Related papers: Cell augmentation framework for topological lattic…
Aligning lattices based on local stress distribution is crucial for achieving exceptional structural stiffness. However, this aspect has primarily been investigated under a single load condition, where stress in 2D can be described by two…
In this work, the second paper of this series, we study the 2+1d version of a Hamiltonian model for topological phases based on higher lattice gauge theory. We construct the ribbon operators that produce the point-like excitations. These…
We present comparatively simple two-dimensional and three-dimensional checkerboard-like optical lattices possessing nontrivial topological properties. By simple tuning of the parameters these lattices can have a topological insulating…
Exponential growth describes an extremely rapid process ubiquitous across mathematics and diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic…
We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…
Engineering non-linear hybrid light-matter states in tailored optical lattices is a central research strategy for the simulation of complex Hamiltonians. Excitons in atomically thin crystals are an ideal active medium for such purposes,…
Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to…
We study Zariski-like topologies on a proper class $X\varsubsetneqq L$ of a complete lattice $\mathcal{L}=(L,\wedge ,\vee ,0,1)$. We consider $X$ with the so called classical Zariski topology $(X,\tau ^{cl})$ and study its topological…
We propose a local reinforcement technique for lattices in the vicinity of a stress-raiser such as a notch, in order to elevate the macroscopic strength and ductility. A spatially non-uniform waviness distribution of sinusoidally-shaped…
Symmetry plays an important role in the topological band theory. In contrary, study on the topological properties of the asymmetric systems is rather limited, especially in higher-dimensional systems. In this work, we explore a new theory…
In this Letter, an elastic twisted kagome lattice at a critical twist angle, called self-dual kagome lattice, is shown to exhibit peculiar finite-frequency topological modes which emerge when certain conditions are satisfied. These states…
The ability to assemble mesoscopic colloidal lattices above a surface is important for fundamental studies related with nucleation and crystallization, but also for a variety of technological applications in photonics and micro-engineering.…
Higher-order topological phase as a generalization of Berry phase attracts an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower and…
Classical spin liquids are frustrated magnetic phases characterized by local constraints, flat bands in reciprocal space, and emergent gauge structures with distinctive signatures such as pinch points. These arise generally in \emph{cluster…
Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic lattices. In this work, we introduce a computational framework that enables continuous reprogramming of a…
We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i)…
This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…