Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9, 3, 1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a ‘shared secret’ related to the group law. ...

Metallo-dielectric photonic crystals with cubic symmetries have been studied here both experimentally and theoretically in the millimeter wavelength region (15-60 mm). In a direct analogy to linear systems, we considered the three-dimensional lattices as a stack of two-dimensional resonating screens. The overall three-dimensional structure was introduced in the calculation through a structural ...

A comparison between experimental and theoretical electron Energy Loss Near Edge Structure (ELNES) of B and N K-edges in cubic boron nitride is presented. The electron energy loss spectra of cubic boron nitride particles were measured using a scanning transmission electron microscope. The theoretical calculation of the ELNES was performed within the framework of density functional theory includ...

We use a simple density functional approach on a diffusional time scale, to address freezing to the body-centered cubic (bcc), hexagonal close-packed (hcp), and face-centered cubic (fcc) structures. We observe faceted equilibrium shapes and diffusion-controlled layerwise crystal growth consistent with two-dimensional nucleation. The predicted growth anisotropies are discussed in relation with r...

The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values of the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid fr...

Alkali halides and alkaline earth halides are strongly ionic compounds that solidify as crystals. The name for the alkali elements (Li, Na, K, Rb and Cs) comes from the Arabic word alqili (ashes of the salt-wort plant that was once used as a source of sodium and potassium for making glass from sand). The name for the halogen elements (F, Cl, Br, I—and the rare radioactive element astatine) come...

this study concerns about quantum chemical modeling behavior of 02 on cr (100)surface by using density functional theory (dft) by lanl2dz and 6 — 31g* basissets, we presented the results of our first principles electronic structure calculationson the 02 molecules and their interface with cr (100) surface. the chromium metalhas the body-centered cubic structure, and chromium cluster has five cr ...

co-fe films were electrodeposited on cu substrate from electrolytes with different co concentration  levels. x-ray diffraction (xrd) was used  to  investigate  the  films  crystal  structures. the  results  indicate that  if  the  co  concentration  is  less  that  the  fe  concentration,  the cubic  structure  appears  in  the  films, while  the  hexagonal  structure dominates when  the co  co...

We present a new cubic γ (Fm3m) Li3N phase discovered above 40(±5) GPa. Structure and spectral distribution of the cubic phase are examined to 200 GPa with synchrotron x-ray diffraction and inelastic x-ray Raman scattering in a diamond anvil cell. First principles calculations predict a factor-of-five band-gap widening at the onset of the β → γ transition, consistent with an observed color chan...

The crystal structure of the highestand second highesttemperature solid phases of choline tetrafluoroborate and iodide was determined by X-ray powder diffraction. The structure in the highest-temperature phase of both salts is NaCl-type cubic (a = 10.16(2) Ä, Z = 4 for tetrafluoroborate; a = 10.08(2) A, Z = 4 for iodide). The second highesttemperature phase of tetrafluoroborate and iodide is Cs...