Narrow Results

This work explores the use of the Higuchi fractal dimension (HFD) to characterize the complexity of the Standard and Poor’s (S&P) Index for the period from 1928 to 2023. It is found that the fractal dimension is not constant but exhibits large time fluctuations. In line with adaptive market hypothesis notions, such a feature can be seen as the response of the stock market to a complex and changing environment formed by a diversity of participants and exogenous shocks. The concept of fractal dimension was extended to consider scale dependence and multifractality. It is shown that the fractality dimension approaches an integer value when the time scale increases, which reflects smoother price fluctuation profiles. It was also shown that the multifractal HFD exhibits large fluctuations for scales of weeks, months, and quarters, which can be linked to the seasonal periods of the operation of the stock market. The impact of salient events was also assessed. It was found that the 1987 and 2008 market crashes had the highest effect on the multifractal HFD, suggesting that these events involved multiple factors. Overall, the results in the present work showed that the fractal dimension tools and notions provide a useful and complementary framework for characterizing the behavior of financial indices.

We present a convergence study for a hybrid Lattice Boltzmann-Molecular Dynamics model for the simulation of dense liquids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The velocity field from the atomistic domain is introduced as forcing terms to the Lattice Boltzmann model of the continuum while the mean field of the continuum imposes mean field conditions for the atomistic domain. In the present paper we investigate the effect of varying the size of the atomistic subdomain in simulations of two dimensional flows of liquid argon past carbon nanotubes and assess the efficiency of the method.

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora and Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.

This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.

The permutation entropy (PE) is a statistical measure which can describe complexity of time series. In recent years, the research on PE is increasing gradually. As part of its application, the complexity–entropy causality plane (CECP) and weighted CECP (WCECP) have been recently used to distinguish the stage of stock market development. In this paper, we focus on weighted Rényi entropy causality plane (WRECP), and then extend WCECP and WRECP into multiscale WCECP (MWCECP) and multiscale WRECP (MWRECP) by introducing a new parameter scale. By data simulating and analyzing, we show the power of WRECP. Besides, we discuss the MWCECP and the MWRECP of adjacent scales. It reveals a gradual relationship between adjacent weighted scale entropies.

Nanopore structure and its multiscale feature significantly affect the shale-gas permeability. This paper employs fractal theory to build a shale-gas permeability model, particularly considering the effects of multiscale flow within a multiscale pore space. Contrary to previous studies which assume a bundle of capillary tubes with equal size, in this research, this model reflects various flow regimes that occur in multiscale pores and takes the measured pore-size distribution into account. The flow regime within different scales is individually determined by the Knudsen number. The gas permeability is an integral value of individual permeabilities contributed from pores of different scales. Through comparing the results of five shale samples, it is confirmed that the gas permeability varies with the pore-size distribution of the samples, even though their intrinsic permeabilities are the same. Due to consideration of multiscale flow, the change of gas permeability with pore pressure becomes more complex. Consequently, it is necessary to cover the effects of multiscale flow while determining shale-gas permeability.