A matrix identity and perturbation expressions

An identity expressing formally the diagonal and off-diagonal elements of an inverse of a matrix is deduced employing operator techniques. Several well-known perturbation expressions for the self-energy are deduced as special cases. A new approximation and other applications following from the above formalism are briefly indicated through illustrations from a perturbed harmonic oscillator, chemisorption approximations and Kelly's result in the problem of electron correlation.

A study of interactions in He2 1 in terms of the electronic forces

The He+He+1 interactions have been studied, as a function of the internuclear separation R, in terms of the electronic forces acting on the nuclei and the change in the charge distribution. The analysis reveals that at large R the atomic densities are polarized inwards, causing an attractive force on each nucleus, while at small R the difference in the nature of the interactions in the 2Σu and 2Σg systems is noted. It is seen that the He+He+1 (2Σu) interaction is less attractive than the He+1+He+1 interaction at lower values of R.

Effect of interface friction on the mechanics of indentation of a finite layer resting on a rigid substrate

Copper strips of 2.5 mm thickness resting on stainless steel anvils were normally indented by wedges under nominal plane strain conditions. Inflections in the hardness-penetration characteristics were identified. Inflections separate stages where each stage has typical mechanics of deformation. These are arrived at by studying the distortion of 0.125 mm spaced grids inscribed on the deformation plane of the strip. The sensitivity of hardness and deformation mechanics to wedge angle and the interfacial friction between strip and anvil were investigated within the framework of existing slip line field models of indentation of semi-infinite and finite blocks.

A Low-Complexity Algorithm for Intrusion Detection in a PIR-Based Wireless Sensor Network

We present a low-complexity algorithm for intrusion detection in the presence of clutter arising from wind-blown vegetation, using Passive Infra-Red (PIR) sensors in a Wireless Sensor Network (WSN). The algorithm is based on a combination of Haar Transform (HT) and Support-Vector-Machine (SVM) based training and was field tested in a network setting comprising of 15-20 sensing nodes. Also contained in this paper is a closed-form expression for the signal generated by an intruder moving at a constant velocity. It is shown how this expression can be exploited to determine the direction of motion information and the velocity of the intruder from the signals of three well-positioned sensors.

The short range interactions between two rare gas atoms

The short range interactions in He2, Ne2 and Ar2 have been studied in terms of the electronic forces as functions of their internuclear separations employing their single configuration SCF wave functions. The results show that the constituent molecular orbitals behave differently in terms of the forces they exert on the nuclei during the interaction process. The different behaviour of the orbitals is also reflected in the redistribution of charges.

Mechanistic Aspects of Nucleophilic Substitution at Half-Sandwich Metal Complexes

The hydrolysis reactions of organometallic ruthenium(II) piano-stool complexes of the type Ru-II(eta(6)-cymene)(L)Cl](0/+) (1-5, where L = kappa(1)- or kappa(2)-1,1-bis(diphenylphosphino)methane,1,1bis-(diphenylphosphino)methane oxide, kappa(1)-mercaptobenzothiazole) have been studied using density functional theory at the B3LYP level. In addition to considering a syn attack in an associative fashion, where the nucleophile approaches from the same side as the leaving group, we have explored alternative paths such as an anti attack in an associative manner, where the nucleophile attacks from the opposite side of the leaving group. During the anti attack, an intermediate is formed and there is a coordination mode change of the arene ring from eta(6) to eta(2) along with its rotation. When the intermediate goes to the product, the arene ring slips back from eta(2) to eta(6) coordination. This coordinated movement of the arene ring makes the associative anti attack an accessible pathway for the substitution process. Our calculations predict very similar activation barriers for both syn and anti attacks. In the dissociative path, the rate-determining step is the generation of a coordinatively unsaturated 16-electron ruthenium species. This turns out to be viable once solvent effects are included. The large size of the ancillary ligands on Ru makes the dissociative process as favorable as the associative process. Activation energy calculations reveal that although the dissociative path is favorable for kappa(1) complexes, both dissociative and associative processes can have significant contribution to the hydrolysis reaction in kappa(2) complexes. Once activated by hydrolysis, these complexes react with guanine and adenine bases of DNA. The thermodynamic stabilities of complexes formed with the nucleobases are also presented.

Barrier crossing in one and three dimensions by a long chain

We consider the Kramers problem for a long chain polymer trapped in a biased double-well potential. Initially the polymer is in the less stable well and it can escape from this well to the other well by the motion of its N beads across the barrier to attain the configuration having lower free energy. In one dimension we simulate the crossing and show that the results are in agreement with the kink mechanism suggested earlier. In three dimensions, it has not been possible to get an analytical `kink solution' for an arbitrary potential; however, one can assume the form of the solution of the nonlinear equation as a kink solution and then find a double-well potential in three dimensions. To verify the kink mechanism, simulations of the dynamics of a discrete Rouse polymer model in a double well in three dimensions are carried out. We find that the time of crossing is proportional to the chain length, which is in agreement with the results for the kink mechanism. The shape of the kink solution is also in agreement with the analytical solution in both one and three dimensions.