Related papers: Spectral triples for nested fractals
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
In the context of metric geometry, we introduce a new necessary and sufficient condition for the convergence of an inductive sequence of quantum compact metric spaces for the Gromov-Hausdorff propinquity, which is a noncommutative analogue…
Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical…
The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface…
A spectral reformulation of the Riemann hypothesis was obtained in [LaMa2] by the second author and H. Maier in terms of an inverse spectral problem for fractal strings. This problem is related to the question "Can one hear the shape of a…
Let $\{a_n(x)\}_{n\geq1}$ be the sequence of digits of $x\in(0,1)$ in infinite iterated function systems with polynomial decay of the derivative. We first study the multifractal spectrum of the convergence exponent defined by the sequence…
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,…
We give a proof of an analogue of Connes' Hochschild character theorem for twisted spectral triples obtained from twisting a spectral triple by scaling automorphisms, under some suitable conditions. We also survey some of the properties of…
Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished…
This Letter presents the first evidence of a new and unique feature of spontaneous reconnection at multiple sites in electron current sheet, viz. nested quadrupole structure of Hall field at electron scales, in Cluster observations. The new…
A multifractal model of neutron evolution in a reactor is considered. For chain reactions, the dimension of the multifractal carrier, information and correlation dimensions, the entropy of the fractal set, the maximum and minimum values of…
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
The neutrino telescopes of the present generation, depending on their specific features, can reconstruct the neutrino spectra from a galactic burst. Since the optical counterpart could be not available, it is desirable to have at hand…
The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…
We establish a Minkowski measurability criterion for a large class of relative fractal drums (or, in short, RFDs), in Euclidean spaces of arbitrary dimension in terms of their complex dimensions, which are defined as the poles of their…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
For a unital spectral triple $(\mathcal{A}, H,D)$, we study when its truncation converges to itself. The spectral truncation is obtained by using the spectral projection $P_{\Lambda}$ of $D$ onto $[-\Lambda,\Lambda]$ to deal with the case…