arXiv subjects

Lev A. Maslov

Publications and source records attributed to Lev A. Maslov.

5 recordsLinked to original sources

arXiv2016

Modeling statistics of the natural aggregation structures and processes with the solution of generalized logistic equation

The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. The general solution of this equation for q=1 is a product of an increasing bounded function and power-law function with stretched exponential cut-off; the power-law distribution is asymptotically nested in the stretched exponential distribution. The relation with Tsallis non-extensive statistics is demonstrated by solving the generalized logistic equation for q>0. In the case 0 1 it models sub-additive structures. The Gutenberg-Richter G-R) formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small α. The solution is applied for modeling distribution of foreshocks and aftershocks in the regions of Napa Valley 2014, and Sumatra 2004 earthquakes fitting the observed data well, both qualitatively and quantitatively.

physics.geo-ph↗

arXiv2014

Self-organization of the Earths climate system versus Milankovitch-Berger astronomical cycles

The Late Pleistocene Antarctic temperature variation curve is decomposed into two components: cyclic and high frequency, stochastic. For each of these components, a mathematical model is developed which shows that the cyclic and stochastic temperature variations are distinct, but interconnected, processes with their own self-organization. To model the cyclic component, a system of ordinary differential equations is written which represent an auto-oscillating, self-organized process with constant period. It is also shown that these equations can be used to model more realistic variations in temperature with changing cycle length. For the stochastic component, the multifractal spectrum is calculated and compared to the multifractal spectrum of a critical sine-circle map. A physical interpretation of relevant mathematical models and discussion of future climate development within the context of this work is given.

physics.ao-ph↗

arXiv2014

Self-organization in the Earth climate system versus Milankovitch-Berger astronomical cycles

The Late Pleistocene Antarctic temperature variation curve is decomposed into two parts: cyclic and stochastic. These two parts represent different but tightly interconnected processes and also represent two different types of self-organization of the Earth climate system. The self-organization in the cyclic component is the non-linear auto-oscillation reaction of the Earth climate system, as a whole, to the input of solar radiation. The self-organization in the stochastic component is a nonlinear critical process, taking energy from, and fluctuating around the cyclic component of the temperature variations. The system of ODEs is written to model the cyclic part of the temperature variation, and the multifractal spectrum of the stochastic part of the temperature variation is calculated. The Earth climate can be characterized as an open, complex, self-organized dynamical system with nonlinear reaction to the input of solar radiation.

physics.ao-ph↗

arXiv2014

Two Levels of Self-Organization in the Earth Climate System

The Late Pleistocene Antarctic temperature variation curve is decomposed into two parts: cyclic and stochastic. These two parts represent different but tightly interconnected processes and also represent two different types of self-organization of the Earth's climate system. The self-organization in the cyclic component is the non-linear auto-oscillation reaction of the Earth's climate system, as a whole, to the input of solar radiation. The self-organization in the stochastic component is a nonlinear critical process, taking energy from and fluctuating around, the cyclic component of the temperature variations. The system of ODEs is written to model the cyclic part of the temperature variation, and the multifractal spectrum of the stochastic part of the temperature variation is calculated. It is shown that the Earth's climate can be characterized as a dynamic system with two levels of self-organization.

physics.ao-ph↗

arXiv2012

Derivation of the Gutenberg-Richter Empirical Formula from the Solution of the Generalized Logistic Equation

We have written a new equation to study the statistics of earthquake distributions. We call this equation "the generalized logistic equation". The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case in approximation of large magnitudes. To illustrate how the found solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N-25N, 5W-35W), Canary Islands, Magellan Mountains (20N-9S, 148E-170E), and the Sea of Japan. This approximation showed the excellent fit between the theoretical curves and observed data for earthquake magnitudes 1<m<9.

physics.geo-ph↗