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A generalized kinetic model of three component mixture of cracks

100%

Czechowski Z.

1998

tom Vol. 46, nr 4

375-388

A kinetic model of nucleation propagation and fusion ofnumerous cracks is derived. The population of three categories of cracks (shear, tensile and shear-tensile) is taken into account. The exponential from of size crack distributions is deduced for constant fusion cross-sections. This is in agreement with the kinetic model for single category of cracks. A set of three simple differential equations for numbers of cracks in each category is obtained and analysed numerically.

A stochastic approach to the cricktip propagation model

100%

Czechowski Z.

2000

tom Vol. 48, nr 1

57-68

System of faults can be regarded as a stochastic non-linear dynamic system. We investigate a dynamic response of such a system to a stochastic input. As an example of the non-linear stochastic differential equation, the model of the cracktip motion is considered. The influence of fault interactions and the medium structure is perceived as the input stochastic process. We are looking for such input distributions for which the stochastic output is consistent with observations (e.g. Gutenberg-Richter law). This allows us to describe the physical nature of internal stresses and the medium avoiding investigations of complex deterministic models of the fault system. It appears that even purely random input processes are transformed by the model into a power-like distribution. Discussion concerning the causes for the appearance of exponential and inverse-power distributions is included.

Ito equations out of domino cellular automaton with efficiency parameters

63%

Czechowski Z. , Białecki M.

Acta Geophysica

2012

tom Vol. 60, no. 3

846-857

Ito equations are derived for simple stochastic cellular automaton with parameters describing efficiencies for avalanche triggering and cell occupation. Analytical results are compared with the numerical one obtained from the histogram method. Good agreement for various parameters supports the wide applicability of the Ito equation as a macroscopic model of some cellular automata and complex natural phenomena which manifest random energy release. Also, the paper is an example of effectiveness of histogram procedure as an adequate method of nonlinear modeling of time series.