Related papers: Analysis on hybrid fractals
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard…
We describe the spectrum structure for the restricted Dirichlet fractional Laplacian in multi-tubes, i.e. domains with cylindrical outlets to infinity. Some new effects in comparison with the local case are discovered. In this version,…
Four-dimensional state space geometry is worked out for the exactly solved one-dimensional spin-3/2 lattice with a Blume-Emery-Griffiths (BEG) Hamiltonian as well as a more general one with a term containing a non-zero field coupling to the…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…
Fractal lattices, featuring the self-similarity symmetry, are often geometric descents of parent crystals, possessing all their discrete symmetries (such as rotations and reflections) except the translational ones. Here, we formulate three…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines…
The geometric structure of the Rh$_8^+$ cation is investigated using a combination of far-infrared multiple photon dissociation spectroscopy and density functional theory (DFT) calculations. The energetic ordering of the different…
The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair…
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…
In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the…
The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the…
We propose a new conceptual approach to reach unattained dissipative properties based on the friction of slender concentric sliding columns. We begin by searching for the optimal topology in the simplest telescopic system of two concentric…
The system of mixed hexagonal and square lattices on a spherical surface is examined, with an emphasis on the exploration of the disclination patterns that form in the square-rich regime. To demonstrate the possible outcomes, the Hertzian…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
Antidot lattices, defined on a two-dimensional electron gas at a semiconductor heterostructure, are a well-studied class of man-made structures with intriguing physical properties. We point out that a closely related system, graphene sheets…
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…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…