Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

Theory of unitarity bounds and low-energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarily. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K-l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

A theory on the migration of an extraneous electron across hydrogen bonds in polypeptides

The migrating electrons in biological systems normally are extraneous and taking this into account the electron delocalisation across the hydrogen bonds in proteins is re-examined. It is seen that an extraneous electron can travel rapidly via the low-lying virtual orbitals of the hydrogen-bonded π-electronic structure of peptide units in proteins. The frequency of electron transfer decreases slowly with an increase in the path length. However, the coupling of electron and protonic motions enhances this frequency. Transfer of electrons across the hydrogen bonds in accordance with the double-exchange mechanism does not appear to be possible. This theory offers a possibility for an extraneous electron to transfer within protein structures.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. I. Theory

Based on a method proposed by Reddy and Daum, the equations governing the steady inviscid nonreacting gasdynamic laser (GDL) flow in a supersonic nozzle are reduced to a universal form so that the solutions depend on a single parameter which combines all the other parameters of the problem. Solutions are obtained for a sample case of available data and compared with existing results to validate the present approach. Also, similar solutions for a sample case are presented.

Weber-Fechner type nonlinear behavior in zigzag edge graphene nanoribbons

Using a continuum Dirac theory, we study the density and spin response of zigzag edge-terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g., width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of organs such as the eye and ear that obey Weber-Fechner law. We validate our analytical results with tight-binding calculations. These results are crucial in understanding important effects of electron-electron interactions in graphene nanoribbons such as edge magnetism, etc., and also suggest possibilities for device applications of graphene nanoribbons.

H I deficiency in cluster spiral galaxies - Dependence on galaxy size

From the available H I data on spiral galaxies in three rich Abell clusters and the Virgo Cluster, it is shown that galaxies with medium to large optical sizes tend to be more severely deficient in atomic hydrogen than the small galaxies. This is so both in terms of the fractional number of galaxies that are deficient and the amount of gas lost by a galaxy. The fraction of H I-deficient galaxies increases with size over most of the size range, saturating or dropping only for the largest galaxies. A comparative study is made of various currently accepted gas removal mechanisms, namely those which are a result of galaxy-intracluster medium interactions, e.g., ram pressure stripping, as well as those due to galaxy-galaxy interactions, i.e., collisions and tidal interactions. It is shown that, with the exception of tidal interactions, all of these mechanisms would produce a size dependence in H I deficiency that is the opposite of that observed. That is, the gas in the largest galaxies would be the least affected by these mechanisms. However, if there is significant mass segregation, these processes may give the trends observed in the size dependence of H I deficiency.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

Structure and superconducting properties of Tl1?yPbyY1?xCaxSr2Cu2O7star, open: Dependence of Tc on hole concentration

Structure and superconducting properties of Tl1?yPbyY1?xCaxSr2Cu2O7 (y=0.0, 0.1, 0.25 and 0.5) , derived from the parent insulator TlYSr2Cu2O7, have been investigated for different values of x. XANES studies show Pb to be in the 4+ state while Tl is in the 3+ state, suggesting thereby that in this series, (x?y) approximately corresponds to the hole concentration. The in-plane Cu---O distance decreases with increase in x for all values of y. The apical Cu---O distance as well as the Tl(Pb)---O(2) distance show anomalies at x=0.5 in the series with y=0.25; at this composition, Tc also reaches a maximum. In general, the composition (value of x) at which the Tc of Tl1?yPbyY1?xCaxSr2Cu2O7 reaches a maximum depends on the Pb content and the maximum Tc itself increases with increase in y, reaching a value of 105 K at y=0.5. More interestingly, a maximum Tc occurs at an (x?y) value of not, vert, similar0.25, which is close to the hole concentration at maximum Tc in other cuprate superconductors containing two CuO2 layers.

Psi-angle dependence of geminal proton–carbonyl-13C coupling constants in peptides. A theoretical investigation†

Theoretical calculations of the geminal carbonyl-13C- proton coupling constant, 2J(C′H), in α-amino acids have been carried out using Dirac Vector model and Penney-Dirac bond order formulations. The results indicate that the couplings are dependent on the backbone torsion angle psi (ψ) of the amino acid residues in peptides. The meagre available experimental data seem to support the theoretical findings.