Statistical properties of the cluster dynamics of the systems of statistical mechanics

Cluster dynamics is the property of dynamics of systems of statistical mechanics when for given time the whole array of particles is decomposed onto finite clusters which move independently during a random interval of time. In this paper we study statistical properties and critical indices related to cluster dynamics.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[3]  H. Kanamori.  The energy release in great earthquakes , 1977 .

[4]  R. Dobrushin,et al.  Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction , 1977 .

[5]  Ilya Zaliapin,et al.  Colliding cascades model for earthquake prediction , 2000 .

[6]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[7]  James H. Stock,et al.  Pre‐recession pattern of six economic indicators in the USA , 2000 .

[8]  Ludwig Boltzmann,et al.  Vorlesungen über Gastheorie , 2009 .

[9]  B. Gutenberg,et al.  Seismicity of the Earth , 1941 .

[10]  B. Tirozzi,et al.  Time evolution of infinite classical systems with singular, long range, two body interactions , 1976 .

[11]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[12]  John K. Tomfohr,et al.  Lecture Notes on Physics , 1879, Nature.

[13]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[14]  A. A. Soloviev,et al.  Nonlinear dynamics of the lithosphere and earthquake prediction , 2003 .

[15]  O. Lanford.  Time evolution of large classical systems , 1975 .

[16]  L. Botvina,et al.  Premonitory transformation of steel fracturing and seismicity , 1997 .

[17]  Ilya Zaliapin,et al.  A Boolean Delay Equation Model of Colliding Cascades. Part II: Prediction of Critical Transitions , 2003 .

[18]  Ilya Zaliapin,et al.  Inverse cascade in a percolation model: hierarchical description of time-dependent scaling. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Ilya Zaliapin,et al.  Short-term earthquake prediction by reverse analysis of lithosphere dynamics , 2006 .

[20]  H. Stanley,et al.  Download details: , 1983 .

[21]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[22]  G. M. Molchan,et al.  Statistical analysis of the results of earthquake prediction, based on bursts of aftershocks , 1990 .

[23]  Newman,et al.  Critical transitions in colliding cascades , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Robert Shcherbakov,et al.  Nonlinear Dynamics of the Lithosphere and Earthquake Prediction , 2003 .