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We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
In previous papers by A. Kameyama and by J. Kigami distances on fractals have been discussed having two different but similar properties. One property is that the maps defining the fractal are Lipschitz of prescribed constants less than 1,…
Short-term variability of X-ray continuum spectra has been reported for several Active Galactic Nuclei. Significant X-ray flux variations are observed within time scales down to 10^3-10^5 seconds. We discuss short variability time scales in…
It is demonstrated on a realistic model of amorphous alloy Si$_{0.9}$Ge$_{0.1}$ with 1000 atoms, that short-range spectral fluctuations of propagons and diffusons are universal and in agreement with random matrix theory. The universality…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
For the statistics of global observables in disordered systems, we discuss the matching between typical fluctuations and large deviations. We focus on the statistics of the ground state energy $E_0$ in two types of disordered models : (i)…
We study here the small-angle scattering structure factor for deterministic fat fractals in the reciprocal space. It is shown that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor,…
We investigate the thermodynamics of model systems exhibiting two-scale fractal spectra. In particular, we present both analytical and numerical studies on the temperature dependence of the vibrational and electronic specific heats. For…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
The spectral fluctuation properties of spherical nuclei are considered by use of NNSD statistic. With employing a generalized Brody distribution included Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters are…
Surface constructs in snakes reflect desirable design traits for technical surface engineering. Their micro-textural patterns, however, do not lend themselves easily to unified analysis due to species-specific variations in surface geometry…
[abridged] Extending the work of Czerny et al. (2004), we model the fractional variability amplitude due to distributions of hot spots co-orbiting on the accretion disk around a supermassive black hole. From defined radial distributions,…
Asymptotics are derived for the scaling of the total diffraction intensity for the set of $k$-free integers near the origin, which is a measure for the degree of patch fluctuations.
The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In paper (I) of this sequence, we described theoretically the refraction of all families of ST wave packets at…
The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
Fluctuation in fluorescence emission of immobilized single molecule is typically ascribed to the chromophore's intrinsic structural conformations and the influence of local environmental factors. Despite extensive research over several…
We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…