Novel approach to estimate fringe order in Moire profilometry

A novel approach to estimate fringe order in Moire topography is proposed. Along with the light source used to create shadow of the grating on the object (as in conventional moire), proposed method uses a second light source which illuminates the object with color bands from the side. Width of each colored band is set to match that height which leads to a 2 pi phase shift in moire fringes. This facilitates one to rule the object with colored bands, which can be used to estimate fringe order using a color camera with relatively low spatial resolution with out any compromise in height sensitivity. Current proposal facilitates one to extract 3D profile of objects with surface discontinuities. It also deals with the possible usage of moire topography (when combined with the proposed method) in extracting 3D surface profile of many objects with height discontinuities using a single 2D image. Present article deals with theory and simulations of this novel side illumination based approach.

A Microscopic Theory of the f.c.c.-b.c.c. Interface .

We present a first-principles theory of the equilibrium b.c.c.-f.c.c. interface at coexistence using the density functional method. We assume that the interfacial region has local body-centred tetragonal (b.c.t.) symmetry and predict typical interfacial widths to be of order 2 to 3 lattice spacings with typical energies close to 0.05 J/m2. These quantities are in good agreement with laboratory measurements on coherent interfaces.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Solvation dynamics in monohydroxy alcohols: Agreement between theory and different experiments

Recently three different experimental studies on ultrafast solvation dynamics in monohydroxy straight-chain alcohols (C-1-C-4) have been carried out, with an aim to quantify the time constant (and the amplitude) of the ultrafast component. The results reported are, however, rather different from different experiments. In order to understand the reason for these differences, we have carried out a detailed theoretical study to investigate the time dependent progress of solvation of both an ionic and a dipolar solute probe in these alcohols. For methanol, the agreement between the theoretical predictions and the experimental results [Bingemann and Ernsting J. Chem. Phys. 1995, 102, 2691 and Horng et al. J: Phys, Chern, 1995, 99, 17311] is excellent. For ethanol, propanol, and butanol, we find no ultrafast component of the time constant of 70 fs or so. For these three liquids, the theoretical results are in almost complete agreement with the experimental results of Horng et al. For ethanol and propanol, the theoretical prediction for ionic solvation is not significantly different from that of dipolar solvation. Thus, the theory suggests that the experiments of Bingemann and Ernsting and those of Horng et al. studied essentially the polar solvation dynamics. The theoretical studies also suggest that the experimental investigations of Joo et al. which report a much faster and larger ultrafast component in the same series of solvents (J. Chem. Phys. 1996, 104, 6089) might have been more sensitive to the nonpolar part of solvation dynamics than the polar part. In addition, a discussion on the validity of the present theoretical approach is presented. In this theory the ultrafast component arises from almost frictionless inertial motion of the individual solvent molecules in the force field of its neighbors.

Mapping adaptive resonance theory onto ring and mesh architectures

In recent years, parallel computers have been attracting attention for simulating artificial neural networks (ANN). This is due to the inherent parallelism in ANN. This work is aimed at studying ways of parallelizing adaptive resonance theory (ART), a popular neural network algorithm. The core computations of ART are separated and different strategies of parallelizing ART are discussed. We present mapping strategies for ART 2-A neural network onto ring and mesh architectures. The required parallel architecture is simulated using a parallel architectural simulator, PROTEUS and parallel programs are written using a superset of C for the algorithms presented. A simulation-based scalability study of the algorithm-architecture match is carried out. The various overheads are identified in order to suggest ways of improving the performance. Our main objective is to find out the performance of the ART2-A network on different parallel architectures. (C) 1999 Elsevier Science B.V. All rights reserved.

Mean-field theory of charge ordering and phase transitions in the colossal-magnetoresistive manganites

We study phase transitions in the colossal-magnetoresistive manganites by using a mean-field theory both at zero and non-zero temperatures. Our Hamiltonian includes double-exchange, superexchange, and Hubbard terms with on-site and nearest-neighbour Coulomb interaction, with the parameters estimated from earlier density-functional calculations. The phase diagrams show magnetic and charge-ordered (or charge-disordered) phases as a result of the competition between the double-exchange, superexchange, and Hubbard terms, the relative effects of which are sensitively dependent on parameters such as doping, bandwidth, and temperature. In accord with the experimental observations, several important features are reproduced from our model, namely, (i) a phase transition from an insulating, charge-ordered antiferromagnetic to a metallic, charge-disordered ferromagnetic state near dopant concentration x = 1/2, (ii) the reduction of the transition temperature TAF-->F by the application of a magnetic field, (iii) melting of the charge order by a magnetic field, and (iv) phase coexistence for certain values of temperature and doping. An important feature, not reproduced in our model, is the antiferromagnetism in the electron-doped systems, e.g., La1-xCaxMnO3 over the entire range of 0.5 less than or equal to x less than or equal to 1, and we suggest that a multi-band model which includes the unoccupied t(2g) orbitals might be an important ingredient for describing this feature.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2epsilon dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an epsilon expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2epsilon dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (theta term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as nu and p, control not only the scaling behavior of the conductances sigma(xx) and sigma(xy) at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (c(v)proportional toT(p)). To extract the numerical values of nu and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.

Theory of polymer breaking under tension

We consider the breaking of a polymer molecule which is fixed at one end and is acted upon by a force at the other. The polymer is assumed to be a linear chain joined together by bonds which satisfy the Morse potential. The applied force is found to modify the Morse potential so that the minimum becomes metastable. Breaking is just the decay of this metastable bond, by causing it to go over the barrier. Increasing the force causes the potential to become more and more distorted and eventually leads to the disappearance of the barrier. The limiting force at which the barrier disappears is D(e)a/2,D-e with a the parameters characterizing the Morse potential. The rate of breaking is first calculated using multidimensional quantum transition state theory. We use the harmonic approximation to account for vibrations of all the units. It includes tunneling contributions to the rate, but is valid only above a certain critical temperature. It is possible to get an analytical expression for the rate of breaking. We have calculated the rate of breaking for a model, which mimics polyethylene. First we calculate the rate of breaking of a single bond, without worrying about the other bonds. Inclusion of other bonds under the harmonic approximation is found to lower this rate by at the most one order of magnitude. Quantum effects are found to increase the rate of breaking and are significant only at temperatures less than 150 K. At 300 K, the calculations predict a bond in polyethylene to have a lifetime of only seconds at a force which is only half the limiting force. Calculations were also done using the Lennard-Jones potential. The results for Lennard-Jones and Morse potentials were rather different, due to the different long-range behaviors of the two potentials. A calculation including friction was carried out, at the classical level, by assuming that each atom of the chain is coupled to its own collection of harmonic oscillators. Comparison of the results with the simulations of Oliveira and Taylor [J. Chem. Phys. 101, 10 118 (1994)] showed the rate to be two to three orders of magnitude higher. As a possible explanation of discrepancy, we consider the translational motion of the ends of the broken chains. Using a continuum approximation for the chain, we find that in the absence of friction, the rate of the process can be limited by the rate at which the two broken ends separate from one another and the lowering of the rate is at the most a factor of 2, for the parameters used in the simulation (for polyethylene). In the presence of friction, we find that the rate can be lowered by one to two orders of magnitude, making our results to be in reasonable agreement with the simulations.

Quantum destruction of spiral order in two-dimensional frustrated magnets

We study the fate of spin-1/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z(2) character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z(2) vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.

A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier's method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.