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This study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces.

The research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality.

The study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions.

This study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models.

The purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.

The paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.

The study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.

The research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.

The study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

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.

The objective of this work is to analyze the necessary conditions for chaotic behavior with fractional order and fractal dimension values of the fractal-fractional operator.

The numerical technique based on the fractal-fractional derivative is implemented over the fractional model and analyzes the condition at the distinct values of fractional order and fractal dimension.

The obtained numerical solution from the numerical technique is analyzed at distinct fractional order and fractal dimension values, and it has been figured out that the behavior of the solution either chaotic or non-chaotic agrees with the condition.

The necessary condition is associated with the fractional order only. So, our work not only studies the condition with fractional order but also examines the model by simultaneously adjusting fractal dimension values. It is found that the model still has chaotic or non-chaotic behavior at certain fractal dimension values and fractional order values corresponding to the condition.

Micro-texture is processed on the surface to reduce the friction of the contact surface, and its application is more and more extensive. The purpose of this paper is to create a texture function model to study the influence of surface parameters on the accuracy of the simulated surface so that it can more accurately reflect the characteristics of the real micro-textured surface.

The microstructure function model of rough surfaces is established based on fractal geometry and polar coordinate theory. The offset angle θ is introduced into the fractal geometry function to make the surface asperity normal perpendicular to the tangent of the surface. The 2D and 3D contour surfaces of the surface groove texture are analyzed by MATLAB simulation. The effects of fractal parameters (D and G) and texture parameter h on the curvature of the surface micro-texture model were studied.

This paper more accurately characterizes the textured 3D curved surface, especially the surface curvature. The scale coefficient G significantly affects curvature, and the influence of fractal dimension D and texture parameters on curvature can be ignored.

The micro-texture model of the rough surface was successfully established, and the range of fractal parameters was determined. It provides a new method for the study of surface micro-texture tribology.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2023-0298/

Multiple jobholding (MJH) is assumed to be a growing phenomenon due to working life changes. This study presents new knowledge on the MJH career paths, from the perspectives of both employers and employees.

The qualitative interview study was focused on retail trade and restaurant and food service industries in Finland, where MJH is a quite common work arrangement compared to other European countries. The data were analyzed with the concepts of the chaos theory of careers and with an abductive thematic content analysis.

According to the results, several events and intertwined factors may lead individual careers gradually to MJH. Changing personal and family situations and leisure time needs attracted the careers towards MJH. MJH was not only a financial necessity to employees, but it also served their flexibility interests. The interviewed employers applied flexible non-standard employment arrangements mainly due to rapidly varying labor needs established in the industries. It was important for them to strengthen the non-standard core employees' sense of belonging to the work community. However, employees with work ability challenges were in risk to end up in peripheral positions at the labor market.

Previous research on multiple jobholding has not combined employers’ perspectives of MJH to employees’ experiences of career paths.

This paper aims to present a low-cost, edge-fed, windmill-shaped, notch-band eliminator, circular monopole antenna which is practically loaded with a complementary split ring resonator (CSRR) in the middle of the radiating conductor and also uses a partial ground to obtain wide-band performance.

To compensate for the reduced value of gain and reflection coefficient because of the full (complete) ground plane at the bottom of the substrate, the antenna is further loaded with a partial ground and a CSRR. The reduction in the length of ground near the feed line improves the impedance bandwidth, and introduced CSRR results in improved gain with an additional resonance spike. This results in a peak gain 3.895dBi at the designed frequency 2.45 GHz. The extending of three arms in the circular patch not only led to an increase of peak gain by 4.044dBi but also eliminated the notch band and improved the fractional bandwidth 1.65–2.92 GHz.

The work reports a –10dB bandwidth from 1.63 GHz to 2.91 GHz, which covers traditional coverage applications and new specific uses applications such as narrow LTE bands for future internet of things (NB-IoT) machine-to-machine communications 1.8/1.9/2.1/2.3/2.5/2.6 GHz, industry, automation and business-critical cases (2.1/2.3/2.6 GHz), industrial, society and medical applications such as Wi-MAX (3.5 GHz), Wi-Fi3 (2.45 GHz), GSM (1.9 GHz), public safety band, Bluetooth (2.40–2.485 GHz), Zigbee (2.40–2.48Ghz), industrial scientific medical (ISM) band (2.4–2.5 GHz), WCDMA (1.9, 2.1 GHz), 3 G (2.1 GHz), 4 G LTE (2.1–2.5 GHz) and other personal communication services applications. The estimated RLC electrical equivalent circuit is also presented at the end.

Because of full coverage of Bluetooth, Zigbee, WiFi3 and ISM band, the proposed fabricated antenna is suitable for low power, low data rate and wireless/wired short-range IoT-enabled medical applications.

The antenna is fabricated on a piece (66.4 mm × 66.4 mm × 1.6 mm) of low-cost low profile FR-4 epoxy substrate (0.54 λ_g × 0.54 λ_g) with a dielectric constant of 4.4, a loss tangent of 0.02 and a thickness of 1.6 mm. The antenna reflection coefficient, impedance and VSWR are tested on the Keysight technology (N9917A) vector network analyzer, and the radiation pattern is measured in an anechoic chamber.

This paper aims to propose a single element, dual feed, polarisation diversity antenna. The proposed antenna operates from 2.9 to 10.6 GHz for covering the entire ultra-wideband (UWB) frequency range. The antenna is designed for usage in massive multiple input multiple output (MIMO) and closed packaging applications.

The size of the antenna is 24 × 24 × 1.6 mm³. The radiating element of the antenna is derived from the Sierpinski–Knopp (SK) fractal geometry for miniaturization of the antenna size. The antenna has a single reflecting stub placed between the two orthogonal feeds, to improve isolation.

The proposed antenna system exhibits S₁₁ < −10 dB, S₂₁ < −15 dB and stable radiation characteristics in the entire operating region. It also offers an envelope correlation coefficient < 0.01, a diversity gain > 9.9 dB and a capacity loss < 0.4 bps/Hz. The simulated and measured outputs were compared and results were found to be in similarity.

The proposed UWB-MIMO antenna has significant size reduction through usage of SK fractal geometry for radiating element. The antenna uses a single radiating element with dual feed. The stub is between the antenna elements which provide a compact and miniaturized MIMO solution for high density packaging applications. The UWB-MIMO antenna provides an isolation better than −20 dB in the entire UWB operating band.

The main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.

This article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.

The proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.

The fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.

In everyday life, people generally wear two layers of clothes (a knitted vest and a knitted t-shirt) during the summer. It is essential to understand which types of innerwear and outerwear maximize comfort. The primary objective of this research is to investigate the influence of layering outerwear on innerwear, as well as the air gap between two layers, on thermal comfort properties.

In this study, a total of 12 combinations were created from four vest fabrics and three T-shirt fabrics. The thermal properties (thermal conductivity, thermal resistance, thermal absorptivity, thermal diffusion and peak heat flow) were evaluated for the individual inner and outer layers. Each inner layer was layered with an outer layer to observe the effect of layering on the thermal properties. An air gap of 2 mm was introduced between the inner and outer layers to study the effect of air gap on thermal properties.

Tencel fibre exhibits higher thermal conductivity and absorptivity than cotton and polyester. Upon layering an outer layer on an inner layer, the thermal conductivity and thermal absorptivity increase to a slight extent, thermal resistance and diffusion increase drastically and the peak heat flow reduces. With an air gap between the two layers, the thermal conductivity did not improve, the difference in thermal resistance among all the combinations reduced, the thermal absorptivity of the combination textiles was lower than that of the innerwear alone, the thermal diffusion increased and the peak heat flow diminished for all the combinations.

In practice, this comprehensive thermal comfort analysis provides specific combinations of inner and outer articles of clothing that are most appropriate for enhancing comfort during the summer season.

Though there are many studies on the effect of multilayer fabrics on thermal properties, no extensive research analyses the influence of innerwear and outerwear combinations on thermal comfort properties.