Effective potentials and Bogoliubov’s quasi-averages

The effective potential method, used in quantum field theory to study spontaneous symmetry violation, is discussed from the point of view of Bogoliubov’s quasi-averaging procedure. It is shown that the effective potential method is a disguised type of this procedure. The catastrophe theory approach to the study of phase transitions is discussed and the existence of the potentials used in that approach is proved from the statistical point of view. It is shown that in the case of broken symmetry, the nonconvex effective potential is not a Legendre transform of the generating functional for connected Green’s functions. Instead, it is a part of the potential used in catastrophe theory. The relationship between the effective potential and the Legendre transform of the generating functional for connected Green’s functions is given by Maxwell’s rule. A rigorous rule for evaluating quasi-averaged quantities within the framework of the effective potential method is established. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 149–161, October, 1997.     

AN ALTERNATIVE SPECIFICATION FOR MODELING GROUNDWATER DYNAMICS

This research extends previous work with dynamic models to manage groundwater quality by using the consumptive nitrate use rate instead of the nitrate application rate. The analysis indicates that misspecification results in overestimation of economic benefits, and supra-optimum nitrogen fertilizer application rates and groundwater nitrate stocks at a steady state.     

Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Fixed-frequency and threshold molecular photoelectron spectra of S 1s, Si 1s and Cl 1s core levels

Fixed-frequency and threshold photoelectron spectra have been recorded for ionization from the S ls shells in SF₆, CS₂ and COS, the Si 1s shells in SiH₄ and SiCl₄ and the Cl 1s shell in SiCl₄ using synchrotron radiation. Fixed-frequency spectra generally showed a single strong ionization feature with associated weak satellite structure due to excited ionized states. Threshold spectra closely resembled X-ray absorption spectra but with an additional feature due to direct ionization. In cases where resonant process enhanced the NEXAFS spectrum direct ionization was not observed.     

Reactivity of sites on Al2O3 surface modified by Ni

It has been established that CO oxidation with excess O₂ on Ni/Al₂O₃ forms an inhomogeneous NiO contact surface that smoothes critical effects in the sharp reactivity change.     

Small angle neutron scattering from oxygen precipitates in silicon

The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×10¹⁷ O_i/cm³ and 13×10¹⁷ O_i/cm³ have been heated at 750° C for 96 h. SiO₂ precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.2 Å^–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å^–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×10¹⁷ O_i/cm³ oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×10¹⁷ O_i/cm³. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam.