Properties of crystal states

It is proved that euclidean invariant states describing crystals are not weakly clustering or equivalently that these states exhibit long range order. Further it is shown that a decomposition of an euclidean invariant state into states all of which are invariant for one specific space group, does not yield states with lattice symmetry.     

Correlations in the XY model and screw dislocations in the solid-on-solid model

An exact relation is proven between the two-point correlation function of the classical XY model and the free energy of a step associated with two screw dislocations on a crystal surface described by a solid-on-solid model. This result suggests a way to obtain the XY critical exponent η_c from Monte Carlo studies of the solid-on-solid model.     

The effect of a variation in the elastic moduli on Saint-Venant's principle for a half-cylinder

A semi-infinite prismatic cylinder composed of a linear anisotropic classical elastic material is in equilibrium under zero body force and either zero displacement or zero traction on the lateral boundary. The elastic moduli become perturbed. Under suitable conditions on the base load decay estimates are derived for the difference between corresponding quantities in the unperturbed and perturbed bodies. The amplitude in each estimate involves a multiplicative factor that tends to zero as the perturbation tends to zero. The analysis, based upon a first-order differential inequality, introduces apparently new modifications of Korn's inequalities of the first and second kind.     

Transverse Decay of Solutions in an Elastic Cylinder

In a semiinfinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strainenergy flux through a plane crossection decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strainenergy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes.This problem is considered in the present paper which discusses a circular semiinfinite cylinder and derives an estimate for the strainenergy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strainenergy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.Sommario. E'noto che in un cilindro semiinfinito composto da materiale elastico lineare anisotropo, caricato sulla base ed incastrato lungo la superficie laterale, la soluzione elastica, misurata, per esempio, dal flusso di energia di deformazione attraverso una sezione trasversale piana, decade con legge al più esponenziale con la distanza dalla base. C'è tuttavia, anche un decadimento radiale della soluzione, misurato, per esempio, dall'energia di deformazione che passa dalla regione vicina all'asse del cilindro a quella vicin alla superficie laterale dove l'energia si annullaQuesto problema è qui studiato. Si discute in particolare un cilindro circolare semiinfinito e si deduce una stima per l'energia di deformazione contenuta in un anello cilindrico ad una distanza assegnata dalla base e di altezza variabile, e la cui superficie esterna coincide con la superficie laterale del cilindro. Si dimostra che l'energia di deformazione decade al più con legge algebrica a zero quando il raggio interno del cilindro si avvicina a quello esterno.     

Uniqueness and Complementary Energy in Nonlinear Elastostatics

Global uniqueness of the smooth stress and deformation to within the usual rigid-body translation and rotation is established in the null traction boundary value problem of nonlinear homogeneous elasticity on a n-dimensional star-shaped region. A complementary energy is postulated to be a function of the Biot stress and to be para-convex and rank-(n-1) convex, conditions analogous to quasi-convexity and rank-(n-2) of the stored energy function. Uniqueness follows immediately from an identity involving the complementary energy and the Piola-Kirchhoff stress. The interrelationship is discussed between the two conditions imposed on the complementary energy, and between these conditions and those known for uniqueness in the linear elastic traction boundary value problem.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.     

Block-spins interactions in the Ising model

We investigate the interactions between block-spins in the large magnetic field region for the nearest neighbour,d-dimensional, Ising model.     

The FT-IR study of the brain tissue of Labeo rohita due to arsenic intoxication

The brain is believed to be particularly vulnerable to arsenic due to its high oxygen consumption rate and high level of polyunsaturated fatty acids and relatively high rate of oxygen free radical generate without commensurable level of arsenic. Hence, in the present work an attempt is made to study the changes in the biochemical contents in the brain tissues of edible fish Labeo rohita due to arsenic intoxication using Fourier Transform Infrared (FT-IR) spectroscopy. FT-IR spectra reveal significant differences in absorbance intensities between the control and arsenic intoxicated brain tissues, reflecting an alteration on the major biochemical constituents, such as lipids, proteins and nucleic acids of the brain tissues of L. rohita due to arsenic intoxication. Further, the administration of antidote DMSA improves the protein and lipid contents significantly in the brain tissues when compared to arsenic intoxicated tissues. The decrease in α-helix structure due to arsenic intoxication might be responsible for the increase in β-sheet secondary structures, which is consistent with the mechanism of β-sheet formation.