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The purpose of this paper is to reveal the multi‐scale relation between power law distribution and correlation of stock returns and to figure out the determinants underlying capital markets.

The multi‐scale relation between power law distribution and correlation is investigated by comparing the original series with the special series. The eliminating intraday trend series approach developed by Liu et al. is utilized to analyze the effects of power law decay change on correlation properties, and shuffling series originated by Viswanathan et al. for the impacts of special type of correlation on power‐law distribution.

It is found that the accelerating decay of power law has an insignificant effect on correlation properties of returns and the empirical results indicate that time scale may also be an important factor maintaining power law property of returns besides correlation. When time scale is under critical point, the effects of correlation are crucial, and the correlation of nonlinear long‐range presents the strongest influence. However, for time scale beyond critical point, the impact of correlation begins to diminish or even finally disappear and then the power law property shows complete dependence on time scale.

The 5‐min high frequency data of the Shanghai market as the empirical benchmark is insufficient to depict the relation over the entire time scale in the Chinese stock market.

The paper identifies the determinants of market dynamics to apply them to risk management through analysis of multi‐scale relations, and supports endeavors to introduce time parameter into further risk measures and control.

The paper provides the empirical evidence that time scale is one of the key determinants of market dynamics by analyzing the multi‐scale relation between power law distribution and correlation.

The purpose of this paper is to emphasize on the impact of endoscope in MHD peristaltic flow of Carreau fluid. Heat and mass transfer phenomena are comprised of Soret and Dufour effects. Influences of mixed convection and viscous dissipation are also accounted. Wall properties and convective boundary conditions are used.

The Navier–Stokes and energy equations used the lubrication approach. The reduced system of equations is executed numerically. The graphical illustration of velocity, temperature, concentration and heat transfer coefficient for various emerging parameters is discussed.

The response of Weissenberg number and power law index is decaying toward velocity and temperature. Moreover impression of Soret and Dufour number on temperature is quite reverse to that of concentration.

The titled problem with the various considered effects has not been solved before, and it is of special importance in various industries. The problem is original.

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.

To provide an eddy‐viscosity turbulence model that accounts for the non‐equilibrium shape of the energy spectrum and for the effect of velocity correlation on turbulent viscosity.

The turbulence model is built using the standard kε model as the starting point. It is suggested that the character of turbulence depends on the time elapsed since its generation. Therefore, a local variable named “age of turbulence” or α, is defined and its transport equation is derived. Two hypotheses are formulated. The first one is that the shape of the energy spectrum depends on α. The second one is that also the effect of velocity correlation on turbulent viscosity is a function of α, in analogy with the dispersion coefficient of a particle in a turbulent flow. Hence, expressions for the characteristic time scaleτ_T and the turbulent viscosity ν_T are proposed and they are integrated in the standard kε model, resulting in a three equation model named here kεα. The expressions of ν_T and τ_T reduce to those of the kε model in decaying turbulence, and deviate from them in recently produced turbulence. The empirical constants are calibrated and various benchmark experiments are simulated.

A comparison between computed results and experimental data show that the kεα model is generally more accurate than the standard kε model.

The “age of turbulence” has not been used previously to characterise turbulence. The work is especially relevant for combustion/reacting applications, where the expression of the characteristic turbulence time scale is crucial for the estimation of the reactant mixing rates.

This paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas.

Numerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi.

An explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model.

Using this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers.

The Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.

This paper explores international trade of the Chinese manufacturing industries through the lenses of network analysis (NA) to visualise the world trade network of the Chinese economy, describe its topology and better explain the international organisation of Chinese manufacturing industries.

The authors built a dataset of 40,550 Chinese companies and their 107,026 subsidiaries in 118 countries from Orbis-BVD and used a NA to investigate the connection between China and other countries. In particular, the authors studied the connections between Chinese companies and their subsidiaries in order to build a network of Chinese industries.

The authors found that the network of Chinese companies is ramified but not wide and it can be divided into two clusters. Moreover, the relations between China and other peripheral countries are strongly mediated by a few leading locations (e.g. Hong Kong and the USA).

This paper contributes to the literature in several ways. First, the authors provide empirical evidence on the magnitude and ramifications of Chinese enterprises in the world. The existing studies generally focus on applying NA to sectoral insights (Mao and Yang, 2012; Shaikh et al., 2016; Zheng et al., 2016; Wanzenbö ck, 2018; Krichene et al., 2019), whereas in this work the authors take a comprehensive view of the entire Chinese manufacturing system. Second, this paper complements the existing literature identifying the difference between cluster levels in Chinese manufacturing (Wu and Jiang, 2011) by proposing a cluster centralisation method to analyse the international network of Chinese firms rather than just the national network. Finally, the results also shed light on the international trade relationship between China, Hong Kong and the USA.

In this work the experimental effect of a slow decay of the photoluminescence is studied theoretically in the case of quantum dots with an indirect energy band gap. The slow decay of the photoluminescence is considered as decay in time of the luminescence intensity, following the excitation of the quantum dot sample electronic system by a short optical pulse. In the presented theoretical treatment the process is studied as a single dot property. The inter-valley deformation potential interaction of the excited conduction band electrons with lattice vibrations is considered in the self-consistent Born approximation to the electronic self-energy. The theory is built on the non-equilibrium electronic quantum transport theory. The time dependence of the photoluminescence decay is estimated upon using a simple effective mass model. The numerical calculation of the considered model shows the power-law time characteristics of the photoluminescence decay in the long-time limit of the decay. We demonstrate that the nonadiabatic influence of the interaction of the conduction band electrons with the lattice vibrations provides a mechanism giving us the power-law time dependence of the photoluminescence intensity signal. This theoretical result emphasizes the role of the electron-phonon interaction in the nanostructures.

Fat‐tailed distributions have been found in many financial and economic variables ranging from forecasting returns on financial assets to modeling recovery distributions in bankruptcies. They have also been found in numerous insurance applications such as catastrophic insurance claims and in value‐at‐risk measures employed by risk managers. Financial applications include:

The purpose of this study is to examine the growth patterns of tag vocabulary in collaborative tagging systems to verify the sustainability and stabilization of tag distributions. Both sustainability and stabilization are essential to the mining and categorization of information driven by tagging behaviors.

The study was based on time series data of CiteULike from November 2004 to April 2010. Power law distributions were detected to reveal statistical regularities and tagging patterns. Logistic regression analysis with time‐dependent covariates was conducted to identify the factors affecting the growth of distinct tags for articles. The significance of the effects and the time taken for a given article to reach its tagging maturity were also explored.

Time series plots and trend analysis illustrated the continuous growth of the tagging system. Exploratory analysis of power law distribution fittings indicated a sign of system stability known as scale invariance. Logistic regression results demonstrated that for a particular article, the number of users who tagged the article, the initial date when the article was tagged, and the life span of the article are statistically significant to the ratio of the distinct tag number to the total tag number for a given article. These results confirmed that the distinct tag ratio of an article gives rise to a stable pattern.

Though extensive work has been done on the patterns of tag vocabulary, it is not clear how the growth of distinctive tags behaves in relation to the total number of tag applications, considering time‐dependent covariates such as the number of users, and the longevity of an article. This paper sets to complement the literature on the existing methodology and investigate this property in detail.