Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Crack stability in edge-notched clamped beam specimens: modeling and experiments

Stability of a fracture toughness testing geometry is important to determine the crack trajectory and R-curve behavior of the specimen. Few configurations provide for inherent geometric stability, especially when the specimen being tested is brittle. We propose a new geometrical construction called the single edge notched clamped bend specimen (SENCB), a modified form of three point bending, yielding stable cracking under load control. It is shown to be particularly suitable for small-scale structures which cannot be made free-standing, (e.g., thin films, coatings). The SENCB is elastically clamped at the two ends to its parent material. A notch is inserted at the bottom center and loaded in bending, to fracture. Numerical simulations are carried out through extended finite element method to derive the geometrical factor f(a/W) and for different beam dimensions. Experimental corroborations of the FEM results are carried out on both micro-scale and macro-scale brittle specimens. A plot of vs a/W, is shown to rise initially and fall off, beyond a critical a/W ratio. The difference between conventional SENB and SENCB is highlighted in terms of and FEM simulated stress contours across the beam cross-section. The `s of bulk NiAl and Si determined experimentally are shown to match closely with literature values. Crack stability and R-curve effect is demonstrated in a PtNiAl bond coat sample and compared with predicted crack trajectories from the simulations. The stability of SENCB is shown for a critical range of a/W ratios, proving that it can be used to get controlled crack growth even in brittle samples under load control.

Fienup Algorithm With Sparsity Constraints: Application to Frequency-Domain Optical-Coherence Tomography

We address the problem of reconstructing a sparse signal from its DFT magnitude. We refer to this problem as the sparse phase retrieval (SPR) problem, which finds applications in tomography, digital holography, electron microscopy, etc. We develop a Fienup-type iterative algorithm, referred to as the Max-K algorithm, to enforce sparsity and successively refine the estimate of phase. We show that the Max-K algorithm possesses Cauchy convergence properties under certain conditions, that is, the MSE of reconstruction does not increase with iterations. We also formulate the problem of SPR as a feasibility problem, where the goal is to find a signal that is sparse in a known basis and whose Fourier transform magnitude is consistent with the measurement. Subsequently, we interpret the Max-K algorithm as alternating projections onto the object-domain and measurement-domain constraint sets and generalize it to a parameterized relaxation, known as the relaxed averaged alternating reflections (RAAR) algorithm. On the application front, we work with measurements acquired using a frequency-domain optical-coherence tomography (FDOCT) experimental setup. Experimental results on measured data show that the proposed algorithms exhibit good reconstruction performance compared with the direct inversion technique, homomorphic technique, and the classical Fienup algorithm without sparsity constraint; specifically, the autocorrelation artifacts and background noise are suppressed to a significant extent. We also demonstrate that the RAAR algorithm offers a broader framework for FDOCT reconstruction, of which the direct inversion technique and the proposed Max-K algorithm become special instances corresponding to specific values of the relaxation parameter.

Frequency-domain stimulated and spontaneous light emission signals at molecular junctions

Using a diagrammatic superoperator formalism we calculate optical signals at molecular junctions where a single molecule is coupled to two metal leads which are held at different chemical potentials. The molecule starts in a nonequilibrium steady state whereby it continuously exchanges electrons with the leads with a constant electron flux. Expressions for frequency domain optical signals measured in response to continuous laser fields are derived by expanding the molecular correlation functions in terms of its many-body states. The nonunitary evolution of molecular states is described by the quantum master equation. (C) 2014 AIP Publishing LLC.

Super-Resolution Reconstruction in Frequency-Domain Optical-Coherence Tomography Using the Finite-Rate-of-Innovation Principle

The standard approach to signal reconstruction in frequency-domain optical-coherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new super-resolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite-rate-of-innovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the high-resolution Prony method and show that high-quality, super-resolved reconstruction is possible with fewer measurements (about one-fourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singular-value decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the Cramer-Rao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal-to-reconstruction noise offered by the proposed method in comparison with the standard approach.

Low-frequency modes in an equatorial shallow-water model with moisture gradients

Motivated by observations of the mean state of tropical precipitable water (PW), a moist, first baroclinic mode, shallow-water system on an equatorial beta-plane with a background saturation profile that depends on latitude and longitude is studied. In the presence of a latitudinal moisture gradient, linear analysis of the non-rotating problem reveals large-scale, symmetric, eastward and westward propagating unstable modes. The introduction of a zonal moisture gradient breaks the east-west symmetry of the unstable modes. The effects of rotation are then included by numerically solving the resulting eigenvalue problem on an equatorial beta-plane. With a purely meridional moisture gradient, the system supports large-scale, low-frequency, eastward and westward moving neutral modes. Some of the similarities, and some of the discrepancies of these modes with intraseasonal tropical waves are pointed out. Finally, a zonal moisture gradient in the presence of rotation renders some of the aforementioned neutral modes unstable. In particular, according to observations of large-scale, low-frequency tropical variability, it is seen that regions where the background saturation profile increases (decreases) to the east favour eastward (westward) moving moist modes.

Interference Alignment With Diversity for the 2 x 2 X-Network With Four Antennas

A transmission scheme based on the Alamouti code, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was recently proposed for the 2 x 2 X-network i.e., two-transmitter (Tx) two-receiver X-network] with two antennas at each node. This scheme was claimed to achieve a sum degrees of freedom (DoF) of 8/3 and also a diversity gain of two when fixed finite constellations are employed at each Tx. Furthermore, each Tx required the knowledge of only its own channel unlike the Jafar-Shamai scheme which required global CSIT to achieve the maximum possible sum DoF of 8/3. In this paper, we extend the LJJ scheme to the 2 x 2 X-network with four antennas at each node. The proposed scheme also assumes only local channel knowledge at each Tx. We prove that the proposed scheme achieves the maximum possible sum DoF of 16/3. In addition, we also prove that, using any fixed finite constellation with appropriate rotation at each Tx, the proposed scheme achieves a diversity gain of at least four.

On-line Estimation of Fundamental and Ripple Components of Line Currents in a Voltage-Source Inverter Operated at Low Switching Frequency

High-power voltage-source inverters (VSI) are often switched at low frequencies due to switching loss constraints. Numerous low-switching-frequency PWM techniques have been reported, which are quite successful in reducing the total harmonic distortion under open-loop conditions at such low operating frequencies. However, the line current still contains low-frequency components (though of reduced amplitudes), which are fed back to the current loop controller during closed-loop operation. Since the harmonic frequencies are quite low and are not much higher than the bandwidth of the current loop, these are amplified by the current controller, causing oscillations and instability. Hence, only the fundamental current should be fed back. Filtering out these harmonics from the measured current (before feeding back) leads to phase shift and attenuation of the fundamental component, while not eliminating the harmonics totally. This paper proposes a method for on-line extraction of the fundamental current in induction motor drives, modulated with low-switching-frequency PWM. The proposed method is validated through simulations on MATLAB/Simulink. Further, the proposed algorithm is implemented on Cyclone FPGA based controller board. Experimental results are presented for an R-L load.

Time resolved terahertz spectroscopy of low frequency electronic resonances and optical pump-induced terahertz photoconductivity in reduced graphene oxide membrane

Towards ultrafast optoelectronic applications of single and a few layer reduced graphene oxide (RGO), we study time domain terahertz spectroscopy and optical pump induced changes in terahertz conductivity of self-supported RGO membrane in the spectral window of 0.5-3.5 THz. The real and imaginary parts of conductivity spectra clearly reveal low frequency resonances, attributed to the energy gaps due to the van Hove singularities in the density of states flanking the Dirac points arising due to the relative rotation of the graphene layers. Further, optical pump induced terahertz conductivity is positive, pointing to the dominance of intraband scattering processes. The relaxation dynamics of the photo-excited carriers consists of three cooling pathways: the faster (similar to 450 fs) one due to optical phonon emission followed by disorder mediated large momentum and large energy acoustic phonon emission with a time constant of a few ps (called the super-collision mechanism) and a very large time (similar to 100 ps) arising from the deep trap states. The frequency dependence of the dynamic conductivity at different delay times is analyzed in term of Drude-Smith model. (C) 2014 Published by Elsevier Ltd.

Frequency and Temperature-Independent Electrical Transport Properties of 2BaO-0.5Na(2)O-2.5Nb(2)O(5)-4.5B(2)O(3) Glass-Ceramics

The temperature (300-973K) and frequency (100Hz-10MHz) response of the dielectric and impedance characteristics of 2BaO-0.5Na(2)O-2.5Nb(2)O(5)-4.5B(2)O(3) glasses and glass nanocrystal composites were studied. The dielectric constant of the glass was found to be almost independent of frequency (100Hz-10MHz) and temperature (300-600K). The temperature coefficient of dielectric constant was 8 +/- 3ppm/K in the 300-600K temperature range. The relaxation and conduction phenomena were rationalized using modulus formalism and universal AC conductivity exponential power law, respectively. The observed relaxation behavior was found to be thermally activated. The complex impedance data were fitted using the least square method. Dispersion of Barium Sodium Niobate (BNN) phase at nanoscale in a glass matrix resulted in the formation of space charge around crystal-glass interface, leading to a high value of effective dielectric constant especially for the samples heat-treated at higher temperatures. The fabricated glass nanocrystal composites exhibited P versus E hysteresis loops at room temperature and the remnant polarization (P-r) increased with the increase in crystallite size.

Ferrimagnetism and magnetic phase separation in Nd1-xYxMnO3 studied by magnetization and high frequency electron paramagnetic resonance

Ferrimagnetism and metamagnetic features tunable by composition are observed in the magnetic response of Nd1-xYxMnO3, for x=0.1-0.5. For all values of x in the series, the compound crystallizes in orthorhombic Pbnm space group similar to NdMnO3. Magnetization studies reveal a phase transition of the Mn-sublattice below T-N(Mn) approximate to 80 K for all compositions, which, decreases up on diluting the Nd-site with Yttrium. For x=0.35, ferrimagnetism is observed. At 5 K, metamagnetic transition is observed for all compositions x < 0.4. The evolution of magnetic ground states and appearance of ferrimagnetism in Nd1-xYxMnO3 can be accounted for by invoking the scenario of magnetic phase separation. The high frequency electron paramagnetic resonance measurements on x=0.4 sample, which is close to the critical composition for phase separation, revealed complex temperature dependent lineshapes clearly supporting the assumption of magnetic phase separation. (C) 2014 Elsevier B.V. All rights reserved.

Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India

Significant changes are reported in extreme rainfall characteristics over India in recent studies though there are disagreements on the spatial uniformity and causes of trends. Based on recent theoretical advancements in the Extreme Value Theory (EVT), we analyze changes in extreme rainfall characteristics over India using a high-resolution daily gridded (1 degrees latitude x 1 degrees longitude) dataset. Intensity, duration and frequency of excess rain over a high threshold in the summer monsoon season are modeled by non-stationary distributions whose parameters vary with physical covariates like the El-Nino Southern Oscillation index (ENSO-index) which is an indicator of large-scale natural variability, global average temperature which is an indicator of human-induced global warming and local mean temperatures which possibly indicate more localized changes. Each non-stationary model considers one physical covariate and the best chosen statistical model at each rainfall grid gives the most significant physical driver for each extreme rainfall characteristic at that grid. Intensity, duration and frequency of extreme rainfall exhibit non-stationarity due to different drivers and no spatially uniform pattern is observed in the changes in them across the country. At most of the locations, duration of extreme rainfall spells is found to be stationary, while non-stationary associations between intensity and frequency and local changes in temperature are detected at a large number of locations. This study presents the first application of nonstationary statistical modeling of intensity, duration and frequency of extreme rainfall over India. The developed models are further used for rainfall frequency analysis to show changes in the 100-year extreme rainfall event. Our findings indicate the varying nature of each extreme rainfall characteristic and their drivers and emphasize the necessity of a comprehensive framework to assess resulting risks of precipitation induced flooding. (C) 2014 Elsevier B.V. All rights reserved.

Low frequency modulation of jets in quasigeostrophic turbulence

Quasigeostrophic turbulence on a beta-plane with a finite deformation radius is studied numerically, with particular emphasis on frequency and combined wavenumber-frequency domain analyses. Under suitable conditions, simulations with small-scale random forcing and large-scale drag exhibit a spontaneous formation of multiple zonal jets. The first hint of wave-like features is seen in the distribution of kinetic energy as a function of frequency; specifically, for progressively larger deformation scales, there are systematic departures in the form of isolated peaks (at progressively higher frequencies) from a power-law scaling. Concomitantly, there is an inverse flux of kinetic energy in frequency space which extends to lower frequencies for smaller deformation scales. The identification of these peaks as Rossby waves is made possible by examining the energy spectrum in frequency-zonal wavenumber and frequency-meridional wavenumber diagrams. In fact, the modified Rhines scale turns out to be a useful measure of the dominant meridional wavenumber of the modulating Rossby waves; once this is fixed, apart from a spectral peak at the origin (the steady jet), almost all the energy is contained in westward propagating disturbances that follow the theoretical Rossby dispersion relation. Quite consistently, noting that the zonal scale of the modulating waves is restricted to the first few wavenumbers, the energy spectrum is almost entirely contained within the corresponding Rossby dispersion curves on a frequency-meridional wavenumber diagram. Cases when jets do not form are also considered; once again, there is a hint of Rossby wave activity, though the spectral peaks are quite muted. Further, the kinetic energy scaling in frequency domain follows a -5/3 power-law and is distributed much more broadly in frequency-wavenumber diagrams. (C) 2015 AIP Publishing LLC.

Differential Multi-phase DLL for Reconfigurable Radio Frequency Synthesizer

A multi phase, delay-locked loop (DLL) based frequency synthesizer is designed for harmonic rejection mixing in reconfigurable radios. This frequency synthesizer uses a 1 GHz input reference frequency, and achieves <= 20ns settling time by utilizing a wide loop bandwidth. The circuit has been designed in 0.13-mu m CMOS technology. It is designed for a frequency range of 500 MHz to 3 GHz with stuck/harmonic lock removal assist. Index Terms-stuck lock, harmonic lock, delay-locked loops, multi phase, phase detector, frequency synthesis

A critical review of the definition of FRA resonance frequency of transformers as per IEEE Std C57.149-2012

The explanation of resonance given in IEEE Std C57.149-2012 to define resonance during frequency response analysis (FRA) measurements on transformers implicitly uses the conditions prevalent during resonance in a series R-L-C circuit. This dependence is evident from the two assertions made in the definition, viz., resulting in zero net reactive impedance, and, accompanied by a zero value appearing in the phase angle of the frequency response function. These two conditions are satisfied (at resonance) only in a series R-L-C circuit and certainly not in a transformer, as has been assumed in the Standard. This can be proved by considering a ladder-network model. Circuit analysis of this ladder network reveals the origin of this fallacy and proves that, at resonance, neither is the ladder network purely resistive and nor is the phase angle (between input voltage and input current) always zero. Also, during FRA measurements, it is often seen that phase angle does not traverse the conventional cyclic path from +90 degrees to -90 degrees (or vice versa) at all resonant frequencies. This peculiar feature can also be explained using pole-zero maps. Simple derivations, simulations and experimental results on an actual winding are presented. In summary, authors believe that this study dispels existing misconceptions about definition of FRA resonance and provides material for its correction in IEEE Std C57.149-2012. (C) 2014 Elsevier B.V. All rights reserved.