Warren F. Perger

Ab-initio calculation of elastic constants of crystalline systems with the CRYSTAL code

An automated procedure for calculating second-order elastic constants for crystalline systems of any symmetry using the CRYSTAL program is described. Second derivatives with respect to strain are evaluated numerically from analytical gradients. The internal co-ordinates are re-optimized with each applied strain. Point group symmetry is exploited to reduce the number of needed deformations according to Laue classes. A set of test cases covering many of the crystal classes is used to document the numerical accuracy of the scheme, and to define default values of the computational parameters so as to reduce the input file to a single keyword.

Thermo-chemical and thermo-physical properties of the high-pressure phase anhydrous B (Mg14Si5O24): An ab-initio all-electron investigation

Abstract Using the hybrid B3LYP density functional method, we computed the ab-initio thermo-chemical and -physical properties of the mineral anhydrous B (Anh-B), which has been recently suggested as a potential phase responsible for the X-discontinuity in the Earth’s mantle at ~300 km depth through the reaction forsterite + periclase = Anh-B, and also to likely split the 410 km discontinuity within the interior of a cold slab through the reaction wadsleyite/ringwoodite = Anh-B + stishovite. We first conducted an investigation of the static properties through a symmetry-preserving relaxation procedure and then computed, on the equilibrium structure, harmonic vibrational modes at the longwavelength limit corresponding to the center of the Brillouin zone (k → 0). While optic modes are the eigenvectors of the Hessian matrix at Γ point, acoustic modes were obtained by solving the non-zero components of the strain matrix. Following the Kieffer model, acoustic branches were assumed to follow sine wave dispersion when traveling within the Brillouin zone. All thermodynamic properties that depend on vibrational frequencies namely, heat capacities, thermal expansion, thermal derivative of the bulk modulus, thermal correction to internal energy, enthalpy, Gibbs free energy, thermal pressure and Debye temperature, were computed on the basis of quasi-harmonic mode-gamma analysis of the volume effects on vibrational frequencies. Moreover, the strain tensor was used to calculate several thermo-physical properties of geophysical interest (transverse and longitudinal wave velocities, shear modulus, Young’s modulus, and Poisson’s ratio). The ab-initio results derived in this study and the available data on molar volumes were used to calculate the univariant equilibrium forsterite + periclase = Anh-B. The results are in satisfactory agreement with the reversed experimental data of Ganguly and Frost (2006).

Calculation of band gaps in molecular crystals using hybrid functional theory

Hybrid functional theory is applied for calculation of band gaps in the molecular crystals anthracene, pentaerythritol (PE), pentaerythritol tetranitrate (PETN), and cyclotrimethylene trinitramine (RDX). The B3LYP hybrid functional is observed to produce band gap estimates in reasonable agreement with experiment for anthracene and RDX. This approach, which has been successfully used recently for other materials, is efficient and practical, which is especially important for these large molecular crystals.

Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes

Abstract A numerical evaluator for the confluent hypergeometric function for complexarguments with large magnitudes using a direct summation of Kummers series is described. Extended precision subroutines using large integer arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to thirteen significant figures, and on rare occasion accurate to only nine for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow, however, the evaluator remains valuable as a benchmark even in such cases.

Algorithm 707: CONHYP: a numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes

A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummers series is presented. Extended precision subroutines using large arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to 13 significant figures, and on rare occasion accurate to only 9 for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow; however, the evaluator remains valuable as a benchmark even in such cases.

A numerical evaluator for the generalized hypergeometric series

Abstract The generalized hypergeometric series is numerically evaluated using extended precision subroutines. Cases involving large, complex arguments are shown to be accurate up to 12 significant figures.

Shielding effectiveness of carbon-filled polypropylene composites:

Adding conductive carbon fillers to insulating thermoplastic resins increases composite shielding effectiveness. In this study, varying amounts of three different carbons (carbon black, synthetic graphite particles, and carbon nanotubes) were added to polypropylene resin. The resulting single filler composites were tested for shielding effectiveness. The effects of single fillers and combinations of two different carbon fillers were studied via a factorial design. At the highest single filler loadings, the following shielding effectiveness results were obtained at 800 MHz: 23.4 dB for 10 wt% carbon black/polypropylene, 34.7 dB for 70 wt% synthetic graphite/polypropylene, and 45.9 dB for 15 wt% carbon nanotubes/polypropylene. The factorial results indicated that for the composites containing only single fillers, carbon nanotubes, carbon black, and synthetic graphite cause a statistically significant increase in composite shielding effectiveness. All composites containing combinations of two different fillers had a statistically significant effect which increased shielding effectiveness. The shielding effectiveness values for the 2.5 wt% carbon black/65 wt% synthetic graphite/polypropylene and 65 wt% synthetic graphite/6 wt% carbon nanotubes/polypropylene composites are >60 dB, which is higher than that of many metals.

Effects of Ground Constituent Parameters on Array Mutual Coupling for DOA Estimation

Effects of ground constituent parameters on the mutual coupling (MC) of monopole antenna array are investigated. This work augments an existing MC compensation technique for ground-based antennas and proposes reduction in mutual coupling for antennas over finite ground as compared to the perfect ground. The work is investigated by finite element method analysis, and numerical results are presented. A factor of 4 decrease in both the real and imaginary parts of the mutual coupling is observed when considering a poor ground versus a perfectly conducting one, for quarter-wave monopoles in receiving mode. A simulated result to show the errors in direction-of-arrival (DOA) estimation with actual realization of the environment is also presented.

SCA calculations of the inner shell ionization with Dirac-Fock electronic wave functions

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is onL- andM-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in theV(N−1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases.

Integrating symbolic and numeric techniques in atomic physics

The article describes ISNAP, a program for calculating atomic properties that uses an integrated symbolic and numerical approach for arbitrary excitations from closed-shell atoms. This program generates transition matrix elements and energy formulas up to third-order perturbation via the symbolic programming language Mathematica.