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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 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.

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.

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.

The problems of designing supply networks and traffic flow routing and scheduling are the subject of intensive research. The problems encompass the management of the supply of a variety of goods using multi-modal transportation. This research also takes into account the various constraints related to route topology, the parameters of the available fleet of vehicles, order values, delivery due dates, etc. Assuming that the structure of a supply network, constrained by a transport network topology that determines its behavior, we develop a declarative model which would enable the analysis of the relationships between the structure of a supply network and its potential behavior resulting in a set of desired delivery-flows. The problem in question can be reduced to determining sufficient conditions that ensure smooth flow in a transport network with a fractal structure. The proposed approach, which assumes a recursive, fractal network structure, enables the assessment of alternative delivery routes and associated schedules in polynomial time. An illustrative example showing the quantitative and qualitative relationships between the morphological characteristics of the investigated supply networks and the functional parameters of the assumed delivery-flows is provided.

We have studied the Stefan problem with Caputo fractional order time derivatives. The difference scheme is built. The algorithm and the program for a numerical solution of the Stefan problem with fractional differentiation operator are created. For the given entry conditions and freezing ground parameters we have obtained the space-time temperature dependences for different values of parameter α. The functional dependences of the interface motion for the generalized Stefan conditions depending on the value of α are estimated. Finally we have found that the freezing process is slowed down during the transition to fractional derivatives.

In this paper, we prove the identity dim H ( F ) = d · dim H ( α − 1 ( F ) ) , where dim H denotes Hausdorff dimension, F ⊆ R d , and α : [ 0 , 1 ] → [ 0 , 1 ] d is a function whose constructive definition is addressed from the viewpoint of the powerful concept of a fractal structure. Such a result stands particularly from some other results stated in a more general setting. Thus, Hausdorff dimension of higher dimensional subsets can be calculated from Hausdorff dimension of 1-dimensional subsets of [ 0 , 1 ] . As a consequence, Hausdorff dimension becomes available to deal with the effective calculation of the fractal dimension in applications by applying a procedure contributed by the authors in previous works. It is also worth pointing out that our results generalize both Skubalska-Rafajłowicz and García-Mora-Redtwitz theorems.

This paper presents a novel hybrid medical stent device. This hybrid stent device formed by fractal mesh structures provides a flow-diverting effect and stent-assisted coil embolization. Flow-diverter stents decrease blood flow into an aneurysm to prevent its rupture. In general, the mesh size of a flow-diverter stent needs to be small enough to prevent blood flow into the aneurysm. Conventional flow-diverter stents are not available for stent-assisted coil embolization, which is an effective method for aneurysm occlusion, because the mesh size is too small to insert a micro-catheter for coil embolization. The proposed hybrid stent device is capable of stent-assisted coil embolization while simultaneously providing a flow-diverting effect. The fractal stent device is composed of mesh structures with fine and rough mesh areas. The rough mesh area can be used to insert a micro-catheter for stent-assisted coil embolization. Flow-diverting effects of two fractal stent designs were composed to three commercially available stent designs. Flow-diverting effects were analyzed using computational fluid dynamics (CFD) analysis and particle image velocimetry (PIV) experiment. Based on the CFD and PIV results, the fractal stent devices reduce the flow velocity inside an aneurism just as much as the commercially available flow-diverting stents while allowing stent-assisted coil embolization. [ABSTRACT FROM AUTHOR]