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Mathematical models of heat and moisture transfer for anisotropic materials, based on the use of the fractional calculus of integro-differentiation, are considered because such two-factor fractal models have not been proposed in the literature so far. The numerical implementation of mathematical models for determining changes in heat exchange and moisture exchange is based on the adaptation of the fractal neural network method, grounded in the physics of processes. A fractal physics-informed neural network architecture with a decoupled structure is proposed, based on loss functions informed by the physical process under study. Fractional differential formulas are applied to the expressions of non-integer operators, and finite difference schemes are developed for all components of the loss functions. A step-by-step method for network training is proposed. An algorithm for the implementation of the fractal physics-informed neural network is developed. The efficiency of the new method is substantiated by comparing the obtained numerical results with numerical approximation by finite differences and experimental data for particular cases. [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.

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]

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]

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]

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.

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]

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 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.

Mathematical models of heat and moisture transfer for anisotropic materials, based on the use of the fractional calculus of integro-differentiation, are considered because such two-factor fractal models have not been proposed in the literature so far. The numerical implementation of mathematical models for determining changes in heat exchange and moisture exchange is based on the adaptation of the fractal neural network method, grounded in the physics of processes. A fractal physics-informed neural network architecture with a decoupled structure is proposed, based on loss functions informed by the physical process under study. Fractional differential formulas are applied to the expressions of non-integer operators, and finite difference schemes are developed for all components of the loss functions. A step-by-step method for network training is proposed. An algorithm for the implementation of the fractal physics-informed neural network is developed. The efficiency of the new method is substantiated by comparing the obtained numerical results with numerical approximation by finite differences and experimental data for particular cases.

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]

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]

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]

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.

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.

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]

• This study proposes a group tree modeling approach to examine the modal properties of fractal sympodial trees analytically. • Modal properties of sympodial trees are characterized by the emerging and the self-similar modes. • The self-similar modes prevent the trunk and lower order branches from vibration. • Recursive closed-form formulas are presented to estimate the modal properties of trees. • A sympodial tree with infinite tree order and infinite branching number resembles to a branchless tree. This study examines the intricate relationship between the hierarchical architecture of fractal trees and their dynamic properties, namely modal frequencies and mode shapes. It focuses on idealized sympodial trees under small, linear elastic lateral vibrations. This study proposes a group tree modeling approach that condenses the branches into simple structures, reducing the complexity of the model as appropriate. With the aid of a renormalization technique, the analysis proves that the sympodial tree is characterized by two families of vibration modes, i.e., the "emerging" and the "self-similar" modes. It further shows that the sympodial tree inherits all modes from the previous tree order (i.e., fractal level). Crucially, these inherited modes are self-similar, and beneficial in mitigating the vibration of the trunk by localizing the vibration of the tree at higher order branches. The study derives recursive closed-form solutions for both self-similar modal frequencies and mode shapes. Further, the analysis of sympodial trees with infinite tree order shows that their modal frequencies converge to stable values as the tree order increases. Accordingly, the study proposes analytical formulas to estimate these frequency limits from the fractal parameters of the sympodial trees. Results reveal that the natural frequency of a sympodial tree with infinite tree order and infinite branching number approaches asymptotically to that of a branchless tree. The proposed approach is then validated with numerical simulations and compared with independent studies. These findings are promising towards new bio-mimicking design concepts for civil engineering structures with improved dynamic behaviour. [ABSTRACT FROM AUTHOR]

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.

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 frequency-selective surface (FSS) optimization method combining a curve-fitting technique and an improved bacterial foraging optimization (IBFO) algorithm is proposed. In the method, novel Koch curve-like FSS and Minkowski fractal islands FSS were designed with a desired resonance center frequency and bandwidth. The bacteria foraging optimization (BFO) algorithm is improved to enhance the performance of the FSS. A curve-fitting technique is provided to allow an intuitive and numerical analysis of the correspondence between the FSS structural parameters and the frequency response. The curve-fitting results are used to evaluate the fitness function of the IBFO algorithm, replacing multiple repeated calls to the electromagnetic simulation software with the curve-fitting equation and thus speeding up the design process. IBFO is compared with the classical BFO algorithm, the hybrid BFO-particle swarm optimization algorithm (BSO), and the artificial bee colony algorithm (ABC) to demonstrate its superior performance. The designed fractal FSS is fabricated and tested to verify the experimental results. The simulation and measurement results show that the proposed FSS has a fractional bandwidth of 91.7 % in the frequency range of 3.41–9.19 GHz (S, C, and X-bands). In addition, the structure is very thin, with only 0.025 λ and 0.067 λ at the lowest and highest frequencies, respectively. The proposed fractal FSS has shown stable performance for both TE and TM polarizations at oblique incidence angles up to 45°. according to simulations and measurements. [ABSTRACT FROM AUTHOR]

Recent studies have shown that it is possible to construct a probability measure from a fractal structure defined on a space. On the other hand, a theory on cumulative distribution functions from an order on a separable linearly ordered topological space has been developed. In this paper, we show how to define a linear order on a space with a fractal structure, so that these two theories can be used interchangeably in both topological contexts. [ABSTRACT FROM AUTHOR]

[Display omitted] • Hydrophilic/hydrophobic dual metal–organic frameworks Janus network is prepared on bio-inspired leaf vein (LV) structure for fog harvesting. • The integrated strategy by mimicking cactus needles, Janus wettability and bionic LV network in fog collection can be regulated by the multi-cooperation theory. • The Janus LV devices yields a high fog collection efficiency and intelligent interfacial materials. The leaf vein (LV) structure is an evolutionarily optimized quasi-fractal network responsible for efficient capture and transport of water with minimum energy consumption. For the first time, a bio-inspired dual-metal organic framework (MOF) functionalized LV network was proposed for water collection. Two MOFs with distinct wettabilities and microstructures are in-situ grown on opposite side of a metallic LV network, yielding a Janus LV (J-LV) network. The integrated strategy by mimicking cactus needles, Janus structures and bionic LV network in water harvesting can be regulated by the multi-cooperation theory in the processes of droplet caption, transport and collection. As such, the fog collection efficiency of J-LV devices can reach 1.23 ± 0.07 g cm-2h−1, which is a 292.9 % increase compared to that of the bare LV. Moreover, the J-LV has excellent interfacial floatability, showing capability of not only carrying objects weighing 149.5 times its own weight while keeping afloat, but also attaching firmly to the air–water interface under harsh airflow. We demonstrate that such Janus quasi-fractal LVs networks by in-situ dual-MOF growth will inspire new insight for designing highly efficient fog water collectors and intelligent Janus interface materials. [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 λg3, while the electrical length of the antenna with the meander line is only 0.445 × 0.445 × 0.036 λg3, 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.

Life, as the most mysterious and unique phenomenon on the Earth, has confused humans since time began. Why does life exist as it does and how has the diversity of life developed? We, herein, propose a new theory of energetic life, based on existing energy laws, to interpret the evolution and categorization of physical life forms, from microscopic life to macroscopic life. According to this theory, life is a process in which a mass of energy flows and diffuses in the environment. This energy takes DNA as the three-dimensional blueprint, protein as the basic material unit, and fractal network structure as the framework, so as to solidify from energy and form a semi-solid structure. DNA base pairs simultaneously have dual properties as protein pointers and spatial coordinates, and the multi-level self-similar fractal helix structure ultimately guides the formation of different levels of the fractal structure of organisms. This theory organically links the life phenomenon from microscopic to macroscopic levels, from gene, cell and organ to organism, and it provides a new perspective on life, which may inspire biologists to better reveal the mystery of life. [ABSTRACT FROM AUTHOR]

The fractal structure of porous carbon materials (PCMs) obtained by hydrothermal carbonization of plant raw materials in the temperature range of 600 ÷ 1100 °С is investigated using the low-temperature porometry method. It is set that materials with a developed microporous structure and a surface fractal dimension of 2.58 are formed at carbonization temperatures of 600 ÷ 800 °C. At higher carbonization temperatures, the value of the fractal dimension of the surface decreases to 2.17, which indicates the formation of an almost smooth surface due to the intensive removal of carbon atoms from the surface layers of the material particles, a decrease in the number of micropores with their transition to mesopores, the combination of small carbon clusters in larger and the formation of microparticles of non-porous carbon material. [ABSTRACT FROM AUTHOR]

This work addresses the long-standing debate over fractal models of packing structure in metallic glasses (MGs). Through detailed fractal and percolation analyses of MG structures, derived from simulations spanning a range of compositions and quenching rates, we conclude that there is no fractal atomic-level structure associated with the packing of all atoms or solute-centered clusters. The results are in contradiction with conclusions derived from previous studies based on analyses of shifts in radial distribution function and structure factor peaks associated with volume changes induced by pressure and compositional variations. The interpretation of such shifts is shown to be challenged by the heterogeneous nature of MG structure and deformation at the atomic scale. Moreover, our analysis in the present work illustrates clearly the percolation theory applied to MGs, for example, the percolation threshold and characteristics of percolation clusters formed by subsets of atoms, which can have important consequences for structure-property relationships in these amorphous materials.

We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of ϕ 6 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. [ABSTRACT FROM AUTHOR]

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.

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.

Fractal structures appear very often in open Hamiltonian systems, and can be identified in the deposition of chaotic magnetic field line on the plates of a tokamak divertor. Indeed, tokamaks with divertors are used to control the magnetic confinement of plasmas, such that the field lines created by electric currents have escape channels, through which plasma particles can be diverted out of the tokamak wall and redirected to divertor plates. In this work, we use a symplectic map to investigate the deposition patterns on the plates of a divertor. We show that the pattern of magnetic footprints on divertor plates (deposition patterns) underlying the chaotic orbits involves a number of fractal structures related to the existence of a nonattractive invariant chaotic set. In order to investigate the fractal characteristic of magnetic footprints, we analyze quantitatively the degree of stability of the fractal structure by calculating the entropy of the basin. These numerical analyses indicate that the fractal pattern on the divertor plates depends sensibly on the magnetic field structure. We show qualitative evidences of the Wada property. [ABSTRACT FROM AUTHOR]

The presence of gas content in medium- and high-rank coal poses a threat to safety production. Safe gas extraction is based on a correct understanding of the pore structure of coal. This work investigates the pore structure characteristics of medium- and high-rank coal and evaluates their fractal structure. The coal samples were collected from Huainan Coalfield and Qinshui Coalfield, and divided into four types, according to the difference in surface bright characteristics. Through adopting low-temperature liquid nitrogen adsorption and desorption, and applying Kelvin equation, we obtain the main pore structure types and main pore size distribution characteristics of various coal briquettes. Electron microscope scanning structure and scientific analysis were used for special adsorption and desorption curves and hysteresis to find the dynamic reason. According to the different adsorption mechanism and Frenkel–Halsey–Hill-based model, with P / P 0 = 0.4 as the dividing point of fractal dimension analysis, the pore structure of coal samples is classified into five grades. The fractal evaluation results are consistent with the results of curve analysis and pore size analysis. [ABSTRACT FROM AUTHOR]

The article explores the effect of citric acid as a pore-forming agent on the structure, morphology and electroconductive properties of porous carbon materials (PCMs) obtained from carbon precursor (saccharose) using the methods of small-angle X-ray scattering, low-temperature porometry and impedance spectroscopy. It was found that the volumetric fractal structure is formed in the samples, and the fractal dimension Dv decreases from 2.15 to 1.91 with the addition of citric acid due to surface loosening. It was set that the use of 20 wt.% of citric acid causes the most effective modification of the porous structure of the material, i.e. an increase in specific surface area of 1.35 times, total pore volume of 1.14 times and a significant development of micro- and mesoporosity. It is shown that the use of citric acid as a pore-forming agent leads to an increase in the specific electrical conductivity of PCMs almost 5 times.

Purpose – This paper aims at developing a behavioral agent-based model for interacting financial markets. Additionally, the effect of imposing Tobin taxes on market dynamics is explored. Design/methodology/approach – The agent-based approach is followed to capture the highly complex, dynamic nature of financial markets. The model represents the interaction between two different financial markets located in two countries. The artificial markets are populated with heterogeneous, boundedly rational agents. There are two types of agents populating the markets; market makers and traders. Each time step, traders decide on which market to participate in and which trading strategy to follow. Traders can follow technical trading strategy, fundamental trading strategy or abstain from trading. The time-varying weight of each trading strategy depends on the current and past performance of this strategy. However, technical traders are loss-averse, where losses are perceived twice the equivalent gains. Market makers settle asset prices according to the net submitted orders. Findings – The proposed framework can replicate important stylized facts observed empirically such as bubbles and crashes, excess volatility, clustered volatility, power-law tails, persistent autocorrelation in absolute returns and fractal structure. Practical implications – Artificial models linking micro to macro behavior facilitate exploring the effect of different fiscal and monetary policies. The results of imposing Tobin taxes indicate that a small levy may raise government revenues without causing market distortion or instability. Originality/value – This paper proposes a novel approach to explore the effect of loss aversion on the decision-making process in interacting financial markets framework.

In this paper, a novel antenna design comprising planar monopole with fractal slot defected ground structure for circularly polarized radiation is proposed. In the proposed antenna geometry, circular polarization radiation characteristics are obtained by defecting the ground structure with fractal slot. In this approach, CP characteristics are achieved by intensifying the level of cross polar component of the linearly polarized antenna upto a certain level by means of fractal slot inserted in ground structure. Antenna prototype with third order iterative tuning fork shaped fractal slot is fabricated and tested for the validation of simulated results. Parametric studies are also performed to exemplify the process of CP radiations. From the simulated and measured results, it is confirmed that the proposed antenna can be proficiently produced 10 dB return loss bandwidth (BW) nearly ≈37.4%, while 3-dB AR bandwidth (ARBW) is 15.5%, respectively. The proposed antenna can be a credible applicant for LTE Band 13/cellular/PCS /ASW/WiMAX and Wi-Fi applications.

Progressively, more dredged sediments are being reused for engineering projects. For example, the Marker Wadden is a new wetland constructed in lake Markermeer, the Netherlands, with dredged cohesive sediments originating from the bed of the lake. Such dredged sediments are often dominated by cohesive sediment particles with varying amounts of sand and organic matter. In addition, during and after the construction process, the material consolidates and is often compressed from a very loose state into a significantly denser condition. To assess the mechanical behavior of this material, the compressibility of the Markermeer dredged sediment samples with various sand and organic matter contents was analyzed with incremental loading oedometer tests, whereas the undrained shear strength was studied using the fall cone test. The behavior was theoretically analyzed assuming a fractal structure of the sediment and applying power law constitutive equations for effective stress, hydraulic conductivity, and undrained shear strength. These constitutive equations, usually used at low initial sediment densities, worked well at the relatively high initial densities studied and proved to be a useful tool to identify the transition fines content TFC. The constitutive equations were put in context with indicators traditionally used in soil mechanics. Samples, each with an identical composition of the fines fraction (particles< 63 μm), but with a sand content varying from 9 to 40%, showed the same compressibility and undrained shear strength behavior when considering the sand a filler material. For a natural sand content of 70%, the behavior was dominated by sand. The organic matter oxidation was observed to drastically decrease the compressibility and the shear strength, and even to decrease the amount of sand needed to exhibit sand-dominated behavior, showing the importance of the reactivity or state of organic matter on the TFC.

A frequency-selective surface (FSS) optimization method combining a curve-fitting technique and an improved bacterial foraging optimization (IBFO) algorithm is proposed. In the method, novel Koch curve-like FSS and Minkowski fractal islands FSS were designed with a desired resonance center frequency and bandwidth. The bacteria foraging optimization (BFO) algorithm is improved to enhance the performance of the FSS. A curve-fitting technique is provided to allow an intuitive and numerical analysis of the correspondence between the FSS structural parameters and the frequency response. The curve-fitting results are used to evaluate the fitness function of the IBFO algorithm, replacing multiple repeated calls to the electromagnetic simulation software with the curve-fitting equation and thus speeding up the design process. IBFO is compared with the classical BFO algorithm, the hybrid BFO-particle swarm optimization algorithm (BSO), and the artificial bee colony algorithm (ABC) to demonstrate its superior performance. The designed fractal FSS is fabricated and tested to verify the experimental results. The simulation and measurement results show that the proposed FSS has a fractional bandwidth of 91.7% in the frequency range of 3.41–9.19 GHz (S, C, and X-bands). In addition, the structure is very thin, with only 0.025λ and 0.067λ at the lowest and highest frequencies, respectively. The proposed fractal FSS has shown stable performance for both TE and TM polarizations at oblique incidence angles up to 45°. according to simulations and measurements.

Although the term “genius loci” has been known and used since ancient civilizations, it was considered almost unimportant in a technically industrialized and competitive world. However, the pursuit of a more dignified life for the human communities has again revealed its undeniable importance as an inner cohesion force, applied in partial territorial-social structures. In an integrating world, it may be a useful tool to transform historically created hierarchical structures into more humanly functional fractal structures. This possibility is documented in the study by regional examples from Slovakia and the Czech Republic.

In this study, we report the emergence of two-dimensional (2D) branching fractal structures (BFS) in the nanoconfinement between the active and the support layer of a thin-film-composite polyamide (TFC-PA) nanofiltration membrane. These BFS are crystal dendrites of NaCl formed when salts are either added to the piperazine solution during the interfacial polymerization process or introduced to the nascently formed TFC-PA membrane before drying. The NaCl dosing concentration and the curing temperature have an impact on the size of the BFS but not on the fractal dimension (~1.76). The BFS can be removed from the TFC-PA membranes by simply dissolving the crystal dendrites in deionized water, and the resulting TFC-PA membranes have substantially higher water fluxes (three-to fourfold) without compromised solute rejection. The flux enhancement is believed to be attributable to the distributed reduction in physical binding between the PA active layer and the support layer, caused by the exertion of crystallization pressure when the BFS formed. This reduced physical binding leads to an increase in the effective area for water transport, which, in turn, results in higher water flux. The BFS-templating method, which includes the interesting characteristics of 2D crystal dendrites, represents a facile, low-cost, and highly practical method of enhancing the performance of the TFC-PA nanofiltration membrane without having to alter the existing infrastructure of membrane fabrication. [ABSTRACT FROM AUTHOR]

Abstract This study performs natural sand-based synthesis using the sonochemical route for preparing Zn-doped magnetite nanoparticles. The nanoparticles were dispersed in water as a carrier liquid to form Zn-doped magnetite aqueous ferrofluids. Structural data analysis indicated that the Zn-doped magnetite nanoparticles formed a nanosized spinel structure. With an increase in the Zn content, the lattice parameters of the Zn-doped magnetite nanoparticles tended to increase because Zn2+ has a larger ionic radius than those of Fe3+ and Fe2+. The existence of Zn–O and Fe–O functional groups in tetrahedral and octahedral sites were observed in the wavenumber range of 400–700 cm–1. The primary particles of the Zn-doped magnetite ferrofluids tended to construct chain-like structures with fractal dimensions of 1.2–1.9. The gas-like compression (GMC) plays as a better model than the Langevin theory to fit the saturation magnetization of the ferrofluids. The ferrofluids exhibited a superparamagnetic character, with their magnetization was contributed by aggregation. The Zn-doped magnetite ferrofluids exhibited excellent antibacterial activity against gram-positive and negative bacteria. It is suggested that the presence of the negatively charged surface and the nanoparticle size may contribute to the high antibacterial activity of Zn-doped magnetite ferrofluids and making them potentially suitable for advanced biomedical.

Recent studies have shown that it is possible to construct a probability measure from a fractal structure defined on a space. On the other hand, a theory on cumulative distribution functions from an order on a separable linearly ordered topological space has been developed. In this paper, we show how to define a linear order on a space with a fractal structure, so that these two theories can be used interchangeably in both topological contexts.

Life, as the most mysterious and unique phenomenon on the Earth, has confused humans since time began. Why does life exist as it does and how has the diversity of life developed? We, herein, propose a new theory of energetic life, based on existing energy laws, to interpret the evolution and categorization of physical life forms, from microscopic life to macroscopic life. According to this theory, life is a process in which a mass of energy flows and diffuses in the environment. This energy takes DNA as the three-dimensional blueprint, protein as the basic material unit, and fractal network structure as the framework, so as to solidify from energy and form a semi-solid structure. DNA base pairs simultaneously have dual properties as protein pointers and spatial coordinates, and the multi-level self-similar fractal helix structure ultimately guides the formation of different levels of the fractal structure of organisms. This theory organically links the life phenomenon from microscopic to macroscopic levels, from gene, cell and organ to organism, and it provides a new perspective on life, which may inspire biologists to better reveal the mystery of life.

• The Thermal conductivity of nano-grained graphite was investigated with MD method. • Both the equilibrium and non-equilibrium molecular dynamics methods were adopted. • Nano-grained graphite models with various grain sizes and arrangements were designed. • The atomic fractal structures of different fractal dimensions and stages were built. • Obtained results of MD simulations were verified with theoretical-model predictions. The thermal conductivity of isotropic graphite is a crucial parameter in mechanical and nuclear engineering. However, obtaining its value accurately is still difficult, especially under irradiation and high ambient temperature conditions. In this study, the nano-grained graphite models with different grain sizes and arrangements are designed, and corresponding thermal conductivity is calculated with equilibrium and non-equilibrium molecular dynamics methods. The results show that the thermal conductivity of nano-grained graphite varies between 3 to 5 W/(m·K) and decreases exponentially with the increase of the number of nanograins, while the arrangement of nanograins has almost no effect on the thermal conductivity. In addition, the effect of porosity of nano-polycrystalline graphite is analyzed by constructing fractal porous structures with different fractal dimensions and stages, of which the pore characteristics are determined with the initial zero-stage structure. The thermal conductivity of porous graphite increases with increasing fractal dimension and decreasing fractal porosity and the outcomes of molecular dynamics simulations are verified with the theoretical model results. [ABSTRACT FROM AUTHOR]