Gaussian Spectrum Research Articles

An Optimized K-Edge Signal Extraction Method for K-Edge Decomposition Imaging Using a Photon Counting Detector

In K-edge decomposition imaging for the multienergy system with the photon counting detectors (PCDs), the energy bins significantly affect the intensity of the extracted K-edge signal. Optimized energy bins can provide a better K-edge signal to improve the quality of the decomposition images and have the potential to reduce the amount of contrast agents. In this article, we present the Gaussian spectrum selection method (GSSM) for the multienergy K-edge decomposition imaging which can extract an optimized K-edge signal by optimizing energy bins compared with the conventional theoretical attenuation selection method (TASM). GSSM decides the width and locations of the energy bins using a simple but effective model of the imaging system, which takes the degraded energy resolution of the detector and the continuous x-ray spectrum into consideration. Besides, we establish the objective function, difference of attenuation to relative standard deviation ratio (DAR), to determine the optimal energy bins which maximize the K-edge signal. The results show that GSSM gets a better K-edge signal than TASM especially at the lower concentration level of contrast agents. The new method has the potential to improve the contrast and reduce the amount of contrast agents.

The distribution of vacua in random landscape potentials

Landscape cosmology posits the existence of a convoluted, multidimensional, scalar potential—the “landscape”—with vast numbers of metastable minima. Random matrices and random functions in many dimensions provide toy models of the landscape, allowing the exploration of conceptual issues associated with these scenarios. We compute the relative number and slopes of minima as a function of the vacuum energy Λ in an N-dimensional Gaussian random potential, quantifying the associated probability density, p(Λ). After normalisations p(Λ) depends only on the dimensionality N and a single free parameter γ, which is related to the power spectrum of the random function. For a Gaussian landscape with a Gaussian power spectrum, the fraction of positive minima shrinks super-exponentially with N; at N=100, p(Λ>0) ≈ 10−1197. Likewise, typical eigenvalues of the Hessian matrices reveal that the flattest approaches to typical minima grow flatter with N, while the ratio of the slopes of the two flattest directions grows with N. We discuss the implications of these results for both swampland and conventional anthropic constraints on landscape cosmologies. In particular, for parameter values when positive minima are extremely rare, the flattest approaches to minima where Λ ≈ 0 are much flatter than for typical minima, increasingly the viability of quintessence solutions.

Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes

We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a stochastic field represents broadband light emitted by quantum dot superluminescent diodes.

Gaussian process foreground subtraction and power spectrum estimation for 21 cm cosmology

ABSTRACT One of the primary challenges in enabling the scientific potential of 21 cm intensity mapping at the epoch of reionization (EoR) is the separation of astrophysical foreground contamination. Recent works have claimed that Gaussian process regression (GPR) can robustly perform this separation, particularly at low Fourier k wavenumbers where the EoR signal reaches its peak signal-to-noise ratio. We revisit this topic by casting GPR foreground subtraction (GPR-FS) into the quadratic estimator formalism, thereby putting its statistical properties on stronger theoretical footing. We find that GPR-FS can distort the window functions at these low k modes, which, without proper decorrelation, make it difficult to probe the EoR power spectrum. Incidentally, we also show that GPR-FS is in fact closely related to the widely studied inverse covariance weighting of the optimal quadratic estimator. As a case study, we look at recent power spectrum upper limits from the Low-Frequency Array (LOFAR) that utilized GPR-FS. We pay close attention to their normalization scheme, showing that it is particularly sensitive to signal loss when the EoR covariance is misestimated. This has possible ramifications for recent astrophysical interpretations of the LOFAR limits, because many of the EoR models ruled out do not fall within the bounds of the covariance models explored by LOFAR. Being more robust to this bias, we conclude that the quadratic estimator is a more natural framework for implementing GPR-FS and computing the 21 cm power spectrum.

Rapid spectral evolution of steep surface wave groups with directional spreading

Abstract

Single-pixel identification of 2-dimensional objects by using complex Laguerre–Gaussian spectrum containing both azimuthal and radial modal indices

We simulate and experimentally demonstrate the optical single-pixel identification of two-dimensional (2D) objects by analyzing the corresponding complex-valued (i.e, amplitude and phase) Laguerre–Gaussian​ (LGl,p) spectra containing both the azimuthal (i.e., l) and radial (i.e., p) indices. A sequence of optical beams, each carrying a different superposition of one LG mode and one fundamental Gaussian mode, propagate through the objects. The amplitude and phase contributions of each LG modal component are then obtained by four sequential power measurements using a single-pixel detector. We reconstruct the 2D spatial structures of fan-shaped objects with different orientation angles and an “SC” logo using the measured complex LG spectra that contain 31 different azimuthal and 31 different radial index values. The simulation and experimental results show that (i) the minima positions of the amplitude-only LG sub-spectra (fixed l=0, varying p) are dependent on the object’s spatial information along its radial direction, (ii) the amplitude-only LG spectrum is likely to be insensitive to the object’s orientation angle, and (iii) the slopes of the phase-only LG sub-spectra (fixed p, varying l) are linearly proportional to the object’s orientation angle.

Effect of spectral resolution on weak-value based parameter estimation

There was a long-standing postulation that the precision of weak-value based metrology using post-selection and spectral analysis is limited by the resolution of spectrometer. Current proposals releasing this limitation require either initially Gaussian spectrum or giving up the weak value amplification approximation, both of which make extra restrictions and increase the difficulty of implementation. However, we find that this compromise is unnecessary. Rather than the spectral resolution, the precision of weak-value based metrology mainly relies on how accurate we know about the initial pointer state. Moreover, the relation between knowledge of the initial pointer state and the error-ratio of output is provided and numerically simulated. Our results suggest that the detection devices of weak-value based metrology can be significantly simplified, thus made it a more convenient technique for real-world applications.

Performance Assessment of NaI detector Spectrometer for Safeguard Measurements

NUCLEAR Safeguards Measurement Methods are developed by design characteristics as well as performance specifications for several systems of the gamma-ray assay. A NaI(Tl) gamma detector was characterized with respect to count rate performance, detector efficiency, dead time (DT), low-level discriminator, and threshold effects using low, medium, and high-energy radioactive point sources. Spectral data are collected using inorganic scintillation detectors NaI (Tl). Besides, the response functions of the NaI(T1) 2 × 2” detector were determined where detector efficiency and FWHM were measured at diverse sources using energy lines (356.02 keV of 133Ba, 661.7 keV of 137Cs and1173.2 and 1332.5 keV of 60Co) and calculated by using MCNP method. The Gaussian spectra generated by MCNP-5 code were compared with the experimental work. To validate the simulated result, the Gaussian Energy Broadening (GEB) card was used, yielding the best results. When comparing the obtained findings derived from MNCP calculations with the experimental findings, they showed a good agreement in their values.

Integrability and spectral form factor in Chern–Simons formulation

We study the integrability from the spectral form factor in the Chern–Simons formulation. The effective action in the higher spin sector was not derived so far. Therefore, we begin from the SL(3) Chern–Simons higher spin theory. Then the dimensional reduction in this Chern–Simons theory gives the SL(3) reparametrization invariant Schwarzian theory, which is the boundary theory of an interacting theory between the spin-2 and spin-3 fields at the infrared or massless limit. We show that the Lorentzian SL(3) Schwarzian theory is dual to the integrable model, SL(3) open Toda chain theory. Finally, we demonstrate the application of open Toda chain theory from the SL(2) case. The numerical result shows that the spectral form factor loses the dip-ramp-plateau behavior, consistent with integrability. The spectrum is not a Gaussian random matrix spectrum. We also give an exact solution of the spectral form factor for the SL(3) theory. This solution provides a similar form to the SL(2) case for [Formula: see text]. Hence the SL(3) theory should also do not have a Gaussian random matrix spectrum.

Effect of pH value on photoluminescence properties of Eu3+/Tb3+ co-doped ZnO

In this work, we studied the effect of different pH values on morphology, band gap and photoluminescence (PL) properties of Eu3+/Tb3+ co-doped ZnO prepared by coprecipitation method. Experimental results show that alkaline condition is more favorable for the doping of Eu3+ and Tb3+ ions which reduce the band gap and increases the PL intensity of UV emission (385 nm) and visible emission (400—600 nm) of ZnO. Gaussian deconvolution PL spectra show that the defects on the surface of ZnO are decreased when it is synthesized under alkaline conditions. Furthermore, both the intrinsic orange emission of Eu3+ ions (611 nm) and the intrinsic green emission of the Tb3+ ions (495 nm) of ZnO in this case are obtained at the same time. High intensity green and orange emission indicates that Eu3+/Tb3+ co-doped ZnO is a promising PL material and has potential in emission devices.

An Analytical Method for High-Frequency Electromagnetic Scattering of Arbitrary Undulating Rough Surfaces

This article presents a new approach to analytically compute high-frequency (HF) electromagnetic (EM) scattering from an arbitrary undulating rough surface according to the statistical characteristics of its geometric fluctuation. The integral expression of the scattering coefficient is derived from Kirchhoff approximation (KA) and extended to arbitrary spectra. Two methods are presented to calculate the integral: 1) the discrete Fourier transforming method based on the autocorrelation function (ACF) (KAC) and 2) the convolution method based on the power spectrum density function (KAW). For some analytically expressed spectra, the scattering coefficients can be calculated directly by the KAW and KAC methods according to its power spectrum density (PSD). The analytical expressions of classical KA for Gaussian and exponential spectrum are used to validate the proposed methods. For the case of unknown undulation height spectra of rough surfaces, the ACF is statistically calculated first, and then the KAC and KAW methods are used to calculate the average scattering coefficients numerically. Moreover, the numerical results show that the KAW method takes up more memory to retain enough energy of the ACF for accurate scattering coefficients. The two new methods are effective in the range of $\theta _{i} $ from 0° to 45° and have broad application prospects for real scenarios.

Nonlinear statistics of primordial black holes from Gaussian curvature perturbations

We develop the non-linear statistics of primordial black holes generated by a gaussian spectrum of primordial curvature perturbations. This is done by employing the compaction function as the main statistical variable under the constraints that: a) the over-density has a high peak at a point $\vec{x}_0$, b) the compaction function has a maximum at a smoothing scale $R$, and finally, c) the compaction function amplitude at its maximum is higher than the threshold necessary to trigger a gravitational collapse into a black hole of the initial over-density. Our calculation allows for the fact that the patches which are destined to form PBHs may have a variety of profile shapes and sizes. The predicted PBH abundances depend on the power spectrum of primordial fluctuations. For a very peaked power spectrum, our non-linear statistics, the one based on the linear over-density and the one based on the use of curvature perturbations, all predict a narrow distribution of PBH masses and comparable abundance. For broader power spectra the linear over-density statistics over-estimate the abundance of primordial black holes while the curvature-based approach under-estimates it. Additionally, for very large smoothing scales, the abundance is no longer dominated by the contribution of a mean over-density but rather by the whole statistical realisations of it.

Proton acceleration via the TNSA mechanism using a smoothed laser focus

In this work, we present the results of an experiment aiming at proton acceleration using a focus with a homogeneous intensity distribution, called smoothed focus. To achieve this goal, we implemented a phase plate before the pre-amplifier of the Petawatt High-Energy Laser for Heavy Ion EXperiments laser facility. The phase plate was used for the first time at a high-power short-pulse laser. Demonstrating a low divergent ion beam was the main goal of this work. Numerical simulations using the particle-in-cell code Extendable PIC Open Collaboration estimated a 2–5 times reduction in the angular divergence of the proton beam using a phase plate due to a smoother sheath at the rear side of the target. However, the reduction in the angular divergence was not sensible according to the experimental data. A positive point is that the spectrum of protons that are generated with the smoothed beam is shifted toward lower energies, provided that the laser absorption is kept in check, compared to the Gaussian proton spectrum. Moreover, the number of protons that are generated with the smoothed beam is higher than the ones generated with the Gaussian beam.

35 fs, all-polarization-maintaining MOPA laser system

We have experimentally observed ultrashort pulse in a simple, all-polarization-maintaining fiber, master oscillator and power amplifier laser. A semiconductor saturable mirror (SESAM) module is used as the mode locker. The ultrashort pulse exhibits perfect Gaussian spectrum without any fine structure. The 20 dB pulse spectral width is 28 nm, and the pulse duration directly output from the oscillator is 268.6 fs. Via a two-stage amplifier, the pulse spectrum is greatly broadened to 43 nm, and the pulse duration lengths to 0.9 ps. Moreover, after compression, a typical saddle-shaped spectrum appears and the spectral bandwidth broadens to 121 nm; the pulse duration is compressed to ~35 fs with a pulse peak power of 22.79 kW, which is high enough to stimulate a one-octave supercontinuum spectrum. Due to the polarization-maintaining structure and high reliability of SESAM, the whole system exhibits strong environmental stability. Experimental observation reveals that such a fiber laser with a very simple structure exhibits excellent performance, and could be applied in the area of optical frequency comb.

Improvement of emission and thermal stability induced by selected occupation of Al3+ in Ba3Si6O12N2:Eu2+ phosphors

Oxynitride Ba3Si6O12N2:Eu2+ phosphor can usually exhibit high color purity emission spectrum and outstanding thermal stability because of its rigid structure which can be widely used in WLEDs. With the aim of further optimizing the emission intensity, color purity and thermal stability, Al3+-doped Ba3Si6O12N2:Eu2+ green phosphors were successfully prepared by a high-temperature sintering method in the current work. The crystal structure was clearly investigated by the XRD patterns and Rietveld refinement. The expanding volume and elemental analysis proved that Si4+ ions can be efficiently substituted by Al3+ ions in the Ba3Si6O12N2:Eu2+ phosphor. With increasing doping of Al3+ ions, the full width at half maximum decreased from 66.88 to 65.12 nm with an optimal color purity of 65.95%, and the reason was clearly elucidated by the Gaussian fitting spectrum and decay times. Moreover, the emission intensity of Ba3Si6O12N2:0.1Eu2+, 0.03Al3+ was 120% of the intensity of the Al-free sample, and the internal quantum efficiency could reach 70%. The thermal stability was also remarkably enhanced as Al3+ substituted Si4+ in Ba3Si6O12N2:0.1Eu2+, and Ba3Si6O12N2:0.1Eu2+, 0.03Al3+ exhibited only 8% emission loss at 200 °C compared with that at ambient temperature. The outstanding thermal stability was clearly explained by the thermoluminescence spectra and configurational coordinate diagram. The results indicate that the introduction of Al3+ ions can be a versatile method to improve the optical properties of silicon oxynitride.

Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves

A methodology is proposed for efficient and accurate modeling and simulation of correlated non-Gaussian wind velocity time histories along long-span structures at an arbitrarily large number of points. Currently, the most common approach is to model wind velocities as discrete components of a stochastic vector process, characterized by a Cross-Spectral Density Matrix (CSDM). To generate sample functions of the vector process, the Spectral Representation Method is one of the most commonly used, involving a Cholesky decomposition of the CSDM. However, it is a well-documented problem that as the length of the structure – and consequently the size of the vector process – increases, this Cholesky decomposition breaks down numerically. This paper extends a methodology introduced by the second and fourth authors to model wind velocities as a Gaussian stochastic wave (continuous in both space and time) by considering the stochastic wave to be non-Gaussian. The non-Gaussian wave is characterized by its frequency–wavenumber (FK) spectrum and marginal probability density function (PDF). This allows the non-Gaussian wind velocities to be modeled at a virtually infinite number of points along the length of the structure. The compatibility of the FK spectrum and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method introduced by the second and third authors, where the underlying Gaussian FK spectrum is upgraded iteratively using the directly computed (through translation process theory) non-Gaussian FK spectrum. After a small number of computationally extremely efficient iterations, the underlying Gaussian FK spectrum is established and generation of non-Gaussian sample functions of the stochastic wave is straightforward without the need of iterations. Numerical examples are provided demonstrating that the simulated non-Gaussian wave samples exhibit the desired spectral and marginal PDF characteristics.

Development of a novel fatigue damage model for Gaussian wide band stress responses using numerical approximation methods

A significant development has been made on a new fatigue damage model applicable to Gaussian wide band stress response spectra using numerical approximation methods such as data processing, time simulation, and regression analysis. So far, most of the alternative approximate models provide slightly underestimated or overestimated damage results compared with the rain-flow counting distribution. A more reliable approximate model that can minimize the damage differences between exact and approximate solutions is required for the practical design of ships and offshore structures. The present paper provides a detailed description of the development process of a new fatigue damage model. Based on the principle of the Gaussian wide band model, this study aims to develop the best approximate fatigue damage model. To obtain highly accurate damage distributions, this study deals with some prominent research findings, i.e., the moment of rain-flow range distribution MRR(n), the special bandwidth parameter μk, the empirical closed form model consisting of four probability density functions, and the correction factor QC. Sequential prerequisite data processes, such as creation of various stress spectra, extraction of stress time history, and the rain-flow counting stress process, are conducted so that these research findings provide much better results. Through comparison studies, the proposed model shows more reliable and accurate damage distributions, very close to those of the rain-flow counting solution. Several significant achievements and findings obtained from this study are suggested. Further work is needed to apply the new developed model to crack growth prediction under a random stress process in view of the engineering critical assessment of offshore structures. The present developed formulation and procedure also need to be extended to non-Gaussian wide band processes.

Characteristics of 3D Printed Plastic Scintillator

Digital Light Processing (DLP) 3D printing technique can be a powerful tool to fabricate plastic scintillator with a geometrically desired shape in innovatively fast time. Plastic scintillator with the size of 30 mm × 30 mm × 10 mm was fabricated by using the plastic resin and the DLP 3D printer (ASIGA, Pico2HD). The characteristics of decay time, energy resolution, intrinsic detection efficiency were analyzed and compared between the fabricated 3D printing plastic scintillator and a commercial plastic scintillator BC408 (Saint-Gobain Crystal). Decay time profile of the tested plastic scintillators was measured for 137Cs Compton maximum electron 477 keV by using a modified time correlated single photon counting (TCSPC) setup. The time profile was fitted by reconvolution function, and each decay time component and contribution was analyzed. For energy resolution of plastic scintillator, the Gaussian spectrum for 137Cs Compton maximum electron 477 keV was selectively measured by using the γ-γ coincidence experimental setup. As a result, it was confirmed that the 3D printing plastic scintillator showed average decay time 15.6 ns and energy resolution 15.4%. These characteristics demonstrates the feasibility of 3D printing plastic scintillator as a radiation detector.

Modeling and Simulation of GNSS-R Observables With Effects of Swell

Global navigation satellite system-reflectometry (GNSS-R) has attracted much attention in remote sensing, such as sea wind speed detection, soil moisture, and sea ice. In order to verify the algorithm of GNSS-R, the simulation of GNSS-R plays an important role in this research field. Delay waveform (DW) and delay-Doppler map (DDM) are the main observables in GNSS-R simulation, and are usually effects by the complex ocean environment, such as wind and swell. Besides the effects of wind, this article focuses on analyzing the influence of swell on the simulation of GNSS-R. In this article, a complex model of DW and DDM is presented with effects of swell. Swell modeled here by narrow-band Gaussian spectrum, and the influence of swell on the sea surface scattering coefficient, which can be calculated using Kirchhoff approximation-geometric optics. Observables obtained from the simulation in the space-borne scene are analyzed. The simulation results show that swell has a stable and significant impact on the simulation of GNSS-R observables. Compared with models under no consideration of swell, the model with effects of swell has higher accuracy.

Suppression of Small-Scale Magnetic Field Generation by Transformation of the Kinetic Energy Spectrum

The stabilization of a small-scale dynamo caused by a change in the energy spectrum of a conducting plasma flow is investigated. Such a change in kinetic properties can be due to the reverse conversion of generated magnetic energy into kinetic energy. We model the reverse conversion process using the classical Kazantsev model, which describes the operation of a small-scale dynamo in a mirror-symmetric turbulent flow. Our results suggest that the appearance of magnetic energy at small scales in the kinetic spectrum can stop the generation process. This stabilization turns out to be no less efficient than the braking of a turbulent dynamo through the conservation of total magnetic and kinetic energies. However, it looks more realistic, because for most dynamo systems the observed magnetic energy is lower than the kinetic one by several orders of magnitude. We show that in this method of nonlinear suppression just the appearance of energy at small scales is often not enough; in particular, a simple shift of the Gaussian spectrum toward small scales only amplifies the generation. In this paper, we describe a reasonable spectrum transformation method that allows the generation in both critical and supercritical regimes of small-scale dynamo operation to be stabilized. The fact that the described spectrum transformation can be directly recorded in an experimental test is equally important.