Oldrich Zmeskal

Fractal–Cantorian geometry, Hausdorff dimension and the fundamental laws of physics

Abstract Fractal geometry is widely used nowadays in many scientific areas. The authors are trying to link its uses to a description of fractal basis of fundamental physical laws. Fractals seem to be very powerful in describing natural objects on all scales. Fractal dimension and fractal measure, are crucial parameters for such description. They imply that there are no different laws, which act on different scales but there is a small set of universal properties, which act in different dimensional spaces as in El Naschie’s Cantorian e(∞) theory. The article describes the relation between fractal–Cantorian geometry and fundamental physical laws. It shows dependence between fractal describing parameters and quantities, which characterize properties of real world.

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.

Field and potential of fractal–Cantorian structures and El Naschie’s E(∞) theory

Abstract In this paper the complex description of conservative forces of fractal fields in the Euclidean space is presented. The physical quantities used for the description of different properties of physical reality (electrical, gravitational, thermal, acoustic, etc.) are defined. The mathematic of fractal–Cantorian geometry is used for the description of properties of the electrical field of systems with different mass distribution, electrical properties of semiconductors, thermal properties of ideal gas and properties of high-energy elementary particles following El Naschie’s E (∞) theory.

Study of the thermal properties of filaments for 3D printing

Various materials are used for 3D printing, most commonly Acrylonitrile butadiene styrene (ABS), Polylactic acid (PLA), Polyethylene (PET) and Polypropylene (PP). These materials differ mainly in their melting point, which significantly influences the properties of the final products. Filaments are melted in the print head during the printing process. The temperature range is from 150 °C to 250 °C depending on the technology used. The optimum temperature for the cooling substrate on which printing is carried out is chosen so as to ensure uniform cooling and deformation. It generally varies between (40 – 100) °C. From the above it is clear that both temperatures can significantly affect the properties of the printed 3D object. It is therefore important to determine the thermal parameters (thermal conductivity, specific heat and thermal diffusivity) of the materials used across the entire range of temperatures. For evaluating the properties of different types of PLA materials, the step transient method was ...

Thermal properties of an erythritol derivative

Erythritol (C4H10O4) is a sugar alcohol (or polyol) that is commonly used in the food industry. Its molar mass is 122.12 g·mol−1 and mass density 1450 kg·m−3. Erythritol, an odorless crystalline powder, can also be characterized by other physical parameters like melting temperature (121 °C) and boiling temperature (329 °C). The substance can be used for the accumulation of energy in heat exchangers based on various oils or water. The PlusICE A118 product manufactured by the PCM Products Ltd. company (melting temperature Θ = 118 °C, specific heat capacity cp = 2.70 kJ.K−1.kg−1, mass density 1450 kg·m−3, latent heat capacity 340 kJ.kg−1, volumetric heat capacity 493 MJ.m−3) is based on an erythritol-type medium. Thermal properties of the PlusICE A118 product in both solid and liquid phase were investigated for this purpose in terms of potential applications. Temperature dependences of its thermal parameters (thermal diffusivity, thermal conductivity, and specific heat) were determined using a transient (ste...

Study of thermal properties of insulating materials

This paper describes a new method of thermal parameters determination. It is based on the measurement of temperature responses after delivery of heat from a heat source. The method is based on the combination of a step-wise and a ramp-wise heating. It can be used for the study of solid and liquid materials and give new information about temperature dependences of transport and thermal parameters in one step. The measured data are used as input of multi parametric regression method for the determination of transport parameters (the diffusion and relaxation time, and heat absorption coefficient). The thermal parameters (the thermal diffusivity a, thermal conductivity λ, and specific heat c) can be also determined from the transport parameters. The dependences of all parameters together with the heat source quality coefficient α (or the source fractal dimension D) and losses parameter R on temperature from interval 20 °C to 33 °C were calculated.

Fractal Analysis of Fitness Landscapes

Complex optimization problems may have fitness landscapes with fractal characteristics. This chapter reviews landscapes obtained from basic artificial test functions as well as cost functions of real application problems which have the property to be fractal. We will discuss the description, structure and complexity of these fractal fitness landscapes. A major topic of this chapter is to use elements from fractal geometry to measure attributes of fractal landscapes. Also, structural as well as functional properties of the landscape are discussed. The examples used in this chapter are two-dimensional, however it is possible to extend the proposed analysis to n dimensions.

Physical properties investigation of reduced graphene oxide thin films prepared by material inkjet printing

The article is focused on the study of the optical properties of inkjet-printed graphene oxide (GO) layers by spectroscopic ellipsometry. Due to its unique optical and electrical properties, GO can be used as, for example, a transparent and flexible electrode material in organic and printed electronics. Spectroscopic ellipsometry was used to characterize the optical response of the GO layer and its reduced form (rGO, obtainable, for example, by reduction of prepared layers by either annealing, UV radiation, or chemical reduction) in the visible range. The thicknesses of the layers were determined by a mechanical profilometer and used as an input parameter for optical modeling. Ellipsometric spectra were analyzed according to the dispersion model and the influence of the reduction of GO on optical constants is discussed. Thus, detailed analysis of the ellipsometric data provides a unique tool for qualitative and also quantitative description of the optical properties of GO thin films for electronic applications.

Thermal properties of alkali-activated aluminosilicates

The paper is focused on measurements and evaluation of thermal properties of alkali-activated aluminosilicates (AAA) with various carbon admixtures. Such composites consisting of blast-furnace slag, quartz sand, water glass as alkali activator and small amount of electrically conductive carbon admixture exhibit better electric and thermal properties than the reference material. Such enhancement opens up new practical applications, such as designing of snow-melting, de-icing or self-sensing systems that do not need any external sensors to detect current condition of building material. Thermal properties of the studied materials were measured by the step-wise transient method and mutually compared.

Optical Characterization of Graphene Oxide Films by Spectroscopic Ellipsometry

The paper deals with the study of optical properties of graphene oxide (GO) by inkjet printing. Defined structure of GO can be obtained by reducing of prepared layers either by heating or by UV radiation (rGO). The dispersion function for refractive index and extinction coefficient of GO and both rGO thin films were measured by spectroscopic ellipsometry in the wavelength range of 200 – 850 nm. Spectroscopic ellipsometry (SE) was used characterize the optical response of layer of GO reduced by UV and thermal reduction GO in visible range.