Related papers: Spectral Asymptotics for $V$-variable Sierpinski G…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
Simplicial complexes are increasingly used to study complex system structure and dynamics including diffusion, synchronization and epidemic spreading. The spectral dimension of the graph Laplacian is known to determine the diffusion…
We propose to employ an optical spectroscopy technique to monitor the superconductivity and properties of superconductors in the fluctuating regime. This technique is operational close to the plasmon resonance frequency of the material, and…
The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
A famous result going back to Eric Kostlan states that the moduli of the eigenvalues of random normal matrices with radial potential are independent yet non identically distributed. This phenomenon is at the heart of the asymptotic analysis…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Vicsek fractal graphs are an important class of infinite graphs with self similar properties, polynomial growth and treelike features, on which several dynamical processes such as random walks or Abelian sandpiles can be rigorously analyzed…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
We prove on some nested fractals scale invariant $L^p$-Poincar\'e inequalities on metric balls in the range $1 \le p \le 2$. Our proof is based on the development of the local $L^p$-theory of Korevaar-Schoen-Sobolev spaces on fractals using…
Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuations without performing any unfolding procedure. Here, SVD…
We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily Zariski dense, but…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law…
We relate the intermittent fluctuations of velocity gradients in turbulence to a whole range of local dissipation scales generalizing the picture of a single mean dissipation length. The statistical distribution of these local dissipation…
The variation of fine structure constant with the variation of velocity of light has been studied considering contribution to the permeability and permittivity of the vacuum and incorporating contribution of fractal potential originated…
Vortices, phase singularities, and topological defects of any kind often reflect information that is crucial for understanding physical systems in which such entities arise. With near-field experiments supported by numerical calculations,…