The structural description of disordered systems has been a longstanding challenge in physical science. We propose an atomic cluster alignment method to reveal the development of three-dimensional topological ordering in a metallic liquid as it undercools to form a glass. By analyzing molecular dynamic (MD) simulation trajectories of a Cu(64.5)Zr(35.5) alloy, we show that medium-range order (MR...

A discrete Fourier analysis on the fundamental domain Ωd of the d-dimensional lattice of type Ad is studied, where Ω2 is the regular hexagon and Ω3 is the rhombic dodecahedron, and analogous results on d-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas o...

Human type 3 adenovirus dodecahedron (a virus like particle made of twelve penton bases) features the ability to enter cells through Heparan Sulphate Proteoglycans (HSPGs) and integrins interaction and is used as a versatile vector to deliver DNA or proteins. Cryo-EM reconstruction of the pseudoviral particle with Heparan Sulphate (HS) oligosaccharide shows an extradensity on the RGD loop. A se...

In this paper, we present a novel 2-refinement algorithm for adaptive all-hexahedral mesh generation based on two tree structures: octree and rhombic dodecahedral tree. Given a smooth boundary surface, we first use a pre-defined error function to detect the main surface features, and build a strongly-balanced octree. Then a novel 2-refinement algorithm is developed to eliminate all hanging node...

The rational design of metal-organic frameworks (MOFs) with hollow features and tunable porosity at the nanoscale can enhance their intrinsic properties and stimulates increasing attentions. In this Communication, we demonstrate that methanol can affect the coordination mode of ZIF-67 in the presence of Co(2+) and induces a mild phase transformation under solvothermal conditions. By applying th...

An elastoviscoplastic finite element model of aluminum alloys is used to compare mechanical response among meshes formed with several different grain shapes. Tetrahedral elements are used to form grains of cubic, rhombic dodecahedral and truncated octahedral shape. The influence of the grain shape on the aggregate response is examined in terms of the stress variation and the aggregate elastic m...

Compact hyperbolic 3-manifolds are used in cosmological models. Their topology is characterized by their homotopy group π1(M) whose elements multiply by path concatenation. The universal covering of the compact manifold M is the hyperbolic space H or the hyperbolic ball B. They share with M a Riemannian metric of constant negative curvature and allow for the isometric action of the group Sl(2, ...

Let VI = GF(211), regarded as an 11-dimensional vector space over GF(2), and form V = V, @ (71,). Define vi = 01~ + v, (i = O,..., 22). Since f(X) is irreducible over GF(2), {v. ,..., v 1o, v,} is a basis for V, and so for 11 < i < 22, we can write vi = CzEr, v,, for certain sets Xi _C X = (0 ,..., 10, w}. Moreover, the sets X, can very quickly be computed explicitly by calculating the powers o...