Discrete-continuous model conversion

This paper presents methods for model conversions of continuous-time state-space equations and discrete-time state-space equations. An improved geometric-series method is presented for converting continuous-time models to equivalent discrete-time models. Also, a direct truncation method, a matrix continued fraction method and a geometric-series method are presented for converting discrete models to equivalent continuous models. As a result, many well-developed theorems and methods in either continuous or discrete domains can be effectively applied to a suitable model in either domain.     

Quantum chemical studies on electrophilic addition

The geometries of the 2-aminoethyl cation and the isomeric protonated aziridine have been optimized using ab initio molecular orbital calculations employing the split-valence shell 4-31G basis set. The protonated aziridine is computed to be the more stable ion by 46.5 kcal/mole (4-31G level) and 44.9 kcal/mole (double-zeta basis set). The profile to interconversion is found to have a barrier of less than 15 kcal/mole (relative to the 2-aminoethyl cation) and this profile is compared with those computed for the similar ions XCH₂CH ₂ ⁺ where X=OH, F, SH and Cl.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Thermodynamic properties of phenol–formaldehyde resin

Characterization measurements of a commercial phenol-formaldehyde resin prepared from constituents including phenol and formaldehyde in the molar ratio 1:1.33 are reported. The measurements consist of (1) the linear thermal expansion coefficient between approximately 85 and 270°K; (2) the specific heat capacity between approximately 6 and 100°K; (3) the Young's modulus at room temperature. A critical examination of the data reveals that: (1) the vibrational behavior is predominantly that of a three-dimensional assembly; (2) as far as data available from other sources permit an assessment to be made, the principle of additivity appears to be applicable to the specific heat capacity between approximately 50 and 100°K; and (3) the data lie near the limit of an empirical relationship observed between the Young's modulus and linear thermal expansion coefficient of other polymers.     

On a simple modification of the glauber collision amplitude

The connection between the Glauber many-particle amplitude function and the generalized Born series is demonstrated. The correspondence suggests the introduction of a mean excitation energy to improve the inclusion of virtual excitations of the target.     

A theoretical study of the heats of formation of some small molecules using non-empirical wavefunctions

Total energies, obtained from non-empirical LCAO-MO-SCF calculations on a series of reactions involving only closed-shell molecules and ions, have been used to calculate the heats of formation H ₂₉₈ ⁰ of a large number of small molecules. The Double- basis set calculations, after empirical corrections for inadequacies in the basis set and systematic errors found in all calculations involving oxygen and carbon atoms, usually predict the heats of formation within 10 kcal/mole of the experimental value. A series of similar calculations predicts the heats of formation of some negative ions for which experimental values are either not available or are unreliable.