Michal Vesely

Entropy of fractal systems

The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Renyi entropy. A special case of Renyi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension can be defined in an E-dimensional space. The Renyi entropy and generalized fractal dimension are connected by a straight relation.

The influence of various deposition techniques on the photoelectrochemical properties of the titanium dioxide thin film

Thin sol–gel TiO2 layers deposited on the conductive ITO glass by means of three various deposition techniques (dip-coating, inkjet printing and spray-coating) were used as photoanode in the three-compartment electrochemical cell. The thin TiO2 films were treated at 450 °C and after calcination all samples possessed the crystallographic form of anatase. The relationship between surface structure and photo-induced conductivity of the nanostructured layers was investigated. It was found that the used deposition method significantly influenced the structural properties of prepared layers; mainly, the formation of defects and their quantity in the prepared films. The surface properties of the calcined layers were determined by XRD, Raman spectroscopy, SEM, AFM, UV–Vis analyses and by the optical microscopy. The photo-induced properties of nanoparticulate TiO2/ITO photoanode were studied by electrochemical measurements combined with UV irradiation.

Optical Properties of Titania Coatings Prepared by Inkjet Direct Patterning of a Reverse Micelles Sol-Gel Composition.

Thin layers of titanium dioxide were fabricated by direct inkjet patterning of a reverse micelles sol-gel composition onto soda-lime glass plates. Several series of variable thickness samples were produced by repeated overprinting and these were further calcined at different temperatures. The resulting layers were inspected by optical and scanning electronic microscopy and their optical properties were investigated by spectroscopic ellipsometry in the range of 200–1000 nm. Thus the influence of the calcination temperature on material as well as optical properties of the patterned micellar titania was studied. The additive nature of the deposition process was demonstrated by a linear dependence of total thickness on the number of printed layers without being significantly affected by the calcination temperature. The micellar imprints structure of the titania layer resulted into significant deviation of measured optical constants from the values reported for bulk titania. The introduction of a void layer into the ellipsometric model was found necessary for this particular type of titania and enabled correct ellipsometric determination of layer thickness, well matching the thickness values from mechanical profilometry.

Statistics of Fractal Systems

Distribution functions are used for the description of energy distribution of elementary particles, atoms, and molecules in dynamic systems. These distribution functions depend on the energy of the system and on its properties. The paper focuses on the generalization of the relationships commonly used to study the statistical properties of particles in 3D space so that they become generally applicable onto an E-dimensional space. These relationships can then be applied e.g. for studying the properties of the particles in 2D and in 1D space.

Energy and Entropy of Fractal Objects: Application to Gravitational Field

Various different approaches to the definition of entropy and their connections with fractal dimensions of systems were described in the paper Entropy of Fractal Systems presented at the conference Nostaradamus 2012. In the second part of the paper, the described findings were applied to study the fractal properties of image structures.