Assessment of technogenic load of Nizhny Tagil city pond and environmental risk management based on multifractal dynamics

Algoremediation which is a method of natural and waste water treatment due to the metabolic potential of chlorococcal microalgae is based on the principle of system stability. The method of pollution degree estimation of anthropogenic loaded water object based on the application of fractal calculation is shown. Factor analysis has been used to determine the parameters of the environmental system of Nizhny Tagil city pond which are the basis for a new approach to evaluating the efficiency of environmental protection measures through geoecological risk management.

On Tail Dependence and Multifractality

We study whether, and if yes then how, a varying auto-correlation structure in different parts of distributions is reflected in the multifractal properties of a dynamic process. Utilizing the quantile autoregressive process with Gaussian copula using three popular estimators of the generalized Hurst exponent, our Monte Carlo simulation study shows that such dynamics translate into multifractal dynamics of the generated series. The tail-dependence of the auto-correlations forms strong enough non-linear dependencies to be reflected in the estimated multifractal spectra and separated from the case of the standard auto-regressive process. With a quick empirical example from financial markets, we argue that the interaction is more important for the asymmetric tail dependence. In addition, we discuss and explain the often reported paradox of higher multifractality of shuffled series compared to the original financial series. In short, the quantile-dependent auto-correlation structures qualify as sources of multifractality and they are worth further theoretical examination.

Toward Interactions through Information in a Multifractal Paradigm

In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities’ geometry becomes, through the Cayley–Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.

Modeling and Analysis of Algolization Process of a Technological Pond of the Novolipetsk Metallurgical Plant Based on Multifractal Dynamics

A method for modeling and analyzing the dynamics of regulation of ecosystem states based on the construction of multifractal models taking into account the multilevel of its biodiversity is proposed. It is proposed to evaluate the integral response of the ecosystem to control actions by superimposing its multifractal image on the selected forms of critical organization that meet the limits of restoration of the ecosystem structure.