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Compression behavior of nanoparticle powder is still unclear, while it could largely affect its applications in additive manufacturing. Considering the fractal structure of aggregates in nanoparticle powder, from the van der Waal's state equation, the relation between porosity and compression pressure of nanoparticle powder was modeled theoretically, i.e. (P + c)(φ -a)=(1-a)c, here P is pressure, φ is porosity, a and c are parameters defined in main text. The model could capture the compression behavior of nanoparticle powders well. Under the same compression pressure, smaller nanoparticles will lead to larger porosity and thus lower thermal conductivity of nanoparticle packed beds, due to the easier aggregate of smaller nanoparticles. The compression behavior and the thermal conductivity of nanoparticle powders or packed beds are expected to supply information for powder spreading and sintering treatment respectively in additive manufacturing. [ABSTRACT FROM AUTHOR]

This study examines the structure of the universe during its high-energy era. In this context, we examine Barrow’s proposal of entropy, which forecasts a fractal configuration for the geometric properties of the black hole’s horizon. By applying the principles of thermodynamics, we get the equation of motion using the Barrow entropic consideration. A quasi-de Sitter phase, in which fractal and non-fractal states may coexist, is determined. This is an uncertainty state (coexistence of fractal and non-fractal states), and so a deformation for de Sitter spacetime, which contains a high-energy scale in the framework of the COBE normalization. With the kinetic energy term of the inflation field, we remove this ambiguity owing to the field oscillations. However, the oscillatory behavior of the inflation field continues and causes the universe to enter a new phase state. At this point, in which the inflation field oscillations are over, we obtain a solution that provides the universe transition to the radiation and dust phases. [ABSTRACT FROM AUTHOR]

Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment. [ABSTRACT FROM AUTHOR]

Abstract Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment.

We offer a detailed description of our previously published new concept of the evolution of the biosphere as an integral system of its states over time, united by development trends. The structure of the biosphere is considered as a hierarchical fractal system, and the elementary unit of the biosphere is an ecosystem. The fractal structure of the biosphere corresponds to the emergent principle: each lower level is an element of a more complex system and has its own properties. The proposed concept of biosphere evolution is based on the general categories of dialectics: states and interstates, continuity and discreteness, reproducibility and uniqueness. The evolutionary history of the biosphere is a metameric picture of changing states and interstates. The most important feature of the biosphere organization in space–time is a complex system of continua. The development of an integral biospheric system occurs in a time continuum: in the biosphere, the differences between the early and subsequent states are quite significant and obvious. Moreover, these differences are associated with fundamental complications, development, which is, in fact, evolution. The states of the biosphere in certain periods are linked by trends that form an evolutionary system. Continuing states, when the system remains self-identical for a long period, are replaced by new states through interstates. Based on the principle of actualism, the problems of the biosphere’s future and evolutionary trends of the biosphere under anthropogenic impact are considered.

We offer a detailed description of our previously published new concept of the evolution of the biosphere as an integral system of its states over time, united by development trends. The structure of the biosphere is considered as a hierarchical fractal system, and the elementary unit of the biosphere is an ecosystem. The fractal structure of the biosphere corresponds to the emergent principle: each lower level is an element of a more complex system and has its own properties. The proposed concept of biosphere evolution is based on the general categories of dialectics: states and interstates, continuity and discreteness, reproducibility and uniqueness. The evolutionary history of the biosphere is a metameric picture of changing states and interstates. The most important feature of the biosphere organization in space–time is a complex system of continua. The development of an integral biospheric system occurs in a time continuum: in the biosphere, the differences between the early and subsequent states are quite significant and obvious. Moreover, these differences are associated with fundamental complications, development, which is, in fact, evolution. The states of the biosphere in certain periods are linked by trends that form an evolutionary system. Continuing states, when the system remains self-identical for a long period, are replaced by new states through interstates. Based on the principle of actualism, the problems of the biosphere's future and evolutionary trends of the biosphere under anthropogenic impact are considered. [ABSTRACT FROM AUTHOR]

In this study, a two-port network-based microwave sensor for liquid characterization is presented. The suggested sensor is built as a miniature microwave resonator using the third iteration of Hilbert's fractal architecture. The suggested structure is used with the T-resonator to raise the sensor quality factor. The suggested sensor is printed on a FR4 substrate and has a footprint of 40 × 60 × 1.6 mm 3 . Analytically, a theoretical investigation is made to clarify how the suggested sensor might function. The suggested sensor is created and put to the test in an experiment. Later, two pans to contain the urine Sample Under Test (SUT) are printed on the sensor. Before loading the SUT, it is discovered that the suggested structure's frequency resonance is 0.46 GHz. An 18 MHz frequency shift is added to the initial resonance after the pans are printed. They monitor the S-parameters in terms of S12 regarding the change in water content in the urine samples, allowing for the sensing component to be completed. As a result, 10 different samples with varying urine percentages are added to the suggested sensor to evaluate its ability to detect the presence of urine. Finally, it is discovered that the suggested process' measurements and corresponding simulated outcomes agreed quite well. [ABSTRACT FROM AUTHOR]

We argue the merits of having a simplified method to simulate equatorial plasma bubble (EPB) plume structures for practical usage. The capability to realistically model EPB plume structures in simulations would be advantageous when assessing the severity of ionospheric threats. Such advantages would arise because a realistic model of EPB plume structures could allow nonstationary scintillation signals to be simulated. Although EPB plume structures can be modeled via first-principle physics-based models, these models tend to be computationally demanding. High-performance computing facilities might be able to offer some remedy, but serious handicaps would remain for those without access to such advanced facilities. We investigated multiple options that utilize the diffusion-limited aggregation (DLA) fractal process to generate bifurcating structures that resemble typical EPB plume structures. We combined the DLA algorithm with the International Reference Ionosphere model to simulate EPBs in three dimensions. Initial tests of this modeling approach indicate promising results. [ABSTRACT FROM AUTHOR]

[Objectives]In order to solve the problem of poor ventilation areas of grain pile, the effect of the fractal structure on the ventilation uniformity in the ventilation process was explored. [Methods]A porous medium(sand)packing wrapped non-uniform section ventilation pipeline ventilation system was proposed. The relevant parameters of fractal structure were obtained by the minimum flow resistance optimization method of rectangular unit configuration. Combining the fractal branch pipelines designed according to the optimization parameters with the non-uniform section ventilation pipelines, a porous medium packing wrapped non-uniform section pipelines and fractal structure ventilation system was proposed. The grain type was selected as rice, and the porous medium material of the packing zone was selected as sand. The ventilation and cooling simulation of the two ventilation systems was carried out. The study simulated the cooling process of the granary with an initial temperature of 300 K and cold inlet air with a constant temperature of 293 K. The ventilation time lasted for 7.5 days. The ventilation velocity field, temperature field of the two ventilation systems were compared and verified. [Results]In the non-fractal ventilation system, most of the poor ventilation areas were in the packing zone, and the ventilation intensity of the grain pile was guaranteed. However, the strong ventilation and strong cooling areas were concentrated near and above the ventilation pipelines, and the cooling uniformity was not good. In the fractal ventilation system, the poor ventilation areas were suppressed under the ventilation pipelines and the fractal branch pipelines. From the velocity field, the ventilation uniformity and the cooling uniformity in the grain pile were better, and the maximum temperature difference was reduced from 2.8 K to 1.3 K. From the ventilation uniformity index, the ventilation uniformity of the fractal ventilation system was good, and exponent of uniformity was 0.919. [Conclusions]The sand packing zone could help the grain pile avoid most of the poor ventilation areas. The fractal structure could effectively enhance the ventilation intensity in the weak ventilation areas of the velocity field, and the temperature field had excellent effect in improving the uniformity of cooling. [ABSTRACT FROM AUTHOR]

Polymer‐based magnetic particles have been widely used for the separation of biological samples including nucleic acids, proteins, virus, and cells. Existing magnetic particles are almost prepared by coating polymers on magnetic nanoparticles (NPs). However, this strategy usually encounters the problem of poor magnetic NPs loading capacity. Here, a series of nanofractal magnetic particles (nanoFMPs) synthesized by a strategy of mediator monomer regulated emulsion interfacial polymerization is presented, which allows effective magnetic NPs loading and show efficient nucleic acid separation performance. The mediator monomers facilitate the dispersion of magnetic NPs in internal phase to achieve higher loading, and the hydrophilic monomers use electrostatic interactions to form surface nanofractal structures with functional groups. Compared with magnetic particles without nanofractal structure, nanoFMPs exhibit a higher nucleic acid extraction capability. This strategy offers an effective and versatile way for the synthesis of nanoFMPs toward efficient separation in various fields from clinical diagnosis to food safety and environmental monitoring. [ABSTRACT FROM AUTHOR]

The study of the fractal properties of the surface of Nd100 – xFex alloys in a wide range of concentrations х (х = 20–90) was carried out in the framework of the fractal thermodynamics model. To this end, we performed an analysis of scanning electron microscopy images of the surfaces of a series of Nd100 – xFex alloys synthesized by induction melting. A high degree of proximity of the surface structure of all the studied samples, both before and after etching, to fractals is shown. The values of the parameter δ characterizing the relative deviation of the studied samples from the fractal are in the range of 0.017–0.029. Three-dimensional diagrams of the fractal parameters Sf, Tf, Ef, and x and two-dimensional diagrams of the same parameters Sf, Tf, Ef, and x reflecting the nature of the state of the surfaces of Nd100 – xFex alloy samples before and after etching are constructed. For all investigated alloy samples, the values of the parameters of the fractal equations of state are calculated. The correlation of the maximum value of the coercive force Hc = 4.8 kE with the values of fractal entropy Sf = 39.86, fractal temperature Tf = 529, and fractal dimension D = 2.6530 of the Nd100 – xFex alloys at x = 20 has been established. [ABSTRACT FROM AUTHOR]

A fractal structure featuring symmetric/asymmetric airfoil fins is embedded within the smooth channels of the printed circuit heat exchanger (PCHE), significantly enhancing its heat transfer performance. In this study, a horizontally installed two-layer channel configuration is examined, with hot CO2 flowing through the upper channel and cold CO2 through the lower channel. Two distinct airfoil fin designs, namely NACA 0021 symmetric and NACA 4822 asymmetric, are tested for their channel reinforcement effect. The numerical analysis reveals that channels equipped with these fins exhibit substantially improved heat transfer compared to smooth channels. Notably, the comprehensive evaluation index for the asymmetric airfoil fin channel is enhanced by a factor ranging from 1.05 to 3.76. Moreover, despite a modest increase in pressure drop, indicated by a dimensionless friction factor of 0.67–1.31, the heat transfer performance remains superior. Crucially, optimal heat transfer does not rely solely on high fluid flow rates but instead demands an apt flow matching between the hot and cold fluid channels.

We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of ϕ6 theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and show that the coupling between two oscillation modes modulate the emergence of the missing bounce windows. By numerical calculation, we present that the two bounce resonance corresponds to the lower eigenfrequency of the toy model.

The distribution of velocity and temperature field inside the granary can be used to evaluate ventilation quality. A well-ventilated system with uniform air-flow and cooling can effectively prevent moisture accumulation. To address the issue of poor uniformity in ventilation and cooling, this research introduces two new ventilation systems: the non-fractal ventilation system and the fractal ventilation system. The fractal structure was designed based on optimized parameters obtained from rectangular elements with minimum flow resistance. Numerical simulation methods were employed to verify the effectiveness of these ventilation systems. A comparative analysis was conducted, examining the velocity field, temperature field, and velocity uniformity of the two systems. The results demonstrated that the presence of a sand packing zone helped the grain pile zone avoid most of the areas with poor ventilation. The discontinuous pores at the interface between the sand packing zone and the grain pile zone significantly increased flow resistance, effectively reducing the velocity of high speed ventilation into the grain pile zone and decreasing the permeability of the grain pile zone towards the poorly ventilated areas of the sand pile zone. Furthermore, the fractal structure greatly enhanced ventilation intensity in areas with poor ventilation in the velocity field, while also improving the uniformity of cooling in the temperature field. This research presents an innovative solution for ventilation in room-type warehouses, offering a new option for effective and efficient ventilation. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optically transparent dual-band metamaterial absorber (MMA) that uses Ag nanowire screen-printed fractal structures. The proposed MMA exhibits near-perfect absorption in the C- and K-bands. This dual-band absorption property is achieved through two inductive–capacitive (L-C) resonances located at 6.45 and 21.14 GHz, which are generated by the second-order fractal structures. We analyzed the microwave absorbing mechanisms through the distributions of the surface current and electromagnetic field on the top and bottom layers. The MMA demonstrates an optical transmittance of 63.1% at a wavelength of 550 nm. This high optical transmittance is attained by screen printing transparent Ag nanowire ink onto a transparent PET substrate. Since screen printing is a simple and low-cost fabrication method, the proposed MMA offers the advantages of being low cost while having the properties of optical transparency and effective dual-band absorption. Consequently, it holds great potential for the radar stealth application of C- and K-bands in that it can be attached to the windows of stealth aircraft due to its optical transparency and dual-band near-perfect absorption property. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain some variable separation solitary solutions of (2 + 1)-dimensional nonlinear long water wave (LWW) equation through symbolic computation. By applying Riccati equation mapping method, the localized dromion excitations are constructed and different number of M × N multi-dromions are described by selecting appropriate functions for the LWW equations, which provide a model of the interaction between two waves propagation consequently, the solition solutions are obtained in different forms of dynamical structures. Moreover, the collision phenomena between two multidromions are explored he fractal structure was also investigated. The results have rich physical structures that are helpful to explain the nonlinear solitary phenomena in nonlinear physics. [ABSTRACT FROM AUTHOR]

Spotted hyaenas live in unusually large social groups for a carnivore. Since, all else equal, the ‘infertility trap’ (a negative relationship between fertility and the number of females in a group) limits social group sizes to ~5 reproductive females in mammals, hyaena must, like other very social species, have found a way to mitigate the stresses involved in order to do so. From a comparative analysis of data from 19 well‐studied Crocuta crocuta populations, I show (1) that the distribution of hyaena clan sizes is multimodal, with a fractal scaling ratio close to 3 and a base unit of 12–15 individuals (3–5 reproductive females), (2) that fertility is a negative function of number of females in the group and (3) that there is a trade‐off between the benefits of having more males in the group and the costs incurred by having more females. Although females do buffer themselves against the infertility trap by forming matrilineal alliances (thereby creating a primate‐like multilevel structure), males seem to play an important role, such that, in areas with a low density of males, clan sizes are much smaller. [ABSTRACT FROM AUTHOR]

In this work we start developing a Riemann-type integration theory on spaces which are equipped with a fractal structure. These topological structures have a recursive nature, which allows us to guarantee a good approximation to the true value of a certain integral with respect to some measure defined on the Borel σ -algebra of the space. We give the notion of Darboux sums and lower and upper Riemann integrals of a bounded function when given a measure and a fractal structure. Furthermore, we give the notion of a Riemann-integrable function in this context and prove that each μ -measurable function is Riemann-integrable with respect to μ. Moreover, if μ is the Lebesgue measure, then the Lebesgue integral on a bounded set of R n meets the Riemann integral with respect to the Lebesgue measure in the context of measures and fractal structures. Finally, we give some examples showing that we can calculate improper integrals and integrals on fractal sets. [ABSTRACT FROM AUTHOR]

Purpose: A new mechanical metamaterial with a periodic fractal honeycomb structure was designed and optimized based on the vibration and noise reduction demand in engineering applications. Methods: The dynamic stiffness matrix of the structure was derived based on the spectral element method, and the frequency response curves were plotted. The feasibility and correctness of the band gap results calculated by the spectral element method were also confirmed by comparison with the finite element method. Results: Based on the finite element method, the energy band structure and vibration transmission characteristics of different order fractal structures are analyzed and calculated, and the effect of a structural fractal on the vibration band gap of different order structures is investigated. The influence of these factors on the band gap is explored by changing the structural fractal ratio and the internal concave angle when designing the optimized structure. Conclusions: The feasibility and correctness of the spectral element method are verified by comparing the calculation results of the finite element and spectral element methods. By comparing the band gaps of fractal structures of different orders, it is found that the band gaps generated by the second-order structures are lower frequency and wider frequency, which are more compatible with the current applications in engineering. By varying the fractal ratio and the internal concave angle of the structure, it is found that the larger the value of the fractal ratio, the lower the frequency at which the band gap is generated. At the same time, the increase of the internal concave angle shifts the band gap of the fractal structure toward the high-frequency range. By optimizing the design, the structural band gap is gradually shifted to the position of low-frequency broadband, and the vibration and noise reduction performance is improved. [ABSTRACT FROM AUTHOR]

The dialectics of evolution is that the development of various systems, complication is determined by several principles, which themselves are similar to emergent systems based on opposite but dialectically complementary categories and concepts. A new concept of evolution of the biosphere as an integral system of its successive states united by development trends is proposed. The structure of the biosphere is considered as a fractal system with the ecosystem as its elementary unit. The next fractal levels are biogeomes and biospheromerons. The fractal structure corresponds to the principle of emergence. The proposed concept of biosphere evolution is based on general naturalistic principles and categories of dialectics, such as states and interstates, continuity and discreteness, reproducibility and uniqueness, the hypothesis of information channels or trends, the concept of biosphere organisation in a specific evolutionary space-time. In general, the evolutionary history of the biosphere is a metameric picture of changing states and interstates. A complex system of continuums is the most important feature of the biosphere’s organisation in space-time. Continuity of the first kind can be observed when there is a continuum of indistinguishability within a continuing state: during a long geological time, there were no cardinal changes in the structure of biosphere elements and connections between them. At the same time, the development of an integral biosphere system occurs in a continuum of the second kind: given the continuity of life, the differences between the early and subsequent states are very significant and obvious in the biosphere. Moreover, these differences are associated with complication, development, which is, in fact, evolution. The states of the biosphere in certain periods are connected by trends, which form an evolutionary system. Continuing states, when the system remains self-identical for a long period, are replaced by new states through interstates. Thus, a specific type of continuum, the metameric continuum, is formed. The taxonomic, ecomorphic, symbiotic, and ecosystem trends are identified and considered as the main ones in the evolution of the biosphere. The Vernadsky–Margalef hypothesis of the origin of life and biosphere in the form of protoecosystems is considered and supported.

In the 1970s, it was proved that a bounded linearly convex domain with smooth boundary in is homeomorphic to an open ball. If the boundary of a bounded linearly convex domain in is allowed not to be smooth, then the domain may be of a different topological type. The projection of the complex plane onto the Hartogs diagram in with symmetry plane has a simple geometric shape only for : in that case, this is a circular cone with vertex in the plane . This fact allows one to construct linearly convex Hartogs domains in with symmetry plane whose projections onto the Hartogs diagram have a fractal structure. [ABSTRACT FROM AUTHOR]

Nonintegrable dynamical systems have complex structures in their phase space. Due to the axisymmetry of the system, motion of a test charged particle in a dipole magnetic field can be reduced to a two-degree-of-freedom (2-DoF) nonintegrable Hamiltonian system (Störmer, Radium (Paris) 4(1):2–5, 1907; Dragt, Rev Geophys, https://doi.org/10.1029/RG003i002p00255, 1965). We carried out a systematic study of orbits of charged particles with an azimuthal initial velocity in a dipole field via calculation of their Lyapunov characteristic exponents (LCEs) and escape times for a dimensionless energy, respectively, less and greater than 1/32, above which most particles will escape from the magnetic dipole to infinity. Meridian plane periodic orbits symmetric with respect to the equatorial plane of the magnetic dipole are then identified. We found that (1) symmetric periodic orbits can be classified into several classes based on their number of crossing points on the equatorial plane; (2) the initial conditions of these classes locate on closed loops or closed curves going through the origin; (3) most isolated regions of stable quasi-periodic orbits are associated asymmetric stable periodic orbits; (4) classes of asymmetric periodic orbits either go through the origin or terminate at flat equatorial plane orbits with the other end approaching centers of spiral structures; (5) there are apparent self-similarities in the above features with the decrease of energy. These results can be used to guide the search for stable orbits that may have applications in broad physical contexts. [ABSTRACT FROM AUTHOR]

A sinuous antenna is a frequency-independent antenna known for its wide bandwidth and consistent gain, which makes it valuable in broadband applications such as ultrawideband (UWB) radar and ground-penetrating radar (GPR). However, sinuous antennas tend to be rather large. Consequently, numerous studies have explored miniaturization methods, with the gap-loading method emerging as a prominent approach. Unfortunately, it is still difficult to achieve broad bandwidths for conventional miniaturized sinuous antennas. In this paper, we use a novel approach incorporating a meander shape into the sinuous curve and employing gap loading with meandering. This innovative technique results in the development of a fractal-structured two-arm sinuous antenna characterized by an ultra-compact size and significantly expanded bandwidth. Adding a meander line in the outermost part maximizes the capacitance, thereby enhancing the gap-loading effect and minimizing the overall size of the sinuous antenna. In addition, the introduction of an inner meander line increases the inductance, contributing to a further expansion of the antenna's bandwidth. For example, the electrical length of the antenna without the meander line is 0.552 × 0.552 × 0.052 λ g 3 , while the electrical length of the antenna with the meander line is only 0.445 × 0.445 × 0.036   λ g 3 , i.e., 19.4% smaller. The antenna lacking the outermost meander line exhibits a 10 dB impedance bandwidth, spanning from 0.74 to 10.53 GHz. In contrast, the antenna featuring the outermost meander line has a 10 dB impedance bandwidth, extending from 0.51 to 10.72 GHz, which results in a remarkable enhancement in the fractional bandwidth (by 8.1%). Hence, the proposed antenna design is a good candidate for broadband applications that require miniaturization. [ABSTRACT FROM AUTHOR]

This paper systematically classifies and summarizes the current state of research on the enhancement of heat transfer in microchannels with bionic fractal structure, including fractal structures such as leaf veins, tree branches, lung trachea, spider webs and other biomimetic microchannels. The fractal topology microchannels are also discussed with theoretical models and experimental numerical verification, which shows their advantages by comparing with conventional microchannels. Finally, the existing challenges and future directions of fractal structured microchannel are analyzed in depth and prospected, respectively. This study can provide new research ideas for the development of heat transfer process strengthening and provide the corresponding theoretical basis and scientific guidance for industrial application. [ABSTRACT FROM AUTHOR]

In order to obtain the local structural solutions of nonlinear integrable systems, a (3 + 1)-dimensional nonlinear integrable equation is studied by using the multi-linear variable separation method, and the soliton, dromion, breather and instanton solutions containing arbitrary functions are obtained. Then, the abundant local excitations for the proposed equations are constructed by appropriately setting arbitrary function forms, and the evolution characteristics of system's dromion solutions with time are investigated. In addition, the fractal structure of the separable solution of the system was described. The results show that the proposed method can obtain some special solutions and this method has been extended in different ways so as to enroll more low-dimensional functions in the solution. [ABSTRACT FROM AUTHOR]

In order to explore the electromagnetic transmission performance of frequency selective fabrics (FSFs) with fractal units, six samples of Y-shaped fractal parameters with different sizes were prepared by computer embroidery technology, and tested using anechoic chamber test method. The effects of unit type, polarization mode, incident angle and unit size parameters on the transmission performance of different samples were respectively analyzed in depth. The results show that for the aperture type and patch type FSFs, the incident angle has a certain influence. When the incident angle of the two groups of samples is 0°, the resonance peak is the largest. When the incident angle increases to 45°, there are two resonance peaks of different amplitudes in the range of 4 GHz ∼ 20 GHz. The size and spacing of the unit pattern have both visible effects on the transmission coefficient, but the former has a greater impact on the transmission coefficient. There is a certain tension and contraction between the base fabrics during the preparation of the flexible FSFs, which are controlled to make the sample size more accurate. In addition, in order to reduce the calculation time and improve the design efficiency, two kinds of patch type and aperture type with the same size were simulated and optimized using HFSS algorithm. Comparison of measured and simulated results verify the effectiveness of simulation design. [ABSTRACT FROM AUTHOR]

The fractal structure was applied to the fin optimization of latent heat storage (LHS) technology based on the fractal principle. By numerical simulation, the performances of LHS units with fractal tree-shaped fins were compared with those with traditional plate fins, and the effects of fin structure parameters based on the fractal principle on heat storage and release performances were studied. The results show that the heat storage performance and heat release performance of LHS units with fractal tree-shaped fins are clearly improved, and the optimal fractal structure parameters allow the LHS units to achieve optimal performance. A nonlinear surface fitting function method was used to obtain the functional relation between the branching angle and length index and the heat storage time of the LHS unit. In fractal tree-shaped fins, the optimal length index is 1.141, the optimal width ratio is 1, and the branching angle is 73.55°. In comparison to the LHS unit with traditional plate fins, the LHS unit with the optimum fractal structure parameters has a 35.85% faster melting rate and a 63.39% faster heat release rate. The least entransy dissipation, least thermal resistance and best reversibility are all characteristics of the LHS unit with the optimal fractal structure parameters. [ABSTRACT FROM AUTHOR]

Like all raw materials of plant origin, persimmon fruits are considered a material rich in carbohydrates. This subtropical plant grows almost throughout the entire territory of the Republic of Azerbaijan. Despite the widespread distribution of this plant in the republic, very few types of products are produced from it. The main reason why persimmon fruits are not used effectively from a production point of view is that they have astringent properties. Since fruit carbohydrates play an important role in eliminating the tart taste of persimmons, the study of the carbohydrate complex was considered as a basic condition. After fractionation of carbohydrates with a water-alcohol mixture, certain stresses arise in the filter residue, which consists of cellulose-lignin. These stresses are analyzed using tensors. It has been established that the size of the filter pores is about 0.005÷0.05 microns, and the volume of these pores is 0.062÷0.195 cm³/g. The clearance coefficient averaged 19.97 %. It is known that the outer layer of a plant cell consists of cellulose and other structural compounds. These substances determine the porosity of the material. The mass fraction of the final product of the fractional residue, more precisely cellulose, averaged 0.63 %. The use of the resulting filter membrane in the clarification of fruit juices has shown its usefulness in industry. It has been established that the selectivity of these membranes for various amino acids is 5÷18 %, and for minerals 1÷30 %. The lipid resistance of the membranes was high. It should be noted that cellulose has the ability to restore its structure and at the last stage acts only as a filter membrane. This explains the usefulness of the celluloselignin mixture as a membrane material. [ABSTRACT FROM AUTHOR]

In this study, a two-port network-based microwave sensor for liquid characterization is presented. The suggested sensor is built as a miniature microwave resonator using the third iteration of Hilbert’s fractal architecture. The suggested structure is used with the T-resonator to raise the sensor quality factor. The suggested sensor is printed on a FR4 substrate and has a footprint of 40×60×1.6mm3. Analytically, a theoretical investigation is made to clarify how the suggested sensor might function. The suggested sensor is created and put to the test in an experiment. Later, two pans to contain the urine Sample Under Test (SUT) are printed on the sensor. Before loading the SUT, it is discovered that the suggested structure’s frequency resonance is 0.46 GHz. An 18 MHz frequency shift is added to the initial resonance after the pans are printed. They monitor the S-parameters in terms of S12 regarding the change in water content in the urine samples, allowing for the sensing component to be completed. As a result, 10 different samples with varying urine percentages are added to the suggested sensor to evaluate its ability to detect the presence of urine. Finally, it is discovered that the suggested process’ measurements and corresponding simulated outcomes agreed quite well.

The model of (2 + 1)-dimensional breaking soliton equation is proposed, and the novel soliton solutions are derived by using the variable separation and extended mapping approach of Riccati equation and then, the propagation dynamics of the solutions which include multi-dromions, ring breather, fusion solitons and other multi-solitons are also constructed. Furthermore, the rich local excitations and fractal structures are investigated. The simulation results verify the proposed scheme. It can get more abundant local excitation structures than the (1 + 1)-dimensional nonlinear systems and it has potential values for certain applications in optical field. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optically transparent dual-band metamaterial absorber (MMA) that uses Ag nanowire screen-printed fractal structures. The proposed MMA exhibits near-perfect absorption in the C- and K-bands. This dual-band absorption property is achieved through two inductive–capacitive (L-C) resonances located at 6.45 and 21.14 GHz, which are generated by the second-order fractal structures. We analyzed the microwave absorbing mechanisms through the distributions of the surface current and electromagnetic field on the top and bottom layers. The MMA demonstrates an optical transmittance of 63.1% at a wavelength of 550 nm. This high optical transmittance is attained by screen printing transparent Ag nanowire ink onto a transparent PET substrate. Since screen printing is a simple and low-cost fabrication method, the proposed MMA offers the advantages of being low cost while having the properties of optical transparency and effective dual-band absorption. Consequently, it holds great potential for the radar stealth application of C- and K-bands in that it can be attached to the windows of stealth aircraft due to its optical transparency and dual-band near-perfect absorption property.

In this work we start developing a Riemann-type integration theory on spaces which are equipped with a fractal structure. These topological structures have a recursive nature, which allows us to guarantee a good approximation to the true value of a certain integral with respect to some measure defined on the Borel σ-algebra of the space. We give the notion of Darboux sums and lower and upper Riemann integrals of a bounded function when given a measure and a fractal structure. Furthermore, we give the notion of a Riemann-integrable function in this context and prove that each μ-measurable function is Riemann-integrable with respect to μ. Moreover, if μ is the Lebesgue measure, then the Lebesgue integral on a bounded set of Rn meets the Riemann integral with respect to the Lebesgue measure in the context of measures and fractal structures. Finally, we give some examples showing that we can calculate improper integrals and integrals on fractal sets.

A (1 + 1)-dimensional Korteweg-de Vries (KdV) equation is studied. Using the extended Tanh-function method, the analytical soliton solutions are obtained by symbolic calculation, and the localized coherent structures containing the compacton, the peakon, periodic multi-solitons and fractal soliton structures are constructed. Through the analysis of various images, the properties of soliton solutions excited by different local structures are discussed and the fractal structure of soliton solutions are further discussed.

Fractal structure investigations of materials have a recent tradition in physics with applications to the natural sciences and technology. A new approach of fractal geometry in solids is analyzed, which allows the accurate evaluation of thermodynamic quantities for various values of fractional dimensions. Based on a fractal concept, the modified Einstein–Debye model and its application of thermodynamics are presented, which contribute to the evaluation of thermal properties as well as many materials. The reliable modified analytical expressions of the energy, heat capacities, entropy, enthalpy, and Gibbs free energy are established on the basis of modified Einstein–Debye approximation. This shows the perspective of the utilizing the fractal, describing quantities and parameters that analyze properties of nature. [ABSTRACT FROM AUTHOR]

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In this article, a miniaturized patch antenna using fractal DGS and SRR DMS for GSM1800, C band and WiMAX applications is presented and investigated. Antenna miniaturization and multiband are accomplished by employing a fractal loop on the DGS structure and a split ring resonator slot in the patch. The proposed radiator has a hexagonal shape that operates at 6.8 GHz. To achieve downsize of 20.58, 38.22, 55.14 and 72.75% an antenna is designed using DGS and DMS structures for quad-band application appearing at 1.85, 3.05, 4.2, and 5.4 GHz. Simulated and tested data are investigated. The prototype antenna has adequate advantages, with a simple structure, compact size, multiband, and uniform radiation patterns. [ABSTRACT FROM AUTHOR]

В работе рассматривается численно-аналитический метод эффективного поиска приближенного решения видоизменной задачи Коши для дифференциального уравнения параболического типа с дробной производной по времени в смысле Римана-Лиувилля, естественно возникающей при изучении нелинейных особенностей процессов влагосолепереноса в средах с фрактальной структурой порового пространства.

In conventional ceramic–metal matrix composites, with the addition of the ceramic phase, although it can significantly improve the performance of the material in one aspect, it tends to weaken some of the excellent properties of the metal matrix as well. In order to meet the high toughness and high strength requirements of composites for practical production applications, researchers have searched for possible reinforcing structures from nature. They found that fractal structures, which are widely found in nature, have the potential to improve the mechanical properties of materials. However, it is often not feasible to manufacture these geometric structures using conventional processes. In this study, alumina ceramic fractal structures were prepared by 3D printing technology, and aluminum composites containing fractal ceramic structures were fabricated by spark plasma sintering technology. We have studied the effect of the fractal structure of alumina ceramics on the mechanical properties of composites. The compression strength of samples was measured by a universal testing machine and the torsional properties of samples were measured by a torsional modulus meter. The results show that a fractal structure improves the compressive strength of aluminum/alumina ceramic composites by 10.97% and the torsional properties by 17.45%. The results of the study will provide a new method for improving the mechanical properties of materials. [ABSTRACT FROM AUTHOR]

Studies on the erosion products of tungsten plasma-facing components (films, surfaces, and dust) for thermonuclear fusion reactors by spectroscopic methods are considered and compared with those of carbon deposits. The latter includes: carbon–deuterium CDx (x ~ 0.5) smooth films deposited at the vacuum chamber during the erosion of the graphite limiters in the T-10 tokamak and mixed CHx-Me films (Me = W, Fe, etc.) formed by irradiating a tungsten target with an intense H-plasma flux in a QSPA-T plasma accelerator. It is shown that the formerly developed technique for studying CDx films with 15 methods, including spectroscopic methods, such as XPS, TDS, EPR, Raman, and FT-IR, is universal and can be supplemented by a number of new methods for tungsten materials, including in situ analysis of the MAPP type using XPS, SEM, TEM, and probe methods, and nuclear reaction method. In addition, the analysis of the fractality of the CDx films using SAXS + WAXS is compared with the analysis of the fractal structures formed on tungsten and carbon surfaces under the action of high-intensity plasma fluxes. A comparative analysis of spectroscopic studies on carbon and tungsten deposits makes it possible to identify the problems of the safe operation of thermonuclear fusion reactors. [ABSTRACT FROM AUTHOR]