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In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create geometric models of complicated fractals, we developed fractal construction models, visualization tools, and fractal measurement approaches. We introduced a novel recursive fractal modeling (RFM) method designed to generate intricate fractal patterns with enhanced control over symmetry, scaling, and self-similarity. The RFM method builds upon traditional fractal generation techniques but introduces adaptive recursion and symmetry-preserving transformations to produce fractals with applications in domains such as medical imaging, textile design, and digital art. Our approach differs from existing methods like Barnsley's IFS and Jacquin's fractal coding by offering faster convergence, higher precision, and increased flexibility in pattern customization. We used the RFM method to create a mathematical model of fractal objects that allowed for the viewing of polygonal, Koch curves, Cayley trees, Serpin curves, Cantor set, star shapes, circulars, intersecting circles, and tree-shaped fractals. Using the proposed models, the fractal dimensions of these shapes were found, which made it possible to create complex fractal patterns using a wide variety of complicated geometric shapes. Moreover, we created a software tool that automates the visualization of fractal structures. This tool may be used for a variety of applications, including the ornamentation of building items, interior and exterior design, and pattern construction in the textile industry. [ABSTRACT FROM AUTHOR]

Failures of water supply pipes are undesirable events with a random nature, yet they are an inevitable part of the operation of water infrastructure. Therefore, ongoing research is being conducted to develop methods for minimising their effects or securing underground infrastructure. One of the methods of limiting the effects of the suffosion phenomenon is determination of the water outflow zone, within which water will possibly flow to the soil surface after a pipe leak. The aim of this paper was to assess hypothetical structures created by outflowing water in terms of their potential use in determining the water outflow zone on the soil surface after a water pipe failure. Based on the laboratory test results, the Monte Carlo method was applied to generate the hypothetical population of points representing the places of water outflow. Three parameters characterising hypothetical structures were analysed: fractal dimension, length of a section, and the product of above parameters. The conducted research showed that it is possible to build a reliable hypothetical structure that allows for estimating the water outflow zone radius, knowledge of which would facilitate sustainable management of the water supply network by water utilities by enabling the estimation of the water outflow zone radius in practice. [ABSTRACT FROM AUTHOR]

The fundamental objective of acoustic barriers is to preserve the inhabitants of nearby areas from the high noise generated by road traffic. It is possible to significantly improve the performance of conventional acoustic barriers by attaching small acoustic diffusers on their upper part (caps) that do not imply an appreciable height increase of the barrier, thereby adhering to any height regulation or restriction. This work deepens and yields findings in the study of the acoustic performance of barriers with diffusers of different shapes, number and arrangement through the calculation of their insertion losses (IL). In this research, a design of four Y-shaped diffusing elements arranged according to the well-known fractal pattern called Cantor set is presented and validated through two types of traffic noise sources ('Car' and 'Ambulance'), one listener and a wide frequency band up to 10 kHz. The results demonstrate that the proposed diffuser provides a significant increase in acoustic losses compared to the results obtained in previous works without raising the height of the barrier. To the best of the authors' knowledge, there are no diffuser structures like the one presented here that have been installed or even proposed/analysed. [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method. We perform numerical experiments with these algorithms using Zetafast as a benchmark and apply the algorithms for the visualizations of fractal structures associated with the Riemann zeta function. [ABSTRACT FROM AUTHOR]

The Luanchuan polymetallic mining district (LPMD) covers many major deposits of the East Qinling metallogenic belt in Henan Province, central China. It has attracted much attention because of its various types of minerals, abundant mineral reserves and huge metallogenic potential. Systematic research on the geology of LPMD has been carried out previously, and it is concluded that the formation of the ore deposits is dominantly controlled by fault structure. However, there are few reports on the quantitative characterization of fault structure and spatial distribution of deposits and the coupling relationship between them. This study applies fractal theory to the illustration of the characteristics of inter-relationship between fault structure and spatial distribution of the ore deposits in LPMD, which then may serve as a basis for further ore exploration. Our results indicate that the capacity dimension (CPDs) of integrated fault structure, NW-trend fault and NE-trend fault for the area investigated are 1.7206, 1.6539 and 1.2145, respectively; while the information dimension (IND) of which is 1.7143, 1.6559 and 1.2222, respectively. The studied area has superior geological environment for potential ore deposits, with major contribution from the NW-trend fault. Spatial distribution dimension value of metallic ore is 0.8873. Quantity fractal dimension and Density fractal dimension values of the metallic deposits are 1.1154 and 1.115, respectively. Quantitatively, the main ore deposits discovered in this area mainly fall on either CPD ≥ 1.49, IND ≥ 1.38 or 1.49 > CPD ≥ 1.00, 1.38 > IND ≥ 1.00. Qualitatively, conditions that facilitate ore deposits require higher fractal dimension values. Among the areas studied, we found that Rank I area is the most ideal region that fulfilled the quantitative and qualitative conditions, which is consistent with the actual location of the ore deposits discovered.

Clinoptilolite (CP) was successfully synthesized via a hydrothermal route in the presence of polyethylene glycol (PEG), and it was then delaminated by washing using Zn2+ containing acid. HKUST-1, as one kind of the Cu-based MOFs, showed a high CO2 adsorption capacity owing to its large pore volume and specific surface area. In the present work, we selected one of the most efficient ways for preparing the HKUST-1@CP compounds via coordination between exchanged Cu2+ and ligand (trimesic acid). Their structural and textural properties were characterized by XRD, SAXS, N2 sorption isotherms, SEM, and TG-DSC profiles. Particularly, the effect of the additive PEG (average molecular weight of 600) on the induction (nucleation) periods and growth behaviors were detailed and investigated in the hydrothermal crystallization procedures of synthetic CPs. The corresponding activation energies of induction (En) and growth (Eg) periods during crystallization intervals were calculated. Meanwhile, the pore size of the inter-particles of HKUST-1@CP was 14.16 nm, and the BET specific area and pore volume were 55.2 m2/g and 0.20 cm3/g, respectively. Their CO2 and CH4 adsorption capacities and selectivity were preliminarily explored, showing 0.93 mmol/g for HKUST-1@CP at 298 K with the highest selective factor of 5.87 for CO2/CH4, and the dynamic separation performance was evaluated in column breakthrough experiments. These results suggested an efficient way of preparing zeolites and MOFs composites that is conducive to being a promising adsorbent for applications in gas separation. [ABSTRACT FROM AUTHOR]

Extensive engineering applications have confirmed the necessity of introducing stochastic disturbance into the permanent magnet synchronous motor (PMSM) system. Therefore the stochastic stability and bifurcation of the system under Gaussian white noise are investigated in this study. The stochastic average method transforms the system equation into Itô stochastic differential equation. Further, the stability of the model under white noise excitation is analysed based on the theoretical calculation process. Notably, the mechanism of P-bifurcation of the system is revealed by simulating the evolution process of probability density function with the change in noise intensity. Moreover, the complex dynamics of the system in two-parameter space are explored using multiple numerical tools, in which extensive fish-shaped periodic regions appear. It is particularly interesting that the noise inevitably erodes the boundaries of these fish-shaped periodic regions. Besides, it is noteworthy that a new phenomenon is found from the numerical simulation results that noise intensity can induce convergence behaviour in the periodic oscillation region, which also shows the two-sidedness of noise effect on the system. [ABSTRACT FROM AUTHOR]

Fe(III)-modified clinoptilolites (Fe-CPs) were prepared by hydrothermal treatment. The collapse of the heulandite skeletons was avoided by adjusting the pH value using HCl solution, showing the maximum relative crystallinity of the Fe-CPs at an optimal pH of 1.3. The competitive exchange performances between Fe3+ ions and H+ with Na+ (and K+) suggested that the exchange sites were more easily occupied by H+. Various characterizations verified that the hydrothermal treatments had a strong influence on the dispersion and morphology of the isolated and clustered Fe species. The high catalytic activity of the oxygen evolution reaction indicated the insertion of Fe3+ into the skeletons and the occurrences of isomorphic substitution. The fractal evolutions revealed that hydrothermal treatments with the increase of Fe content strongly affected the morphologies of Fe species with rough and disordered surfaces. Meanwhile, the Fe(III)-modified performances of the CPs were systematically investigated, showing that the maximum Fe-exchange capacity was up to 10.6 mg/g. Their thermodynamic parameters and kinetic performances suggested that the Fe(III)-modified procedures belonged to spontaneous, endothermic, and entropy-increasing behaviors. Finally, their adsorption capacities of CO2 at 273 and 298 K were preliminarily evaluated, showing high CO2 adsorption capacity (up to 1.67 mmol/g at 273 K). [ABSTRACT FROM AUTHOR]

Natural organic matter, including humic substances (HS), comprises complex secondary structures with no defined covalent chemical bonds and stabilized by inter- and intra-molecular interactions, such as hydrogen bonding, Van der Waal's forces, and pi-pi interactions. The latest view describes HS aggregates as a hydrogel-like structure comprised by a hydrophobic core of aromatic residues surrounded by polar and amphiphilic molecules akin a self-assembled soft material. A different view is based on the classification of this material as either mass or surface fractals. The former is intended as made by the clustering of macromolecules generating dendritic networks, while the latter have been modelled in terms of a solvent-impenetrable core surrounded by a layer of lyophilic material. This study reviews the evolution of the increasingly refined models that appeared in the literature, all capable to describing the physicochemical properties of HS. All the models are critically examined and revisited in terms of their ability to provide key information on the structural organization of HS. Understanding how the molecular association pathway influences aggregation of HS also provides a key acknowledgment of their role in the environment. [ABSTRACT FROM AUTHOR]

The particle formation in spray flame synthesis (SFS) is a fast and complex process involving many sub-steps that may happen simultaneously. To investigate the mechanisms that typically lead to small aggregated primary particles, a sophisticated technique for in situ measurements in the flame is necessary to provide information about primary particles and the aggregates as well. This work describes the development of an in situ measurement setup using small angle X-ray scattering (SAXS) to investigate the entire particle formation mechanism of zirconia nanoparticles in and above a turbulent spray flame. In preparation for the in situ measurements, a beamline for single crystal diffractometry at Karlsruhe Research Accelerator (KARA) was adapted for low scattering SAXS experiments including optimizations of the optics and measurement protocol. As a result, a significant dependence of scattering intensity was detected as a function of the height above the burner. A detailed analysis of the SAXS data and comparison with TEM images allow insights into the primary particle growth, the development of fractal properties and the aggregation process. [ABSTRACT FROM AUTHOR]

• A new fractal multi-cell square tube (FMST) based on the Sierpinski carpet fractal is proposed. • Energy absorption performance of the FMST are numerically and theoretically studied. • The SEA of the 3rd order FMST is 100 % than that of the 0th order FMST. • The theoretical predictions of the MCF agree well with the numerical results. In this study, a new fractal multi-cell square tube (FMST) based on the fractal design of the Sierpinski carpet is proposed for energy absorption. The dynamic crushing performance and energy absorption characteristics of the FMST are numerically and theoretically investigated. Extensive numerical simulations are carried out for the FMST structures with different fractal orders and masses of the structures. The findings reveal that the specific energy absorption of the 3rd order FMST is significantly higher, exhibiting a remarkable 100 % increase compared to the 0th order FMST. Furthermore, the undulation of the load-carrying capacity of the 3rd order FMST is reduced by up to 88.5 % compared to a conventional square tube, indicating the substantial potential of the FMST for designing highly efficient energy absorbers. Comparative analysis against other hierarchical multi-cell square tubes reported in the literature confirms that the specific energy absorption of the FMST surpasses existing designs. In addition, a theoretical study is presented for the mean crushing force of the proposed FMST, employing the simplified super folding element theory. The theoretical predictions agree well with the numerical results, further validating the effectiveness of the proposed design. This study provides an innovative design of a multi-cell energy absorber with exceptional energy absorption efficiency. The incorporation of fractal principle in the FMST design holds promise for advancing the field of energy absorption, with potential applications in various industries. [ABSTRACT FROM AUTHOR]

Natural images are scale invariant with structures at all length scales.We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs.We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation.

The asymmetry of heat conduction in thermal diodes is attributed to the thermal regulation in thermal logic circuits, thermal control devices, etc. Currently, thermal rectification devices, however, are constrained by either specific on/off switching thresholds, or low sensitivity to manufacturing errors, as well as the restrictions for specific roughness and material characteristics. Here, a thermal diode based on fractal structures (inverted tapered branch channel, 5.7 mm branch length, and 4 branches) with liquid metal/insulator interface is proposed to avoid these existing constraints. The thermal rectification coefficient reaches 0.4704 (16.43 times larger than that of the basic structures) when the filling fraction only increases 1.33 times. The maximum temperature difference for the optimized thermal diodes is 18.31 °C when the heating temperature is 80 °C. By different arrangements of two thermal diodes mounted on chambers' surfaces, the interior temperatures range from 16.06 to 52.34 °C in the same ambient conditions (23.49 °C), indicating the excellent thermal regulation effect of the thermal diodes. These controlled temperature chambers can be applied in greenhouses or cold chain storage devices, more combinations with higher degree of thermal‐threshold tunability offer possibilities in solving complicated thermal management problems and promote the energy utilization efficiency. [ABSTRACT FROM AUTHOR]

В работе рассмотрены подходы к моделированию различных наносистем с использованием с модельных парных межатомных потенциалов. Рассмотрены случаи наночастиц, нанотрубок, молекул фуллерена и зондов атомно-силового микроскопа.

Abstract The main objective of this paper is to understand the impact of the fractal characteristics of fractured reservoirs on their pressure behavior, flow rate decline, and productivity index. The paper proposes a new methodology for developing several analytical models for describing the wellbore pressure distribution and the flow rate decline trend. The proposed models consider including the fractal characteristics such as the mass fractal dimension, conductivity index of anomalous diffusion flow mechanism, fractal-network parameters, fractional-derivative order, and matrix/fracture-interaction index as well as dual-porosity media characteristics such as the storativity and interporosity flow coefficient in the analytical models of the pressure, rate, and productivity index. The study has found that: (1) Some of the fractal characteristics have a significant impact on reservoir performance, while others may not have a significant impact. (2) Fractal reservoirs exhibit better performance than the standard geometry reservoirs of single and dual-porosity media.

In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method. We perform numerical experiments with these algorithms using Zetafast as a benchmark and apply the algorithms for the visualizations of fractal structures associated with the Riemann zeta function.

In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method. We perform numerical experiments with these algorithms using Zetafast as a benchmark and apply the algorithms for the visualizations of fractal structures associated with the Riemann zeta function. [ABSTRACT FROM AUTHOR]

Natural organic matter, including humic substances (HS), comprises complex secondary structures with no defined covalent chemical bonds and stabilized by inter- and intra-molecular interactions, such as hydrogen bonding, Van der Waal’s forces, and pi-pi interactions. The latest view describes HS aggregates as a hydrogel-like structure comprised by a hydrophobic core of aromatic residues surrounded by polar and amphiphilic molecules akin a self-assembled soft material. A different view is based on the classification of this material as either mass or surface fractals. The former is intended as made by the clustering of macromolecules generating dendritic networks, while the latter have been modelled in terms of a solvent-impenetrable core surrounded by a layer of lyophilic material. This study reviews the evolution of the increasingly refined models that appeared in the literature, all capable to describing the physicochemical properties of HS. All the models are critically examined and revisited in terms of their ability to provide key information on the structural organization of HS. Understanding how the molecular association pathway influences aggregation of HS also provides a key acknowledgment of their role in the environment.

The high rate of urbanization in the modern world requires a conscious approach to architectural design. A person needs an environment that fills him with new strength and does not drown out his creative potential with monotonous routine. Due to its natural feature, fractal architecture meets these requirements. The article examines the signs of fractal systems in relation to architecture, highlights the concept - "the principle of fragmentation of a fractal", the term "self-similarity" is broader. In addition, the existing experience of fractal architecture has been analyzed, and the relationship between fractality and the success of the project has been revealed using the example of existing objects. The materials of this article can serve for the further development of the theory of creating fractal architecture.

The aim of the present paper is to construct a set of high order strong matrices for a key-exchange matrix algorithm on an open channel and to create a high-speed one-way matrix function. Fractal structures are synthesized from band matrices. Square matrices are considered over a Galois field of GF (2). Each initial n-th order square matrix is primitive (the degree value is equal to 2n - 1) or its degree value is a Mersenne number 2j - 1, when j < n (except n = 18). [ABSTRACT FROM AUTHOR]

The main types of structures consisting of adjacent and/or intersecting helices 30/11 formed by tetrahedrally coordinated atoms have been investigated. These structures are fundamentally noncrystalline. Nevertheless, they can take form of regularly folded large helices, lattices, a planar layer, rod structures, and different-level approximations to fractal structures. It is shown that such bound-water structures correspond in metric parameters, symmetry, and topology to crystals of biological macromolecules, protein shells of viruses, and biological tissues. In addition, they can store energy. [ABSTRACT FROM AUTHOR]

The paper continues the study of efficient algorithms for the computation of zeta functions over the complex plane. We aim to apply the modifications of algorithms to the investigation of underlying fractal structures associated with the Riemann zeta function. We discuss the computational complexity and numerical aspects of the implemented algorithms based on series with binomial-like coefficients.

In this paper, a new tri-band metamaterial absorber based on crossed sun fractal structure for Radar Cross Section (RCS) reduction is presented. The proposed metamaterial absorber (MMA) exhibits three distinct absorption peaks at 2.2, 5.9 and 6.8 GHz with peak absorption values of 97, 91.6 and 93.3 % respectively. The proposed MMA unit cell is printed on FR-4 substrate with thickness 1.6 mm (0.0117λ0) and compact size 40 mm × 40 mm (0.293 λ0 × 0.293λ0), where λ0 is the free-space wavelength with respect to the lowest resonance frequency. Thanks to the new proposed fractal sun shape with sharp edges, we achieve the highest absorption rate at the lowest resonant frequency in comparison with the other published works. In addition, the simple equivalent circuit model is proposed to analyze and predict the frequency of the absorption phenomena of the proposed design. Radar target is characterized by Radar Cross Section (RCS). The surface currents and electric field distributions have been illustrated to understand the mechanism of the structure. In this paper we simulated and calculated the RCS of Perfect Electric Conductor (PEC) and compared this result by a PEC covered by metamaterial sheet. The proposed absorber structure can be used in different applications such as electro-magnetic protections, military and medical applications. All simulation results are performed using the Computer Simulation Technology (CST) Microwave Studio 2018 software, Advanced Design System (ADS) 2017 software, and Mathworks simulation tool MATLAB ver. 2011. In this paper, a new tri-band metamaterial absorber based on crossed sun fractal structure for Radar Cross Section (RCS) reduction is presented. The proposed metamaterial absorber (MMA) exhibits three distinct absorption peaks at 2.2, 5.9 and 6.8 GHz with peak absorption values of 97, 91.6 and 93.3 % respectively. The proposed MMA unit cell is printed on FR-4 substrate with thickness 1.6 mm (0.0117 λ0) and compact size 40 mm × 40 mm (0.293 λ0 × 0.293 λ0 ), where λ0 is the free-space wavelength with respect to the lowest resonance frequency. Thanks to the new proposed fractal sun shape with sharp edges, we achieve the highest absorption rate at the lowest resonant frequency in comparison with the other published works. In addition, the simple equivalent circuit model is proposed to analyze and predict the frequency of the absorption phenomena of the proposed design. Radar target is characterized by Radar Cross Section (RCS). The surface currents and electric field distributions have been illustrated to understand the mechanism of the structure. In this paper we simulated and calculated the RCS of Perfect Electric Conductor (PEC) and compared this result by a PEC covered by metamaterial sheet. The proposed absorber structure can be used in different applications such as electro-magnetic protections, military and medical applications. All simulation results are performed using the Computer Simulation Technology (CST) Microwave Studio 2018 software, Advanced Design System (ADS) 2017 software, and Mathworks simulation tool MATLAB ver. 2011. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to understand the impact of the fractal characteristics of fractured reservoirs on their pressure behavior, flow rate decline, and productivity index. The paper proposes a new methodology for developing several analytical models for describing the wellbore pressure distribution and the flow rate decline trend. The proposed models consider including the fractal characteristics such as the mass fractal dimension, conductivity index of anomalous diffusion flow mechanism, fractal-network parameters, fractional-derivative order, and matrix/fracture-interaction index as well as dual-porosity media characteristics such as the storativity and interporosity flow coefficient in the analytical models of the pressure, rate, and productivity index. The study has found that: (1) Some of the fractal characteristics have a significant impact on reservoir performance, while others may not have a significant impact. (2) Fractal reservoirs exhibit better performance than the standard geometry reservoirs of single and dual-porosity media. [ABSTRACT FROM AUTHOR]

Ibuprofen was encapsulated into pH-sensitive hybrid nanocomposite using amine-modified bimodal mesopores silica (BMMs) as core and poly(methylacrylic acid) (PMAA) as the shell. The various characterizations showed that PMAA-coated shell played a pH-dependent "open–close" switch, and BMMs as a stored drug carrier. The high drug loading and pH-responsive release performances in vitro could be successfully monitored by SAXS techniques, demonstrating the evolution of mass fractal with surface roughness and structural irregularities. The release mechanism was proposed, showing a "diffusion-controlled" profile in both acidic and alkaline medium. Finally, the pharmacokinetics of released-IBU in mice through intravenous injection was preliminarily explored. The mesoporous hybrid P/NN-BMMs with core-shell structure showed a strong pH- responsible performance for IBU release, their fractal features and pharmacokinetics were elucidated. [ABSTRACT FROM AUTHOR]

Thin-walled structures are used in automotive industry due to their excellent lightweight and crashworthiness properties. This paper proposes a vertex fractal multi-cell hexagonal structure to develop a novel lightweight energy absorber. Experimental analysis and numerical modeling are performed to investigate the crashworthiness of the fractal multi-cell hexagonal structures. The numerical results indicate that fractal configurations and geometrical parameters of the fractal hexagonal structure have significant effect on the crashworthiness. In addition, the multi-objective design optimization is performed to seek the optimal crashworthiness parameters and explore the optimal crashworthiness of the fractal hexagonal structure. The results show that the fractal multi-cell hexagonal structure outperforms non-fractal hexagonal structure. [ABSTRACT FROM AUTHOR]

As there is a great demand of 2D metal networks, especially out of gold for a plethora of applications we show a universal synthetic method via phase boundary gelation which allows the fabrication of networks displaying areas of up to 2 cm2. They are transferred to many different substrates: glass, glassy carbon, silicon, or polymers such as PDMS. In addition to the standardly used web thickness, the networks are parametrized by their fractal dimension. By variation of experimental conditions, we produced web thicknesses between 4.1 nm and 14.7 nm and fractal dimensions in the span of 1.56 to 1.76 which allows to tailor the structures to fit for various applications. Furthermore, the morphology can be tailored by stacking sheets of the networks. For each different metal network, we determined its optical transmission and sheet resistance. The obtained values of up to 97 % transparency and sheet resistances as low as 55.9 Ω/sq highlight the great potential of the obtained materials. [ABSTRACT FROM AUTHOR]

Polymeric nanocomposites containing nanodiamonds are attractive multifunctional materials with a growing range of applications. Since the microstructure of the system determines its properties, it is an important task to establish the features of structure formation of nanodiamonds in the polymer matrix. The structural features of nanocomposites based on polyethylene glycol (PEG) and ultradispersed nanodiamonds (UDNDs) were investigated using the methods of wide-angle and small-angle X-ray scattering. Systems based on nanodiamonds of detonation synthesis and crystalline PEG were prepared by ultrasonic dispersion in melt. The studied UDNDs are found to be polydispersed particles with a narrow size distribution. The average radius of the UDNDs primary particles is 20 nm. It is shown that as the content of nanodiamonds in the system increases, the aggregation processes increase. The structure of such systems is well described within the model with multilevel fractal aggregation. Fractal analysis identified the type of fractal aggregates of each structural level and determined their sizes. Depending on the content of the filler in the system, particles of UDNDs form different types of aggregates. At low filler content, dense mass fractal aggregates and surface aggregates with a smooth surface are formed. At high contents, dense aggregates of surface-fractal type with a rough surface are formed. It is established that aggregates with an average size of 60-75 nm are formed at the first structural level, and aggregates with an average size of 225-240 nm are formed at the second level. [ABSTRACT FROM AUTHOR]

Nanostructured conductive surfaces have been exploited for a variety of applications in photonics and optical sensing due to the broad spectral tunability of the localized surface plasmon resonances and the subsequent electromagnetic field confinement in the vicinity of the structures. Herein, we report on the second-order nonlinear optical properties of dendritic fractal structures with specific geometries that were optimized to yield resonances at both the fundamental and the second-harmonic wavelengths. Using a femtosecond excitation at 800 nm, second-harmonic generation microscopy experiments were conducted on a series of gold fractal dendritic structures with and without center of inversion. The polarized second-harmonic maps reveal the local character of the second-harmonic generation (SHG) emission and even structures with center of inversion show SHG activity in the periphery of the core dendron where non-centrosymmetric features are forming the higher fractal generations. The experiments were correlated using finite-difference time-domain electromagnetic time modelling performed at both the fundamental and second-harmonic wavelengths. [ABSTRACT FROM AUTHOR]

The article is designated to the prospects of earthquakes prediction via monitoring of the accompanying phenomena such as conformation change of aerosols by measuring the mosaic ionization. Based on the synoptic analysis, we propose a predictive model of the recording of electric discharge processes that cause the formation of ball lightings under conditions of volumetric concentration of unlike particles of aerosols and multichannel condition of their interaction. [ABSTRACT FROM AUTHOR]

The mesoporous hybrid silicas (P@BMMs) with core-shell structure were successfully synthesized via seed polymerization method using bimodal mesoporous silica materials (BMMs) as core and dual pH- and temperature-responsive poly(N-isopropylacryl-acrylamide)-co-poly(acrylic acid) (P(NIPAM-co-AA)) copolymer as shell. Meanwhile, the obtained P@BMMs were physicochemically and morphologically characterized via X-ray diffraction, N2 adsorption-desorption isotherms, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared, ultraviolet visible diffused reflection spectrum, small angle X-ray scattering (SAXS), dynamic light scattering, and thermogravimetric analysis techniques. The results indicated that P(NIPAM-co-AA) was successfully coated onto the mesoporous surface of used BMMs, while the uniform mesoporous structure of obtained P@BMMs was still preserved. Using ibuprofen (IBU) as a model drug, the influence of the P(NIPAM-co-AA) shell on the release kinetics of IBU was explored, and its performances elucidated that the P@BMMs nanoparticles presented an apparent thermo/pH-responsive properties, which could be regulated via adjusting mass ratio of AA to NIPAM, and their IBU-release kinetic profiles were favorable to Korsmeyer-Peppas model. Specially, SAXS patterns were employed to evaluate the fractal evolution of P@BMMs along with releasing time, showing the decline tendency for mass fractal value from 2.89 to 2.56 during the release time of 0.25–24 h. [ABSTRACT FROM AUTHOR]

Architecture is characterized by a correction of design approaches that take into account new discoveries. Changing scientific paradigm also influences this process by introducing extra details into the architectural objects workflows. The synergistic paradigm that influences mostly appears in the tendency to create architecture that meets the ideal standards of sustainable design, capable design which is of self-development and self-regulation. A unique feature of the synergistic paradigm that can fundamentally change the approach to design is its relation to the evolutionary process. According to this concept, evolution in its path passes through points of bifuciation – special states of instability – when possible ways of further development are clear and it becomes possible for us to choose and follow one of them. This approach takes into account changing data and corrects decisions during the process. This is especially relevant when designing architectural objects for harsh climate conditions, as additional difficulties may arise in the process of construction and operation, and the unexpectedly arising issues, which may unanticipated arise itself during the usage of the object and can have a disastrous effects on it.

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature’s drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients’ entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

The present paper is devoted to constructing a set of high order strong matrices for an open channel key exchange matrix algorithm and creating a quick one-way matrix function. A high order fractal matrix set consisting of primitive matrices was constructed. The fractal family consisting of matrices and used in the cryptographic algorithm was studied. This issue concerns a global problem. [ABSTRACT FROM AUTHOR]

In this study, Cu and Ag dendrites, as well as Ag dendrite decorated with gold nanoparticles (NPs) are designed for improving the efficiency of plasminic TiO 2 dye sensitized solar cells (DSSCs). The main challenge in plasmonic DSSCs is adjusting the plasmonic peak at suitable position. Herein, it is shown that how an engineered structure can enhance the efficiency of DSSC by an intense plasmonic effect in extended wavelength range. This is addressed by engineering plasmonic peak of noble metal through controlling their morphology. Moreover, the importance of the protection of the morphology-controlled nobel metal additive by Polyvinylpyrrolidone (PVP) polymer against corrosive electrolyte is shown. PVP-capped Ag dendrites, PVP-capped Cu dendrites and PVP-capped Ag dendrites decorated by gold NPs are prepared and are applied in dye sensitized solar cells. [ABSTRACT FROM AUTHOR]

Fractal nature of porous silicon (Si), where porous nanowires (NWs) of Si has been observed inside the porous membrane matrix, has been revisited this time by metal assisted chemical etching (MACE) also known as metal induced etching or MIE. While carrying out MACE of Si wafer with silver nanoparticles (AgNPs) as the etching metal, it is observed that non vertical chemical etching take place. An SEM study reveals that the usual well aligned SiNWs, approximately 50 nm thick, consists of nanometer wide pores in themselves. The nanometer sized pores in turn results in Si NSs of a few nanometers in these thick looking SiNWs and are capable of showing quantum confinement effects. The SEM and TEM studies have been consolidated to model the growth mechanism for the observed fractal porous Si. [ABSTRACT FROM AUTHOR]

Self-assembled hierarchical CuO nanostructures with fractal structures were prepared by a mild method and exhibited excellent lithium storage properties, certain of which even demonstrated a high reversible capacity of 827 mAh g −1 at a rate of 0.1 C. An interesting phenomenon was observed that the electrochemical performance varies along with the structure complexity, and the products with higher surface factal dimensions exhibited larger capability and better cyclability. Structural and electrochemical analysis methods were used to explore the lithiation kinetics of the samples and the reasons for the outstanding electrochemical performances related to the complexities of hierarchical nanostructures and the irregularities of surface and mass distribution. [ABSTRACT FROM AUTHOR]