Shape Of Spectral Density Research Articles

Spectral and temporal shaping of spectrally incoherent pulses in the infrared and ultraviolet.

Laser-plasma instabilities (LPIs) hinder the interaction of high-energy laser pulses with targets. Simulations show that broadband spectrally incoherent pulses can mitigate these instabilities. Optimizing laser operation and target interaction requires controlling the properties of these optical pulses. We demonstrate closed-loop control of the spectral density and pulse shape of nanosecond spectrally incoherent pulses after optical parametric amplification in the infrared (∼1053 nm) and sum-frequency generation to the ultraviolet (∼351 nm) using spectral and temporal modulation in the fiber front end. The high versatility of the demonstrated approaches can support the generation of high-energy, spectrally incoherent pulses by future laser facilities for improved LPI mitigation.

Spectra of Temperature Fluctuations in the Solar Wind

Turbulent cascade transferring the free energy contained within the large scale fluctuations of the magnetic field, velocity and density into the smaller ones is probably one of the most important mechanisms responsible for heating of the solar corona and solar wind, thus the turbulent behavior of these quantities is intensively studied. The temperature is also highly fluctuating quantity but its variations are studied only rarely. There are probably two reasons, first the temperature is tensor and, second, an experimental determination of temperature variations requires knowledge of the full velocity distribution with an appropriate time resolution but such measurements are scarce. To overcome this problem, the Bright Monitor of the Solar Wind (BMSW) on board Spektr-R used the Maxwellian approximation and provided the thermal velocity with a 32 ms resolution, investigating factors influencing the temperature power spectral density shape. We discuss the question whether the temperature spectra determined from Faraday cups are real or apparent and analyze mutual relations of power spectral densities of parameters like the density, parallel and perpendicular components of the velocity and magnetic field fluctuations. Finally, we compare their spectral slopes with the slopes of the thermal velocity in both inertial and kinetic ranges and their evolution in course of solar wind expansion.

Exciton Lifetime Distributions and Population Dynamics in the FMO Protein Complex from Prosthecochloris aestuarii.

Significant protein rearrangement upon excitation and energy transfer in Fenna–Matthews–Olson protein of Prosthecochloris aestuarii results in a modified energy landscape, which induces more changes in pigment site energies than predicted by the “standard” hole-burning theory. The energy changes are elucidated by simulations while investigating the effects of site-dependent disorder, both static (site-energy distribution widths) and dynamic (spectral density shapes). The resulting optimized site energies and their fluctuations are consistent with relative differences observed in inhomogeneous widths calculated by recent molecular dynamic simulations. Two sets of different spectral densities reveal how their shapes affect the population dynamics and distribution of exciton lifetimes. Calculations revealed the wavelength-dependent distributions of exciton lifetimes (T1) in the femtosecond to picosecond time frame. We suggest that the calculated multimodal and asymmetric wavelength-dependent T1 distributions offer more insight into the interpretation of resonant hole-burned (HB) spectra, kinetic traces in two-dimensional (2D) electronic spectroscopy experiments, and widely used global analyses in fitting data from transient absorption experiments.

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.

Pseudonoise Waveform Design for Spectrum Sharing Systems

With an increasing demand for high-resolution radar and wideband communication systems, the frequency spectrum is becoming a limited resource. Many such systems must coexist in a given frequency band. In order to minimize interference among these systems, a radar waveform design is used. Without a priori knowledge of the transmission channel and communication waveform, one viable strategy is to use spectral nulls for the frequencies used by communication system. This article describes an improved method for generating pseudonoise waveforms with limited range and Doppler sidelobes. The algorithm permits adjustable power spectral density of the generated waveform. An additional parameter, “significance factor,” is a tradeoff between power spectral density shape and sidelobe suppression depth. The method also allows the generation of a set of mutually orthogonal waveforms for multitransmitter scenarios. Effectiveness of the algorithm is confirmed by both numerical simulation and field trials.

Analytical derivation of equilibrium state for open quantum system.

Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.

Bayesian Spectral Modeling for Multiple Time Series

ABSTRACT We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets and used for spectral analysis of multichannel electroencephalographic recordings, which provides a key motivating application for the proposed methodology.

Statistical analysis of variability properties of the Kepler blazar W2R 1926+42

We analyzed Kepler light curves of the blazar W2R 1926+42 that provided nearly continuous coverage from quarter 11 through quarter 17 (589 days between 2011 and 2013) and examined some of their flux variability properties. We investigate the possibility that the light curve is dominated by a large number of individual flares and adopt exponential rise and decay models to investigate the symmetry properties of flares. We found that those variations of W2R 1926+42 are predominantly asymmetric with weak tendencies toward positive asymmetry (rapid rise and slow decay). The durations (D) and the amplitudes (F0) of flares can be fit with log-normal distributions. The energy (E) of each flare is also estimated for the first time. There are positive correlations between logD and logE with a slope of 1.36, and between logF0 and logE with a slope of 1.12. Lomb-Scargle periodograms are used to estimate the power spectral density (PSD) shape. It is well described by a power law with an index ranging between -1.1 and -1.5. The sizes of the emission regions, R, are estimated to be in the range of 1.1*10^15 cm - 6.6*10^16 cm. The flare asymmetry is difficult to explain by a light travel time effect but may be caused by differences between the timescales for acceleration and dissipation of high-energy particles in the relativistic jet. A jet-in-jet model also could produce the observed log-normal distributions.

NEW AR/ARMA MODEL SELECTION METHOD FOR FINITE LENGTH TIME SERIES WITH APPLICATION TO PREDICTION OF PRETERM DELIVERIES

In this paper, we proposed a new method able to select, simultaneously, from finite length time-series sequence, the suitable model type; pure Autoregressive (AR) or Autoregressive Moving Average (ARMA), which best describes the process that generated data. This is also a new way for estimating ARMA model order. The proposed method is different in its concept from all other methods found in the literature, direct and far simpler to implement. We proposed new empirical criteria basing on specific AR order selection criteria for finite length time series. We tested the proposed criteria on 10000 realizations of different broadband and narrow band processes. We also studied effects of additive noise and data length on their performance. The best mean recognition rate of model type was 92%. [Formula: see text]-value of Fisher’s exact test was always strictly under [Formula: see text]. Power spectral densities of selected models managed to recover the true Power spectral density (PSDs) shapes by resolving close spectral peaks and by finding their positions and their bandwidths with negligible spectral biases. Efficiency of our method was proved by its application in automatic segmentation of electrohysterographic signals (EHG) in the aim of predicting preterm deliveries with a mean rate of 90%.

Signature of inverse Compton emission from blazars

Blazars are classified into high, intermediate and low energy peaked sources based on the location of their synchrotron peak. This lies in infra-red/optical to ultra-violet bands for low and intermediate peaked blazars. The transition from synchrotron to inverse Compton emission falls in the X-ray bands for such sources. We present the spectral and timing analysis of 14 low and intermediate energy peaked blazars ob- served with XMMNewton spanning 31 epochs. Parametric fits to X-ray spectra helps constrain the possible location of transition from the high energy end of the syn- chrotron to the low energy end of the inverse Compton emission. In seven sources in our sample, we infer such a transition and constrain the break energy in the range 0.6 10 keV. The Lomb-Scargle periodogram is used to estimate the power spectral density (PSD) shape. It is well described by a power law in a majority of light curves, the index being flatter compared to general expectation from AGN, ranging here between 0.01 and 1.12, possibly due to short observation durations resulting in an absence of long term trends. A toy model involving synchrotron self-Compton (SSC) and exter- nal Compton (EC; disk, broad line region, torus) mechanisms are used to estimate magnetic field strength 6 0.03 - 0.88 G in sources displaying the energy break and infer a prominent EC contribution. The timescale for variability being shorter than synchrotron cooling implies steeper PSD slopes which are inferred in these sources.

Numerical generation of road profile through spectral description for simulation of vehicle suspension

This paper presents the generation of random road profile (Gaussian random signal) in spatial and time domain through power spectral density. For this purpose the two methods viz. white noise filtration and superposition of harmonics are described and used to generate the single track road elevation profiles corresponding to the ISO road through numerical simulation. The statistical analysis of the generated road profile is presented using power spectral density, probability density function and statistical moments to evaluate efficacy of the proposed methods. The terms associated with the spectral description of road profile are reviewed, well defined and described to resolve the ambiguity regarding the use of these terms. A modified expression is proposed for the spectrum of white noise filtration method to make it consistent with the ISO road classification. A parameter, low frequency cutoff of the white noise filtration method is properly defined and a methodology is presented for its estimation. A generalized formula is proposed for the method of superposition of harmonics to generate the signal and its successive differentiations without going through the numerical differentiation to avoid the numerical errors. It is shown that the method of superposition of harmonics is a flexible and powerful technique for generating the Gaussian random signal from spectral description as it can handle any practical shape of spectral density not only continuous but discrete split spectrum also. In addition, the use of higher sampling frequency has negligible effect on the contribution of high frequency spectral either in elevation or, especially in gradient of the generated profile as contrast to the method of white noise filtration.

Effect of Spectral Density Shapes on the Excitonic Structure and Dynamics of the Fenna–Matthews–Olson Trimer from Chlorobaculum tepidum

The Fenna-Matthews-Olson (FMO) trimer (composed of identical subunits) from the green sulfur bacterium Chlorobaculum tepidum is an important protein model system to study exciton dynamics and excitation energy transfer (EET) in photosynthetic complexes. In addition, FMO is a popular model for excitonic calculations, with many theoretical parameter sets reported describing different linear and nonlinear optical spectra. Due to fast exciton relaxation within each subunit, intermonomer EET results predominantly from the lowest energy exciton states (contributed to by BChl a 3 and 4). Using experimentally determined shapes for the spectral densities, simulated optical spectra are obtained for the entire FMO trimer. Simultaneous fits of low-temperature absorption, fluorescence, and hole-burned spectra place constraints on the determined pigment site energies, providing a new Hamiltonian that should be further tested to improve modeling of 2D electronic spectroscopy data and our understanding of coherent and dissipation effects in this important protein complex.

Kepler light-curve analysis of the blazar W2R 1926+42

We study the long term Kepler light curve of the blazar W2R 1926+42 ($\sim$ 1.6 years) which indicates a variety of variability properties during different intervals of observation. The normalized excess variance, $F_{\rm var}$ ranges from 1.8 % in the quiescent phase and 43.3 % in the outburst phase. We find no significant deviation from linearity in the $F_{\rm var}$-flux relation. Time series analysis is conducted using the Fourier power spectrum and the wavelet analysis methods to study the power spectral density (PSD) shape, infer characteristic timescales and statistically significant quasi-periodic oscillations (QPOs). A bending power law with an associated timescale of $T_B = 6.2^{+6.4}_{-3.1}$ hours is inferred in the PSD analysis. We obtain a black hole mass of $M_\bullet = (1.5 - 5.9) \times 10^7 M_\odot$ for the first time using $F_{\rm var}$ and the bend timescale for this source. From a mean outburst lifetime of days, we infer a distance from the jet base $r \leq 1.75$ pc indicating that the outburst originates due to a shock. A possible QPO peaked at 9.1 days and lasting 3.4 cycles is inferred from the wavelet analysis. Assuming that the QPO is a true feature, $r = (152 - 378)~ G M_\bullet/c^2$ and supported by the other timing analysis products such as a weighted mean PSD slope of $-1.5 \pm 0.2$ from the PSD analysis, we argue that the observed variability and the weak and short duration QPO could be due to jet based processes including orbital features in a relativistic helical jet and others such as shocks and turbulence.

Frequency-dependent core shifts and parameter estimation for the blazar 3C 454.3

We study the core shift effect in the parsec scale jet of the blazar 3C 454.3 using the 4.8 GHz - 36.8 GHz radio light curves obtained from three decades of continuous monitoring. From a piecewise Gaussian fit to each flare, time lags $\Delta t$ between the observation frequencies $\nu$ and spectral indices $\alpha$ based on peak amplitudes $A$ are determined. From the fit $\Delta t \propto \nu^{1/k_r}$, $k_r = 1.10 \pm 0.18$ indicating equipartition between the magnetic field energy density and the particle energy density. From the fit $A \propto \nu^\alpha$, $\alpha$ is in the range $-0.24$ to $1.52$. A mean magnetic field strength at 1 pc, $B_1 = 0.5 \pm 0.2$ G, and at the core, $B_{\rm core} = 46 \pm 16$ mG, are inferred, consistent with previous estimates. The measure of core position offset is $\Omega_{r\nu} = 6.4 \pm 2.8$ pc GHz$^{1/k_r}$ when averaged over all frequency pairs. Based on the statistical trend shown by the measured core radius $r_{\rm core}$ as a function of $\nu$, we infer that the synchrotron opacity model may not be valid for all cases. A Fourier periodogram analysis yields power law slopes in the range $-1.6$ to $-3.5$ describing the power spectral density shape and gives bend timescales in the range $0.52 - 0.66~$yr. This result, and both positive and negative $\alpha$, indicate that the flares originate from multiple shocks in a small region. Important objectives met in our study include: the demonstration of the computational efficiency and statistical basis of the piecewise Gaussian fit; consistency with previously reported results; evidence for the core shift dependence on observation frequency and its utility in jet diagnostics in the region close to the resolving limit of very long baseline interferometry observations.

KINEMATICS OF AND EMISSION FROM HELICALLY ORBITING BLOBS IN A RELATIVISTIC MAGNETIZED JET

We present a general relativistic (GR) model of jet variability in active galactic nuclei due to orbiting blobs in helical motion along a funnel or cone shaped magnetic surface anchored to the accretion disk near the black hole. Considering a radiation pressure driven flow in the inner region, we find that it stabilizes the flow, yielding Lorentz factors ranging between 1.1 and 7 at small radii for reasonable initial conditions. Assuming these as inputs, simulated light curves (LCs) for the funnel model include Doppler and gravitational shifts, aberration, light bending, and time delay. These LCs are studied for quasi-periodic oscillations (QPOs) and the power spectral density (PSD) shape and yield an increased amplitude ($\sim$ 12 %); a beamed portion and a systematic phase shift with respect to that from a previous special relativistic model. The results strongly justify implementing a realistic magnetic surface geometry in Schwarzschild geometry to describe effects on emission from orbital features in the jet close to the horizon radius. A power law shaped PSD with a typical slope of $-2$ and QPOs with timescales in the range of $(1.37 - 130.7)$ days consistent with optical variability in Blazars, emerges from the simulations for black hole masses $M_{\bullet} = (0.5 - 5) \times 10^8 M_{\odot}$ and initial Lorentz factors $\gamma_{jet,i} = 2 - 10$. The models presented here can be applied to explain radio, optical, and X-ray variability from a range of jetted sources including active galactic nuclei, X-ray binaries and neutron stars.

Broad-Band Variability in Accreting Compact Objects

Cataclysmic variable stars are in many ways similar to X-ray binaries. Both types of systems possess an accretion disk, which in most cases can reach the surface (or event horizon) of the central compact object. The main difference is that the embedded gravitational potential well in X-ray binaries is much deeper than those found in cataclysmic variables. As a result, X-ray binaries emit most of their radiation at X-ray wavelengths, as opposed to cataclysmic variables which emit mostly at optical/ultraviolet wavelengths. Both types of systems display aperiodic broad-band variability which can be associated to the accretion disk. Here, the properties of the observed X-ray variability in XRBs are compared to those observed at optical wavelengths in CVs. In most cases the variability properties of both types of systems are qualitatively similar once the relevant timescales associated with the inner accretion disk regions have been taken into account. The similarities include the observed power spectral density shapes, the rms-flux relation as well as Fourier-dependant time lags. Here a brief overview on these similarities is given, placing them in the context of the fluctuating accretion disk model which seeks to reproduce the observed variability.

Effect of Temperature Variation on Vibration Monitoring of Prestressed Concrete Girders

The effect of temperature variation on vibration monitoring of prestressed concrete (PSC) girders is experimentally analyzed. Firstly, vibration features such as autoregressive (AR) coefficient, correlation coefficient of power spectral density (CC of PSD), natural frequency, and mode shape are selected to estimate the effect of temperature variation on vibration characteristics of PSC girders. Secondly, vibration experiments on a lab-scale PSC girder are performed under the condition of temperature variation. Finally, the vibration features with respect to the temperature variation are analyzed to estimate the effect of temperature in vibration characteristics of the PSC girder.

X-RAY VARIABILITY AND THE INNER REGION IN ACTIVE GALACTIC NUCLEI

We present theoretical models of X-ray variability attributable to orbital signatures from an accretion disk including emission region size, quasi-periodic oscillations (QPOs) and its quality factor $Q$, and the emergence of a break frequency in the power spectral density shape. We find a fractional variability amplitude of $F_{var}\propto M^{-0.4}_{\bullet}$. We conduct a time series analysis on X-ray light curves ($0.3-10$ keV) of a sample of active galactic nuclei (AGNs). A statistically significant bend frequency is inferred in 9 of 58 light curves (16 %) from 3 AGNs for which the break timescale is consistent with the reported BH spin but not with the reported BH mass. Upper limits of $2.85 \times 10^7 M_\odot$ in NGC 4051, $8.02 \times 10^7 M_\odot$ in MRK 766 and $4.68 \times 10^7 M_\odot$ in MCG-6-30-15 are inferred for maximally spinning BHs. For REJ 1034+396, where a QPO at 3733 s was reported, we obtain an emission region size of $(6 - 6.5) M$ and a BH spin $a\lesssim$ 0.08. The relativistic inner region of a thin disk, dominated by radiation pressure and electron scattering is likely to host the orbital features as the simulated $Q$ ranges from $6.3 \times 10^{-2}$ to $4.25 \times 10^6$, containing the observed $Q$. The derived value of $Q \sim$ 32 for REJ 1034+396 therefore suggests that the AGN hosts a thin disk.

Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

Consider a real-valued and second-order stationary time series with mean zero. The aim is to estimate its spectral density. A minimax solution of this problem is known when either the time series is observed directly, or some observations are missed according to an independent Bernoulli process, or for some special cases when the time series is multiplied by an amplitude-modulating time series with known distribution. It is shown that if a time series of interest, a Bernoulli time series defining missing mechanism, and an amplitude-modulating time series are mutually independent, then the shape of spectral density of an underlying time series of interest can be estimated with the minimax rate known for the case of direct observations. Furthermore, in some special cases the spectral density can be estimated with the minimax rate known for directly observed time series of interest.

Multistage Procedure for Isolation of Diagnostic Parameters of Radial Artery Pulsation

A procedure for analysis of radial artery pulse signal is described. The procedure is used to estimate the diagnostic significance of different signal parameters in analyses using increasingly complex algorithms. The procedure can be used to elucidate and employ typological features of the signal shape and the spectral functions for some signal parameters of time series. At every step of the procedure, a particular parameter set is chosen. It is the informative set at this step that is important for diagnostically significant decision rules construction for the disease under consideration. A multi-step pulse signal analysis procedure was implemented with respect to diagnostic problem of identification of early stage pediatric arterial hypertension. This identification was based on large-scale experimental material received during clinical survey. Three analysis stages are described: signal shape analysis, analysis of spectral density shape of quasi-periodic time series, and analysis of spectral density parameters of pulse signal dicrotic wave time series. The multi-step pulse signal analysis procedure allows the reliability of early stage pediatric arterial hypertension identification to be increased significantly.