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Antenna miniaturization, multiband operation and wider operational bandwidth are vital to achieve optimal design for modern wireless communication devices. Using fractal geometries is recognized as one of the most promising solutions to attain these characteristics. The purpose of this paper is to present a unique structure of patch antenna using hybrid fractal technique to enhance the performance characteristics for various wireless applications and to achieve better miniaturization.

In this paper, the authors propose a novel hybrid fractal antenna by combining Koch and Minkowski (K-M) fractal geometries. A microstrip patch antenna (MPA) operating at 1.8 GHz is incorporated with a novel K-M hybrid fractal geometry. The proposed fractal antenna is designed and simulated in CST Microwave studio and compared with existing Koch fractal geometry. The prototype for the third iteration of the K-M fractal antenna is then fabricated on FR-4 substrate and tested through vector network analyzer for operating band/voltage standing wave ratio.

The third iteration of the proposed K-M fractal geometry results in achieving a 20% size reduction as compared to an ordinary MPA for the same resonant frequency with impedance bandwidth of 16.25 MHz and a directional gain of 6.48 dB, respectively. The operating frequency of MPA also lowers down to 1.44 GHz.

Further testing for the radiation patterns in an anechoic chamber shows good agreement to those of simulated results.

Digital design technologies play a significant role in assisting the designer through conceptual architectural design. Computer supported design systems can generate various images at the early design phase and can contribute to seeking alternative architectural forms. Currently, different design approaches are being employed in the formation of architectural products. Examples of architecture that produce unusual forms are often encountered within unique conceptual approaches. The development of new design examples is supported by the digital production of forms, and three-dimensional models through varying geometric approaches. In this study, a design approach that uses computer aided architectural design to produce architectural forms will be suggested. This approach utilizes principles existing in the unique fractal dimension of elements based on a vocabulary relevant to a specific architectural language. By relying on the fractal dimension and features of an existing architectural pattern, this generative design approach supports creativity in the production of new forms. The proposed approach is evaluated as a creative tool in architectural design. The subject of architecture; buildings, spaces, surroundings, symbols of that particular society are also the elements of a meta-language which creates a fractal geometry based relation. It is possible to analyse this relation through a fractal geometry-based principle. In short, a fractal geometrical generative method is suggested. Also, recently-surfaced discussions about "Chaos Theory" and its effects on the design process via "Chaos and Self - Similarity" are studied. The significance of these different phenomena and disciplines upon architectural design are also studied for developing a possible creative tool.

The purpose of this paper is to investigate the influence of the resolution with which interfaces of fractal geometry are represented, on the contact area and consequently on the contact interfacial stresses. The study is based on a numerical approach. The paper focuses on the differences between the cases of elastic and inelastic materials having as primary parameter the resolution of the interface.

A multi‐resolution parametric analysis is performed for fractal interfaces dividing a plane structure into two parts. On these interfaces, unilateral contact conditions are assumed to hold. The computer‐generated surfaces adopted here are self‐affine curves, characterized by a precise value of the resolution δ of the fractal set. Different contact simulations are studied by applying a horizontal displacement s on the upper part of the structure. For every value of s, a solution is taken in terms of normal forces and displacements at the interface. The procedure is repeated for different values of the resolution δ. At each scale, a classical Euclidean problem is solved by using finite element models. In the limit of the finest resolution, fractal behaviour is achieved.

The paper leads to a number of interesting conclusions. In the case of linear elastic analysis, the contact area and, consequently, the contact interfacial stresses depend strongly on the resolution of the fractal interface. Contrary, in the case of inelastic analysis, this dependence is verified only for the lower resolution values. As the resolution becomes higher, the contact area tends to become independent from the resolution.

The originality of the paper lies on the results and the corresponding conclusions obtained for the case of inelastic material behaviour, while the results for the case of elastic analysis verify the findings of other researchers.

Application of electromagnetic band gap (EBG) i.e. electromagnetic band gap technique and its use in the design of microstrip antenna and MIC i.e. microwave integrated circuits is becoming more attractive. This paper aims to propose a new type of EBG fractal square patch microstrip multi band fractal antenna structures that are designed and developed. Their performance parameters with and without EBG structures are investigated and minutely compared with respect to the resonance frequency, return loss, a gain of the antenna and voltage standing wave ratio.

The fractal antenna geometries are designed from the fundamental square patch and then EBG structures are introduced. The antenna geometry is optimized using IE3D simulation tool and fabricated on low cost glass epoxy FR4, with 1.6 mm height and dielectric materials constant of 4.4. The prototype is examined by means of the vector network analyzer and antenna patterns are tested on the anechoic chamber.

Combining the square fractal patch antenna with an application of EBG techniques, the gain of microstrip antenna has been risen up and attained good return loss as compared to the antennas without EBG structures. The designs exhibit multi-frequency band characteristics extending in between 1.70 and 7.40 GHz. Also, a decrease in antenna size of 34.84 and 59.02 per cent for the first and second iteration, respectively, is achieved for the antenna second and third without EBG. The experimental results agree with that of simulated values. The presented microstrip antenna finds uses in industrial, scientific and medical (ISM) band, Wi-Fi and C band. This antenna can also be used for satellite and radio detection and range devices for communication purposes.

A new type of EBG fractal square patch microstrip antenna structures are designed, developed and compared with and without EBG. Because of the application of EBG techniques, the gain of microstrip antenna has been risen up and attained good return loss as compared to the antennas without EBG structures. The designs exhibit multi-frequency band characteristics extending in between 1.70 and 7.40 GHz, which are useful for Wi-Fi, ISM and C band wireless communication.

This paper aims to study the relationship between normal contact stiffness and contact load. It purpose a new calculation model of the normal contact stiffness of joint surfaces by considering the elastic–plastic critical deformation change of asperities contact.

The paper described the surface topography of joint surfaces based on fractal geometry, and fractal parameters and of fractal function derived from measurement data. According to the plastic–elastic contact theory, the contact deformation characteristic of asperities was analyzed; the critical deformation estimation model was presented, which expressed critical deformation as the function of fractal parameters and contact deformation; the contact stiffness calculation model of single asperity was brought forward by considering critical deformation change.

The paper combined the surface topography description function, analyzed the asperity contact states by considering the critical deformation change, and calculated normal contact stiffness based on fractal theory and contact deformation analysis. The comparison between theoretical contact stiffness and experimental data indicated that the theoretical normal contact stiffness agreed with the experimental data, and the estimation model for normal contact stiffness was appropriate.

Owing to the possibility of plastic deformation during the loading process, the experimental curve between the contact stiffness and the contact load is nonlinear, resulting in an error between the experimental results and the theoretical calculation results.

The paper established the relationship between critical deformation and fractal surface topography by constructing asperity distribution function. The paper proposed a new normal contact stiffness calculation model of joint surfaces by considering the variation of critical deformation in contact process.

Compact and wideband antennas are the need of modern wireless systems that preferably work with compact, low-profile and easy-to-install devices that provide a wider coverage of operating frequencies. The purpose of this paper is to propose a novel compact and ultrawideband (UWB) microstrip patch antenna intended for high frequency wireless applications.

A square microstrip patch antenna was initially modeled on finite element method-based electromagnetic simulation tool high frequency structure simulator. It was then loaded with a rectangular slit and Koch snowflake-shaped fractal notches for bandwidth enhancement. The fabricated prototype was tested by using vector network analyzer from Agilent Technologies, N5247A, Santa Clara, California, United States (US).

The designed Koch fractal patch antenna is highly compact with dimensions of 10 × 10 mm only and possesses UWB characteristics with multiple resonances in the operating band. The −10 dB measured impedance bandwidth was observed to be approximately 13.65 GHz in the frequency range (23.20–36.85 GHz).

Owing to its simple and compact structure, positive and substantial gain values, high radiation efficiency and stable radiation patterns throughout the frequency band of interest, the proposed antenna is a suitable candidate for high frequency wireless applications in the K (18–27 GHz) and Ka (26.5–40 GHz) microwave bands.

Wolverine hairs with superior heat transfer properties have been used as fur ruffs for extreme cold-weather clothing. In order to understand the exclusive mechanism of wolverine surviving in the cold areas of circumpolar, the purpose of this paper is to establish a one-dimensional fractional heat transfer equation to reveal the hidden mechanism for the hairs, and also calculate the fractal dimension of the wolverine hair using the box counting method to verify the proposed theory. The observed results (from the proposed model) found to be in good agreement with the box counting method. This model can explain the phenomenon which offers the theoretical foundation for the design of extreme cold weather clothing.

The authors calculated the fractal dimension of the wolverine hair using the box counting method to verify the proposed theory. The observed results (from the proposed model) found to be in good agreement with the box counting method.

The box counting method proves that the theoretical model is applicable.

The authors propose the first heat transfer model for the wolverine hair.

The objective of the present work is to find an alternative approach for gearbox condition monitoring using wear particle characterization incorporated with image vision systems.

It is a quite well‐known phenomenon that wear generates whenever two metallic bodies have contact with each; other hence the present work tries to investigate the effect of improper lubrication in the gearbox due to wear particle generation between gear wheels. Since the identification of wear for machine condition monitoring needs much expertise knowledge and is time‐consuming using the conventional process, fractal mathematics with image morphological analysis has been utilized to overcome this situation in the present work.

The type of wear has been found for the present method by utilizing the lubricant used in the system ferrographically and a great deal of image processing has been done to characterize the type of particle so that the proper maintenance strategy can be undertaken.

Wear particle characterization is a quite common method in maintenance engineering, especially when fault diagnosis of any equipment is concerned. In the present work, the CCD acquisition of the images has been done for different particles, but one analysis amongst them has been shown in this paper. Among all other methodologies, the new technique of fractal mathematics has been used in the present work to minimize the imaging hazards and to make the system more user‐friendly.

Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus.

This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given.

Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations.

Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.

The purpose of this paper is to consider and compare different ways of using numbers to value aspects of nature-beyond-the-human through case analysis of ecological and natural capital accounting practices in the UK that create standardised numerical-economic values for beyond-human natures. In addition, to contrast underlying ontological and ethical assumptions of these arithmetical approaches in ecological accounting with those associated with Pythagorean nature-numbering practices and fractal geometry. In doing so, to draw out distinctions between arithmetical and geometrical ontologies of nature and their relevance for “valuing nature”.

Close reading and review of policy texts and associated calculations in: UK natural capital accounts for “opening stock” inventories in 2007 and 2014; and in the experimental implementation of biodiversity offsetting (BDO) in land-use planning in England. Tracking the iterative calculations of biodiversity offset requirements in a specific planning case. Conceptual review, drawing on and contrasting different numbering practices being applied so as to generate numerical-economic values for natures-beyond-the-human.

In the cases of ecological accounting practices analysed here, the natures thus numbered are valued and “accounted for” using arithmetical methodologies that create commensurability and facilitate appropriation of the values so created. Notions of non-monetary value, and associated practices, are marginalised. Instead of creating standardisation and clarity, however, the accounting practices considered here for natural capital accounts and BDO create nature-signalling numbers that are struggled over and contested.

This is the first critical engagement with the specific policy texts and case applications considered here, and, the authors believe, the first attempt to contrast arithmetical and geometrical numbering practices in their application to the understanding and valuing of natures-beyond-the-human.