Related papers: Analysis on hybrid fractals
We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form…
Magneto-transport of interacting electrons in a Sierpinski gasket fractal is studied within a mean field approach. We work out the three-terminal transport and study the interplay of the magnetic flux threading the planar gasket and the…
We define a new set of excitations in the XY model which we call ``fractional vortices''. In the frustrated XY model containing $\pi$ bonds, we make the ansatz that the ground state configurations can be characterized by pairs of oppositely…
A structural model of hydrogenated amorphous silicon containing an isolated dangling bond is used to investigate the effects of electron interactions on the electronic level splittings, localization of charge and spin, and fluctuations in…
We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg-shells under two different loading conditions: impact…
It has recently been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities.…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
A two-parameter extension of the density-scaled double hybrid approach of Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)] is presented. It is based on the explicit treatment of a fraction of multideterminantal exact exchange. The…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic…
The physical properties of blends of distinct homopolymers, cross-linked beyond the gelation point, are addressed via a Landau approach involving a pair of coupled order-parameter fields: one describing vulcanisation, the other describing…
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for electrons…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
We study the spectral decomposition of the Laplacian on a family of fractals $\mathcal{VS}_n$ that includes the Vicsek set for $n=2$, extending earlier research on the Sierpinski Gasket. We implement an algorithm [24] for spectral…
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…
We describe a new hybrid framework to model non-thermal spectral signatures from highly energetic particles embedded in a large-scale classical or relativistic MHD flow. Our method makes use of \textit{Lagrangian} particles moving through…
In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…
Labyrinth fractals are self-similar fractals that were introduced and studied in recent work by Cristea and Steinsky. In the present paper we define and study more general objects, called mixed labyrinth fractals, that are in general not…