Comments on “Wirtinger-based integral inequality: Application to time-delay systems [Automatica 49 (2013) 2860–2866]”

In a recent paper (Automatica 49 (2013) 2860–2866), the Wirtinger-based inequality has been introduced to derive tractable stability conditions for time-delay or sampled-data systems. We point out that there exist two errors in Theorem 8 for the stability analysis of sampled-data systems, and the correct theorem is presented.

Time delay between photoemission from the 2p and 2s subshells of neon

The R-matrix incorporating time (RMT) method is a method developed recently for solving the time-dependent Schrödinger equation for multielectron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a 2p orbital in a neon atom with respect to one released from a 2s orbital following absorption of an attosecond xuv pulse. Time delays due to xuv pulses in the range 76-105 eV are presented. For an xuv pulse at the experimentally relevant energy of 105.2 eV, we calculate the time delay to be 10.2±1.3 attoseconds (as), somewhat larger than estimated by other theoretical calculations, but still a factor of 2 smaller than experiment. We repeated the calculation for a photon energy of 89.8 eV with a larger basis set capable of modeling correlated-electron dynamics within the neon atom and the residual Ne ion. A time delay of 14.5±1.5 as was observed, compared to a 16.7±1.5 as result using a single-configuration representation of the residual Ne⁺ ion. 

Time delay between singly and doubly ionizing wavepackets in laser-driven helium

We present calculations of the time delay between single and double ionization of helium, obtained from full-dimensionality numerical integrations of the helium-laser Schroedinger equation. The notion of a quantum mechanical time delay is defined in terms of the interval between correlated bursts of single and double ionization. Calculations are performed at 390 and 780 nm in laser intensities that range from 2 X 10^14 to 14 X 10^14 W /cm^2. We find results consistent with the rescattering model of double ionization but supporting its classical interpretation only at 780 nm.

Eigenvalues of the time-delay matrix in overlapping resonances

We discuss the properties of the lifetime or the time-delay matrix Q(E) for multichannel scattering, which is related to the scattering matrix S(E) by Q = i?S(dS†/dE). For two overlapping resonances occurring at energies E with widths G(? = 1, 2), with an energy-independent background, only two eigenvalues of Q(E) are proved to be different from zero and to show typical avoided-crossing behaviour. These eigenvalues are expressible in terms of the four resonance parameters (E , G) and a parameter representing the strength of the interaction of the resonances. An example of the strong and weak interaction in an overlapping double resonance is presented for the positronium negative ion. When more than two resonances overlap (? = 1, ..., N), no simple representation of each eigenvalue has been found. However, the formula for the trace of the Q-matrix leads to the expression d(E) = -?arctan[(G/2)/(E - E)] + d(E) for the eigenphase sum d(E) and the background eigenphase sum d(E), in agreement with the known form of the state density. The formulae presented in this paper are useful in a parameter fitting of overlapping resonances. © 2006 IOP Publishing Ltd.

Time domain wave separation using multiple microphones

Methods of measuring the acoustic behavior of tubular systems can be broadly characterized as steady state measurements, where the measured signals are analyzed in terms of infinite duration sinusoids, and reflectometry measurements which exploit causality to separate the forward and backward going waves in a duct. This paper sets out a multiple microphone reflectometry technique which performs wave separation by using time domain convolution to track the forward and backward going waves in a cylindrical source tube. The current work uses two calibration runs (one for forward going waves and one for backward going waves) to measure the time domain transfer functions for each pair of microphones. These time domain transfer functions encode the time delay, frequency dependent losses and microphone gain ratios for travel between microphones. This approach is applied to the measurement of wave separation, bore profile and input impedance. The work differs from existing frequency domain methods in that it combines the information of multiple microphones within a time domain algorithm, and differs from existing time domain methods in its inclusion of the effect of losses and gain ratios in intermicrophone transfer functions.

Effect of temporal separation on synchronization in rhythmic performance

A variety of short time delays inserted between pairs of subjects were found to affect their ability to synchronize a musical task. The subjects performed a clapping rhythm together from separate sound-isolated rooms via headphones and without visual contact. One-way time delays between pairs were manipulated electronically in the range of 3 to 78 ms. We are interested in quantifying the envelope of time delay within which two individuals produce synchronous per- formances. The results indicate that there are distinct regimes of mutually coupled behavior, and that `natural time delay'o¨delay within the narrow range associated with travel times across spatial arrangements of groups and ensembleso¨supports the most stable performance. Conditions outside of this envelope, with time delays both below and above it, create characteristic interaction dynamics in the mutually coupled actions of the duo. Trials at extremely short delays (corresponding to unnaturally close proximity) had a tendency to accelerate from anticipation. Synchronization lagged at longer delays (larger than usual physical distances) and produced an increasingly severe deceleration and then deterioration of performed rhythms. The study has implications for music collaboration over the Internet and suggests that stable rhythmic performance can be achieved by `wired ensembles' across distances of thousands of kilometers.

Time series wind power forecasting based on variant Gaussian process and TLBO

Due to the variability and stochastic nature of wind power system, accurate wind power forecasting has an important role in developing reliable and economic power system operation and control strategies. As wind variability is stochastic, Gaussian Process regression has recently been introduced to capture the randomness of wind energy. However, the disadvantages of Gaussian Process regression include its computation complexity and incapability to adapt to time varying time-series systems. A variant Gaussian Process for time series forecasting is introduced in this study to address these issues. This new method is shown to be capable of reducing computational complexity and increasing prediction accuracy. It is further proved that the forecasting result converges as the number of available data approaches innite. Further, a teaching learning based optimization (TLBO) method is used to train the model and to accelerate
the learning rate. The proposed modelling and optimization method is applied to forecast both the wind power generation of Ireland and that from a single wind farm to show the eectiveness of the proposed method.

Probabilistic program analysis for parallelizing compilers

Parallelizing compilers have difficulty analysing and optimising complex code. To address this, some analysis may be delayed until run-time, and techniques such as speculative execution used. Furthermore, to enhance performance, a feedback loop may be setup between the compile time and run-time analysis systems, as in iterative compilation. To extend this, it is proposed that the run-time analysis collects information about the values of variables not already determined, and estimates a probability measure for the sampled values. These measures may be used to guide optimisations in further analyses of the program. To address the problem of variables with measures as values, this paper also presents an outline of a novel combination of previous probabilistic denotational semantics models, applied to a simple imperative language.

Dissociation of H2+ from a short, intense, infrared laser pulse: proton emission spectra and pulse calibration

The proton energy spectrum from photodissociation of the hydrogen molecular ion by short intense pulses of infrared light is calculated. The time-dependent Schrödinger equation is discretized and integrated. For few-cycle pulses one can resolve vibrational structure, arising from the experimental preparation of the molecular ion. We calculate the corresponding energy spectrum and analyse the dependence on the pulse time delay, pulse length and intensity of the laser for ? ~ 790 nm. We conclude that the proton spectrum is a sensitive probe of both the vibrational populations and phases, and allows us to distinguish between adiabatic and nonadiabatic dissociation. Furthermore, the sensitivity of the proton spectrum from H2+ is a practical means of calibrating the pulse. Our results are compared with recent measurements of the proton spectrum for 65 fs pulses using a Ti:Sapphire laser (? ~ 790 nm) including molecular orientation and focal-volume averaging. Integrating over the laser focal volume, for the intensity I ~ 3 × 1015 W cm-2, we find our results are in excellent agreement with these experiments.

Multi-pulse scheme for enhancing electron localization through vibrational wavepacket manipulation

A novel scheme for enhancing electron localization in intense-field dissociation is outlined. Through manipulation of a bound vibrational wavepacket in the exemplar deuterium molecular ion, simulations demonstrate that the application of multiple phase-locked, few-cycle IR pulses can provide a powerful scheme for directing the molecular dissociation pathway. By tuning the time delay and carrier–envelope–phase for a sequence of pulse interactions, the probability of the electron being localized to a chosen nucleus can be enhanced to above 80%.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

Two-colour pulsed Raman studies of the lowest excited singlet state of tetraphenylporphyrin: band assignments and electronic structure

The resonance Raman spectra of the lowest lying singlet (S-1) state of free-base tetraphenylporphyrin and seven of its isotopomers were recorded under pump-and-probe conditions with a time delay of -2 ns between pump and probe laser pulses, In the S-1 spectra of the isotopomers, as in the ground state, there are dramatic splittings of what appear to be single bands in the natural isotopic abundance spectrum. The most structurally significant bands of the S-1 state were assigned on the basis of the isotope data, In some cases it was necessary to curve fit unresolved bands in the excited-state spectra in order to account for observed intensity ratios and to rationalize isotope shifts, The changes in band positions on excitation to the S-1 state were compared with those from earlier studies on the T-1 state. The changes in band positions were found to be similar For both excited states. Most notable was the similar shift in nu(2), the most widely used marker band for orbital character. The data are interpreted as implying that the lowest lying singlet state is a configuration interaction admixture of b(1u)b(2g) + a(u)b(3g) configurations with the coefficients weighted heavily in favour of b(1n)b(2g), which Is the configuration of the T-1 state. Copyright (C) 2000 John Wiley & Sons, Ltd.

Microflare Activity Driven By Forced Magnetic Reconnection.

High cadence, multiwavelength, optical observations of a solar active region, obtained with the Swedish Solar Telescope, are presented. Two magnetic bright points are seen to separate in opposite directions at a constant velocity of 2.8 km s(-1). After a separation distance of approximate to 4400 km is reached, multiple Ellerman bombs are observed in both Ha and Ca-K images. As a result of the Ellerman bombs, periodic velocity perturbations in the vicinity of the magnetic neutral line, derived from simultaneous Michelson Doppler Imager data, are generated with amplitude +/-6 km s(-1) and wavelength approximate to 1000 km. The velocity oscillations are followed by an impulsive brightening visible in Ha and Ca-K, with a peak intensity enhancement of 63%. We interpret these velocity perturbations as the magnetic field deformation necessary to trigger forced reconnection. A time delay of approximate to 3 minutes between the Ha-wing and Ca-K observations indicates that the observed magnetic reconnection occurs at a height of similar to 200 km above the solar surface. These observations are consistent with theoretical predictions and provide the first observational evidence of microflare activity driven by forced magnetic reconnection.

Rotman lens based-retrodirective array

A new type of broadband retrodirective array, which has been constructed using a microstrip Rotman lens, is presented. Automatic tracking of targets is obtained by exploiting the conjugate phase response of the beamforming network which is exhibited when the input ports are terminated with either open or short circuits. In addition, the true time-delay property of the Rotman lens gives broadband operation of the self-tracking array when used in conjunction with Vivaldi antennas. The simulated and measured bistatic and monostatic radar cross-section (RCS) patterns of a structure consisting of 13 beamports and 12 array ports are presented at frequencies in the range 8-12 GHz. Significantly enhanced RCS within the scan coverage ±40° is demonstrated by comparing the retrodirective behavior of a 12-element Vivaldi array terminated with and without the Rotman lens. © 2006 IEEE.