Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

An Observation on the Experimental Measurement of Dislocation Density

The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points to the importance of spatial variations of the elastic strain field in relation to its magnitude in inferring estimates of dislocation density from measurements.     

Os(VIII)-catalysed oxidation of sulfides by sodium salt of N-chlorobenzenesulfonamide

Catalytic activity of Os(VIII) in the oxidation of some twenty organic sulfides with sodium salt of N-chlorobenzenesulfonamide (CAB) has been investigated in alkaline (pH8.7) t-butanol–water (1:1 v/v) medium. Significant retarding influence of [OH⁻] on the reactivity is exhibited. The catalysed reaction is strongly accelerated in the presence of Hg(II). Imperfections are observed in the linear Hammett relationship in the case of –NO₂ substituents.     

Stability and related results in linear elastodynamics on unbounded regions

Communicated by K. R. Rajagopal     

Raman spectroscopic investigation on the microenvironment of the liver tissues of Zebrafish (Danio rerio) due to titanium dioxide exposure

Nano titanium dioxide (nTiO₂), generally considered to be toxicologically inert, is manufactured in large quantities and extensively applied in consumer products. The small size and large surface area endow them with an active group or intrinsic toxicity. Advances in instrumentation are making Raman spectroscopy the tool of choice for an increasing number of (bio) chemical applications. One of the great advantages of this technique is its ability to provide information on the concentration, structure and interaction of biochemical molecules in their microenvironments within intact cells and tissues, non-destructively. Zebrafish (Danio rerio), one of the most important vertebrate model organisms used in developmental biology, are increasingly used in biomedical research, particularly as a model of human disease. In the present work, an attempt is made to study the effect of titanium dioxide, both nano and bulk, on the microenvironment of the liver tissues of Zebrafish using FT-Raman spectroscopy. The results of the present study suggest that TiO₂ exposure demonstrate a marked influence on the microenvironments of the liver tissues of Zebrafish. A shift to a higher wavenumber and an increase in the intensity of the band at ∼1087 cm⁻¹ in the TiO₂ exposed tissues suggest that some of the conformational changes resulting from the alkali recovery process takes place due to TiO₂ exposure. The decreased intensity ratio (I₃₂₂₀/I₃₄₀₀) observed in the titanium-exposed tissues suggests a decreased water domain size, which could be interpreted in terms of weaker hydrogen-bonded molecular species of water in the TiO₂ exposed tissues. The observed shift of COO⁻ bands to higher frequencies shows the disruption of salt bridges as a result of a change in the oppositely charged partners and due to the enhanced random coil conformation. The variation in the intensity ratio of the tyrosyl doublet (I₈₅₈/I₈₂₅) indicates variation in the hydrogen bonding of the phenolic hydroxyl group due to TiO₂ exposure. The results further suggest that the microenvironments are greatly altered due to titanium nano exposure when compared to titanium bulk. In conclusion, the results indicate that FT-Raman spectroscopy might be a useful tool for rapid assessment of nano particle biological interactions.     

Some convexity considerations for a two-dimensional traction problem

Summary A rectangular strip, consisting of homogeneous, isotropic, elastic material, is in an equilibrium state of plane stress, due to actions applied to a pair of opposite edges, the remaining pair being traction-free. The convexity of certain cross-sectional measures of stress is established; and a generalized convexity property is also established for one such measure, leading to an explicit decay estimate for the measure in the case of a semi-infinite strip, one end of which is subjected to a self-equilibrated load.     

Modulated phases in Ising models with diluted frustration

A particular class of periodic Ising models with diluted frustration is studied using a simple recursion relation for spinor correlation functions. A modulated phase is found at T = 0 which extends into a modulated paramagnetic phase for finite temperatures. The disorder line at which this latter phase changes into a paramagnetic phase is located. In a study of the ground state excitations of the model contact is made with results known for the ANNNI-model.     

Momentum space renormalization for the sine-Gordon model

A momentum space renormalization is presented for the sine-Gordon model with an arbitrary cut-off function. In contrast to previous work the present method reproduces the slope of the critical line as found from the Kosterlitz renormalization of the equivalent Coulomb gas and is also applicable to the case of a sharp cut-off function.