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We study the variation of average powers and spectral indices of electric field fluctuations with respect to the angle between average flow direction and the mean magnetic field in solar wind turbulence. Cluster spacecraft data from the…
The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have…
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we…
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…
The spectral properties of the restricted fractional Dirichlet Laplacian in ${\sf V}$-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[\Lambda_\dagger, +\infty)$…
In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…
We study the scale function of the spectrally negative phase-type Levy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phase-type…
A model for strong kinetic Alfv\'en plasma turbulence at scales smaller than the ion gyroscale is proposed. It is argued that magnetic and density fluctuations are concentrated mostly at two-dimensional structures, which leads to their…
For a family of fractal measures, we find an explicit Fourier duality. The measures in the pair have compact support in $\br^d$, and they both have the same matrix scaling. But the two use different translation vectors, one by a subset $B$…
We perform an analysis of preliminary data on strange particles yields and fluctuations within the Statistical hadronization model. We begin by describing the theoretical disagreements between different statistical models currently on the…
We consider a two-dimensional gas of colliding charged particles confined to finite size containers of various geometries and subjected to a uniform orthogonal magnetic field. The gas spectral densities are characterized by a broad peak at…
We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter…
This paper illustrated the possible relationship between the occurrences of the earthquake and the anomalous line-of-sight propagations in the very high frequency band by the fast Fourier transform spectral analysis. Despite many anomalous…
In this survey article, we investigate the spectral properties of fractal differential operators on self-similar fractals. In particular, we discuss the decimation method, which introduces a renormalization map whose dynamics describes the…
We study the dissipative bi-stable Duffing oscillator with equal energy wells and observe fractal patterns in the parameter space of driving frequency, forcing amplitude, and damping ratio. Our numerical investigation reveals the Hausdorff…
Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this…
We discuss the spin fluctuations and the role played by the magnetic susceptibility in an atomic Fermi gas interacting with positive scattering length. Both thermal and quantum fluctuations are considered. Using a sum rule approach and…
We confirm, in a more general framework, a part of the conjecture posed by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpi\'nski gasket, Indiana Univ. Math. J. 63 (2014), 831--868] on the…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.