Multifractal Signals Research Articles

Multi-Fractal Signal Simulation of Local Instantaneous Pressure in a Bubbling Gas-Fluidized Bed—Part 2: Chaos Assessment

The purpose of this paper, in two parts, is to (1) determine the fractal characteristics of time-series pressure data from gas-fluidized bed, (2) evaluate the possibility of using the Weierstrass-Mandelbrot (WM) function to simulate the fractal and dynamic characteristics of such pressure data, (3) refine the method of signal simulation introduced by Humphrey et al. (1992) for turbulence data, and (4) to investigate the nonlinear, fractal, and physical phenomena of pressure in a fluidized bed as a function of angular position around a cylinder, location in the bed, and the fluidization ratio. Part 2 is specifically devoted to (1) assessing the nonlinear dynamical, or chaotic, characteristics of the simulated data, and (2) relating chaos measures to physical phenomena as a function of operating conditions.

Multi-Fractal Signal Simulation of Local Instantaneous Pressure in a Bubbling Gas-Fluidized Bed—Part 1: Signal Simulation

The purpose of this paper, in two parts, is to (1) determine the fractal characteristics of time-series pressure data from gas-fluidized bed, (2) evaluate the possibility of using the Weierstrass-Mandelbrot (WM) function to simulate the fractal and dynamic characteristics of such pressure data, (3) refine the method of signal simulation introduced by Humphrey et al. (1992) for turbulence data, and (4) to investigate the nonlinear, fractal, and physical phenomena of pressure in a fluidized bed as a function of angular position around a cylinder, location in the bed, and the fluidization ratio. Part 1, (1) provides evidence that pressure signals from a bubbling fluidized bed are fractal, and delineates the range of scales over which these signals are fractal, (2) demonstrates that simulated signals have statistical measures essentially identical to experimental signals, and (3) relates parameters of the WM function to the physics of pressure fluctuations in fluidized beds. In addition, a refinement to the method of simulation employed by Humphrey et al. (1992) is proposed that employs the method presented by Higuchi (1988) to identify the fractal dimension and upper scaling frequency. Also, a direct means of specifying the amplitude of the fractal component of the signal results from using the peak-to-peak pressure of the experimental signal.

MFGA-IDT2 workshop: Astrophysical and geophysical fluid mechanics: the impact of data on turbulence theories

MFGA-IDT2 workshop: Astrophysical and geophysical fluid mechanics: the impact of data on turbulence theories

Fractional differentiability of nowhere differentiable functions and dimensions.

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals. (c) 1996 American Institute of Physics.

Fractal structure of cosmic ray intensity variations

Time series of cosmic ray (CR) intensity recorded at a low cut-off rigidity neutron monitor, Calgary (CA), are checked for scaling properties. Three years of 5-min data from CA and ten days of 10-sec measurements at Lomnický stit (LS) are analyzed. Power spectrum analysis, and two methods of checking fractality, namely the yardstick length method and the method of scaling exponent, are applied to the 214 data points. As compared to CRs at higher energies, the examined data have a more complicated scaling structure, affected by disturbances in the heliosphere. Regions, where fractal description is appropriate, are 30 – 300 hours and 40 min – 8 hours. While the 40-minute limit is probably the signature of a vanishing effect of interplanetary magnetic field (IMF) on CRs, the other limits are due to diurnal and 27 day variations. Scaling of the higher moments of CR time series involves the signature of multifractality. However, the present statistical significance is not sufficient for a detailed investigation of this problem.