Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Flow and heat transfer in steady laminar compressible boundary layer swirling flow in a nozzle

The axisymmetric steady laminar compressible boundary layer swirling flow of a gas with variable properties in a nozzle has been investigated. The partial differential equations governing the non-similar flow have been transformed into new co-ordinates having finite ranges by means of a transformation which maps an infinite range into a finite one. The resulting equations have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for compressible swirling flow through a convergent conical nozzle. The results indicate that the swirl exerts a strong influence on the longitudinal skin friction, but its effect on the tangential skin friction and heat transfer is comparatively small. The effect of the variation of the density-viscosity product across the boundary layer is appreciable only at low-wall temperature. The results are in good agreement with those of the local-similarity method for small values of the longitudinal distance.

Free vibration of circular plates of arbitrary thickness

Free vibration of circular plates of arbitrary thickness is investigated using the method of initial functions. State-space approach is used to derive the governing equations of the above method. The formulation is such that theories of any desired order can be obtained by deleting higher terms in the infinite-order differential equations. Numerical results are obtained for flexural and extensional vibration of circular plates. Results are also computed using Mindlin's theory and they are in agreement with the present analysis.

Theoretical Treatment of Interaction Parameters in Multicomponent Metallic Solutions

A new theoretical equation for interaction parameter in multicomponent metallic solutions is developed using the pseudopotential formalism coupled with the free energy of the hard sphere system. The approximate expression for the pseudopotential term is given in terms of the heat of solution at infinite dilution, to allow easy evaluation of the interaction parameter in various multicomponent systems. This theory has been applied to 23 non-ferrous alloys based on Pb, Sn, Bi and indium. Comparison with the results of previous theoretical calculations using only the hard sphere model suggests that the inclusion of the pseudopotential term yields a quantitatively more correct prediction of interaction parameters in multicomponent metallic solutions. Numerical calculations were also made for 320 Fe-base solutions relevant to steelmaking and the agreement between calculation and experimental data appears reasonable, with 90% reliability in predicting the correct sign.

Volume effects and associations in liquid alloys

The regular associated solution model for binary systems has been modified by incorporating the size of the complex as an explicit variable. The thermodynamic properties of the liquid alloy and the interactions between theA ?B type of complex and the unassociated atoms in anA-B binary have been evaluated as a function of relative size of the complex using the activity coefficients at infinite dilution and activity data at one other composition in the binary. The computational procedure adopted for determining the concentration of clusters and interaction energies in the associated liquid is similar to that proposed by Lele and Rao. The analysis has been applied to the thermodynamic mixing functions of liquid Al-Ca alloys believed to contain Al2Ca associates. It is found that the size of the cluster significantly affects the interaction energies between the complex and the unassociated atoms, while the equilibrium constant and enthalpy change for the association reaction exhibit only minor variation, when the equations are fitted to experimental data. The interaction energy between unassociated free atoms remains virtually unaltered as the size of the complex is varied between extreme values. Accurate data on free energy, enthalpy, and volume of mixing at the same temperature on alloy systems with compound forming tendency would permit a rigorous test of the proposed model.

X-ray studies on crystalline complexes involving amino acids and peptides. XV. Crystal structures of L-lysine D-glutamate and L-lysine D-aspartate monohydrate and the effect of chirality on molecular aggregation

L-Lysine D-glutamate crystallizes in the monoclinic space group P2(1) with a = 4.902, b = 30.719, c = 9.679 A, beta = 90 degrees and Z = 4. The crystals of L-lysine D-aspartate monohydrate belong to the orthorhombic space group P2(1)2(1)2(1) with a = 5.458, b = 7.152, c = 36.022 A and Z = 4. The structures were solved by the direct methods and refined to R values of 0.125 and 0.040 respectively for 1412 and 1503 observed reflections. The glutamate complex is highly pseudosymmetric. The lysine molecules in it assume a conformation with the side chain staggered between the alpha-amino and the alpha-carboxylate groups. The interactions of the side chain amino groups of lysine in the two complexes are such that they form infinite sequences containing alternating amino and carboxylate groups. The molecular aggregation in the glutamate complex is very similar to that observed in L-arginine D-aspartate and L-arginine D-glutamate trihydrate, with the formation of double layers consisting of both types of molecules. In contrast to the situation in the other three LD complexes, the unlike molecules in L-lysine D-aspartate monohydrate aggregate into alternating layers as in the case of most LL complexes. The arrangement of molecules in the lysine layer is nearly the same as in L-lysine L-aspartate, with head-to-tail sequences as the central feature. The arrangement of aspartate ions in the layers containing them is, however, somewhat unusual. Thus the comparison between the LL and the LD complexes analyzed so far indicates that the reversal of chirality of one of the components in a complex leads to profound changes in molecular aggregation, but these changes could be of more than one type.

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.

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Effect of interface friction on the mechanics of indentation of a finite layer resting on a rigid substrate

Copper strips of 2.5 mm thickness resting on stainless steel anvils were normally indented by wedges under nominal plane strain conditions. Inflections in the hardness-penetration characteristics were identified. Inflections separate stages where each stage has typical mechanics of deformation. These are arrived at by studying the distortion of 0.125 mm spaced grids inscribed on the deformation plane of the strip. The sensitivity of hardness and deformation mechanics to wedge angle and the interfacial friction between strip and anvil were investigated within the framework of existing slip line field models of indentation of semi-infinite and finite blocks.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

A simple and inexpensive two channel boxcar integrator

A two-channel boxcar integrator with an analog to digital converter was constructed using integrated circuits wherever convenient. The digital output can be instantaneously displayed or displayed after accumulating many samplings in the totaliser. The totaliser mode provides averaging at the digitiser level and hence the integrator has an infinite holding time. When used in the double boxcar mode the instrument overcomes the problem of any base line instability.

The first structurally characterized diruthenium(II,III) complex with four bridging arylcarboxylato ligands

The diruthenium(II,III) compound [Ru2Cl(O2CC6H4-p-OMe)4](H2O)0.25 (1) has been prepared and its crystal structure determined by X-ray studies. The crystals belong to the triclinic space group, PImage , and the asymmetric unit consists of one full dimer and two half dimers. The {Ru2(O2CC6H4-p-OMe)4+} units are bridged by chloride ions into an infinite zigzag chain, with an average Ru---Cl distance and Ru---Cl---Ru angle of 2.567(2) Å and 121.0(1)°, respectively. The average Ru---Ru distance of 2.286(1) Å in 1 is comparable with that in analogous tetra-alkylcarboxylates, Ru2Cl(O2CR)4 and tetra-amidates, Ru2Cl(ArCONH)4.

The contribution of polarons, bipolarons and intersite tunneling to low temperature conductivity in doped polypyrrole

The conductivity of highly doped polypyrrole is less than that of intermediately doped samples, by two orders of magnitude, at 4.2 K. This may be due to more number of bipolarons in highly doped samples. Bipolarons require four times more activation energy than single polarons to hop by thermally induced virtual transitions to intermediate dissociated polaron states than by the nondissociated process. The conduction process in these polyconjugated systems involve ionization from deep trapped states, having a View the MathML source dependence, hopping from localised states, having View the MathML source dependence, and intersite tunnel percolation, having T−1 dependence. The interplay of these factors leads to a better fit by View the MathML source. The mechanism for this exponential behaviour need not be same as that of Motts variable range hopping. Conduction by percolation is possible, if an infinite cluster of chains can be connected by impurity centers created by dopant ions. The tendency for the saturation of conductivity at very low temperatures is due to the possibility of intersite tunnel percolation is disordered polaronic systems.