Fractals, Materials and Energy Technologies

World’s perennial need for energy yields the whole spectra of technological challenges and scientific tasks. An important stream in finding new solutions leads over materials characterized by precise microstructural architecture based on fractal geometry/analysis covering wide size ranges down to nano scale. Having such a deep geometric hierarchy opens new possibilities in energy storage capacities supported by fractal resources. These novel ideas are natural continuation of some early fractal applications have been used as a tool in energy research, applying on diverse energy technologies, from photovoltaics to fuel cells and carbon capture. All three items that are essential regarding energetic questions, free energy stocks location, energy harvesting and short/ long term energy storage have their specific common points with fractal nature. Also, the concept of energy as physical objects property, share some features characteristic to fractal objects. In other words, fractal, as a crucial concept of modern theoretical-experimental physics is tightly connected with the process of cultivating the wild energy as well. Here, the above items will be discussed. The term “geometry” as it is custom in plain language, understands “shape” rather than the science of geometry. In this sense, “geometry” describes property of hierarchy that is more present in every day’s life than we are usually aware of. Just note that all our senses often convey information on the quality of some matter by absorbing certain hierarchical order. The touch feeling of smooth or rough surface, olfactory or taste data differ by energetic level that generates according to geometry of particles or clusters that follow fractal patterns. Adjusting specific, a priori constructed fractal micro or nano architecture make the energetic flow more effective by decrease losses made by non-conformal geometry

Curie-Weiss Law Fractal Corrections and Clausius-Mossotti Equation

The Clausius–Mossotti relation emerged as a combination of the analysis of indices of refraction (by Rudolf Clausius) and the relationship between the dielectric constants of two different media (Ottaviano-Fabrizio Mossotti). Since it connects dipole’s polarizability with the electric permittivity of a material made of those dipoles, it is one of the fundamental relationship that can be derived from Maxwell’s conductivity equation. Also, it is tightly connected both the Curie and Curie–Weiss laws which are correlation relations. Using fractal approach in Curie–Weiss equation and fractal correction applied recently by the authors, the Clausius–Mossotti relation is also subjected to modification with respect to ferroelectric materials fractal nature. The correction is operationally performed by introducing fractal correction factor a0 > 1, as a multiplier to the usual dielectric constant er to gain the bigger value a0er. This shows that the Clausius–Mossotti relation is also “permeated” by fractal nature being inherited from the material’s morphology. Our experiments were carried out on BaTiO3-ceramics as characteristic representative of perovskites but the conclusions can be applied on any other ceramics materials as well as on thin film layers and coating in general. By shapes control and contact surfaces numbers on the entire BaTiO3-ceramic sample level, the control over structural properties of these ceramics can be done, with the aim of correlation between material electronic properties and corresponding microstructure. The fractal correction has wide consequences on many phenomena like PTC, ferroelectrics, ferromagnetics, piezo- and optoelectronic properties as well as electrochemical thermodynamic and fluid dynamics parameters

Comparative fractal analysis of Valeriana officinalis roots shrinkage during drying

Valerian plant roots (Valeriana officinalis)shrinkage was investigated during the convective hot air drying. Combined fractal and image analysis was performed in this study.The samples were prepared for light microscopy observation by standard paraffin wax method, sectioned by sliding microtome and stained by Alcian blue and Safranin. The fractal dimensions of sample images were calculated using the box counting method.Both polar and orthogonal meshes were used. The normalized changes of fractal dimension of the microstructural images were used to describe the shrinkage process of biomaterial. The changes of physical properties and microstructure of roots strongly depends on drying regime and drying agent properties. Comparative analysis of fresh and dry root samples shows thatmicrostructural changes in bio material can be correlated with drying parameters during the dehydration process. Fractal dimension was found to be a good indicator of the microstructural changes of an investigated bio-material

Towards Electronic Materials Fractal Theory

We are witnesses of blowing-up of new technologies and materials that nowadays are being introduced by the increasing rate. With huge diversity of electrophysical properties as well as difference between dimensions of 12 orders of magnitude, from nano tubes to boulders of ore which makes the length scale 10-9 to 103 m yields a demand of introducing an universal analytic tool that will independent from both dimension and phenomenology. Next remark is that these materials are usually of amorphous, amorphous-crystals and crystals solid state ceramics, and thou of very irregular geometry, with characteristic example of powder metallurgy. There are also evidences of self-similar phenomena upon different magnitude of magnification of materials’ grains or intergranular pores. Besides, the grains themselves possesses very irregular contours which makes difficult calculating their surface area or probability of intergranular contacts. All of these arguments makes reasonable to treat such materials as fractal objects and apply fractal analysis to extract new information about their inner properties regardless dimension range or underlying phenomena. The existing literature as well as our experiments and results show that materials like different ceramics, especially electronics ceramics materials, semiconductors, electromagnetics, ferroelectrics, multiferroics, thin films, diamond films etc., already have fractal nature. As practical outcome we propose introducing suitable correction quantities that would take care of fractal reality as well as involvement of important physical laws. Especially, these fractal nature analysis approaches do open a new perspective for deeper and higher level electronics integrations within the new fractal electronics ideas

New materials and technologies in aero and space research

Space technology plays an integral and indispensable role in our daily lives. Whether we are talking about live broadcasts of World Cup matches, satellite-assisted emergency management efforts, or the nightly weather forecast, one thing is true: our lives would be very different without satellite images or satellite-based communication and navigation systems. Space technology is key to our modern, knowledge-based society. Today space makes a vital contribution when it comes to promoting research and development, education and innovation, economic growth, providing highly qualified jobs, improving our quality of life, protecting the Earth, ensuring our security and defence and furthering international cooperation. Military platforms—such as ships, aircraft, and ground vehicles— rely on advanced materials to make them lighter, stronger, and more resistant to harsh environmental conditions. Currently, the process for developing new materials frequently takes longer than a decade. This lengthy process often means that developers of new military platforms are forced to rely on decades-old, mature materials, because potentially more advanced materials are still being developed and tested and are considered too large a risk to be implemented into platform designs. Al alloys have been the primary material for the structural parts of aircraft because of their well known performance, well established design methods, manufacturing and reliable inspection techniques. Fiber reinforced polymer composites have been increasingly used in aerospace. Fiber Metal Laminate (FML) is a new kind of hybrid composite. Materials used to construct spacecraft and protective gear—including the International Space Station and space suits for astronauts—must be lightweight yet strong enough to guard against cosmic dust that travels at hypervelocity

Quantitative metallography modern metods

This paper has been concerned with the classical Stereological targets V, S, L, and N only, namely with so-called first-order properties. Stereology is now drifting rapidly toward second-order methods, aimed at quantifying spatial pattern for the elements of a structure (e.g. clustering, repulsion, etc., between the elements) as well as the nature and degree of association between different structures. Second-order statistical methods are widely available for point patterns. Important devices for the second-order analysis of cells and organelles when regarded as points in space have recently been devised. Analogous methods extend to higher dimensional quantities such as surface areas and volumes

Fractal nature Heywang model correction and Brownian motions

Ceramics grains contacts are essential for understanding complex dielectric properties of electronic ceramics materials. Since the actual contact surface is an irregular object, the theory of fractal sets is applied. Also, the Heywang model of intergranular capacity are introduced as a basic idea for relations with fractal structure. The BaTiO3-ceramics has fractal form in, at least, two levels: shapes and distributions of grains and intergranular contacts. Using fractal modeling approach, reconstruction of microstructure, like shapes of grains or intergranular contacts can be successfully done. Furthermore, the area of grains surface is calculated by using fractal correction that expresses the irregularity of grains surface through fractal dimension. It is known that BaTiO3 and similar ceramics have fractal nature based on three different phenomena. First, there is process of Brownian-fractal motions inside the material during sintering in the form of flowing micro-particles –ions, atoms, electrons which is an essentially fractal phenomena. This motion has fractal structure and can be undergo the process of fractal modification. Second, there are so called “negative space” made of pores and intergranular space. Being extremely complex, the pore space plays an important role in microelectronic, PTC and other phenomena. Third, ceramic grains have fractal shape seeing as a contour in cross section or as grain’s surface. These triple factors, in combination, make the microelectronic environment of very peculiar electro-static and dynamics microelectronic environment. In order to obtain an equivalent circuit model, which provides a more realistic representation of the electronic materials electrical properties, in this article an intergranular contacts model for the BaTiO3 electrical properties characterization were determined and implemented. Considering obtained results, the directions of possible BaTiO3-ceramics materials properties prognosis are determined according to the correlations synthesisstructure- properties

Material characterization SEM modern methods

Detailed analysis was carried out and systematization of methods used in the characterization of materials using SEM. We analyzed its operation. Attention was paid to its major parts. Specially to the electron gun and lens. Also, comparisons of forming character oprickim microscope and SEM. In further analysis we have studied differences between EDS and WDS.. The EDS features measurement with a small probe current, short-time acquisition of spectra, etc. WDS features a high energy (wavelength) resolution, detection of trace elements. Most SEMs are equipped with an EDS, whereas a WDS is generally used as an Electron Probe Microanalyzer (EPMA) that mainly performs elemental analysis

New trends in the development of battery

Among civilized priorities and challenges for humanity, energy occupies the most important and certainly the most attractive place in terms of research as well as in scientific and technological developments. The question of energy, in relation trinity energy-materials-information (EMI) is directly correlated with the triad of the synthesis (the technological process of obtaining materials)- structure of- material properties (srb. sinteza-struktura-svojstva materijala (SSS)). Storage of energy (electricity, heat, cooling energy ...) is an important issue and a weak point in the energy sector. Fossil fuels provide the internal storage of energy which is not the case for wind, solar, etc. The nanostructure of materials can be a useful for the storage of heat or for the isolation of heat storage. Storing electrochemical energy is widely applied, especially in portable devices, which are mainly related to the battery. Li, as the material is the most used because it is the lightest metal and has a very high energy density. Due to the lack of lithium in the United States, and the world, new research substitute lithium for magnesium ions, for already listed battery system. These studies are done at the Illinois State University, in Chicago. After the commercialization of lithium-ion battery research for the cathode active material concentrates on lithium that contains at the forefront the transition-metal oxides with a 4V class high electromotive force because it can serve as a lithium of carbonic negative electrode. Unfortunately all classes 4V rechargeable cathode: LiCoO2, LiNiO2, LiMn2O4, have a core problem of costs and environmental impact, because their cathodes include the use of rare metals such as redox center. The problems become more serious, especially for the most expensive LiCoO2, with further expansions of the market for electric vehicles, which are expected in the near future

Fractal tools in terrorist and financial crime prevention

Information society imposes globalization and universality of values. In these circumstances, terrorism, institutional political violence which targets trying to achieve the morbid fear of provoking a spectacular way, inappropriately given conditions, becomes a real threat not only to the nations but also to politics on the global level. In 1996, the International Monetary Fund estimated that 2–5% of the worldwide global economy involved laundered money. Today, intelligence activities in preventing and combating terrorism include financial investigations and money laundering for the purpose of financing terrorism, resulting in broadening of the scope of data to the level which makes it impossible for human logical evaluation. Technologies development that enables increasing capacity of speed and the amount of data processing has enabled defining, analyzing and exploring more and more models. This led to the idea of computer experiments and simulations trying to get to more complex planning and forecasting for the purpose of countering terrorism and “dirty” money transaction, as highly dangerous, complex and variable phenomena. This presentation aims at quotation the wide spectrum of mathematically founded fractal concepts suited to generate computer models of anti-terrorist activities. In this sense, the logistic behind the items connected with detecting and recognizing degree of terroristic threat by comparing fractal structure of people’s faces, fast search through the databases of faces and fingerprints. The speed of searching processes is of vital importance which promotes the crucial importance of compression and data reduction with preservation of regularity. Especially important are analytic forecasting of missing visual data and forms, to supplement the empirical evidences and records. All these operations are possible with higher degree of knowledge utilization and adaptation of virtual reality in the fight against terrorism and different forms of money laundering. The results indicate that the achievements implementation of the concept of fractals depends on substantial prior knowledge, environmental influences, subsystem integration, decentralization and synchronization, and allows us to come up with similar high information technology models, but not necessarily to enable identification of the authentic features of the various anomalies that result in objectively a social consequences. In this sense, we conclude that the application of information technology in the fight against terrorism, based on the concept of fractals has its place in the arsenal of anti-terroristic prevention