Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Limit Analysis of Slabs with Free Edge

The general method earlier developed by the writers for obtaining valid lower bound solutions to slabs under uniformly distributed load and supported along all edges is extended to the slabs with a free edge. Lower bound solutions with normal moment criterion are presented for six cases of orthotropically reinforced slabs, with one of the short edges being free and the other three edges being any combination of fixed and simply supported conditions. The expressions for moment field and collapse load are given for each slab. The lower bounds have been compared with the corresponding upper bound values obtained from the yield line theory with simple straight yield line modes of failure. They are also compared with Nielsen’s solutions available for two cases with isotropic reinforcement.

Analysis of Long Cantilever Cylindrical Shell Subjected to Wind Loading

Bending analysis of closed cylindrical shells subjected to asymmetric load and having different support conditions is of interest in the design of chimneys, water towers, oil storage tanks, etc. A simple method of analyzing a long cantilever cylindrical shell, subjected to asymmetric load, is presented in the paper, using Schorer’s shell theory and orthogonal functions. The application of the solution has been illustrated with an example of a cantilever shell subjected to wind loads. The results obtained for this problem have been compared with the previously available results to illustrate the accuracy of the results obtained here. The solution presented can also be extended to a cylindrical shell with other support conditions, as well as to the study of free vibration of a cylindrical shell. The present solution will be very useful for designers who need to obtain numerical results for specific problems with minimum computational effort.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Topological analysis off charge density distribution in concomitant polymorphs of 3-acetylcoumarin, a case off packing polymorphism

Detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin in terms of experimental and theoretical densities shows significant differences in the intermolecular features when analyzed based on the topological properties via the quantum theory of atoms in molecules. The two forms, triclinic and monoclinic (Form A and Form B), pack in the crystal lattice via weak C-H---O and C-H---pi interactions. Form A results in a head-to-head molecular stack, while Form B generates a head-to-tail stack. Form A crystallizes in PI (Z' = 2) and Form B crystallizes in P2(1)/n (Z = 1). The electron density maps of the polymorphs demonstrate the differences in the nature of the charge density distribution in general. The charges derived from experimental and theoretical analysis show significant differences with respect to the polymorphic forms. The molecular dipole moments differ significantly for the two forms. The lattice energies evaluated at the HF and DFT (B3LYP) methods with 6-31G** basis set for the two forms clearly suggest that Form A is the thermodynamically stable form as compared to Form B. Mapping of electrostatic potential over the molecular surface shows dominant variations in the electronegative region, which bring out the differences between the two forms.

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.

Kinetic theory for the density plateau in the granular flow down an inclined plane

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is O(delta(2)) smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter delta = (d/(1 - e(n))H-1/2), d is the particle diameter, en is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small delta. Numerical estimates of both the parameter delta and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.

Infrared Spectra of Dimethylquinolines in the Gas Phase: Experiment and Theory

Infrared spectra of atmospherically important dimethylquinolines (DMQs), namely 2,4-DMQ, 2,6-DMQ, 2,7-DMQ, and 2,8-DMQ in the gas phase at 80 degrees C were recorded using a long variable path-length cell. DFT calculations were carried out to assign the bands in the experimentally observed spectra at the B3LYP/6-31G* level of theory. The spectral assignments particularly for the C-H stretching modes could not be made unambiguously using calculated anharmonic or scaled harmonic frequencies. To resolve this problem, a scaled force field method of assignment was used. Assignment of fundamental modes was confirmed by potential energy distributions (PEDs) of the normal modes derived by the scaled force fields using a modified version of the UMAT program in the QCPE package. We demonstrate that for large molecules such as the DMQs, the scaling of the force field is more effective in arriving at the correct assignment of the fundamentals for a quantitative vibrational analysis. An error analysis of the mean deviation of the calculated harmonic, anharmonic, and force field fitted frequencies from the observed frequency provides strong evidence for the correctness of the assignment.

Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

First-principles analysis of electron correlation, spin ordering and phonons in the normal state of FeSe1-x

We present first-principles density-functional-theory-based calculations to determine the effects of the strength of on-site electron correlation, magnetic ordering, pressure and Se vacancies on phonon frequencies and electronic structure of FeSe1-x. The theoretical equilibrium structure (lattice parameters) of FeSe depends sensitively on the value of the Hubbard parameter U of on-site correlation and magnetic ordering. Our results suggest that there is a competition between different antiferromagnetic states due to comparable magnetic exchange couplings between first- and second-neighbor Fe sites. As a result, a short range order of stripe antiferromagnetic type is shown to be relevant to the normal state of FeSe at low temperature. We show that there is a strong spin-phonon coupling in FeSe (comparable to its superconducting transition temperature) as reflected in large changes in the frequencies of certain phonons with different magnetic ordering, which is used to explain the observed hardening of a Raman-active phonon at temperatures (similar to 100 K) where magnetic ordering sets in. The symmetry of the stripe antiferromagnetic phase permits an induced stress with orthorhombic symmetry, leading to orthorhombic strain as a secondary order parameter at the temperature of magnetic ordering. The presence of Se vacancies in FeSe gives rise to a large peak in the density of states near the Fermi energy, which could enhance the superconducting transition temperature within the BCS-like picture.

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.

Improved hybrid elements for structural analysis

Hybrid elements, which are based on a two-field variational formulation with the displacements and stresses interpolated separately, are known to deliver very high accuracy, and to alleviate to a large extent problems of locking that plague standard displacement-based formulations. The choice of the stress interpolation functions is of course critical in ensuring the high accuracy and robustness of the method. Generally, an attempt is made to keep the stress interpolation to the minimum number of terms that will ensure that the stiffness matrix has no spurious zero-energy modes, since it is known that the stiffness increases with the increase in the number of terms. Although using such a strategy of keeping the number of interpolation terms to a minimum works very well in static problems, it results either in instabilities or fails to converge in transient problems. This is because choosing the stress interpolation functions merely on the basis of removing spurious energy modes can violate some basic principles that interpolation functions should obey. In this work, we address the issue of choosing the interpolation functions based on such basic principles of interpolation theory and mechanics. Although this procedure results in the use of more number of terms than the minimum (and hence in slightly increased stiffness) in many elements, we show that the performance continues to be far superior to displacement-based formulations, and, more importantly, that it also results in considerably increased robustness.

Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Bayesian Analysis of a Superimposed Renewal Process

Stochastic behavior of an aero-engine failure/repair process has been analyzed from a Bayesian perspective. Number of failures/repairs in the component-sockets of this multi-component system are assumed to follow independent renewal processes with Weibull inter-arrival times. Based on the field failure/repair data of a large number of such engines and independent Gamma priors on the scale parameters and log-concave priors on the shape parameters, an exact method of sampling from the resulting posterior distributions of the parameters has been proposed. These generated parameter values are next utilised in obtaining the posteriors of the expected number of system repairs, system failure rate, and the conditional intensity function, which are computed using a recursive formula.