Related papers: Random-h Fractional-Dimensional Lattices Reveal En…
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.…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant…
Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…
We study the mutual percolation of two interdependent lattice networks ranging from two to seven dimensions, denoted as $D$. We impose that the length of interdependent links connecting nodes in the two lattices be less than or equal to a…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network.…
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian.…
We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long…
In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…
Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. To explain the…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
We show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{\'e} approximants of the mean cluster number $S(p)$ for site and bond percolation on general $d$-dimensional lattices are upper bounds on this quantity in any Euclidean…
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and…
We propose an interdependent random geometric graph (RGG) model for interdependent networks. Based on this model, we study the robustness of two interdependent spatially embedded networks where interdependence exists between geographically…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…