Flexure of composite plates

A new higher order shear deformation theory of laminated composite plates is developed. The basic displacement variables in this theory are two partial normal displacements and two in-plane displacement parameters. The governing equations are presented in the form of four simultaneous partial differential equations. The shear deformation theories of Bhimareddy and Stevens, and of Reddy are special cases of this formulation. In their models, transverse shear strains will become zero at points in the plate where displacements are constrained to be zero such as those on fixed edges. This limitation has been overcome in the present formulation.

Macromechanical behaviour of composite laminates

An improved higher order transverse shear deformation theory is employed to arrive at modified constitutive relations which can be used in the flexural, buckling and vibration analysis of laminated plates and shells. The strain energy for such systems is then expressed in terms of the displacements and the rotations for ready reference and use. Numerical values of vibration frequencies are obtained using this formulation employing Ritz's method of analysis. The results are compared with those available in the literature to validate the analysis presented.

A fluctuation-based probe to athermal phase transitions

We focus on athermal phase transitions where in discrete and dissipative avalanches are observed in physical observables as the system jumps from one metastable state to another, when driven by an external field. Using higher order statistics of time dependent avalanches, or noise, in electrical resistivity during temperature-driven martensite transformation in thin nickel-titanium films, we demonstrate evidence suggesting the existence of a singular `global instability' or divergence of the correlation length as a function of temperature at the transition. These results not only establish a mapping of non-equilibrium first order phase transition and equilibrium critical phenomena, but perhaps also call for a re-evaluation of many existing experimental claims of self-organized criticality.

Dispersion in Unilateral Finlines on Anisotropic Substrates

The dispersion characteristics of the dominant and higher order modes in unilateral firdines on uniaxially anisotropic substrates have been obtained. The solution has been obtained by applying the equivalent transmission-line concept in the spectral domain and by using Galerkhr’s method. Numericaf results for the propagation constant as a function of the slot-width ratio and freqnency are presented.

Quest for new materials: Inorganic chemistry plays a crucial role

There is an endless quest for new materials to meet the demands of advancing technology. Thus, we need new magnetic and metallic/semiconducting materials for spintronics, new low-loss dielectrics for telecommunication, new multi-ferroic materials that combine both ferroelectricity and ferromagnetism for memory devices, new piezoelectrics that do not contain lead, new lithium containing solids for application as cathode/anode/electrolyte in lithium batteries, hydrogen storage materials for mobile/transport applications and catalyst materials that can convert, for example, methane to higher hydrocarbons, and the list is endless! Fortunately for us, chemistry - inorganic chemistry in particular - plays a crucial role in this quest. Most of the functional materials mentioned above are inorganic non-molecular solids, while much of the conventional inorganic chemistry deals with isolated molecules or molecular solids. Even so, the basic concepts that we learn in inorganic chemistry, for example, acidity/basicity, oxidation/reduction (potentials), crystal field theory, low spin-high spin/inner sphere-outer sphere complexes, role of d-electrons in transition metal chemistry, electron-transfer reactions, coordination geometries around metal atoms, Jahn-Teller distortion, metal-metal bonds, cation-anion (metal-nonmetal) redox competition in the stabilization of oxidation states - all find crucial application in the design and synthesis of inorganic solids possessing technologically important properties. An attempt has been made here to illustrate the role of inorganic chemistry in this endeavour, drawing examples from the literature its well as from the research work of my group.

Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

Fournier polarography revisited

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.

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.

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt. (C) 2010 Elsevier B.V. All rights reserved.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Noise minimization in RC-active filters using generalized impedance converters

A procedure has been given for minimizing the total output noise of a Generalized Impedance Converter (GIC), subject to constraints dictated by signal handling capability of the Operational Amplifiers and ease of microcircuit fabrication. The noise reduction is achieved only by the adjustment of RC elements of the GIC, and the total output noise after optimization in the example cited is close to the theoretical lower limit. The output noise of a higher-order filter can be reduced by RC-optimizing the individual GIC's of the active realization. Experimental results on a 20–24 kHz channel bank band-pass filter demonstrate the effectiveness of the above procedure.

The superfluid as a source of all interactions

The superfluid state of fermion-antifermion fields developed in our previous papers is generalized to include higher orbital and spin states. In addition to single-particle excitations, the system is capable of having real and virtual bound or quasibound composite excitations which are akin to bosons of spinJ P equal to0 �, 1�, 2+, etc. These pseudoscalar, vector, and tensor bosons can be massive or massless and provide the vehicles for strong, electromagnetic, weak, and gravitational interactions. The concept that the basic (unmanifest) fermion-antifermion interaction can lead to a multiplicity of manifest interactions seems to provide a basis for a unified field theory.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.