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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.

Three kinds of observations are usually used in the modelling of general systems: Gallilean observation, observation with informational invariance and scaling observation. All these models presuppose the invariance of the dimension of the system under consideration. The purpose of the present paper is to examine what happens when the observation process increases this dimension. A 1‐D co‐ordinate switches to a 2‐D co‐ordinate. Complex‐valued random variables are used to describe this approach. Prospects of applications are outlined.

To conceptualize a new approach to economic development that fully embraces its fractal complexity, providing a basis for sustained socioeconomic welfare within cultures that encourage collaborative democracy and social learning.

Following the premise that healthy development must follow the natural laws of growth that apply to all ecosystems, the paper examines fractal intricacy as the basis of economic systems that are able to sustain sufficient flows of energy and information to all sub‐systems. Two methodological approaches that emerge for planning are called hierarchical (fractal) coherence and fractal connectivity. The first refers to sufficient density and variety of nodes (firms, economic processes, customers, etc.) at all scales in the hierarchy of an economic system; and the second denotes multiple paths of connection between the nodes, to handle the necessary flows.

This approach highlights the fundamental importance of locally‐based entrepreneurship and democratic control, and also suggests new methods for measuring system interconnectedness at all scales, supplementing economic growth measures such as GDP.

The paper indicates the need for empirical research to calibrate and further refine the approach in real‐world settings.

The paper outlines a fresh planning strategy for dealing with the geometrically worsening dimensions of uneven economic development and poverty, at all levels of scale from the local to the global.

The paper articulates a viable cybernetic alternative to prevailing economic development approaches that are based on the neo‐classical, neo‐liberal, and neo‐conservative models embodied in our present system of economic globalization.

Hydro-viscous drive (HVD) clutches are widely used in equipment requiring soft start, such as fans and pumps, to transmit torque and adjust speed by changing the gap distance between friction pairs. This paper aims to propose a novel two-parameter evaluation method for HVD during the mixed lubrication stage. The objective is to develop an effective model that establishes the relationship between these parameters and the actual surface topography.

In the presented methods, the fractal features of the real manufacturing surface are calculated based on the power spectrum function by the ultra-depth three-dimensional microscope. After that, the hybrid friction model of the friction plate is established based on mixed elasto-hydrodynamic lubrication theory, boundary friction model and fractal theory. Then the torque and load bearing characteristics of the clutch are obtained, and the influences of the surface fractal features are investigated and discussed. Finally, the Weierstrass–Mandelbrot function is adopted for the surface topography characterization and evaluation.

The results indicate that the proposed method exhibits good accuracy, while the speed difference between the friction pair exceeds 2,500 rpm. It is concluded that this paper proposed a way to evaluate the torque and loading capacity of HVD considering the real manufacturing surface topography and is helpful for surface optimization.

The originality and value of this study lie in its development of a novel torque and load bearing capacity evaluation method for HVD in mixed lubrication stage, considering manufacturing surface topography and describing the real manufacturing surface.

The purpose of this paper is to discuss some fundamental aspects regarding the anomalies in the passive scalar field advected by forced homogenous and isotropic turbulence, by inspection of the analytical properties of the governing equations and with the aid of direct numerical simulation (DNS) data.

Results from a pseudo‐spectral DNS of a unitary‐Schmidt‐ number passive scalar advected by a low Reynolds number flow field, Re_λ=50 and 70 (based on the Taylor microscale λ) allow for a preliminary assessment of the developed numerical model.

Manipulation of the governing equations for the scalar field (which are monotonic) reveals that the unboundedness of the scalar gradient magnitude is not ruled out by the mathematical properties of the correspondent conservation equation. Classic intermittency effects in the passive scalar field have been reproduced, such as non‐Gaussian behavior of the passive scalar statistics, loss of local isotropy, and multi‐fractal scaling of scalar structure functions. Moreover, Taylor and Richardson theories are, surprisingly, not confirmed only in the dissipation range (small‐scales anomalies).

The authors suggest that the origin of intermittency (qualitatively pictured here as violent burst in spatial gradient quantities) should be sought in the loss of monotonicity of the evolution equation of the scalar gradient.

Asset pricing dynamics in a multi-asset framework when investors’ trading exhibits the disposition effect is studied. The purpose of this paper is to explore asset pricing dynamics and the switching behavior among multiple assets.

The dynamics of complex financial markets can be best explored by following agent-based modeling approach. The artificial financial market is populated with traders following two heterogeneous trading strategies: the technical and the fundamental trading rules. By simulation, the switching behavior among multiple assets is investigated.

The proposed framework can explain important stylized facts in financial time series, such as random walk price dynamics, bubbles and crashes, fat-tailed return distributions, absence of autocorrelation in raw returns, persistent long memory of volatility, excess volatility, volatility clustering and power-law tails. In addition, asset returns possess fractal structure and self-similarity features; though the switching behavior is only allowed among the asset markets.

The model demonstrates stylized facts of most real financial markets. Thereafter, the proposed model can serve as a testbed for policy makers, scholars and investors.

To the best of knowledge, no research has been conducted to introduce the disposition effect to a multi-asset agent-based model.

The purpose of this study is to develop a normal contact stiffness (NCS) model among three disks of the assembled rotor system, which systematically considers the friction coefficient, the asperities interaction and the elastoplastic contact regime.

Based on the revised fractal theory, considering the friction effect, the elastoplastic contact regime and the asperities interaction in a simple way, the total NCS among three disks of the rod-fastening rotor bearing system is established. Effects of fractal dimension and roughness, friction coefficient, asperities interaction and material properties on the normal stiffness are investigated by simulations and the relevant comparisons are given for examining the reasonability of the proposed model.

NCS will decrease when asperities interaction and friction are included. As the load increases, the influences of asperities interaction and friction on stiffness become serious. NCS will be enhanced when the elastoplastic regime is considered.

A comprehensive NCS model is developed. It provides a theoretical basis for the modeling of the NCS for multi-interfaces.

Unlike previous crisis where investors tend to put their assets in safe havens like gold, the recent coronavirus pandemic is characterised by an increase in the Bitcoin purchasing described as risk heaven. This paper aims to analyse the Bitcoin dynamics and the investor response by focusing on herd biases. Therefore, the main objective of this work is to study the degree of efficiency through multifractal analysis in order to detect herd behaviour leading to build the best predictions and strategies.

This paper develops a novel methodology that detects the presence of herding biases and assesses the inefficiency of Bitcoin through an inefficiency index (MLM) by using statistical indicators defined by measures of persistence. This study, also, investigates the nonlinear dynamical properties of Bitcoin by estimating the Multifractal Detrended Fluctuation Analysis (MFDFA) leading to deduce the effect of COVID-19 on the Bitcoin performance. Besides, this work performs an event study to capture abnormal changes created by COVID-19 related events capable to analyse the Bitcoin market response.

The empirical results of the generalized Hurst exponent GHE estimation indicates that Bitcoin is multifractal before this pandemic and becomes less fractal after the outbreak. Using an efficiency index (MLM), Bitcoin is found to be more efficient after the pandemic. Based on the Hausdorff topology, the authors showed that this pandemic has reduced the herd bias.

The uncertainty of COVID-19 disease and the lasting of its duration make it difficult to make the best prediction.

The main contribution of this study is the evaluation of the Bitcoin value after the COVID19 outbreak. This work has practical implications as it provides new insights on trading opportunities and social reactions.

To the authors’ knowledge, this work represents the first study that analyses the Bitcoin response to different events related to COVID-19 and detects the presence of herding behaviour in such a crisis.

The purpose of this paper is to provide a static friction coefficient prediction model of rough contact surfaces based on the contact mechanics analysis of elastic-plastic fractal surfaces.

In this paper, the continuous deformation stage of the multi-scale asperity is considered, i.e. asperities on joint surfaces go through three deformation stages in succession, the elastic deformation, the elastic-plastic deformation (the first elastic-plastic region and the second elastic-plastic region) and the plastic deformation, rather than the direct transition from the elastic deformation to the plastic deformation. In addition, the contact between rough metal surfaces should be the contact of three-dimensional topography, which corresponds to the fractal dimension D (2 < D < 3), not two-dimensional curves. So, in consideration of the elastic-plastic deformation mechanism of asperities and the three-dimensional topography, the contact mechanics of the elastic-plastic fractal surface is analyzed, and the static friction coefficient nonlinear prediction model of the surface is further established.

There is a boundary value between the normal load and the fractal dimension. In the range smaller than the boundary value, the normal load decreases with fractal dimension; in the range larger than the boundary value, the normal load increases with fractal dimension. Considering the elastic-plastic deformation of the asperity on the contact surface, the total normal contact load is larger than that of ignoring the elastic-plastic deformation of the asperity. There is a proper fractal dimension, which can make the static friction of the contact surface maximum; there is a negative correlation between the static friction coefficient and the fractal scale coefficient.

In the mechanical structure, the research and prediction of the static friction coefficient characteristics of the interface will lay a foundation for the understanding of the mechanism of friction and wear and the interaction relationship between contact surfaces from the micro asperity-scale level, which has an important engineering application value.

The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.

The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.

The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.

The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.