Related papers: Nonlinear Dynamics, Magnitude-Period Formula and F…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…
It is shown that earthquakes do not know how large they will become, at least from the information collected at seismic catalogs. In other words, the magnitude is independent on previous magnitudes as well as on the waiting time between…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…
The dynamic energy balance is essential for earthquake studies. The energy balance approach is one of the most famous developments in fracture mechanics. To interpret seismological data, crack models and sliding on a frictional surface…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…
The GPS derived anomalous TEC disturbances before earthquakes were discovered in the last years using global and regional TEC maps, measurements over individual stations as well as measurements along individual GPS satellite passes. For…
We study a 2D quasi-static discrete {\it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces.…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient…
To the foundation of a principally new short-term forecasting method there has been laid down a theory of surrounding us world's creation and of physical vacuum as a result of interaction of byuons - discrete objects. The definition of the…
The paper represents the VLF/LF electromagnetic radiation as the earthquake's true precursor. It is shown that this parameter is capable of describing the fault formative process in the focal area. Besides, VLF/LF electromagnetic radiation…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic waves, is…
We analyze regional earthquake energy statistics from the Southern California and Japan seismic catalogs and find scale-invariant energy distributions characterized by an exponent $\tau \simeq 1.67$. To quantify how closely scale-invariant…
The Burridge-Knopoff model of earthquakes has recently gained increased interest for the consistency of the predicted energy released by sismic faults, with the Gutenberg-Richter scaling law. The present work suggests an improvement of this…
We present an axiomatic approach to earthquake forecasting in terms of multi-component random fields on a lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of…
Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional Burridge-Knopoff (BK) model obeying the rate- and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the…
The semiclassical gravity describes gravitational back-reactions of the classical spacetime interacting with quantum matter fields but the quantum effects on the background is formally defined as higher derivative curvatures. These induce…