Related papers: Imaginary crystals made real
Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…
Contrary to the finite-dimensional case, the Moebius group admits interesting self-representations when infinite-dimensional. We construct and classify all these self-representations. The proofs are obtained in the equivalent setting of…
In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree $3$. An explicit set of elliptic curves with elements of order $3$ in their Tate-Shafarevich group is constructed. Combining this…
For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous…
Nematic liquid crystals confined to geometrically as well as chemically patterned substrate on one end and a flat substrate with strong anchoring on the other is studied using non-Boltzmann Monte Carlo methods. We observe significant…
We review Bacry and Levy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous…
Let $\Gamma$ be a crystallographic group of dimension $n,$ i.e. a discrete, cocompact subgroup of $\operatorname{Isom}(\mathbb{R}^n)$ = $O(n)\ltimes\mathbb{R}^n.$ For any $n\geq 2,$ we construct a crystallographic group with a trivial…
Here, we investigate the effective response of three-dimensional spacetime crystals formed by spherical scatterers under a travelling-wave modulation. We develop an analytical formalism to homogenize the spacetime crystals that extends the…
Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…
An ant-like observer confined to a two-dimensional surface traversed by stripes would wonder whether this striped landscape could be devised in such a way as to appear to be the same wherever they go. Differently stated, this is the problem…
We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…
Colloidal particles can spontaneously self-assemble into ordered structures, which not only can manipulate the propagation of light, but also vibration or phonons. Using Monte Carlo simulation, we study the self-assembly of perfectly…
The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in…
We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By…
We discuss the suitability of holographically generated optical potentials for the investigation of superfluidity in ultracold atoms. By using a spatial light modulator and a feedback enabled algorithm we generate a smooth ring with…
Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure…
This paper is devoted to the problem of choosing the most suitable model of a geometrical system for describing the real crystallographic space. It has been shown that all 230 crystallographic groups used to describe the crystalline…
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…
In recent years, simulation methods based on the scaling of atomic potential functions, such as quasi-coarse-grained dynamics and coarse-grained dynamics, have shown promising results for modeling crystalline systems at multiple scales.…
We develop a new technique to equip models of spiral galaxies with self-consistent dynamics that match observations. We apply our technique and construct a model for the Milky Way with a dynamical interstellar medium (ISM). In simulations a…