO₂/Si substrate structure were compared. The surface morphology was investigated using atomic force microscopy (AFM) and scanning electron microscopy (SEM). AFM topography of pentacene layer in non-contact mode confirmed the preferable pentacene grain formation on parylene surface in dependence on layer thickness. The distribution of chemical species on the surfaces and composition depth profiles were measured by secondary ion mass spectroscopy (SIMS) and surface imaging. The depth profiles of the analyzed structures show a homogenous pentacene layer, characterized with C or C₂ ions. Relatively sharp interface between pentacene and parylene layers was estimated by characteristic increased intensity of CCl ions peak. For revealing the pentacene phases in the structures the Micro-Raman spectroscopy was utilized. Conformal coatings of parylene and pentacene layers without pinholes resulted from the deposition process as was confirmed by SIMS surface imaging. For the pentacene layers thicker than 20 nm, both thin and bulk pentacene phases were detected by Micro-Raman spectroscopy, while for the pentacene layer thickness of 5 and 10 nm the preferable thin phase was detected. The complete characterisation of pentacene layers deposited on SiO₂ and parylene surface revealed that the formation of large grains suggests 3D pentacene growth at parylene layer with small voids between grains and more than one monolayer step growth. The results will be utilized for optimization of the deposition process.      

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.