The finite-frequency dynamics of the He superfluid phase transition can be formulated in terms of the response of thermally excited vortex loops to an oscillating flow field. The key parameter is the Hausdorff fractal dimension dH of the loops, which affects the dynamics because the frictional force on a loop is proportional to the total perimeter P of the loop, which varies as P ∼ aH where a i...

The Fourier transform and spectral analysis are employed to estimate the fractal dimension and explore the fractal parameter relations of urban growth and form using mathematical experiments and empirical analyses. Based on the models of urban density, two kinds of fractal dimensions of urban form can be evaluated with the scaling relations between the wave number and the spectral density. One ...

We use fractal continuous random media to model visible and near-infrared light scattering by biological tissue and cell suspensions. The power law of the reduced scattering coefficient, the anisotropy factor of scattering, and the phase function are derived with good agreement with experimental results. Implications for spectroscopic tissue diagnosis are discussed.

The spacing intervals of adjacent Riemann zeta zeros (non-trivial) exhibit fractal (irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated with unpredictability or chaos. The power spectra of such fractal space-time fluctuations exhibit inverse power-law form and signify long-range correlations,...

Long-distance dispersal (LDD) plays an important role in many population processes like colonization, range expansion, and epidemics. LDD of small particles like fungal spores is often a result of turbulent wind dispersal and is best described by functions with power-law behavior in the tails ("fat tailed"). The influence of fat-tailed LDD on population genetic structure is reported in this art...

This review first gives an overview on the concept of fractal geometry with definitions and explanations of the most fundamental properties of fractal structures and processes like self-similarity, power law scaling relationship, scale invariance, scaling range and fractal dimensions. Having laid down the grounds of the basics in terminology and mathematical formalism, the authors systematicall...

Atmospheric flows exhibit fractal fluctuations and inverse power law form for power spectra indicating an eddy continuum structure for the selfsimilar fluctuations. A general systems theory for fractal fluctuations developed by the author is based on the simple visualisation that large eddies form by space-time integration of enclosed turbulent eddies, a concept analogous to Kinetic Theory of G...

“Our analysis finds Earth’s lakes are power-law distributed for lakes ≥ 8.5 km2 (Fig. 2). Lakes < 8.5 km2 deviate from the power-law distribution such that there are fewer of these small lakes than expected if small lakes conformed to the same power-law distribution as large lakes. Across the range of lake sizes conforming to a power-law distribution, the tail exponent is τ = 1.97 (+ /− 0.01), ...

The concept of fractal geometry is useful for the analysis of irregular and complex structures often seen in nature. Here we apply this concept to investigate the structural mechanism of the development of pulmonary emphysema in the klotho mouse, which, after milk feeding, exhibits characteristics resembling aging and develops emphysema. We calculated the relationships between perimeter and siz...

• Stock indexes have dual fractal structure which is consistent with previous studies. • The return distribution of emerging markets shows abnormal dual power-law exponents. • External shock of a crisis affects different markets at distinct stages. a b s t r a c t We investigate minute indexes of stock markets in 10 countries during financial crashes by dividing them into several stages accordi...