Related papers: Cracked rotor vibrations by multifractal analysis
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
Rolling bearing fault diagnosis has garnered increased attention in recent years owing to its presence in rotating machinery across various industries, and an ever increasing demand for efficient operations. Prompt detection and accurate…
The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We revisit the fidelity as a measure for the stability and the complexity of the quantum motion of single and many-body systems. Within the context of cold atoms, we present on overview of applications of two fidelities which we call static…
In the present paper, the models of structural analysis and evaluation of efficiency indicators (reliability, fault tolerance, viability, and flexibility) of a multi core processor with variable structure, equipped with multi functional…
Some Mumford-Shah functionals are revisited as perturbed area functionals in connection with brittle damage mechanics. We find minimizers "on paper" for the classical Mumford-Shah functional for some particular two dimensional domains and…
Understanding the microstructural influence on the failure mechanisms in multi-phase materials calls for the identification of the worst-case scenario. This necessitates a statistical approach. By performing simulations directly based on…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.
Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a…
Vibrations of the Jeffcott rotor are modelled by a three degree of freedom system including coupling between lateral and torsional modes. The crack in a rotating shaft of the rotor is introduced via time dependent stiffness with off…
Multi-mode systems can operate in different modes, leading to large numbers of different dynamics. Consequently, applying traditional structural diagnostics to such systems is often untractable. To address this challenge, we present a…
In the domain of rotating machinery, bearings are vulnerable to different mechanical faults, including ball, inner, and outer race faults. Various techniques can be used in condition-based monitoring, from classical signal analysis to deep…
The kicked rotator model is an essential paradigm in nonlinear dynamics, helping us understand the emergence of chaos and bifurcations in dynamical systems. In this study, we analyze a two-dimensional kicked rotator model considering a…