arXiv subjects

Zygmunt Mazur

Publications and source records attributed to Zygmunt Mazur.

4 recordsLinked to original sources

arXiv2013

Impact of scaling range on the effectiveness of detrending methods

We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed. The efficiency and exactness of all three methods towards proper determination of scaling exponent $H$ is discussed, particularly for short series of uncorrelated or persistent data. \end{abstract}

physics.data-an↗

arXiv2012

On the scaling ranges of detrended fluctuation analysis for long-memory correlated short series of data

We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of length $L$ of time series and regression line coefficient $R^2$ at various confidence levels. Next, an analysis of artificial short series with long memory is performed. In both cases the scaling range $λ$ is found to change linearly -- both with $L$ and $R^2$. We show how this dependence can be generalized to a simple unified model describing the relation $λ=λ(L, R^2, H)$ where $H$ ($1/2\leq H \leq 1$) stands for the Hurst exponent of long range autocorrelated data. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where enormous number of short time series has to be examined at once, without possibility for preliminary check of the scaling range of each series separately.

physics.data-an↗

arXiv2007

Numerical Simulation of the Perrin - like Experiments

A simple model of random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be both solved analytically and simulated numerically. The analytic solution gives the known Eistein-Smoluchowski diffusion law $ = Dt$ where the diffusion constant $D$ is expressed by the mass and geometry of a particle, the viscosity of a liquid and the average effective time between consecutive collisions of the tracked particle with liquid molecules. The latter allows to make a simulation of the Perrin experiment and verify in detailed study the influence of the statistics on the expected theoretical results. To avoid the problem of small statistics causing departures from the diffusion law we introduce in the second part of the paper the idea of so called Artificially Increased Statistics (AIS) and prove that within this method of experimental data analysis one can confirm the diffusion law and get a good prediction for the diffusion constant even if trajectories of just few particles immersed in a liquid are considered.

physics.comp-ph↗

arXiv2000

The problem of friction in two-dimensional relative motion

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding most intuitive expectations. In particular, the strong qualitative dependence between behaviour of the system, boundary conditions and parameters involved in its description is emphasised. The problem is intended to be discussed in theoretical framework and might be of interest for physics and mechanics students as well as for physics teachers.

physics.ed-ph↗