Related papers: Geometry- and topology-controlled synchronization …
We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this work we use symmetry as a guide to map…
A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function $f(\theta ) = \sin (\theta +\alpha _1) + h\sin 2(\theta +\alpha _2)$ is investigated based on the generalized…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…
The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase…
Topological boundary states localize at interfaces whenever the interface implies a change of the associated topological invariant encoded in the geometric phase. The generically present dynamic phase, however, which is energy and time…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…
We presented the topological current of Ehrenfest definition of phase transition. It is shown that different topology of the configuration space corresponds to different phase transition, it is marked by the Euler number of the interaction…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
Topological mosaic pattern (TMP) can be formed in two-dimensional (2D) moir\'e superlattices, a set of periodic and spatially separated domains with distinct topologies give rise to periodic edge states on the domain walls. In this study,…
Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable…
Multi-agent systems on nonlinear spaces sometimes fail to synchronize. This is usually attributed to the initial configuration of the agents being too spread out, the graph topology having certain undesired symmetries, or both. Besides…
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing…
Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
We investigate the abrupt transition from low interlayer synchrony to high interlayer synchrony in a system of two identical layers of non-locally coupled Kuramoto-Sakaguchi oscillators using time-switching of the interlayer topology, while…