Modified Power Spectrum Research Articles

Classical versus quantum features of the Berthelot cosmological model

In this paper, we compare and contrast the classical versus quantum dynamics of a cosmological model based on the literature (Modified) Berthelot equation of state for the description of the dark sector of the universe. At the classical background level we identify a Minkowski-like and a de Sitter-like equilibrium epochs, with the latter occurring only beyond a certain threshold for a parameter in the equation of state; at the classical perturbed level we find that this same parameter realizes a duality in the adiabatic speed of sound between the two equilibrium epochs. The quantum evolution of this model is studied in the context of quantum geometrodynamics by solving analytically the Wheeler–DeWitt equation in the Born–Oppenheimer approximation for the scalar field potentials about the two equilibrium epochs. We identify the phenomenon of quantum decoherence to arise at the same threshold which constitutes the bifurcation between the two equilibrium epochs at the classical level. We comment on the quantum modified power spectrum focusing on some consequences dealing with the formation of astrophysical structures within the Press–Schechter framework. Our paper is intended to scrutinize which classical features of a certain cosmological model are preserved at its quantum level, and under which assumptions.

Single star SCIDAR: Atmospheric parameters profiling using the power spectrum of scintillation

Optical parameters of atmospheric turbulence have a significant impact on high angular resolution, adaptive optics, and site testing. The single star SCIDAR technique provides vertical profiles of these parameters, including the refractive index structure constant Cn2(h). Its is based on the analysis of single stars scintillation. This study introduces a new approach for real-time measurement of atmospheric parameters using the Single Star SCIDAR. The key element of this approach is the utilization of a modified power spectrum of atmospheric speckles, that have more significant variation with altitude. By using that modified power spectrum, an objective function is computed, and the minimization process is performed using the Active-Set algorithm. With this approach, we successfully obtained real-time vertical profiles of Cn2(h) with good accuracy. The processing takes approximately 3 s per profile, and the recovery rate (i.e. sum of Cn2(h)) is about 95%. The reliability of this approach is validated through simulation results and a comparison with data obtained from sounding balloons. These validations confirm the accuracy and credibility of this method, which can be useful in many practical applications.

JWST early Universe observations and ΛCDM cosmology

ABSTRACT Deep space observations of the JWST have revealed that the structure and masses of very early Universe galaxies at high redshifts ($z\sim15$), existing at $\sim$0.3 Gyr after the Big Bang, may be as evolved as the galaxies in existence for $\sim10$ Gyr. The JWST findings are thus in strong tension with the ${\rm{\Lambda}}$CDM cosmological model. While tired light (TL) models have been shown to comply with the JWST angular galaxy size data, they cannot satisfactorily explain isotropy of the cosmic microwave background (CMB) observations or fit the supernovae distance modulus versus redshift data well. We have developed hybrid models that include the tired light concept in the expanding universe. The hybrid ${\rm{\Lambda}}$CDM model fits the supernovae type 1a data well but not the JWST observations. We present a model with covarying coupling constants (CCC), starting from the modified FLRW metric and resulting Einstein and Friedmann equations, and a CCC + TL hybrid model. They fit the Pantheon + data admirably, and the CCC + TL model is compliant with the JWST observations. It stretches the age of the Universe to 26.7 Gyr with 5.8 Gyr at $z = 10$ and 3.5 Gyr at $z = 20$, giving enough time to form massive galaxies. It thus resolves the ‘impossible early galaxy’ problem without requiring the existence of primordial black hole seeds or modified power spectrum, rapid formation of massive population III stars, and super Eddington accretion rates. One could infer the CCC model as an extension of the ${\rm{\Lambda}}$CDM model with a dynamic cosmological constant.

Influence of structural length-scale sensitivities on Hermite–Gaussian rectangular vortex beam propagation in biological tissues

A modified power spectrum of biological tissues involving upper length-scale and bottom length-scale was introduced. In addition, the analytical expression of Hermite–Gaussian rectangular vortex beam with the parameter () in free space was derived. By this modified power spectrum, we established the normalized probability model of orbital angular momentum (OAM) states for Hermite–Gaussian rectangular vortex beams propagation in biological tissues. The results revealed that Hermite–Gaussian rectangular vortex beam exhibits a better anti-interference performance than Laguerre–Gaussian beam under the same conditions. The Hermite–Gaussian rectangular vortex beam propagates through a biological tissue with large bottom length-scale, small upper length-scale, small characteristic length of heterogeneity, low the fractal dimensions, and weak fluctuation strength, which produces a large normalized probability of signal OAM states. These results are fundamental to improving light propagation in tissue and provide a quantitative guidance for medical imaging and diagnosis.

Inflationary perturbation spectrum in extended effective field theory of inflation

The effective field theory (EFT) of inflation provides a natural framework to study the new physical effects on primordial perturbations. Recently a healthy extension of the EFT of inflation with high-order operators has been proposed, which avoids ghosts and meanwhile leads to a nonlinear dispersion relation of the scalar perturbations. This paper is devoted to studying the effects of these high-order operators by using the uniform asymptotic approximation method. In particular, we first construct the approximate analytical solution to the mode function of the scalar perturbations. Because of the presence of the high-order operators, the perturbation modes usually experience a period of non-adiabatic evolution before they cross the Hubble radius, which could lead to the production of excited states and modifications of the primordial perturbation spectrum. However, we show that the modified power spectrum is still nearly scale-invariant and the presence of the high-order operators can only affect the overall amplitude of the spectrum. In particular, after showing explicitly the impact of these new effects on particle production rate and perturbation spectrum, we explore their origin in detail.

Rolling bearing fault diagnosis based on time-delayed feedback monostable stochastic resonance and adaptive minimum entropy deconvolution

Rolling bearings are the key components in the modern machinery, and tough operation environments often make them prone to failure. However, due to the influence of the transmission path and background noise, the useful feature information relevant to the bearing fault contained in the vibration signals is weak, which makes it difficult to identify the fault symptom of rolling bearings in time. Therefore, the paper proposes a novel weak signal detection method based on time-delayed feedback monostable stochastic resonance (TFMSR) system and adaptive minimum entropy deconvolution (MED) to realize the fault diagnosis of rolling bearings. The MED method is employed to preprocess the vibration signals, which can deconvolve the effect of transmission path and clarify the defect-induced impulses. And a modified power spectrum kurtosis (MPSK) index is constructed to realize the adaptive selection of filter length in the MED algorithm. By introducing the time-delayed feedback item in to an over-damped monostable system, the TFMSR method can effectively utilize the historical information of input signal to enhance the periodicity of SR output, which is beneficial to the detection of periodic signal. Furthermore, the influence of time delay and feedback intensity on the SR phenomenon is analyzed, and by selecting appropriate time delay, feedback intensity and re-scaling ratio with genetic algorithm, the SR can be produced to realize the resonance detection of weak signal. The combination of the adaptive MED (AMED) method and TFMSR method is conducive to extracting the feature information from strong background noise and realizing the fault diagnosis of rolling bearings. Finally, some experiments and engineering application are performed to evaluate the effectiveness of the proposed AMED-TFMSR method in comparison with a traditional bistable SR method.

Acoustic detection of cracks in the anvil of a large-volume cubic high-pressure apparatus.

A large-volume cubic high-pressure apparatus with three pairs of tungsten carbide anvils is the most popular device for synthetic diamond production. Currently, the consumption of anvils is one of the important costs for the diamond production industry. If one of the anvils is fractured during the production process, the other five anvils in the apparatus may be endangered as a result of a sudden loss of pressure. It is of critical importance to detect and replace cracked anvils before they fracture for reduction of the cost of diamond production and safety. An acoustic detection method is studied in this paper. Two new features, nested power spectrum centroid and modified power spectrum variance, are proposed and combined with linear prediction coefficients to construct a feature vector. A support vector machine model is trained for classification. A sliding time window is proposed for decision-level information fusion. The experiments and analysis show that the recognition rate of anvil cracks is 95%, while the false-alarm rate is as low as 5.8 × 10(-4) during a time window; this false-alarm rate indicates that at most one false alarm occurs every 2 months at a confidence level of 90%. An instrument to monitor anvil cracking was designed based on a digital signal processor and has been running for more than eight months in a diamond production field. In this time, two anvil-crack incidents occurred and were detected by the instrument correctly. In addition, no false alarms occurred.

Testing quantum gravity effects with latest CMB observations

Inspired by quantum gravitational physics, the approach of non-commutative (NC) phase space leads to a modified dispersion relation of gravitational waves. This feature, if applied to the very early universe, gives rise to a modified power spectrum of primordial tensor perturbations with a suppression of power on large scales. We confront this phenomenon with the BICEP2 and Planck experiments, and show that inflation with the modified dispersion relation can simultaneously fit the observations better than the standard inflationary paradigm. In particular, the numerical result implies that with the latest cosmological microwave background (CMB) observations, a quantum gravity modified power spectrum of primordial tensor modes is preferred at a statistical significance of more than 3σ compared with the minimal model. Our study indicates that the potential tension between the BICEP2 and Planck data may be resolved by quantum gravity effects.

INFLATION AND SQUEEZED STATES: LATTICE SCHRÖDINGER PICTURE

In lattice Schrödinger picture, the wave functionals of the squeezed vacuum states of a free real scalar field in de Sitter space are constructed explicitly in momentum space by using the method of instantaneous Hamiltonian diagonalization. The modified power spectrum and particle production in the general mixed, squeezed initial states are also presented. For the massless minimally coupled scalar field which is relevant to slow roll inflationary models, we recover the power spectrum of scalar fluctuations for the squeezed vacuum states, and show that the evolution of the squeezed vacuum states exhibits an attractor behavior. The case of a massless conformally coupled scalar field is also discussed.

Far-field spectral behaviour and spectral switching of super-Gaussian pulses

We have presented the far-field spectral behaviour of a super-Gaussian pulse diffracted through a rectangular aperture. It has been found that the on-axis modified power spectrum is always blue shifted, whose value increases with the increase in the value of the super-Gaussian parameter ( m). For off-axis case, at some critical angle of diffraction, the diffraction induced far-field power spectrum is split into two lines of equal height. The far-field power spectrum is blue shifted when the diffraction angle is greater than the critical angle, whereas it is red shifted when the diffraction angle is less than the critical angle, i.e., spectral switching occurs. The critical angle for switching significantly increases with the increase in the super-Gaussian parameter ( m). An important finding is that the switching frequency, the blue and red shift frequencies can be tuned by varying m.

Pre-inflationary vacuum in the cosmic microwave background

We consider the effects on the primordial power spectrum of a period of radiation-dominated expansion prior to the inflationary era. If inflation lasts a total of only 60 e-folds or so, the boundary condition for quantum modes cannot be taken in the short-wavelength limit as in the standard perturbation calculation. Instead, the boundary condition is set by the vacuum state of the prior radiation-dominated epoch, which only corresponds to the inflationary vacuum state in the ultraviolet limit. This altered vacuum state results in a modulation of the inflationary power spectrum. We calculate the modification to a best-fit model from the WMAP3 data set, and find that power is suppressed at large scales. The modified power spectrum is favored only very weakly by the WMAP3 temperature and polarization data.

White noise from dark matter: 21 cm observations of early baryon collapse

In concordance cosmology, dark matter density perturbations generated by inflation lead to nonlinear, virialized minihalos, into which baryons collapse at redshift $z\ensuremath{\sim}20$. We survey here novel baryon evolution produced by a modification of the power spectrum from white noise density perturbations at scales below $k\ensuremath{\sim}10h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ (the smallest scales currently measured with the Lyman-$\ensuremath{\alpha}$ forest). Exotic dark matter dynamics, such as would arise from scalar dark matter with a late phase transition (similar to an axion, but with lower mass), or primordial black hole dark matter, create such an amplification of small scale power. The dark matter produced in such a phase transition collapses into minihalos, with a size given by the dark matter mass within the horizon at the phase transition. If the mass of the initial minihalos is larger than $\ensuremath{\sim}{10}^{\ensuremath{-}3}{M}_{\ensuremath{\bigodot}}$, the modified power spectrum is found to cause widespread baryon collapse earlier than standard $\ensuremath{\Lambda}\mathrm{CDM}$, leading to earlier gas heating. It also results in higher spin temperature of the baryons in the 21 cm line relative to $\ensuremath{\Lambda}\mathrm{CDM}$ at redshifts $zg20$ if the mass of the minihalo is larger than $1{M}_{\ensuremath{\bigodot}}$. It is estimated that experiments probing 21 cm radiation at high redshift will contribute a significant constraint on dark matter models of this type for initial minihalos larger than $\ensuremath{\sim}10{M}_{\ensuremath{\bigodot}}$. These experiments may also detect (or rule out) primordial black holes as the dark matter in the window $30{M}_{\ensuremath{\bigodot}}\ensuremath{\lesssim}{M}_{H}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{3}{M}_{\ensuremath{\bigodot}}$ still left open by strong microlensing experiments and other astrophysical constraints. Early experiments reaching to $z\ensuremath{\approx}15$ will constrain minihalos down to $\ensuremath{\sim}{10}^{3}{M}_{\ensuremath{\bigodot}}$.

Localized pulses exhibiting a missilelike slow decay

We investigate the quasi-missile behavior of known localized wave solutions, such as the modified power spectrum and splash pulses. We demonstrate that source-free localized waves can exhibit slow decay rates analogous to Wu's missile solutions, which are characterized by an amplitude decay rate slower than 1/R over an unlimited range. When excited from a finite aperture, the missilelike decay is not exhibited by all localized waves showing such behavior in the source-free situation. On the other hand, localized wave missiles generated from a finite aperture have peaks that exhibit quasi-missile decay. In an extended intermediate range between the near- and the far-field regions, these pulses decay at a rate slower than 1/R before switching to the usual 1/R decay.

Two-point Correlation Function and Power Spectrum at Very Large Scales

Subsamples of galaxies with different morphological types have been sorted out from Stromlo-APM redshift survey. Two-point correlation function for each subsample has been calculated. The two-point correlation functions for all subsamples show very large scale fluctuation. We show that the two-point correlation function with fluctuation could be fitted by a modified power spectrum with power excess at wave number comparable to the scale of the fluctuation.

Spatiotemporal evolution of focused single-cycle electromagnetic pulses

We analyze exact solutions of Maxwell's equations that are capable of describing focused single-cycle electromagnetic pulses. These finite energy solutions are a subset of Ziolkowski's ``modified power spectrum'' pulse solutions [Phys. Rev A 39, 2005 (1989)]. They display substantial temporal reshaping, time reversal, and polarity reversals as they pass through the focus. The temporal profiles at the focus and in the far field are related by a Hilbert transform in time. These results are explained in terms of the Gouy phase shift of focused beams. We also show that these pulse solutions are natural spatiotemporal modes of an open resonator and propose methods for their practical realization.

The distribution of empirical periodograms: Lomb-Scargle and PDM spectra

The theoretical probability distributions of periodograms are derived for the assumed variance of noise. In practice, however, the variance is estimated from data and hence it is a random variable itself. The empirical periodograms, i.e. the periodograms normalized using the estimated variance, therefore follow a distribution different from that predicted by theory. We demonstrate that in general many empirical periodograms follow the beta distribution. In particular, as an example we consider a Lomb &38; Scargle (L-S) modified power spectrum with an exponential theoretical distribution. We derive its easy-to-use analytical empirical distribution. We demonstrate that the difference between the tails of the empirical and theoretical distributions is large enough to have a profound effect on the statistical significance of signal detections. The difference persists despite generally good asymptotic convergence of the distributions near their centres. Hence we argue that even for well-behaved statistics (e.g. L-S) one has to use our new empirical beta distributions rather than the theoretical ones. Our conclusions are illustrated by a realistic example. In the example we demonstrate a significant difference between the theoretical and empirical distributions. Additionally, we provide an example of conversion between analysis of variance (AOV), power-spectrum, PDM and χ2 periodograms.

The distribution of empirical periodograms: Lomb-Scargle and PDM spectra

The theoretical probability distributions of periodograms are derived for the assumed variance of noise. In practice, however, the variance is estimated from data and hence it is a random variable itself. The empirical periodograms, i.e. the periodograms normalized using the estimated variance, therefore follow a distribution different from that predicted by theory. We demonstrate that in general many empirical periodograms follow the beta distribution. In particular, as an example we consider a Lomb &38; Scargle (L–S) modified power spectrum with an exponential theoretical distribution. We derive its easy-to-use analytical empirical distribution. We demonstrate that the difference between the tails of the empirical and theoretical distributions is large enough to have a profound effect on the statistical significance of signal detections. The difference persists despite generally good asymptotic convergence of the distributions near their centres. Hence we argue that even for well-behaved statistics (e.g. L–S) one has to use our new empirical beta distributions rather than the theoretical ones. Our conclusions are illustrated by a realistic example. In the example we demonstrate a significant difference between the theoretical and empirical distributions. Additionally, we provide an example of conversion between analysis of variance (AOV), power-spectrum, PDM and χ2 periodograms.

Focused one-cycle electromagnetic pulses.

We describe several families of exact unbounded solutions of Maxwell's equations in vacuum. These solutions depict one- (or 11/2-) cycle electromagnetic pulses whose fields are of either transverse magnetic or transverse electric character and are confined to toroidal wave packets that converge to a focus and then diverge in a manner that is expected from familiar rules of diffraction. These ``focused doughnut'' pulses constitute a subset of the ``modified power spectrum'' pulse solutions discovered by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. We derive the total energy, the energy spectrum, the ability to accelerate an electron, and other properties of these focused doughnut pulse solutions. \textcopyright{} 1996 The American Physical Society.

Scattering of superpositions of localized waves from spheres

Localized wave (LW) solutions of the homogeneous wave equation can represent either focused or extended pulses, depending on the choice of a free parameter present in the solution. One can form finite energy superpositions, with respect to this parameter, and one such superposition, known as a modifiedpowerspectrum (MPS) pulse, has been extensively studied [R. W. Ziolkowski, Phys. Rev. A 39, 2005–2032 (1989)]. In particular, the enhanced near-field LW propagation effect has been demonstrated by others, in the context of multi-time-derivative transmit/receive systems [R. W. Ziolkowski and D. K. Lewis, J. Appl. Phys. 68, 6083–6086 (1990)]. The LW solutions are broadband, so it is perhaps to be expected that one could use this property, along with the enhanced focusing characteristic, to extract target parameters when scattering LW superpositions from objects. The acoustic MPS pulse backscattered spectra from a number of different sized steel and aluminum spheres will be presented. It will be demonstrated that these spectra can be used to extract target size information. [Work supported by NSERC.]

Space/time characteristics of localized transient fields from planar axisymmetric sources

Several approaches are presented to compute the acoustic transient field from planar axisymmetric circular sources vibrating with continuous space/time velocity distributions. These approaches include an impulse response approach for uniformly vibrating sources, and a generalized impulse response approach and a source discretization approach for nonuniformly vibrating sources. Also, two approximations for the far field will be overviewed. As a particular case of interest and importance, the acoustic field generated by a space/time modified power spectrum (MPS) driving pulse will be described using the various approaches. Numerical results are presented to illustrate the localized behavior of the space/time field. These results are compared to analogous results obtained from ordinary cw driving pulses. Methods to optimize the localization power of the MPS pulse are also discussed.