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Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and…

This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…

Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in…

Competing ground states may lead to topologically constrained excitations such as domain walls or quasiparticles, which govern metastable states and their dynamics. Domain walls and more exotic topological excitations are well studied in…

We consider an ultra-small system of polarized bosons on an optical lattice with a ring topology interacting via long range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions…

There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two…

Topological boundary modes, a hallmark of quantum topological phases, remarkably occur in classical mechanical systems through an interesting correspondence with the quantum case. Here, we explore the Maxwell lattice frustrated Mott…

We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected…

We construct a three-dimensional lattice model for biological gels in which straight lines of bonds correspond to filamentous semi-flexible polymers and lattice sites, which are exactly four-fold coordinated, to crosslinks. With only…

We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are…

Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit…

The homogenization of auxetic cellular solids having periodic hexachiral and tetrachiral microstructure is dealt with two different techniques. The first approach is based on the representation of the cellular solid as a beam-lattice to be…

Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections. These phases were suggested and demonstrated not only for electronic systems, but also for…

We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…

Topological magnetic lattices offer a fertile ground for exploring fundamental physics and developing novel spintronic devices. However, current research is predominantly confined to single-Q topologies hosting uniform type of…

The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…

Topological dislocations in otherwise periodic lattices represent global structural defects that, nevertheless, typically leave the lattice periodicity intact far from the dislocation. Such dislocations arise in diverse physical systems…

This paper investigates the extension complexity of polytopes by exploiting the correspondence between non-negative factorizations of slack matrices and randomized communication protocols. We introduce a geometric characterization of…

Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a…

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted…