Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

Trap-assisted tunnelling current in MIM structures

A new model is presented of current transport in Metal Insulator Metal (MIM) structures by quantum mechanical tunnelling. In addition to direct tunnelling through an insulating layer, tunnelling via defects present in the insulating layer plays an important role. Examples of the influence of the material and thickness of the insulating layer, energy distribution of traps, and metal work functions are also provided.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

Elimination Voltammetry of Miniaturized Mercury Drop Electrodes

Elimination voltammetry with linear scan (EVLS) in connection with renewed mini‐ drop mercury electrodes provides valuable information about the character and kinetics of processes at electrode/electrolyte interfaces. Based on the experiment related to the hydrogen evolution, it is presented that the EVLS is more sensitive than other voltammetric methods. Using miniaturized mercury electrodes, the EVLS is capable of detecting the effect of spherical diffusion associated with both the scan rates and the size of an electrode drop.     

Towards Discrimination of Plant Species by Machine Vision: Advanced Statistical Analysis of Chlorophyll Fluorescence Transients

Automatic discrimination of plant species is required for precision farming and for advanced environmental protection. For this task, reflected sunlight has already been tested whereas fluorescence emission has been only scarcely considered. Here, we investigated the discriminative potential of chlorophyll fluorescence imaging in a case study using three closely related plant species of the family Lamiaceae. We compared discriminative potential of eight classifiers and four feature selection methods to identify the fluorescence parameters that can yield the highest contrast between the species. Three plant species: Ocimum basilicum, Origanum majorana and Origanum vulgare were grown separately as well as in pots where all three species were mixed. First, eight statistical classifiers were applied and tested in simulated species discrimination. The performance of the Quadratic Discriminant Classifier was found to be the most efficient. This classifier was further applied in combination with four different methods of feature selection. The Sequential Forward Floating Selection was found as the most efficient method for selecting the best performing subset of fluorescence images. The ability of the combinatorial statistical techniques for discriminating the species was also compared to the resolving power of conventional fluorescence parameters and found to be more efficient.     

Production and hydrolysis of 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine

Summary Condensation of ephedrine with benzaldehyde, an acid catalyzed reversible reaction, producing 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine, was studied. If the starting reaction mixture contained acetic acid, it quantitatively reacted with ephedrine and produced a salt functioning as an acid catalyst. On the contrary, ephedrine hydrochloride had no catalytic effect.     

Ionic Liquid for in situ Vis/NIR and Raman Spectroelectrochemistry: Doping of Carbon Nanostructures

1-butyl-3-methylimidazolium tetrafluoroborate (an ionic liquid) is an advantageous electrolyte for the study of charge-transfer reactions at single-walled carbon nanotubes (SWCNTs) and fullerene peapods (C₆₀@SWCNT). Compared to traditional electrolyte solutions, this medium offers a broader window of electrochemical potentials to be applied, and favorable optical properties for in situ Vis/NIR and Raman spectroelectrochemistry of nano-carbon species. The electrochemistry of both nanotubes and peapods is dominated by their capacitive double-layer charging. Vis/NIR spectroelectrochemistry confirms the charging-induced bleaching of transitions between Van Hove singularities. At high positive potentials, new optical transitions were activated in partly filled valence band. The bleaching of optical transitions is mirrored by the quenching of resonance Raman scattering in the region of tube-related modes. The Raman frequency of the tangential displacement mode of SWCNT shifts to blue upon both anodic and cathodic charging in the ionic liquid. The Raman modes of intratubular C₆₀ exhibit a considerable intensity increase upon anodic doping of peapods.     

A remark on Liouville's formula on small time scales

We present a new proof of the Liouville formula for a d-dimensional linear dynamic system xΔ=A(t)x on a time scale T, where T is in a sense small. Our proof demonstrates that Liouville's formula on small time scales is a direct consequence of its well-known counterpart for ordinary differential equations.