Simon Gluzman

TL;DR: In this article, the authors provide a physical basis for this phenomenological law based on a slider block model using a state and velocity-dependent friction law established in the laboratory, and use the slider block friction model to analyze quantitatively the displacement and velocity data preceding two landslides, Vaiont and La Clapiere.

TL;DR: In this article, a simple physical model was proposed to explain the accelerating displacements preceding some catastrophic landslides, based on a slider-block model with a state and velocity-dependent friction law.

TL;DR: It is suggested that growth processes, rupture, earthquake, and financial crashes seem to be characterized by oscillatory or bounded regular microscopic functions that lead to a slow power-law decay of A(n), giving strong log-periodic amplitudes.

TL;DR: It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions, and provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Padé approximant.

Abstract: An approach is suggested for defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed. The basis of this construction is the self-similar approximation theory. Control functions governing the convergence of exponentially renormalized series are defined from stability and fixed-point conditions and from additional asymptotic conditions when the latter are available. The stability of the calculational procedure is checked by analyzing cascade multipliers. A number of physical examples for different statistical systems illustrate the generality and high accuracy of the approach.