Relaxation system based sub-grid scale modelling for large eddy simulation of Burgers' equation

An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (epsilon) to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a fourth-order CWENO discretisation in space and third-order TVD Runge-Kutta discretisation in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.

Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

Spectroscopic Observation of Oscillations in the Corona During the Total Solar Eclipse of 22 July 2009

We performed high resolution spectroscopy of the solar corona during the total solar eclipse of 22 July 2009 in two emission lines: the green line at 5303 due to Fe xiv and the red line at 6374 due to Fe x, simultaneously from Anji (latitude 30A degrees 28.1' N; longitude 119A degrees 35.4' E; elevation 890 m), China. A two-mirror coelostat with 100 cm focal length lens produced a 9.2 mm image of the Sun. The spectrograph using 140 cm focal length lens in Littrow mode and a grating with 600 lines per millimeter blazed at 2 mu m provided a dispersion of 30 m and 43 m per pixel in the fourth order around the green line and third order around the red line, respectively. Two Peltier cooled 1k x 1k CCD cameras, with a pixel size of 13 mu m square and 14-bit readout at 10 MHz operated in frame transfer mode, were used to obtain the time sequence spectra in two emission lines simultaneously. The duration of totality was 341 s, but we could get spectra for 270 s after a trial exposure at an interval of 5 s. We report here on the detection of intensity, velocity, and line width oscillations with periodicity in the range of 25 -50 s. These oscillations can be interpreted in terms of the presence of fast magnetoacoustic waves or torsional Alfv,n waves. The intensity ratios of green to red emission lines indicate the temperature of the corona to be 1.65 MK in the equatorial region and 1.40 MK in the polar region, relatively higher than the expected temperature during the low activity period. The width variation of the emission lines in different coronal structures suggests different physical conditions in different structures.

Lithium borate-strontium bismuth tantalate glass nanocomposite: a novel material for nonlinear optic and ferroelectric applications

Glass nanocomposites in the system (100 - x)Li2B4O7-xSrBi(2)Ta(2)O(9) (0 less than or equal to x less than or equal to 22.5, in molar ratio) were fabricated via a melt quenching technique followed by controlled heat-treatment. The as-quenched samples were confirmed to be glassy and amorphous by differential thermal analysis (DTA) and X-ray powder diffraction (XRD) techniques, respectively. The phase formation and crystallite size of the heat-treated samples (glass nanocomposites) were monitored by XRD and transmission electron microscopy (TEM). The relative permittivities (epsilon(tau)') of the glass nanocomposites for different compositions were found to lie in between that of the parent host glass (Li2B4O7) and strontium bismuth tantalate (SBT) ceramic in the frequency range 100 Hz-40 MHz at 300 K, whereas the dielectric loss (D) of the glass nanocomposite was less than that of both the parent phases. Among the various dielectric models employed to predict the effective relative permittivity of the glass nanocomposite, the one obtained using the Maxwell's model was in good agreement with the experimentally observed value. Impedance analysis was employed to rationalize the electrical behavior of the glasses and glass nanocomposites. The pyroelectric response of the glasses and glass nanocomposites was monitored as a function of temperature and the pyroelectric coefficient for glass and glass nanocomposite (x = 20) at 300 K were 27 muC m(-2) K-1 and 53 muC m(-2) K-1, respectively. The ferroelectric behavior of these glass nanocomposites was established by P vs. E hysteresis loop studies. The remnant polarization (P-r) of the glass nanocomposite increases with increase in SBT content. The coercive field (E-c) and P-r for the glass nanocomposite (x = 20) were 727 V cm(-1) and 0.527 muC cm(-2), respectively. The optical transmission properties of these glass nanocomposites were found to be composition dependent. The refractive index (n = 1.722), optical polarizability (am = 1.266 6 10 23 cm 3) and third-order nonlinear optical susceptibility (x(3) = 3.046 6 10(-21) cm(3)) of the glass nanocomposite (x = 15) were larger than those of the as-quenched glass. Second harmonic generation (SHG) was observed in transparent glass nanocomposites and the d(eff) for the glass nanocomposite (x = 20) was found to be 0.373 pm V-1.

Turbulent flow computations using upwind RANS technique for a flat plate and an airfoil

Reynolds Averaged Navier Stokes (RANS) equations are solved using third order upwind biased Roe's scheme for the inviscid fluxes and second order central difference scheme for the viscous fluxes. The Baldwin & Lomax turbulence model is employed for Reynolds stresses. The governing equations are solved using finite-volume implicit scheme in body fitted curvilinear coordinate O-grid system. Computations axe reported for a flat plate apart from RAE 2822 and NACA 0012 airfoils. Results for the flat plate at M = 0.3, R-c = 4.0 x 10(6) compare favourably with the analytical solution. Results for the two airfoils are compared with experiment. There is a good agreement in C-p distribution between experiment and computation for both the airfoils. Comparison of C-f distribution with experiment for RAE 2822 airfoil is reasonable.

Optical and structural properties of TiO2 films deposited by Sol-Gel technique

TiO2 thin films were prepared by sol gel method. The structural investigations performed by means of X- ray diffraction (XRD) technique, Scanning electronic microscopy (SEM) showed the shape structure at T=600°C. The optical constants of the deposited film were obtained from the analysis of the experimental recorded transmittance spectral data over the wavelengths range 200-3000 nm. The values of some important parameters (refractive index n, dielectric constant ε ∞ and thickness d), and the third order optical nonlinear susceptibility χ(3) of TiO2 film are determined from these spectra. It has been found that the dispersion data obey the single oscillator relation of the Wemple-DiDomenico model, from which the dispersion parameters and high – frequency dielectric constant were determined. The estimation of the corresponding band gap Eg , χ (3) and ε ∞ are 2.57 eV, 0.021 × 10-10 esu and 5.20,respectively.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]

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.

Magneto-Transport Study of Pure and Co Doped ZnO Thin Films

A detailed low temperature magneto-transport study is carried out to understand the transport mechanism in pure and Co doped ZnO thin films grown by pulsed laser deposition (PLD) technique. A negative transverse magneto-resistance (MR) (with a value similar to 4% at 4.5 K) which decreases monotonically with the increase in temperature, is observed for the undoped ZnO film. A competition between positive and negative MR is observed for the Co doped ZnO samples. In this case at higher field values negative MR contribution dominates over the positive MR, which gives rise to a slope change in the MR data. Our data for MR shows excellent agreement with the semi-empirical formula given by Khosla et al., which is originally proposed for the degenerate semiconductors. This formula incorporates the third order perturbation expansion of the s-d exchange scattering of the conduction electrons from the localised spins. We have also obtained the Hall mobility, carrier conc. and mean free path as function of temperature for the pure ZnO film.

Ultrafast photoinduced enhancement of nonlinear optical response in 15-atom gold clusters on indium tin oxide conducting film

We show that the third order optical nonlinearity of 15-atom gold clusters is significantly enhanced when in contact with indium tin oxide (ITO) conducting film. Open and close aperture z-scan experiments together with non-degenerate pump-probe differential transmission experiments were done using 80 fs laser pulses centered at 395 nm and 790 nm on gold clusters encased inside cyclodextrin cavities. We show that two photon absorption coefficient is enhanced by an order of magnitude as compared to that when the clusters are on pristine glass plate. The enhancement for the nonlinear optical refraction coefficient is similar to 3 times. The photo-induced excited state absorption using pump-probe experiments at pump wavelength of 395 nm and probe at 790 nm also show an enhancement by an order of magnitude. These results attributed to the excited state energy transfer in the coupled gold cluster-ITO system are different from the enhancement seen so far in charge donor-acceptor complexes and nanoparticle-conjugate polymer composites.

Loss and gain signals in broadband stimulated-Raman spectra: Theoretical analysis

Stimulated optical signals obtained by subjecting the system to a narrow band and a broadband pulse show both gain and loss Raman features at the red and blue side of the narrow beam, respectively. Recently observed temperature-dependent asymmetry in these features Mallick et al., J. Raman Spectrosc. 42, 1883 (2011); Dang et al., Phys. Rev. Lett. 107, 043001 (2011)] has been attributed to the Stokes and anti-Stokes components of the third-order susceptibility, chi((3)). By treating the setup as a steady state of an open system coupled to four quantum radiation field modes, we show that Stokes and anti-Stokes processes contribute to both the loss and gain resonances. chi((3)) predicts loss and gain signals with equal intensity for electronically off-resonant excitation. Some asymmetry may exist for resonant excitation. However, this is unrelated to the Stokes vs anti-Stokes processes. Any observed temperature-dependent asymmetry must thus originate from effects lying outside the chi((3)) regime.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (delta(t) similar or equal to 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at delta similar or equal to 0.09 in case of T* = 1.0, phi = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at delta similar or equal to 0.10 (just beyond the solid-liquid transition density at T* = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Analysis and design of split-capacitor resistive-inductive passive damping for LCL filters in grid-connected inverters

Grid-connected inverters require a third-order LCL filter to meet standards such as the IEEE Std. 519-1992 while being compact and cost-effective. LCL filter introduces resonance, which needs to be damped through active or passive methods. Passive damping schemes have less control complexity and are more reliable. This study explores the split-capacitor resistive-inductive (SC-RL) passive damping scheme. The SC-RL damped LCL filter is modelled using state space approach. Using this model, the power loss and damping are analysed. Based on the analysis, the SC-RL scheme is shown to have lower losses than other simpler passive damping methods. This makes the SC-RL scheme suitable for high power applications. A method for component selection that minimises the power loss in the damping resistors while keeping the system well damped is proposed. The design selection takes into account the influence of switching frequency, resonance frequency and the choice of inductance and capacitance values of the filter on the damping component selection. The use of normalised parameters makes it suitable for a wide range of design applications. Analytical results show the losses and quality factor to be in the range of 0.05-0.1% and 2.0-2.5, respectively, which are validated experimentally.