Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

FT-Raman spectroscopy of the reaction of polybutadiene with mercapto-thiadiazoles

Mercapto-thiadiazoles having potential anti-wear behaviour are reacted with polymers with existing viscosity index-improving properties in order to produce materials which may find a use as multifunctional lubricant additives. 2,5-Dimercapto-1,3,4-thiadiazole, 2-amino-5-mercapto-1,3,4-thiadiazole and 2-methyl-5-mercapto-1,3,4-thiadiadiazole were reacted with low MW polybutadiene containing vinyl-1,2, cis-1,4 and trans-1,4 (C=C) groups. The reactions were monitored using FT-Raman spectroscopy in order to determine quantitatively the consumption of the individual structural units when reacted with thiadiazoles. 2,5-Dimercapto-1,3,4-thiadiazole reacted readily with the polybutadiene, achieving 80% reaction within a few hours. The thiadiazole reacted selectively with the order of addition being cis>vinyl>trans. 2-Amino-5-mercapto-1,3,4-thiadiazole and 2-methyl-5-mercapto-1,3,4-thiadiazole were found to react more slowly and hence to a lesser extent (40 and 25%, respectively) over a similar time scale.     

Localized moments in the superconducting Li1+xTi2−xO4 spinel system

Electron spin resonance (ESR) and magnetic-susceptibility measurements on the Li_1+xTi_2?xO₄ spinel system ($\text{0 ≤ x ≤}\text{1}\text{3}$) indicate the presence of two types of localized moments in this material. In both cases, an unpaired electron is trapped as a Ti³⁺ ion in a crystal field that is predominantly octahedral, but with a strong tetragonal component. This type of crystal field cannot arise in the stoichiometric spinel. We propose two types of defect in the title spinel system: an oxygen vacancy and a hydroxyl ion. Unpaired electrons are trapped as Ti³⁺ ions adjacent to these defects, and it is argued that the strong tetragonal field is associated with the formation of a static (TiO)⁺ ion by a displacement of the titanium ion from the defect. Spin relaxation occurs via a thermal ionization of the trapped electron that appears to be associated with a static-dynamic transition in the titanium-ion displacement.     

Alteration of foliar flavonoid chemistry induced by enhanced UV-B radiation in field-grown Pinus ponderosa, Quercus rubra and Pseudotsuga menziesii

Chromatographic analyses of foliage from several tree species illustrate the species-specific effects of UV-B radiation on both quantity and composition of foliar flavonoids. Pinus ponderosa, Quercus rubra and Pseudotsuga menziesii were field-grown under modulated ambient (1x) and enhanced (2x) biologically effective UV-B radiation. Foliage was harvested seasonally over a 3-year period, extracted, purified and the flavonoid fraction applied to a mu Bondapak/C(18) column HPLC system sampling at 254 nm. Total flavonoid concentrations in Quercus rubra foliage were more than twice (leaf area basis) that of the other species; Pseudotsuga menziesii foliage had intermediate levels and P. ponderosa had the lowest concentrations of total flavonoids. No statistically significant UV-B radiation-induced effects were found in total foliar flavonoid concentrations for any species; however, concentrations of specific compounds within each species exhibited significant treatment effects. Higher (but statistically insignificant) levels of flavonoids were induced by UV-B irradiation in 1- and 2-year-old P. ponderosa foliage. Total flavonoid concentrations in 2-year-old needles increased by 50% (1x ambient UV-B radiation) or 70% (2x ambient UV-B radiation) from that of 1-year-old tissue. Foliar flavonoids of Q. rubra under enhanced UV-B radiation tended to shift from early-eluting compounds to less polar flavonoids eluting later. There were no clear patterns of UV-B radiation effects on 1-year-old P. menziesii foliage. However, 2-year-old tissue had slightly higher foliar flavonoids under the 2x UV-B radiation treatment compared to ambient levels. Results suggest that enhanced UV-B radiation will alter foliar flavonoid composition and concentrations in forest tree species, which could impact tissue protection, and ultimately, competition, herbivory or litter decomposition.     

Four-dimensional density and energy density functional

The relations based on an external one-electron operator V( r ) are examined from two view-points, i.e., from the Hohenberg–Kohn approach and the four-dimensional density concept introduced by Wilson and Frost, and extensively studied by Parr and Politzer. The object being to obtain, with the help of the Hellmann–Feynman theorem, new formulas for the energy of atoms and molecules, and to discuss the construction of the universal energy density functional on the basis of the four-dimensional density.     

High pressure-temperature Raman measurements of H2O melting to 22 GPa and 900 K

The melting curve of H(2)O has been measured by in situ Raman spectroscopy in an externally heated diamond anvil cell up to 22 GPa and 900 K. The Raman-active OH-stretching bands and the translational modes of H(2)O as well as optical observations are used to directly and reliably detect melting in ice VII. The observed melting temperatures are higher than previously reported x-ray measurements and significantly lower than recent laser-heating determinations. However, our results are in accord with earlier optical determinations. The frequencies and intensities of the OH-stretching peaks change significantly across the melting line while the translational mode disappears altogether in the liquid phase. The observed OH-stretching bands of liquid water at high pressure are very similar to those obtained in shock-wave Raman measurements.     

The Effects of UVA-I (340-400 nm), UVA-II (320-340 nm) and UVA-I+II on the Photoisomerization of Urocanic Acid in vivo

Abstract— Ultraviolet B radiation (280-320 nm) can systemically suppress contact hypersensitivity (CHS), delayed type hypersensitivity (DTH) and tumor rejection responses in mice. Several models have been postulated for the initiation of this UVB-induced immune suppression and, although the complete mechanism is unclear, our early studies suggested that initiation is via the activation of a photoreceptor in the skin, identified as urocanic acid (UCA). Recent preliminary data from our laboratory and others indicated that UVA (320-400 nm)-emitting broadband sunlamps can also isomerize UCA but may not lead to immune suppression, in contrast to UVB-emitting sunlamps, which cause both effects. Although the reason for this inconsistency is unknown, the emission spectra of UVA lamps contain differing amounts of UVB, UVA-I (340-400 nm) and UVA-II (320-340 nm) from those of UVB sources. In this study we determined a detailed dose-response for the isomerization of UCA in mouse skin using the UVA-I, UVA-II and UVA-I+II wavelength ranges. The dose-response curves obtained were put on an equal energy basis by quantum correction and the possibility of wavelength interaction for this effect investigated. A simple additive wavelength interaction between UVA-I, UVA-II, and UVA-I+II was observed for trans-UCA photoisomerization. This result indicates that the failure of UVA-I, UVA-II or UVA-I+II radiation to induce immune suppression of the CHS response in an animal model is not due to complex wavelength interactions and/or the presence of an in vivo endogenous photosensitizer of UCA isomerization. Other factors, such as downstream blocking by UVA of the cis -UCA generated signal, may be involved.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR