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.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Spectral element approach to wave propagation in uncertain beam structures

This paper presents a study on the uncertainty in material parameters of wave propagation responses in metallic beam structures. Special effort is made to quantify the effect of uncertainty in the wave propagation responses at high frequencies. Both the modulus of elasticity and the density are considered uncertain. The analysis is performed using a Monte Carlo simulation (MCS) under the spectral finite element method (SEM). The randomness in the material properties is characterized by three different distributions, the normal, Weibull and extreme value distributions. Their effect on wave propagation in beams is investigated. The numerical study shows that the CPU time taken for MCS under SEM is about 48 times less than for MCS under a conventional one-dimensional finite element environment for 50 kHz loading. The numerical results presented investigate effects of material uncertainties on high frequency modes. A study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. These studies show that even for a small coefficient of variation, significant changes in the above parameters are noticed. A number of interesting results are presented, showing the true effects of uncertainty response due to dynamic impulse load.

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u(0), w, phi for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

Q-band beam waveguide

A report of the design, development ana periom~ance characteristics of a Q-band (8 nim) confoal. mned, aielectric lens beam waveguide is presented.

Q-Band beam wave-guide

Consideration is given to a 25-foot long Q-band (8 mm) confocal, zoned dielectric lens beam waveguide. Numerical expressions for the axial and radial fields are presented. The experimental set-up consisted of uniformly spaced zoned dielectric lenses, a transmitting horn and a receiving horn. It was found that: (1) the wave beam is reiterated when confocal, zoned dielectric lenses act as phase transformers in place of smooth surfaced transformers in beam waveguides; (2) the axial field is oscillatory near the source and the oscillation persists for about 25 cm from the source; (3) the oscillation disappears after one lens is used; (4) higher order modes with higher attenuation rates die out faster than fundamental modes; (5) phase transformers do not alter beam modes; (6) without any lens the beam cross-section broadens significantly in the Z-direction; (7) with one lens the beam exhibits the reiteration phenomenon; and (8) inserting a second lens on the axial and cross-sectional field distribution shows further the reiteration principle.

Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Theory of the effects of destruction of localization by inelastic scattering in the resistivity of pure thin potassium wires

Measurements of the electrical resistivity of thin potassium wires at temperatures near 1 K have revealed a minimum in the resistivity as a function of temperature. By proposing that the electrons in these wires have undergone localization, albeit with large localization length, and that inelastic-scattering events destroy the coherence of that state, we can explain both the magnitude and shape of the temperature-dependent resistivity data. Localization of electrons in these wires is to be expected because, due to the high purity of the potassium, the elastic mean free path is comparable to the diameters of the thinnest samples, making the Thouless length lT (or inelastic diffusion length) much larger than the diameter, so that the wire is effectively one dimensional. The inelastic events effectively break the wire into a series of localized segments, whose resistances can be added to obtain the total resistance of the wire. The ensemble-averaged resistance for all possible segmented wires, weighted with a Poisson distribution of inelastic-scattering lengths along the wire, yields a length dependence for the resistance that is proportional to [L3/lin(T)], provided that lin(T)?L, where L is the sample length and lin(T) is some effective temperature-dependent one-dimensional inelastic-scattering length. A more sophisticated approach using a Poisson distribution in inelastic-scattering times, which takes into account the diffusive motion of the electrons along the wire through the Thouless length, yields a length- and temperature-dependent resistivity proportional to (L/lT)4 under appropriate conditions. Inelastic-scattering lifetimes are inferred from the temperature-dependent bulk resistivities (i.e., those of thicker, effectively three-dimensional samples), assuming that a minimum amount of energy must be exchanged for a collision to be effective in destroying the phase coherence of the localized state. If the dominant inelastic mechanism is electron-electron scattering, then our result, given the appropriate choice of the channel number parameter, is consistent with the data. If electron-phason scattering were of comparable importance, then our results would remain consistent. However, the inelastic-scattering lifetime inferred from bulk resistivity data is too short. This is because the electron-phason mechanism dominates in the inelastic-scattering rate, although the two mechanisms may be of comparable importance for the bulk resistivity. Possible reasons why the electron-phason mechanism might be less effective in thin wires than in bulk are discussed.

A photoelastic approach to framed structure-foundation beam-soil interaction

The interaction of a framed structure with a foundation beam resting on an elastic medium, representing the soil, has been studied using the photoelastic method. The contact pressure distribution, the fibre stress in the foundation beam and frame structure, as well as the stresses in the elastic medium, have been obtained. These have been compared with theoretical results obtained by idealizing the soil as (a) elastic half plane, and (b) elastic half space. It is shown that the photoelastic method can provide an easy solution to this type of problem if the soil can be idealized as an elastic continuum.

A parity-violatingU4-gravitation theory

The general structure of a metric-torsion theory of gravitation allows a parity-violating contribution to the complete action which is linear in the curvature tensor and vanishes identically in the absence of torsion. The resulting action involves, apart from the constant ¯K E =8pgr/c4, a coupling (B) which governs the strength of the parity interaction mediated by torsion. In this model the Brans-Dicke scalar field generates the torsion field, even though it has zero spin. The interesting consequence of the theory is that its results for the solar-system differ very little from those obtained from Brans-Dicke (BD) theory. Therefore the theory is indistinguishable from BD theory in solar-system experiments.

A Theory of the Lifted Temperature Minimum on Calm Clear Nights

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of $\frac{1}{2}$ m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several hours, and has not so far been satisfactorily explained. We formulate here a theory that considers energy balance between radiation, conduction and free or forced convection in humid air, with surface temperature, humidity and wind incorporated into an appropriate mathematical model as parameters. A complete numerical solution of the coupled air-soil problem is used to validate an approach that specifies the surface temperature boundary condition through a cooling rate parameter. Utilizing a flux-emissivity scheme for computing radiative transfer, the model is numerically solved for various values of turbulent friction velocity. It is shown that a lifted minimum is predicted by the model for values of ground emissivity not too close to unity, and for sufficiently low surface cooling rates and eddy transport. Agreement with observation for reasonable values of the parameters is demonstrated. A heuristic argument is offered to show that radiation substantially increases the critical Rayleigh number for convection, thus circumventing or weakening Rayleigh-Benard instability. The model highlights the key role played by two parameters generally ignored in explanations of the phenomenon, namely surface emissivity and soil thermal conductivity, and shows that it is unnecessary to invoke the presence of such particulate constituents as haze to produce a lifted minimum.

Dynamic response of a beam on elastic foundation of finite depth under a moving force

In this paper, dynamic response of an infinitely long beam resting on a foundation of finite depth, under a moving force is studied. The effect of foundation inertia is included in the analysis by modelling the foundation as a series of closely spaced axially vibrating rods of finite depth, fixed at the bottom and connected to the beam at the top. Viscous damping in the beam and foundation is included in the analysis. Steady state response of the beam-foundation system is obtained. Detailed numerical results are presented to study the effect of various parameters such as foundation mass, velocity of the moving load, damping and axial force on the beam. It is shown that foundation inertia can considerably reduce the critical velocity and can also amplify the beam response.

Electron-beam weld microstructures and properties of aluminium-lithium alloy 8090

Lithium-containing aluminium alloys are of considerable current interest in the aerospace and aircraft industries because lithium additions to aluminium improve the modulus and decrease the density compared to conventional aluminium alloys. Few commercial aluminium-lithium alloys have emerged for use in the aerospace industry. One such candidate is 8090, a precipitation-hardenable Al-Li-Cu-Mg alloy. The influence of electron-beam welding on the microstructure and mechanical properties of alloy 8090 material has been evaluated through microscopical observations and mechanical tests. Microscopic observations of the electronbeam welds revealed an absence of microporosity and hot cracking, but revealed presence of microporosity in the transverse section of the weld. Mechanical tests revealed the electronbeam weld to have lower strength, elongation and joint efficiency. A change in microscopic fracture mode was observed for the welded material when compared to the unwelded counterpart. An attempt is made to rationalize the behaviour in terms of competing mechanistic effects involving the grain structure of the material, the role of matrix deformation characteristics, grain-boundary chemistry and grain-boundary failure.