In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in ...

To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice particles have the Hubble-type radial expansion velocities. As time proceeds, the average density decreases and density fluctuation develops. By using the box cou...

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical ...

Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution between two fractal surfaces follows an unique power law. This is then utilised to show that the elastic energy releases for slips between two rough fractal surfac...

Studies of the power-law relations of seismicity and earthquake source parameters based on the one-dimensional (1-D) Burridge-Knopoff’s (BK) dynamical lattice model, especially those studies conducted by Taiwan’s scientists, are reviewed in this article. In general, velocityand/or state-dependent friction is considered to control faulting. A uniform distribution of breaking strengths (i.e., the...

We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.

MOTIVATION Current growth in the field of genomics has provided a number of exciting approaches to the modeling of evolutionary mechanisms within the genome. Separately, dynamical and statistical analyses of networks such as the World Wide Web and the social interactions existing between humans have shown that these networks can exhibit common fractal properties-including the property of being ...

Continuous periodogram power spectral analyses of fractal fluctuations of frequency distributions of bases A, C, G, T in Drosophila DNA show that the power spectra follow the universal inverse power-law form of the statistical normal distribution. Inverse power-law form for power spectra of space-time fluctuations is generic to dynamical systems in nature and is identified as self-organized cri...

The dissipation of acoustic wave propagation has long been found to obey an empirical power function of frequency, whose exponent parameter varies through different media. This note aims to unveil the inherent relationship between this dissipative frequency power law and 1/f spectral trend. Accordingly, the 1/f spectral trend can physically be interpreted via the media dissipation mechanism, so...