Related papers: Fractality-induced Topology
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
Axial vectors, such as current or magnetization, are commonly used order parameters in time-reversal symmetry breaking systems. These vectors also break isotropy in three dimensional systems, lowering the spatial symmetry. We demonstrate…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
The intersection of topology, symmetry, and magnetism yields a rich structure of possible phases. In this work, we study theoretically the consequences of magnetism on IrF4, which was recently identified as a possible candidate topological…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…
We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
We introduce higher order polariton topological insulator (HOTI) realized with fractal array of microcavity pillars arranged into Sierpinski gasket-like geometry. This system exhibiting self similarity in different generations, can support…
The control of exciton transport in organic materials is of fundamental importance for the development of efficient light-harvesting systems. This transport is easily deteriorated by traps in the disordered energy landscape. Here, we…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…