Critical earthquake input power spectral density function models for engineering structures

The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

Effect of two-level systems on the spectral density of universal conductance fluctuations in doped Si

We have studied the power spectral density [S(f) = gamma/f(alpha)] of universal conductance fluctuations (UCF's) in heavily doped single crystals of Si, when the scatterers themselves act as the primary source of dephasing. We observed that the scatterers, with internal dynamics like two-level-systems, produce a significant, temperature-dependent reduction in the spectral slope alpha when T less than or similar to 10 K, as compared to the bare 1/f (alphaapproximate to1) spectrum at higher temperatures. It is further shown that an upper cutoff frequency (f(m)) in the UCF spectrum is necessary in order to restrict the magnitude of conductance fluctuations, [(deltaG(phi))(2)], per phase coherent region (L-phi(3)) to [(deltaGphi)(2)](1/2) less than or similar to e(2)/h. We find that f(m) approximate to tau(D)(-1), where tau(D) = L-2/D, is the time scale of the diffusive motion of the electron along the active length (L) of the sample (D is the electron diffusivity).

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.

Optimal input cross-power spectra in shake table testing of asymmetric structures

The study considers earthquake shake table testing of bending-torsion coupled structures under multi-component stationary random earthquake excitations. An experimental procedure to arrive at the optimal excitation cross-power spectral density (psd) functions which maximize/minimize the steady state variance of a chosen response variable is proposed. These optimal functions are shown to be derivable in terms of a set of system frequency response functions which could be measured experimentally without necessitating an idealized mathematical model to be postulated for the structure under study. The relationship between these optimized cross-psd functions to the most favourable/least favourable angle of incidence of seismic waves on the structure is noted. The optimal functions are also shown to be system dependent, mathematically the sharpest, and correspond to neither fully correlated motions nor independent motions. The proposed experimental procedure is demonstrated through shake table studies on two laboratory scale building frame models.

Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

Nonstationary Random Critical Seismic Excitations

A method is presented to find nonstationary random seismic excitations with a constraint on mean square value such that the response variance of a given linear system is maximized. It is also possible to incorporate the dominant input frequency into the analysis. The excitation is taken to be the product of a deterministic enveloping function and a zero mean Gaussian stationary random process. The power spectral density function of this process is determined such that the response variance is maximized. Numerical results are presented for a single-degree system and an earth embankment modeled as shear beam.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Performance Analysis of MQAM-OFDM based WLAN in presence of Zigbee interference in AWGN and Rayleigh fading channel

In this paper we give the performance of MQAM OFDM based WLAN in presence of single and multiple channels Zigbee interference. An analytical model for getting symbol error rate (SER) in presence of single and multiple channel Zigbee interference in AWGN and Rayleigh fading channel for MQAM OFDM system is given. Simulation results are compared with analytical symbol error rate (SER) of the MQAM-OFDM system. For analysis we have modeled the Zigbee interference using the power spectral density (PSD) of OQPSK modulation and finding the average interference power for each sub-carrier of the OFDM system. Then we have averaged the SER over all WLAN sub-carriers. Simulations closely match with the analytical models. It is seen from simulation and analytical results that performance of WLAN is severely affected by Zigbee interference. Symbol error rate (SER) for 16QAM and 64QAM OFDM system is of order of 10(-2) for SIR (signal to interference ratio) of 20dB and 30dB respectively in presence of single Zigbee interferer inside the WLAN frequency band for Rayleigh fading channel. For SIR values more than 30dB and 40dB the SER approaches the SER without interference for 16QAM and 64QAM OFDM system respectively.

Correction of Ocular Artifacts in EEG Recordings using Empirical Mode Decomposition

EEG recordings are often contaminated with ocular artifacts such as eye blinks and eye movements. These artifacts may obscure underlying brain activity in the electroencephalogram (EEG) data and make the analysis of the data difficult. In this paper, we explore the use of empirical mode decomposition (EMD) based filtering technique to correct the eye blinks and eye movementartifacts in single channel EEG data. In this method, the single channel EEG data containing ocular artifact is segmented such that the artifact in each of the segment is considered as some type of slowly varying trend in the dataand the EMD is used to remove the trend. The filtering is done using partial reconstruction from components of the decomposition. The method is completely data dependent and hence adaptive and nonlinear. Experimental results are provided to check the applicability of the method on real EEG data and the results are quantified using power spectral density (PSD) as a measure. The method has given fairlygood results and does not make use of any preknowledge of artifacts or the EEG data used.

Stability Training and Measurement System for Sportsperson (P84)

Balance and stability are very important for everybody and especially for sports-person who undergo extreme physical activities. Balance and stability exercises not only have a great impact on the performance of the sportsperson but also play a pivotal role in their rehabilitation. Therefore, it is very essential to have knowledge about a sportsperson’s balance and also to quantify the same. In this work, we propose a system consisting of a wobble board, with a gyro enhanced orientation sensor and a motion display for visual feedback to help the sportsperson improve their stability. The display unit gives in real time the orientation of the wobble board, which can help the sportsperson to apply necessary corrective forces to maintain neutral position. The system is compact and portable. We also quantify balance and stability using power spectral density. The sportsperson is made stand on the wobble board and the angular orientation of the wobble board is recorded for each 0.1 second interval. The signal is analized using discrete Fourier transforms. The power of this signal is related to the stability of the subject. This procedure is used to measure the balance and stability of an elite cricket team. Representative results are shown below: Table 1 represents power comparison of two subjects and Table 2 represents power comparison of left leg and right leg of one subject. This procedure can also be used in clinical practice to monitor improvement in stability dysfunction of sportsperson with injuries or other related problems undergoing rehabilitation.

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these moments are closely related to fundamental physiological parameters, i.e. concentration of moving erythrocytes and blood flow. In particular, we take advantage of the link between moments in the Fourier domain and fractional derivatives in the temporal domain. Using Parseval's theorem, we establish an exact analytical equivalence between the time-domain expression and the conventional frequency-domain counterpart. Moreover, we demonstrate the appropriateness of estimating the zeroth-, first- and second-order moments using Monte Carlo simulations. Finally, we briefly discuss the feasibility of implementing the proposed algorithm in hardware.

Parametric instability of stochastic columns

Columns which have stochastically distributed Young's modulus and mass density and are subjected to deterministic periodic axial loadings are considered. The general case of a column supported on a Winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered. Material property fluctuations are modeled as independent one-dimensional univariate homogeneous real random fields in space. In addition to autocorrelation functions or their equivalent power spectral density functions, the input random fields are characterized by scale of fluctuations or variance functions for their second order properties. The foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables. The system equations of boundary frequencies are obtained using Bolotin's method for deterministic systems. Stochastic FEM is used to obtain the discrete system with random as well as periodic coefficients. Statistical properties of boundary frequencies are derived in terms of input parameter statistics. A complete covariance structure is obtained. The equations developed are illustrated using a numerical example employing a practical correlation structure.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude psi(ij) equivalent to psi(m) = Delta(m) exp(i phi(m)), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form FDelta, phi] = Sigma(m)A Delta(2)(m) + (B/2)Delta(4)(m)] + C Sigma(< mn >) Delta(m) Delta(n) cos(phi(m) - phi(n)) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature T-ms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature T-c(x), and describes superconductivity with d-wave symmetry for positive C. The calculated T-c(x) curve has the observed parabolic shape. The results for the superfluid density rho(s)(x, T), the local gap magnitude , the specific heat C-v(x, T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers.