In the design of asphalt mixtures for paving, the choice of components has a remarkable importance,as requirements of quality and durability must be assured in use, guaranteeing adequate standardsof safety and comfort.

In this paper, an approach of analysis on the aggregate materials using fractal geometry is proposed. Following an analytical and an experimental approach, it was possible to find a correlation betweencharacteristics of the asphalt concrete (specific gravity and porosity) and the fractal dimension ofthe aggregate mixtures.

The studies revealed that this approach allows to draw the optimal fractal dimension and, conse-quently, it can be used to choose an appropriate aggregate gradation for the specific application;once the appropriate initial physical parameters are finalized.

This fractal approach could be employed for predicting the porosity of mixed asphalt concretes,given as input the fractal characteristics of the aggregate mixtures of the concrete materials.

Fractal analysis is one of the rapidly evolving branches of mathematics and finds its application in different analyses such as pore space description. It constitutes a new approach to the issue of their natural irregularity and roughness. To be properly applied, it should be encompassed by an error estimation. The article presents and verifies uncertainties along with imperfections connected with image analysis and expands on the possible ways of their correction. One of key aspects of such research is finding both appropriate place and the number of photos to take. A coarse- grained sandstone thin section was photographed and then pictures were combined into one, bigger image. Fractal parameters distributions show their change and suggest that the accurately gathered group of photos include both highly and less porous regions. Their amount should be representative and adequate to the sample. The resolution influence on the fractal dimension and lacunarity values was examined. For SEM limestone images obtained using backscattered electrons, magnification in the range of 120x to 2000x was used. Additionally, a single pore was examined. The acquired results point to the fact that the values of fractal dimension are similar to a wide range of magnifications, while lacunarity changes each time. This is connected with changing homogeneity of the image. The article also undertakes a problem of determining fractal parameters spatial distribution based on binarization. The available methods assume that it is carried out after or before the image division into rectangles to create fractal dimension and lacunarity values for interpolation. An individual binarization, although time consuming, provides better results that resemble reality to a closer degree. It is not possible to define a single, correct methodology of error elimination. A set of hints has been presented that can improve results of further image analysis of pore space.

The analysis of the fractal dimension becomes one of the new approach features in spatial research. This approach bases on the perception of space as a living structure, an organism which in its complexity and heterogeneity is a multi-scale creation although holistically perceived. The aim of the authors was to determine the nationwide fractal dimensions for the distinguished construction categories and designation of general regularities in these layout.

Combine harvesters are the source a large amount of noise in agriculture. Depending on different working conditions, the noise of such machines can have a significant effect on the hearing condition of drivers. Therefore, it is highly important to study the noise signals caused by these machines and find solutions for reducing the produced noise. The present study was carried out is order to obtain the fractal dimension (FD) of the noise signals in Sampo and John Deere combine harvesters in different operational conditions. The noise signals of the combines were recorded with different engine speeds, operational conditions, gear states, and locations. Four methods of direct estimations of the FD of the waveform in the time domain with three sliding windows with lengths of 50, 100, and 200 ms were employed. The results showed that the Fractal Dimension/Sound Pressure Level [dB] in John Deere and Sampo combines varied in the ranges of 1.44/96.8 to 1.57/103.2 and 1.23/92.3 to 1.51/104.1, respectively. The cabins of Sampo and John Deere combines reduced and enhanced these amounts, respectively. With an increase in the length of the sliding windows and the engine speed of the combines, the amount of FD increased. In other words, the size of the suitable window depends on the extraction method of calculating the FD. The results also showed that the type of the gearbox used in the combines could have a tangible effect on the trend of changes in the FD.

The paper proposes an adaptation of mathematical models derived from the theory of deterministic chaos to short-term power forecasts of wind turbines. The operation of wind power plants and the generated power depend mainly on the wind speed at a given location. It is a stochastic process dependent on many factors and very difficult to predict. Classical forecasting models are often unable to find the existing relationships between the factors influencing wind power output. Therefore, we decided to refer to fractal geometry. Two models based on self-similar processes (M-CO) and (M-COP) and the (M-HUR) model were built. The accuracy of these models was compared with other short-term forecasting models. The modified model of power curve adjusted to local conditions (M-PC) and Canonical Distribution of the Vector of Random Variables Model (CDVRM). Examples of applications confirm the valuable properties of the proposed approaches.

Professor Piotr Pierański, an outstanding Polish physicists, excellent researcher and brilliant lecturer, passed away on the 23rd February 2018. The article quotes some recollections of his numerous friends and coworkers wordwide.

Speech and music signals are multifractal phenomena. The time displacement profile of speech and music signal show strikingly different scaling behaviour. However, a full complexity analysis of their frequency and amplitude has not been made so far. We propose a novel complex network based approach (Visibility Graph) to study the scaling behaviour of frequency wise amplitude variation of speech and music signals over time and then extract their PSVG (Power of Scale freeness of Visibility Graph). From this analysis it emerges that the scaling behaviour of amplitude-profile of music varies a lot from frequency to frequency whereas it’s almost consistent for the speech signal. Our left auditory cortical areas are proposed to be neurocognitively specialised in speech perception and right ones in music. Hence we can conclude that human brain might have adapted to the distinctly different scaling behaviour of speech and music signals and developed different decoding mechanisms, as if following the so called Fractal Darwinism. Using this method, we can capture all non-stationary aspects of the acoustic properties of the source signal to the deepest level, which has huge neurocognitive significance. Further, we propose a novel non-invasive application to detect neurological illness (here autism spectrum disorder, ASD), using the quantitative parameters deduced from the variation of scaling behaviour for speech and music.

Aflexible fractal-like aggregate modelwas used to study deformation and fragmentation of the structure of fractal-like aggregates via their impaction with rigid rough surface.Aggregateswere conveyed one at the time towards a surface under vacuum conditions. The number of primary particles remaining in each fragment, ratio of average fragment radius of gyration after impaction to the average fragment initial radius of gyration and ratio of average coordination number to the initial coordination number were monitored for each individual aggregate. Results demonstrate that depending on the impact velocity, the fractal dimension of the aggregate, the strength of bonds between primary particles, the stiffness of the aggregate structure and the diameter of primary particle composing an aggregate, restructuring or breakage of the aggregate occur. Moreover, in the analysis of the ratio of coordination number of aggregates after impaction to the initial coordination number, three regimes were distinguished: first no deformation at low impact velocities, second restructurisation regime and finally fragmentation regime where partial or total fragmentation of aggregates was observed.

The paper presents the results and provides an analyse of the geometric structure of Fe-Al protective coatings, gas-treated under specified GDS conditions. The analysis of the surface topography was conducted on the basis of the results obtained from the SEM data. Topographic images were converted to three-dimensional maps, scaling the registered amplitude coordinates of specific gray levels to the relative range of 0÷1. This allowed us to assess the degree of surface development by determining the fractal dimension. At the same time, the generated three-dimensional spectra of the autocorrelation function enabled the researchers to determine the autocorrelation length (Sal) and the degree of anisotropy (Str) of the surfaces, in accordance with ISO 25178. Furthermore, the reconstructed three-dimensional images of the topography allowed us to evaluate the functional properties o the studied surfaces based on the Abbott-Firestone curve (A-F), also known as the bearing area curve. The ordinate describing the height of the profile was replaced by the percentage of surface amplitude in this method, so in effect the shares of the height of the three-dimensional topographic map profiles of various load-bearing properties were determined. In this way, both the relative height of peaks, core and recesses as well as their percentages were subsequently established.

The paper presents results of a research on simulation of magnetic tip-surface interaction as a function of the lift height in the magnetic force microscopy. As expected, magnetic signal monotonically decays with increasing lift height, but the question arises, whether or not optimal lift height eventually exists. To estimate such a lift height simple procedure is proposed in the paper based on the minimization of the fractal dimension of the averaged profile of the MFM signal. In this case, the fractal dimension serves as a measure of distortion of a pure tip-surface magnetic coupling by various side effects, e.g. thermal noise and contribution of topographic features. Obtained simulation results apparently agree with experimental data.

One of the main purpose of accurate blasting in open pit mining is to achieve optimum rock fragmentation.

The degree of rock fragmentation plays a significant role in order to control and minimise the

overall production cost including loading, hauling and crushing. In the present paper, the application of

a Number-Size (N-S) fractal model is intended to classify the blast fragmentation size in the Jalal-Abad

iron mine, SW Iran, using GoldSize image analysis software for four blasting with the obtained result

being compared with Kuz-Ram curves. To do this, the fractal dimensions via N-S log-log plots were

generated based on the output of the GoldSize software. The results indicated that the fragmented rocks

have a multifractal nature with four/five different fragmented populations in terms of size namely; the fine

rocks with the size of less than 16 cm, Mean-fragment values between 16 and 45 cm, In-range between

45 and 70 cm and finally, oversize larger than 70 cm.

The analysis of particle size in suspensions carried out with use of the laser diffraction method enables us to obtain not only information about the size of particles, but also about their properties, shape and spatial structure, determined basing on fractal dimension. The fractal dimension permits the evaluation of the interior of aggregates, at the same time showing the degree of complexity of the matter. In literature, much attention is paid to the evaluation of the fractal dimension of flocs in activated sludge, in the aspect of control of single processes, i.e. sedimentation, dehydration, coagulation or flocculation. However, results of research concerning the size of particles and the structure of suspensions existing in raw and treated sewage are still lacking. The study presents optical fractal dimensions D3 and particle size distributions measured with use of laser granulometer in raw and treated sewage and activated sludge collected from six mechanical-biological wastewater treatment plants located in the Lower Silesian region. The obtained test results demonstrate that wastewater treatment plants that use both sequencing batch reactors and continuous flow reactors are more efficient at capturing suspension particles of a size up to 30 μm and are characterized by an increased removal of particles of a size ranging from 30 μm to 550 μm to the outflow. Additionally, in the case of samples of treated sewage and activated sludge collected at the same location, at short intervals, similar particle distributions were observed. As far as the analysis of fractal dimensions is concerned, particles contained in the raw sewage suspension were characterized by the lowest values of the fractal dimension (median equals 1.89), while the highest values occurred in particles of activated sludge (median equals 2.18). This proves that the spatial structure of suspension particles contained in raw sewage was similar to a linear structure, with a large amount of open spaces, while the structure of particles contained in the activated sludge suspension was significantly more complex in the spatial aspect.

The paper presents the concept of a fully planar treeshaped antenna with quasi-fractal geometry. The shape of the proposed radiator is based on a multi-resonant structure. Developed planar tree has symmetrical branches with different length and is fed by a coplanar waveguide (CPW) with modified edge of the ground plane. The antenna of size 29 mm x25 mm has been designed on Taconic - RF-35 substrate (r = 3.5, tg= 0.0018, h = 0.762 mm). The paper shows simulated and measured characteristics of return loss, as well as measured radiation patterns. The proposed antenna could be a good candidate for broadband applications (for instance: wideband imaging for medical application and weather monitoring radars in satellite communication etc.)

The knowledge whether and how chemical species react with tissues is important because of protection against harmful factors, diagnose of dermatological diseases, validation of dermatological procedures as well as effectiveness of topical therapies. In presented work the effects of chemical agents on plates of human fingernails were studied using Atomic Force Microscopy and Scanning Electron Microscopy. Apart from that, mapping of the elastic properties of the nails was also carried out. To obtain reliable measures of spatial evolution of the surface variations, recorded images were analyzed in terms of scaling invariance brought by fractal geometry, instead of common though not unique statistical measures.

Based on recent advances in non-linear analysis, the surface electromyography (sEMG) signal has been studied from the viewpoints of self-affinity and complexity. In this study, we examine usage of critical exponent analysis (CE) method, a fractal dimension (FD) estimator, to study properties of the sEMG signal and to deploy these properties to characterize different movements for gesture recognition. SEMG signals were recorded from thirty subjects with seven hand movements and eight muscle channels. Mean values and coefficient of variations of the CE from all experiments show that there are larger variations between hand movement types but there is small variation within the same type. It also shows that the CE feature related to the self-affine property for the sEMG signal extracted from different activities is in the range of 1.855~2.754. These results have also been evaluated by analysis-of-variance (p-value). Results show that the CE feature is more suitable to use as a learning parameter for a classifier compared with other representative features including root mean square, median frequency and Higuchi's method. Most p-values of the CE feature were less than 0.0001. Thus the FD that is computed by the CE method can be applied to be used as a feature for a wide variety of sEMG applications.

Swing-up control of a single pendulum from the pendant to the upright position is firstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found effective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like figures.

Electrical Discharge Machining (EDM) process with copper tool electrode is used to investigate the machining characteristics of AISI D2 tool steel material. The multi-wall carbon nanotube is mixed with dielectric fluids and its end characteristics like surface roughness, fractal dimension and metal removal rate (MRR) are analysed. In this EDM process, regression model is developed to predict surface roughness. The collection of experimental data is by using L9 Orthogonal Array. This study investigates the optimization of EDM machining parameters for AISI D2 Tool steel using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Analysis of variance (ANOVA) and F-test are used to check the validity of the regression model and to determine the significant parameter affecting the surface roughness. Atomic Force Microscope (AFM) is used to capture the machined image at micro size and using spectroscopy software the surface roughness and fractal dimensions are analysed. Later, the parameters are optimized using MINITAB 15 software, and regression equation is compared with the actual measurements of machining process parameters. The developed mathematical model is further coupled with Genetic Algorithm (GA) to determine the optimum conditions leading to the minimum surface roughness value of the workpiece.