A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term

In this paper, two classes of methods are developed for the solution of two space dimensional wave equations with a nonlinear source term. We have used non-polynomial cubic spline function approximations in both space directions. The methods involve some parameters, by suitable choices of the parameters, a new high accuracy three time level scheme of order O(h ⁴ + k ⁴ + τ ² + τ ² h ² + τ ² k ²) has been obtained. Stability analysis of the methods have been carried out. The results of some test problems are included to demonstrate the practical usefulness of the proposed methods. The numerical results for the solution of two dimensional sine-Gordon equation are compared with those already available in literature.     

Effect of iridium loading on HZSM-5 for isomerization of n-heptane

The effect of iridium loading on the properties and catalytic isomerization of n-heptane over Ir-HZSM-5 is studied. Ir-HZSM-5 was prepared by impregnation method and subjected to isomerization process in the presence of flowing hydrogen gas. XRD and BET studies show that the presence of iridium stabilizes the crystalline structure of HZSM-5, leading to more ordered framework structure and larger surface area. TGA and FTIR results substantiate that iridium species interacts with OH group on the surface of HZSM-5. Pyridine FT-IR study verifies the interaction between iridium and surface OH group slightly increased the Bro¨nsted and Lewis acid sites without changing the lattice structure of HZSM-5. The presence of iridium and the increase of strong Lewis acid sites on HZSM-5 were found to bring an increase about 4.1%, 33.2% and 11.8% in conversion, selectivity and yield of n-heptane isomerization, respectively.     

A study of electron affinities using the initiator approach to full configuration interaction quantum Monte Carlo

For the atoms with Z ≤ 11, energies obtained using the "initiator" extension to full configuration interaction quantum Monte Carlo (i-FCIQMC) come to within statistical errors of the FCIQMC results. As these FCIQMC values have been shown to converge onto FCI results, the i-FCIQMC method allows similar accuracy to be achieved while significantly reducing the scaling with the size of the Slater determinant space. The i-FCIQMC electron affinities of the Z ≤ 11 atoms in the aug-cc-pVXZ basis sets are presented here. In every case, values are obtained to well within chemical accuracy [the mean absolute deviation (MAD) from the relativistically corrected experimental values is 0.41 mE(h)], and significantly improve on coupled cluster with singles, doubles and perturbative triples [CCSD(T)] results. Since the only remaining source of error is basis set incompleteness, we have investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results. By doing so, much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials presented in a previous paper. With this F12 correction, the MAD can be further reduced to 0.13 mE(h) for the electron affinities and 0.31 mE(h) for the ionization potentials.     

Molecular dynamics simulation of NMR powder lineshapes of linear guests in structure I clathrate hydrates

We perform molecular dynamics simulations (up to 6 ns) for the structure I clathrate hydrates of linear molecules CS, CS(2), OCS, and C(2)H(2) in large cages at different temperatures in the stability range to determine the angular distribution and dynamics of the guests in the large cages. The long axes of linear guest molecules in the oblate large structure I clathrate hydrate cages are primarily confined near the equatorial plane of the cage rather than axial regions. This non-uniform spatial distribution leads to well-known anisotropic lineshapes in the solid-state NMR spectra of the guest species. We use the dynamic distribution of guest orientations in the cages during the MD simulations at different temperatures to predict the (13)C NMR powder lineshapes of the guests in the large cages. The length of the guests and intermolecular interactions of the guests in the water cages determine the angular distribution and the mobility of the guests in the sI large cages at different temperatures. At low temperatures the range of motion of the guests in the cages are limited and this is reflected in the skew of the predicted (13)C lineshapes. As the guest molecules reach the fast motion limit at higher temperatures, the lineshapes for CS, OCS, and C(2)H(2) are predicted to have the "standard" powder lineshapes of guest molecules.     

Molecular-dynamics simulation of methane adsorbed on MgO: Evidence for a Kosterlitz-Thouless transition

A realistic model of a monolayer molecular crystal of methane adsorbed on the (100) surface of MgO has been studied by means of molecular dynamics. The model treates the atomicity of the MgO substrate explicitly. Large corrugations in energy are found for both the translational and rotational motion of methane across the substrate. The preferred configurations of adsorption is over an Mg²⁺ ion in a tripod-down orientation. The orientationally ordered low-energy states of the monolayer have been found. Finite-size-scaling calculations on systems of different sizes indicate, however, that the ordered state exhibits only quasi-long-range order. The disclinations in the ordered phase exist in low concentrations and in bound pairs. Evidence is presented for a Kosterlitz-Thouless-type unbinding transition occurring at T _c ≈ 27 K. No evidence is found for a first-order transition. The specific heat exhibits an anomaly at T ≈ 32 K. The disclination density in the region of the transition is reported; below T _c, this density can be fitted to an Arrhenius-type law, yielding an estimate of the core enegy for a bound vortex-antivortex pair.