Lattice dynamics and phase diagrams for hydrogen bonded systems

Abstract

A variational correlated ground state wave-function theory is applied to investigate the high-pressure deformation of hydrogen-bond potential described by a double Morse potential functions. The evolution of the hydrogen bond potential with increasing pressure and the effects of deuterium isotope substitution on the quantum-fluctuation-driven phenomena are discussed. The theory was employed for predicting and interpreting the pressure dependence of the phase transition temperatue for KDP-like ferroelectrics and NQR-frequency coefficients for several deuterated and undeuterated crystals.     

A semiclassical model of the interior of Uranus

Abstract

Using the mass and radius of Uranus, as determined by Voyager, and a particular semiclassical theory of dense matter, a model of its interior has been developed. Details of the model, the underlying theory and possible sources of discrepancies with recent work on this topic are briefly presented.     

Radiation hardness of gas discharge tubes and avalanche diodes used for transient voltage suppression

The widespread use of gas discharge tubes (GDTs) and avalanche diodes for transient voltage suppression (TVS) in many cases results in their exposure to ionizing radiation. The aim of this paper is to investigate the influence of irradiation on these TVS devices’ characteristics, by exposing them to a combined neutron/gamma radiation field. Experimental results show that irradiation of TVS diodes causes a lasting degradation of their protective characteristics. On the other hand, GDTs exhibit a temporary change of performance. The observed effects are presented with the accompanying theoretical interpretations, based on the interaction of radiation with materials constituting the investigated devices.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

Two Hadamard matrices of order 956 of Goethals-Seidel type

No Hadamard matrices of order 956 appear in the literature. In this note we construct two such matrices. They are both of Goethals-Seidel type. As a consequence of this and of a result of Seberry and Yamada, we conclude that there exist 4-Williamson type matrices of order 1913.This work was supported by NSERC of Canada Grants A-5285 and EQP0107539.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Difference equations in statistical mechanics. I. Cluster statistics models

A review and some new results are presented for several cluster statistics models, solutions of which can be reduced to difference equations. Mathematical techniques suitable for solving these equations are surveyed.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

The elliptical gaussian wave transformation due to diffraction by an elliptical hologram

Realized as an interferogram of a spherical and a cylindrical wave, the elliptical hologram is treated as a plane diffracting grating which produces Fresnel diffraction of a simple astigmatic gaussian incident wave. It is shown that if the principal axes of the incident beam coincide with the principal axes of the hologram, the diffracted wave field is composed of three different astigmatic gaussian waves, with their waists situated in parallel but distinct planes. The diffraction pattern, observed on a transverse screen, is the result of the interference of the three diffracted wave components. It consists of three systems of overlapped second-order curves, whose shape depends on the distance of the observation screen from the hologram, as well as on the parameters of the incident wave beam and the hologram. The results are specialized for gratings in the form of circular and linear holograms and for the case of a stigmatic gaussian incident wave, as well as for the normal plane-wave incidence on the three mentioned types of hologram.