This paper describes the fault diagnosis in the operation of industrial ball bearings. In order to cluster the very small differential signals of the four classic fault types of the ball bearing system, the chaos synchronization (CS) concept is used in this study as the chaos system is very sensitive to a system’s variation such as initial conditions or system parameters. In this study, the Che...

Geophysical phenomena of interest to geoscientists include both atmospheric and terrestrial related processes, which can be either static or dynamic. Characterization of such phenomena requires advanced models which often include scale invariance concepts of fractal or multi-fractal type. Recently, there has been much interdisciplinary interest in the application of geophysical processes. The a...

We propose a phenomenological field theoretical approach to the chemical etching of a disordered solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the author's knowledge, this constitutes the...

We construct matter field theories in “theory space” that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant “compactific...

A new scheme for sequence coding based on the iterated functions systems theory is presented. The method relies on a 3D approach in which the sequence is adaptively partitioned. Each partition block can be coded either by using the spatial self similarities or by exploiting temporal redundancies. The proposed system shows very good performances when compared to other existing methods.

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

In this review paper, we recall the successive steps that we have followed in the construction of the theory of scale relativity. The aim of this theory is to derive the physical behavior of a nondifferentiable and fractal space-time and of its geodesics (to which waveparticles are identified), under the constraint of the principle of relativity of all scales in nature. The first step of this c...