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We investigate the particle trapping and scattering properties in a tight-binding network which consists of several subgraphs. The particle trapping condition is proved under which particles can be trapped in a subgraph without leaking.…
We show that bound states moving in a finite periodic volume have an energy correction which is topological in origin and universal in character. The topological volume corrections contain information about the number and mass of the…
We show that finite lattices with arbitrary boundaries may support large degenerate subspaces, stemming from the underlying translational symmetry of the lattice. When the lattice is coupled to an environment, a potentially large number of…
Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive…
Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli…
We numerically explore the behavior of repelling and aligning self-propelled polar particles (boids) in 2D enclosed by a damped flexible and elastic loop-shaped boundary. We observe disordered, polar ordered (or jammed) and circulating…
A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites).…
Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…
We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…
We demonstrate that stacking topologically trivial layers, under enforced symmetry restrictions, yields emergent topological phases with protected boundary states. Remarkably, the number of layers itself acts as a topological switch,…
One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
Recent experiments and simulations have demonstrated that particle-covered interfaces can exist in stable non-spherical shapes as a result of the steric jamming of the interfacially trapped particles, which confers the interface with…
In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have…
We address the problem of stability of one-dimensional non-periodic ground-state configurations with respect to finite-range perturbations of interactions in classical lattice-gas models. We show that a relevant property of non-periodic…
In a dissipationless linear lattice, spatial disorder or incommensurate modulation induce localization of the lattice eigenstates and block spreading of wave packets. Additionally, incommensurate arrays allow for the metal-insulator…