Eigenvalues of large even annulenes in terms ofK 3,S 4 andS 5

Squares of the adjacency matrices of bipartite cycles (C_v) can be block-factored into matrices which correspond to vertex-weighted complete graphs forv = 6, vertex-weighted strongly regular graphs forv = 8 and 10, and vertex-weighted metrically regular graphs forv > 10. Using this fact and some properties of strongly and metrically regular graphs, it is shown that eigenvalues of large bipartite C _v graphs (i.e. large even annulenes) can be expressed by the general formula ± (2 ± (2 ± (... ± (2 +r _p)) ...), wherev = 2 ⁿ ×p,n is the number of surd () signs required andp = 3, 4 and 5. Here,r ₃,r ₄, andr ₅, are the eigenvalues of the complete graphK ₃ and the strongly regular graphsS ₄ andS ₅ respectively. The procedure does not require construction of characteristic polynomials for the determination of eigenvalues, and brings out a common topological origin for the two-fold degeneracies observed in the eigenvalue spectra of all even cycles and many odd cycles.     

Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

Formation energies and swelling of uranium dioxide by point defects

Hybrid density functional theory is used to study the stability and behavior of rare gases in uranium dioxide. Three insertion sites are considered: the octahedral interstitial position and the oxygen and uranium substitution sites. The optimized lattice constant, the volume variation induced by gaseous atom incorporation, and the defect formation energy are studied for each rare gas. Both lattice constants and formation energies increase with increase in radii of the rare gases. The octahedral interstitial position is the most favorable occupation site. The formation energy is found to be negative only for He at an interstitial site.     

Design of a Hybrid Fiber-Optic Network Using 3-D Optical Code Sequences

We present the design of a 3-dimensional (3-D) noncoherent optical hybrid network. We also report the design of a new family of 3-D codes for fiber optic hybrid networks. We show that the hybrid network allows for shorter bit times and a higher number of users, given a set chip rate, compared to previously conceived networks. These newly designed hybrid single-pulse-per-row (HSPR) codes have very low autocorrelation side-lobes and very small cross-correlation peaks. We compare the performance of our hybrid model using our codes with the Optical Orthogonal Codes (OOCs) and Temporal/Spatial (T/S) codes and show that the new network can support a greater number of users and higher data rates than those using OOCs and T/S codes.     

Molecular hydrogen and oxygen interactions with armchair Si nanotubes

Molecular hydrogen and oxygen adsorptions on a (6, 6) armchair silicon nanotube have been studied by optimizing the distances of the admolecules from both inside and outside the tube. Full geometry and spin optimizations have been performed without any symmetry constraints with an all electron 3-21G* basis set and the B3LYP functional. The molecule is originally placed perpendicular or parallel to the tube axis. Hydrogen adsorption with the molecular axis aligned parallel to the surface of the nanotube is less favorable. Hydrogen molecule does not dissociate while oxygen molecule dissociates after optimization. The on-top site is the only preferred site for hydrogen molecule with an adsorption energy of 3.71 eV and an optimized distance of 3.31 for external adsorption whereas the on-top site is the most preferred site with adsorption energy of 3.69 eV for internal adsorption. For oxygen, the molecule dissociates and the most preferred sites are the two bridge sites with an adsorption energy of 9.64 eV, the optimized distance being 1.65/1.68 Å when it is adsorbed from the outside of the tube. When oxygen molecule is originally placed at on-top site it will hold as a molecule after adsorption with a slightly increased bond length. For the internal adsorption of oxygen, the molecules also dissociate in most cases and the zigzag bridge site is the most preferred site. After molecular adsorption for both hydrogen and oxygen, the buckling of the nanotubes increased. Frustration effects in the nanotube due to molecular adsorption are also noted.     

Effect of Si/Ge ratio on resistivity and thermopower in Gd5SixGe4−x magnetocaloric compounds

The effect of Si/Ge ratio on resistivity and thermopower behavior has been investigated in the magnetocaloric ferromagnetic Gd₅Si_xGe_4−x compounds with x=1.7-2.3. Microstructural studies reveal the presence of Gd₅(Si,Ge)₄-matrix phase (5:4-type) along with traces of secondary phases (5:5 or 5:3-type). The x=1.7 and 2.0 samples display the presence of a first order structural transition from orthorhombic to monoclinic phase followed by a magnetic transition of the monoclinic phase. The alloys with x=2.2 and 2.3 display only magnetic transitions of the orthorhombic phase. A low temperature feature apparent in the AC susceptibility and resistivity data below 100 K reflects an antiferromagnetic transition of secondary phase(s) present in these compounds. The resistivity behavior study correlates with microstructural studies. A large change in thermopower of −8 μV/K was obtained at the magneto-structural transition for the x=2 compound.     

A soft-segmentation visualization scheme for magnetic resonance images

Prevalent visualization tools exploit gray value distribution in images through modified histogram equalization and matching technique, referred to as the window width/window level-based method, to improve visibility and enhance diagnostic value. The window width/window level tool is extensively used in magnetic resonance (MR) images to highlight tissue boundaries during image interpretation. However, the identification of different regions and distinct boundaries between them based on gray-level distribution and displayed intensity levels is extremely difficult because of the large dynamic range of tissue intensities inherent in MR images. We propose a soft-segmentation visualization scheme to generate pixel partitions from the histogram of MR image data using a connectionist approach and then generate selective visual depictions of pixel partitions using pseudo color based on an appropriate fuzzy membership function. By applying the display scheme in clinical examples in this study, we could demonstrate additional overlapping regions between distinct tissue types in healthy and diseased areas (in the brain) that could help improve the tissue characterization ability of MR images.     

Absorption spectrometric study of charge transfer complex formation between 4-acetamidophenol (paracetamol) and a series of quinones including vitamin K3

The formation of charge transfer (CT) complexes of 4-acetamidophenol (commonly called 'paracetamol') and a series of quinones (including Vitamin K3) has been studied spectrophotometrically in ethanol medium. The vertical ionisation potential of paracetamol and the degrees of charge transfer of the complexes in their ground state has been estimated from the trends in the charge transfer bands. The oscillator and transition dipole strengths of the complexes have been determined from the CT absorption spectra at 298 K. The complexes have been found by Job's method of continuous variation to have the uncommon 2:1 (paracetamol:quinone) stoichiometry in each case. The enthalpies and entropies of formation of the complexes have been obtained by determining their formation constants at five different temperatures.     

Studies on the molecular interaction of Erythrosine ‘B’ with surfactants

The spectroscopic investigation on anionic dye, Erythrosine ‘B’(EB) with three different types of surfactants such as CTAB (cationic), sodium lauryl sulphate (SLS; anionic) and Triton X-100 (TX-100),Tween-20, 40, 60 and 80 (nonionic) in aqueous media shows that EB forms a 1:1 molecular complex with TX-100, Tweens and CTAB. No interaction is observed between EB and SLS. The thermodynamic and spectrophotometric properties of these complexes suggest that EB forms a strong charge transfer (CT) complex with TX-100 and Tweens whereas the interaction of EB with CTAB is coulombic in nature. Photogalvanic and photoconductometric studies also support the above interactions. In addition to this, the electron-donating ability among the nonionic surfactants, i.e. TX-100 and Tweens towards dye, role of surface in CT interaction, the site of CT interaction and the intensity and stability of CT interaction between EB and nonionic surfactants have been pointed out.