A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.

Structural and dielectric characteristics of Bi2O3-TiO2-SrB4O7 glasses

Glasses of the composition 0.20 Bi2O3 - 0.30 TiO2 - 0.50 SrB4O7 and 0.30 Bi2O3 - 0.45 TiO2 - 0.25 SrB4O7 have been fabricated by conventional glass processing technique. These glasses have been characterized using X-ray powder diffraction (XRD), differential thermal analysis (DTA) and high resolution transmission electron microscopy (HRTEM). The frequency response of the dielectric constant and the loss tangent of these glasses has been studied. The formation of the crystalline bismuth titanate, Bi4Ti3O12 (BiT) phase in the heat treated samples has been confirmed by XRD and HRTEM studies. The measured ET Of the glass-ceramics are found to be in good agreement with those predicted by the logarithmic mixture rule. Optical second harmonic generation (SHG) at 1064 nm has been observed in the heat treated samples and is attributed to the formation of crystalline Bi4Ti3O12 (BiT) phase in the SrB4O7 (SBO) matrix.

Synthesis, growth, and characterization of a new NLO material 3-(2,3-dimethoxyphenyl)-1-(pyridin-2-yl)prop-2-en-1-one

3-(2,3-Dimethoxyphenyl)-1-(pyridin-2-yl)prop-2-en-1-one (DMPP) a potential second harmonic generating (SHG) has been synthesized and grown as a single crystal by the slow evaporation technique at ambient temperature. The structure determination of the grown crystal was done by single crystal X-ray diffraction study. DMPP crystallizes with orthorhombic system with cell parameters a = 20.3106(8)angstrom, b = 4.9574(2)angstrom, c = 13.4863(5)angstrom, alpha = 90 degrees, beta = 90 degrees, gamma = 90 degrees and space group Pca2(1). The crystals were characterized by FT-IR, thermal analysis, UV-vis-NIR spectroscopy and SHG measurements. Various functional groups present in DMPP were ascertained by FTIR analysis. DMPP is thermally stable up to 80 degrees C and optically transparent in the visible region. The crystal exhibits SHG efficiency comparable to that of KDP. (C) 2011 Elsevier B.V. All rights reserved.

Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth

Scattering of water waves by a sphere in a two-layer fluid, where the upper layer has an ice-cover modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves - the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave scattering by a submerged sphere placed in either of the layers. The exciting forces for vertical and horizontal directions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero, the numerical results for the exciting forces for the problem with free surface are recovered as particular cases. (C) 2011 Elsevier Ltd. All rights reserved.

Minimization of the effects of harmonics and voltage dip caused by electric arc furnace

This study examines the thermal efficiency of the operation of arc furnace and the effects of harmonics and voltage dips of a factory located near Bangkok. It also attempts to find ways to improve the performance of the arc furnace operation and minimize the effects of both harmonics and voltage dips. A dynamic model of the arc furnace has been developed incorporating both electrical and thermal characteristics. The model can be used to identify potential areas for improvement of the furnace and its operation. Snapshots of waveforms and measurement of RMS values of voltage, current and power at the furnace, at other feeders and at the point of common coupling were recorded. Harmonic simulation program and electromagnetic transient simulation program were used in the study to model the effects of harmonics and voltage dips and to identify appropriate static and dynamic filters to minimize their effects within the factory. The effects of harmonics and voltage dips were identified in records taken at the point of common coupling of another factory supplied by another feeder of the same substation. Simulation studies were made to examine the results on the second feeder when dynamic filters were used in the factory which operated the arc furnace. The methodology used and the mitigation strategy identified in the study are applicable to general situation in a power distribution system where an arc furnace is a part of the load of a customer

Structural, vibrational and thermal studies of a new nonlinear optical material: L-Asparagine-L-tartaric acid

Crystals of a new nonlinear optical (NLO) material, viz., L-asparagine-L-tartaric acid (LALT)(1) were grown by slow evaporation of an aqueous solution containing equimolar concentrations of L-asparagine and t-tartaric acid. The structure of the title compound which crystallizes in the non-centrosymmetric monoclinic space group P2(1) consists of a molecule of L-asparagine and a molecule of free L-tartaric acid both of which are interlinked by three varieties of H-bonding interactions namely O-H center dot center dot center dot O, N-H center dot center dot center dot O and C-H center dot center dot center dot O. The UV-Vis-NIR spectrum of 1 reveals its transparent nature while the vibrational spectra confirm the presence of the functional groups in 1. The thermal stability and second harmonic generation (SHG) conversion efficiency of 1 were investigated. (C) 2012 Elsevier B.V. All rights reserved.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

Basic principles of ultrafast Raman loss spectroscopy

When a light beam passes through any medium, the effects of interaction of light with the material depend on the field intensity. At low light intensities the response of materials remain linear to the amplitude of the applied electromagnetic field. But for sufficiently high intensities, the optical properties of materials are no longer linear to the amplitude of applied electromagnetic field. In such cases, the interaction of light waves with matter can result in the generation of new frequencies due to nonlinear processes such as higher harmonic generation and mixing of incident fields. One such nonlinear process, namely, the third order nonlinear spectroscopy has become a popular tool to study molecular structure. Thus, the spectroscopy based on the third order optical nonlinearity called stimulated Raman spectroscopy (SRS) is a tool to extract the structural and dynamical information about a molecular system. Ultrafast Raman loss spectroscopy (URLS) is analogous to SRS but is more sensitive than SRS. In this paper, we present the theoretical basis of SRS (URLS) techniques which have been developed in our laboratory.

Isomeric identification of methylated naphthalenes using gas phase infrared spectroscopy

We report gas phase mid-infrared spectra of 1- and 2- methyl naphthalenes at 0.2 cm(-1) resolution. Assignment of observed bands have been made using scaled quantum mechanical (SQM) calculations where the force fields rather the frequencies are scaled to find a close fit between observed and calculated bands. The structure of the molecules has been optimized using B3LYP level of theory in conjunction with standard 6-311G** basis set to obtain the harmonic frequencies. Using the force constants in Cartesian coordinates from the Gaussian output, scaled force field calculations are carried out using a modified version of the UMAT program in the QCPE package. Potential energy distributions of the normal modes obtained from such calculations helped us assign the observed bands and identify the unique features of the spectra of 1- and 2-MNs which are important for their isomeric identification.

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and an infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.

Northeast monsoon over India: variability and prediction

South peninsular India experiences a large portion of the annual rainfall during the northeast monsoon season (October to December). In this study, the facets of diurnal, intra-seasonal and inter-annual variability of the northeast monsoon rainfall (the NEMR) over India have been examined. The analysis of satellite derived hourly rainfall reveals that there are distinct features of diurnal variation over the land and oceans during the season. Over the land, rainfall peaks during the late afternoon/evening, while over the oceans an early morning peak is observed. The harmonic analysis of hourly data reveals that the amplitude and variance are the largest over south peninsular India. The NEMR also exhibits significant intra-seasonal variability on a 20-40 day time scale. Analysis also shows significant northward propagation of the maximum cloud zone from south of equator to the south peninsula during the season. The NEMR exhibits large inter-annual variability with the co-efficient of variation (CV) of 25%. The positive phases of ENSO and the Indian Ocean Dipole (IOD) are conducive for normal to above normal rainfall activity during the northeast monsoon. There are multi-decadal variations in the statistical relationship between ENSO and the NEMR. During the period 2001-2010 the statistical relationship between ENSO and the NEMR has significantly weakened. The analysis of seasonal rainfall hindcasts for the period 1960-2005 produced by the state-of-the-art coupled climate models, ENSEMBLES, reveals that the coupled models have very poor skill in predicting the inter-annual variability of the NEMR. This is mainly due to the inability of the ENSEMBLES models to simulate the positive relationship between ENSO and the NEMR correctly. Copyright (C) 2012 Royal Meteorological Society

Bose-Hubbard models in confining potentials: Inhomogeneous mean-field theory

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

Study of molecular structure and vibrational spectra of poly (beta,-1-malic acid) PMLA] using DFT approach

Poly (beta-L-malic acid) (PMLA) is a biodegradable polymer and it has various important applications in the biomedical field. In the present work the structural and spectral characteristics of PMLA have been studied by methods of infrared. Raman spectroscopy and quantum chemistry. Electrostatic potential surface, optimized geometry, harmonic vibrational frequencies, infrared intensities and activities of Raman scattering were calculated by density functional theory (DFT) using oligomeric approach employing B3LYP with complete relaxation in the potential energy surface using 6-311++G (d, p) basis set. Based on results, we have discussed the correlation between the vibrational modes and the structure of the PMLA. A complete analysis of the experimental infrared and Raman spectra has been reported on the basis of wavenumber of the vibrational bands and potential energy distribution. The calculated HOMO and LUMO energies shows that charge transfer occur within the molecule. The calculated infrared and the Raman spectra of the polymer based on DFT calculations show reasonable agreement with the experimental results. (c) 2012 Elsevier Ltd. All rights reserved.

Infrared Spectra of Dimethylphenanthrenes in the Gas phase

Infrared spectra of atmospherically and astronomically important dimethylphenanthrenes (DMPs), namely 1,9-DMP, 2,4-DMP, and 3,9-DMP, were recorded in the gas phase from 400 to 4000 cm(-1) with a resolution of 0.5 cm(-1) at 110 degrees C using a 7.2 m gas cell. DFT calculations at the B3LYP/6-311G** level were carried out to get the harmonic and anharmonic frequencies and their corresponding intensities for the assignment of the observed bands. However, spectral assignments could not be made unambiguously using anharmonic or selectively scaled harmonic frequencies. Therefore, the scaled quantum mechanical (SQM) force field analysis method was adopted to achieve more accurate assignments. In this method force fields instead of frequencies were scaled. The Cartesian force field matrix obtained from the Gaussian calculations was converted to a nonredundant local coordinate force field matrix and then the force fields were scaled to match experimental frequencies in a consistent manner using a modified version of the UMAT program of the QCPE package. Potential energy distributions (PEDs) of the normal modes in terms of nonredundant local coordinates obtained from these calculations helped us derive the nature of the vibration at each frequency. The intensity of observed bands in the experimental spectra was calculated using estimated vapor pressures of the DMPs. An error analysis of the mean deviation between experimental and calculated intensities reveal that the observed methyl C-H stretching intensity deviates more compared to the aromatic C-H and non C-H stretching bands.

DFT study of structure and vibrational spectra of ceramide 3: comparison to experimental data

The Fourier transform Raman and infrared (IR) spectra of the Ceramide 3 (CER3) have been recorded in the regions 200-3500 cm(-1) and 680-4000 cm(-1), respectively. We have calculated the equilibrium geometry, harmonic vibrational wavenumbers, electrostatic potential surfaces, absolute Raman scattering activities and IR absorption intensities by the density functional theory with B3LYP functionals having extended basis set 6-311G. This work is undertaken to study the vibrational spectra of CER3 completely and to identify the various normal modes with better wavenumber accuracy. Good consistency is found between the calculated results and experimental data for the IR and Raman spectra.