Related papers: Designing isotropic interactions for self-assembly…
Model lattices consisting of balls connected by central-force springs provide much of our understanding of mechanical response and phonon structure of real materials. Their stability depends critically on their coordination number $z$.…
Like the letters in the alphabet forming words, reusing components of a heterogeneous mixture is an efficient strategy for assembling a large number of target structures. Examples range from synthetic DNA origami to proteins self-assembling…
Self-assembly is one of the crucial mechanisms allowing to design multifunctional materials. Soft hybrid materials contain components of different nature and exhibit competitive interactions which drive self-organisation into structures of…
Controlling anisotropy in self-assembled structures enables engineering of materials with highly directional response. Here, we harness the anisotropic growth of ice walls in a thermal gradient to assemble an anisotropic refractory metal…
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular,…
We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated…
We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…
We devise a generic recipe for constructing $D$-dimensional lattice models whose $d$-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying…
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 obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two…
We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: $m_1\ne m_2$. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich…
This article investigates phonons and elastic response in randomly diluted lattices constructed by combining (via the addition of next-nearest bonds) a twisted kagome lattice, with bulk modulus $B=0$ and shear modulus $G>0$, with either a…
Understanding the complex self-assembly of biomacromolecules is a major outstanding question. Microtubules are one example of a biopolymer that possesses characteristics quite distinct from standard synthetic polymers that are derived from…
Despite tremendous progress in the research on self-assembled nanotechnological building blocks such as macromolecules, nanowires, and two-dimensional materials, synthetic self-assembly methods bridging nanoscopic to macroscopic dimensions…
In automated manufacturing, robots must reliably assemble parts of various geometries and low tolerances. Ideally, they plan the required motions autonomously. This poses a substantial challenge due to high-dimensional state spaces and…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…