Related papers: Linearized spectral decimation in fractals
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
We revisited the problem of describing, on average, a fractal distribution of matter using a Lemaitre-Tolman-Bondi (LTB) solution. Here we study the fractal structure of our local universe having a fractal dimension and a scale transition,…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
We use a binary sequential decay model in order to describe the fragmentation of a nucleus induced by the high energy collisions of protons with Au nuclei. Overall agreement between measured and calculated physical observables is obtained.…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
When circuits are set up and dismantled dynamically in elastic optical networks, spectrum tends to become fragmented in the fiber links. The fragmentation limits the available path choices and may lead to significant blocking of connection…
Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…
We construct a one-parameter family of Laplacians on the Sierpinski Gasket that are symmetric and self-similar for the 9-map iterated function system obtained by iterating the standard 3-map iterated function system. Our main result is the…
Using group theoretical and numerical methods we have calculated the exact energy spectrum of the two-dimensional Hubbard model on square lattices with four electrons for a wide range of the interaction strength. All known symmetries, i.e.\…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which…
We have designed a new experimental setup able to investigate fracture of soft materials at small scales. At high crack velocity, where energy is mostly dissipated through viscoelastic processes, we observe an increasingly large high strain…
This paper discusses some features of the spectral line profile theory used in the treatment of measured atomic transitions. It is shown that going beyond the established linear approximation for the spectral line contour in the case of its…
We study topological, metric and fractal properties of set of numbers $[0;1]$ with given asymptotic mean of digits in their ternary representation. We investigate connection of these numbers and numbers with a given frequency of digits.
The quantization of the transverse motion energy in the continuous potentials of atomic strings and planes can take place under passage of fast charged particles through crystals. The energy levels for electron moving in axial channeling…
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…