Functional Renormalization Prediction of Rupture

Abstract

We develop theoretical formulas for the prediction of the rupture of systems which are known to exhibit a critical behavior, based solely on the knowledge of the early time evolution of an observable, such as the acoustic emission rate as a function of time or of stress. From the parameterization of such early time evolution in terms of a low-order polynomial, we use the functional renormalization approach introduced by Yukalov and Gluzman to transform this polynomial into a function which is asymptotically a power law. The value of the critical time t c , conditioned on the assumption that t c exists, is thus determined from the knowledge of the coefficients of the polynomials. We test with success this prediction scheme with respect to the order of the polynomials and as a function of noise.

Interplay between Approximation Theory and Renormalization Group

“…In addition to the cited publications, it is possible to mention here several more applications. For example, self-similar approximants were used for describing systems with Bose-Einstein condensate [280][281][282][283][284], barrier crossing processes [285,286], stochastic processes [287], seismological phenomena [288][289][290], and time series [291,292]. Self-similar approximants have been widely used for a large class of problems in the theory of structured media [293,294].…”