A three-dimensional solution for plates and laminates

A general three-dimensional solution is presented for statics and dynamics of plates, homogeneous or laminated, of orthotropic materials. The solution is in series form. Using parts of the general solution a variety of problems, especially of rectangular configurations, can be solved. As Mindlin's approximate analysis for vibration of thick plates is often adequate for specific practical purposes, a general solution for Mindlin's analysis is also given.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Open manifolds, Ozsvath-Szabo invariants and exotic R-4 ` S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R-4 for which the invariant is non-trivial,showing that X is an exotic R-4. This is the first invariant that detects exotic R-4' s. (C) 2009 Published by Elsevier GmbH.

Structure and dynamics of benzene in one-dimensional channels

Molecular dynamics investigation of benzene in one-dimensional channel systems A1PO(4)-5, VPI-5, and carbon nanotube is reported. The results suggest that, in all the three host systems, the plane of benzene is almost perpendicular to the channel axis when the molecule is near the center of the channel and the plane of benzene is parallel to the channel axis when the molecule is near the wall of the channel. The density distribution of benzene as a function of channel length, z and the radial distance, r, from the channel axis is also different in the three host structures. Anisotropy in translational diffusion coefficient, calculated in body-fixed frame of benzene, suggests that benzene prefers to move with its plane parallel to the direction of motion in A1PO(4)-5 and VPI-5 whereas in carbon nanotube the motion occurs predominantly with the plane of the benzene perpendicular to the direction of motion.;Anisotropy associated with the rotational motion is seen to alter significantly in confinement as compared to liquid benzene. In A1PO(4)-5, the rotational anisotropy is reversed as compared to liquid benzene thereby suggesting that anisotropy arising out of molecular geometry can be reduced. Reorientational correlation times for C-6 and C-2 axes Of benzene are reported. Apart from the inertial decay of reorientational correlation function due to free, rotation, two other distinct regimes of decay are observed in narrower channels (AIPO(4)-5 and carbon nanotube): (i) an initial fast decay (0.5-2 ps) and (ii) a slower decay (>2 ps) of reorientational correlation function where C-6 decays slower than C-2 Similar to what is observed in liquid benzene. In the initial fast decay, it is seen that the decay for C-6 is faster than C-2 which is in contrast to what is observed in liquid benzene or for benzene confined in VPI-5.

Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values

Structural and spectral perspectives of a novel thiosemicarbazone synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide

A new thiosemicarbazone, HL is synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide and structurally and spectrochemically characterized. H-1 NMR, C-13 NMR, COSY, HMQC and IR spectra of the compound are studied and the proton magnetic resonance spectrum reveals some unprecedented observations. The thione form is predominant in the solid state, as supported by the crystal structure and IR data, while a thiol-thione equilibrium is proposed in the solution state by NMR studies. The compound crystallizes into a monoclinic lattice with space group C2/c and the ZE conformation is exhibited by the thiosemicarbazone. Intra- and intermolecular hydrogen-bonding interactions give rise to a two-dimensional packing in the crystal lattice

A note on the equivalence of shock manifold equations

The shock manifold equation is a first order nonlinear partial differential equation, which describes the kinematics of a shockfront in an ideal gas with constant specific heats. However, it was found that there was more than one of these shock manifold equations, and the shock surface could be embedded in a one parameter family of surfaces, obtained as a solution of any of these shock manifold equations. Associated with each shock manifold equation is a set of characteristic curves called lsquoshock raysrsquo. This paper investigates the nature of various associated shock ray equations.

A two-dimensional model for crack closure effect in plates under bending

A two-dimensional model is proposed for taking into account the establishment of contact on the compression side of crack faces in plates under bending. An approximate but simple method is developed for evaluating reduction of stress intensity factor due to such ‘crack closure’. Analysis is first carried out permitting interference of the crack faces. Contact forces are then introduced on the crack faces and their magnitudes determined from the consideration that the interference is just eliminated. The method is based partly on finite element analysis and partly on a continuum analysis using Irwin's solution for point loads on the crack line.

Resistance fluctuations, phase randomness and noise in one-dimensional conductors with a long-range correlated potential

When the size (L) of a one-dimensional metallic conductor is less than the correlation length λ-1 of the Gaussian random potential, one expects transport properties to show ballistic behaviour. Using an invariant imbedding method, we study the exact distribution of the resistance, of the phase θ of the reflection amplitude of an incident electron of wave number k0, and of dθ/dk0, for λL ll 1. The resistance is non-self-averaging and the n-th resistance moment varies periodically as (1 - cos 2k0L)n. The charge fluctuation noise, determined by the distribution of dθ/dk0, is constant at low frequencies.

Structural and spectral perspectives of a novel thiosemicarbazone synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide

A new thiosemicarbazone, HL is synthesized from di-2-pyridyl ketone and 4-phenyl-3-thiosemicarbazide and structurally and spectrochemically characterized. H-1 NMR, C-13 NMR, COSY, HMQC and IR spectra of the compound are studied and the proton magnetic resonance spectrum reveals some unprecedented observations. The thione form is predominant in the solid state, as supported by the crystal structure and IR data, while a thiol-thione equilibrium is proposed in the solution state by NMR studies. The compound crystallizes into a monoclinic lattice with space group C2/c and the ZE conformation is exhibited by the thiosemicarbazone. Intra- and intermolecular hydrogen-bonding interactions give rise to a two-dimensional packing in the crystal lattice. (c) 2005 Elsevier B.V. All rights reserved.