Primitive Square Research Articles

On silver and golden optical orthogonal codes

It is several years that no theoretical construction for optimal (v, k, 1) optical orthogonal codes (OOCs) with new parameters has been discovered. In particular, the literature almost completely lacks optimal (v, k, 1)-OOCs with k > 3 which are not regular. In this paper we will show how some elementary difference multisets allow to obtain three new classes of optimal but not regular (3p, 4, 1)-, (5p, 5, 1)-, and (2p, 4, 1)-OOCs which are describable in terms of Pell and Fibonacci numbers. The OOCs of the first two classes (resp. third class) will be called silver (resp. golden) since they exist provided that the square of a silver element (resp. golden element) of ℤp is a primitive square of ℤp.

Correlation Effects in Diffusion of CH4/CF4 Mixtures in MFI Zeolite. A Study Linking MD Simulations with the Maxwell−Stefan Formulation

Correlation effects in diffusion of CH4 and CF4 in MFI zeolite have been investigated with the help of molecular dynamics (MD) simulations and the Maxwell−Stefan (M−S) formulation. For single-component diffusion, the correlations are captured by the self-exchange coefficient ; in the published literature this coefficient has been assumed to be equal to the single-component M−S diffusivity, Đi. A detailed analysis of single-component diffusivity data from MD, along with published kinetic Monte Carlo (KMC) simulations, reveals that /Đi is a decreasing function of the molecular loading, depends on the guest−host combination, and is affected by intermolecular repulsion (attraction) forces. A comparison of published KMC simulations for diffusion of various molecules in MFI, with those of primitive square and cubic lattices, shows that the self-exchange coefficient increases with increasing connectivity. Correlations in CH4/CF4 binary mixtures are described by the binary exchange coefficient ; this exchange coefficient has been examined using Onsager transport coefficients computed from MD simulations. Analysis of the MD data leads to the development of a logarithmic interpolation formula to relate with the self-exchange coefficient of the constituents. The suggested procedure for estimation of is validated by comparison with MD simulations of the Onsager and Fick transport coefficients for a variety of loadings and compositions. Our studies show that a combination of the M−S formulation and the ideal adsorbed solution theory allows good predictions of binary mixture transport on the basis of only pure component diffusion and sorption data.

Binary Phases of C60 and C70 Buckminsterfullerenes: An Electron Crystallographic Study

Binary combinations of the fullerenes C60 and C70, in molar ratios spanning the concentration interval between the two pure components, were crystallized from dilute benzene solution to study their copacking in the solid state. From electron diffraction patterns, the hexagonal close packed structure was found to persist across the entire concentration interval, becoming more and more disordered when higher concentrations of C70 were present. The ordered face-centered cubic structure of C60, with crystals oriented along [111], disappeared when C70 was present at a molar concentration somewhat above 0.40. At high C70 concentrations (including the pure material), electron diffraction patterns indicated that a new primitive cubic structure, with a unit cell spacing a = 10.63 Å, might be present, even though such a molecular packing should not be energetically favored. It is shown, however, that such patterns can be produced when initially solvated three-dimensional crystals collapse to form a randomly displaced packing (shear direction: 〈110〉) of primitive square lattice layers as the solvent is rapidly evaporated. The disordered structure is, therefore, a distortion of the C70 fcc crystal structure oriented along [001].