Nonlinear Dust lattice modes are studied in a hexagonal two-dimensional dusty plasma lattice, in presence of charge gradient of dust particles. In this lattice, such gradients affect nonlinear behavior of dust lattice waves. The amplitude modulation of off-plane transverse dust lattice wave packets is investigated considering the anisotropy of interactions, caused by the height-dependent char...

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more g...

In this study, the hybrid Au-Ag hexagonal lattice of triangular and square lattice of quadrate periodic nanoparticle arrays (PNAs) were designed to investigate their extinction spectra of the localized surface plasmon resonances (LSPRs). First, their simulating extinction spectra were calculated by discrete dipole approximation (DDA) numerical method by changing the media refractive index. Simu...

In this talk, we first introduce the concept of the lattice discrete Fourier transform (lattice DFT). Then we build a theory of matrix-vector division with remainder to represent multi-dimensional integer indices. As an application, a divide-and-conquer technique is developed for fast evaluation of the hexagonal lattice DFT, which is finally reduced to a variety of the Cooley-Tukey algorithms. ...

Edestin, a legumin class reserve protein from hemp seeds having six identical subunits was crystallized from ammonium phosphate at pH 5 and subsequently characterized by X-ray diffraction. The crystals are of space group R32 with a = 127 A and gamma = 116 degrees having an equivalent triply centered hexagonal cell of a = b = 215 A, c = 80 A. There is one hexameric protein in the rhombohedral un...

Based on crystal chemistry considerations and quantum density functional theory ground state calculations, rhombohedral rh-C3 hexagonal h-C6 carbon allotropes are proposed energetically calculated as new stable ultra-hard phases likewise lonsdaleite. Along the two kinds of in linear C2-C1-C2 lattice, distorted tetrahedra C2(sp3) with an angle 106.17{\deg} (smaller than ideal 109.4{\deg}) C1(sp)...

A recent experiment [1] suggested that bismuth forms hexagonal close packed (HCP) films on the Ni(111) surface, of heights 3, 5 and 7 layers. A quantum size effect based on free electrons was proposed in explanation. To test this idea, we calculate the total energies of Bi on the Ni(111) surface using density functional theory. We find that HCP film stabilities disagree with the observed odd la...

Mercury has perhaps the strangest behavior of any of the metals. Although the other metals in column IIB have an hcp ground state, mercury’s ground state is the body centered tetragonal βHg phase. The most common phase of mercury is the rhombohedral αHg phase, which is stable from 79K to the melting point and meta-stable below 79K. Another rhombohedral phase, γHg, is believed to exist at low te...