scholarly journals Double peaks of gravitational wave spectrum induced from inflection point inflation

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Tie-Jun Gao ◽  
Xiu-Yi Yang
Keyword(s):  
Energy Spectrum ◽  
Power Spectrum ◽  
Inflection Point ◽  
Wave Spectrum ◽  
Primordial Black Holes ◽  
Double Peak ◽  
Polynomial Potential ◽  
Double Peaks ◽  
Inflection Points ◽  
Peak Energy

AbstractWe investigate the possibility of inducing the gravitational waves (GWs) with double peak energy spectrum from primordial scalar perturbations in inflationary models with three inflection points. Here the inflection points can be generated from a polynomial potential or generated from a Higgs-like $$\phi ^4$$ ϕ 4 potential with the running of quartic coupling. In such models, the inflection point at large scales predicts the scalar spectral index and tensor-to-scalar ratio to be consistent with current CMB constraints, and the other two inflection points generate two large peaks in the scalar power spectrum at small scales, which can induce GWs with a double peak energy spectrum. We find that for some choices of the parameters the double peak spectrum can be detected by future GW detectors, and one of the peaks around $$f\simeq 10^{-9}{-}10^{-8}$$ f ≃ 10 - 9 - 10 - 8  Hz can also explain the recent NANOGrav signal. Moreover, the peaks of the power spectrum allow for the generation of primordial black holes, which accounts for a significant fraction of dark matter.

scholarly journals Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

2020 ◽  
Author(s):  
Chul-Moon Yoo ◽  
Tomohiro Harada ◽  
Shin’ichi Hirano ◽  
Kazunori Kohri
Keyword(s):  
Mass Spectrum ◽  
Power Spectrum ◽  
Environmental Effect ◽  
Window Function ◽  
Radial Coordinate ◽  
Primordial Black Holes ◽  
Scale Invariant ◽  
Curvature Perturbation ◽  
Arbitrary Power ◽  
Nonlinear Relation

Abstract We modify the procedure to estimate PBH abundance proposed in Ref. [1] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation △ ζ and use the values of △ ζ and △ △ ζ at each peak to specify the profile of ζ as a function of the radial coordinate while the values of ζ and △ ζ are used in Ref. [1]. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in Ref. [1]. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the k-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the k-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

scholarly journals Resistance behaviour of carbon fibre-reinforced polymers subjected to lightning strikes: Experimental investigation and application

2019 ◽  
Vol 28 ◽  
pp. 2633366X1989227 ◽  
Author(s):  
Jian Chen ◽  
Zhengcai Fu ◽  
Yang Zhao
Keyword(s):  
Carbon Fibre ◽  
Surface Resistance ◽  
Inflection Point ◽  
Front Surface ◽  
Resistance Change ◽  
Reinforced Polymers ◽  
Change Rate ◽  
Lightning Strikes ◽  
Inflection Points ◽  
Carbon Fibre Reinforced Polymers

It is difficult to monitor lightning damage to carbon fibre-reinforced polymers (CFRPs) online. This work experimentally investigates the changes associated with the electrical resistance of CFRPs subjected to lightning strikes. Two kinds of simulated lightning currents with different amplitudes in the range of 10–80 kA were injected into the CFRP samples. By measuring and comparing the changes in the struck-side (front) surface resistance, the surface resistance of the side opposite to the struck-side (back) and the oblique resistance of each sample before and after the lightning strike, it was observed that inflection points exist in the curve of the resistance change rate. The resistance decreases with increasing peak currents before the inflection point and increases when the peak current goes beyond the inflection point. The change rate of the front surface resistance is more sensitive to the lightning damage than are those of the back surface resistance and the oblique resistance. Different simulated lightning currents have approximately the same action integrals at the inflection points of resistance change rate. The characteristics indicate that resistance change detection could be a possible method for the online monitoring of CFRP lightning damage.

scholarly journals Study on Possible Double Peaks in Cutoff Frequency Characteristics of AlGaAs/GaAs HBTs by Energy Transport Simulation

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 437-442
Author(s):  
T. Okada ◽  
K. Horio
Keyword(s):  
Heterojunction Bipolar Transistors ◽  
Energy Transport ◽  
Transport Model ◽  
Cutoff Frequency ◽  
Bipolar Transistors ◽  
Electron Velocity ◽  
Collector Current ◽  
Double Peak ◽  
Double Peaks ◽  
Energy Profiles

By using an energy transport model, we simulate cutoff frequency fT  versus collector current density IC characteristics of npn−n AlGaAs/GaAs heterojunction bipolar transistors (HBTs) with various n−-collector thickness and n−-doping densities. It is found that the calculated fT  characteristics show double peak behavior when the n−- layer is thick enough and the n−-doping is high enough to allow existence of neutral n−- region. The mechanism of the double peak behavior is discussed by studying energy band diagrams, electron-energy profiles and electron-velocity profiles. Particularly, we discuss the origin of the second peak (at higher IC) which is not usually reported experimentally.

scholarly journals A GROWTH STUDY OF BEEF CATTLE

1981 ◽  
Vol 61 (4) ◽  
pp. 1041-1048 ◽  
Author(s):  
L. A. GOONEWARDENE ◽  
R. T. BERG ◽  
R. T. HARDIN
Keyword(s):  
Birth Weight ◽  
Beef Cattle ◽  
Inflection Point ◽  
Prediction Errors ◽  
Von Bertalanffy ◽  
University Of Alberta ◽  
Inflection Points ◽  
Richards Function ◽  
Residual Variances ◽  
The University

Four growth equations (Richards, Brody, Von Bertalanffy and Logistic) were fitted to data from two breed groups of female beef cattle, purebred Hereford (HE) and synthetic of Charolais, Angus and Galloway (SY), which were maintained at the University of Alberta beef breeding research ranch at Kinsella, Alberta. All functions fitted three common parameters (an asymptote, an integration constant and a maturing rate parameter). Two functions (Von Bertalanffy and Logistic) had fixed inflection points while the Richards function fitted the inflection point as a fourth parameter. The Brody function had no inflection point. Based on the R2, mean prediction errors (MPE) and residual variances, the Richards function, with a variable inflection point, provided the best overall and the most consistent fit to both sets of data, followed by the Brody function with no inflection point. The Richards was the only function that could predict birth weight with any degree of accuracy. The Logistic and Von Bertalanffy functions, with fixed inflection points, provided poor estimates of actual weights at each end of the growth curve, overestimating birth weight and converging too early leading to underestimation of adult weight or the asymptote. Intermediate weights were reasonably well estimated by these functions. The HE group showed a 28% greater maturing rate compared with the SY based on the Richards function.

scholarly journals Steepest growth of the power spectrum and primordial black holes

2019 ◽  
Vol 2019 (06) ◽  
pp. 028-028 ◽  
Author(s):  
Christian T. Byrnes ◽  
Philippa S. Cole ◽  
Subodh P. Patil
Keyword(s):  
Black Holes ◽  
Power Spectrum ◽  
Primordial Black Holes

Uncertainties of Wind Sea and Swell Prediction From the Torsethaugen Spectrum

2009 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Alessandro Toffoli
Keyword(s):  
Continental Shelf ◽  
Wave Spectrum ◽  
Single Mode ◽  
Offshore Structures ◽  
Reasonable Accuracy ◽  
Double Peak ◽  
Design Work ◽  
Practical Applications ◽  
Wind Sea ◽  
Norwegian Continental Shelf

In practical applications, it is usually assumed that the wave spectrum is of a single mode form, and well modelled by a JONSWAP or Pierson-Moskowitz spectrum. This assumption is of a reasonable accuracy for severe sea states. However, moderated and low sea states are often of a combined nature, consisting of both wind-sea and swell and should be characterized by a double peak spectrum. Bimodal seas can have a significant impact on the design and operability of fixed and floating offshore structures as well as LNG terminals. Although several separation procedures for the wave components exist the bimodal Torsethaugen spectrum is probably the only one well established in design work. This spectrum was developed primarily for one location at the Norwegian Continental Shelf (Statfjord Field) but in qualitative terms is expected to be of much broader validity. The present study discusses applicability of the Torsethaugen spectrum for locations outside the Norwegian Continental Shelf and uncertainties related to use of the spectrum.

scholarly journals The Distribution of Contact Pressures in the Rolling of Metals

1959 ◽  
Vol 81 (4) ◽  
pp. 669-679 ◽  
Author(s):  
C. W. MacGregor ◽  
R. B. Palme
Keyword(s):  
Contact Pressure ◽  
The Other ◽  
Center Line ◽  
Strip Rolling ◽  
Double Peak ◽  
Double Peaks ◽  
Pressure Distributions ◽  
Strain Data ◽  
Pressure Peak ◽  
Contact Pressures

A comparison is made between the experimentally determined contact pressure distributions obtained on square bars and flat strips. The former showed double peaks in the pressure, one near entry and the other near the roll center line. A pressure peak is obtained near the center line only for strip-rolling. Two independent analyses were made. One allowed the double peak for the square bars to be predicted with fair accuracy from stress-strain data. The second, based on the local elastic deformation of the rolls, also showed the transition in pressure distributions from billet to strip-rolling.

scholarly journals Generation of 3-hr Long-Crested Waves of Extreme Sea States With HOS-NWT Solver

2020 ◽  
Author(s):  
Maxime Canard ◽  
Guillaume Ducrozet ◽  
Benjamin Bouscasse
Keyword(s):  
Energy Spectrum ◽  
Wave Energy ◽  
Wave Spectrum ◽  
Wave Structure ◽  
Spatial Discretization ◽  
Ocean Engineering ◽  
Sea State ◽  
Wave Condition ◽  
Highly Nonlinear ◽  
Wave Energy Spectrum

Abstract The accurate control of wave fields generated in experiments and numerical simulations is of great interest for the ocean engineering community. In the context of wave-structure interactions, the recommended practices of classification societies are indeed based on the definition of a wave spectrum, that needs to be reproduced. The present work intends to address this problem from the numerical point of view, using a Numerical Wave Tank equipped with a wavemaker and an absorbing beach, based on the High-Order Spectral method (HOS-NWT). The challenging case of the generation of 3-hours long-crested extreme sea states is studied in details. An iterative procedure to reproduce a target wave spectrum at a given distance from the wavemaker is proposed. The quality of the sea state obtained is evaluated using several criteria defined from spectral quantities. A validation is first performed with a highly nonlinear but non-breaking sea-state. Statistical crest distributions obtained are compared with the Forristall and Huang distributions [1,2]. Then, the Gulf of Mexico 1,000 Year Return Period wave condition is generated. This corresponds to an extreme sea state with significant wave breaking occurrence. The numerical solver needs to be able to account for this phenomenon [3]. The Tian breaking model [4, 5] is calibrated to realistically reproduce the dissipation due to breaking, with particular attention paid to the spatial discretization, enlightening its significant effect on breaking model actions. Consequences on the iterative correction process are studied. The computed statistical quantities appear to be significantly different changing the spatial discretization, while the wave energy spectrum stands the same. It questions the relevance of the characterization of a sea state with the sole wave energy spectrum.

scholarly journals A Proper Increasing in the Testosterone Level May Be Associated With Better Pregnancy Outcomes for Patients With Tubal or Male Infertility During in vitro Fertilization/Intracytoplasmic Sperm Injection

2021 ◽  
Vol 12 ◽  
Author(s):  
Zhiyan Chen ◽  
Duoduo Zhang ◽  
Zhengyi Sun ◽  
Qi Yu
Keyword(s):  
Male Infertility ◽  
Pregnancy Outcomes ◽  
Inflection Point ◽  
Upward Trend ◽  
Time Points ◽  
Inflection Points ◽  
Group 3 ◽  
The Relationship ◽  
Group 1

We aimed to investigate the relationship between testosterone (T) levels and pregnancy outcomes in patients with tubal or male infertility at different times during in vitro fertilization (IVF)/intracytoplasmic sperm injection (ICSI) cycles. Patients with tubal or male infertility and normal androgen levels undergoing IVF/ICSI were consecutively recruited. We performed a longitudinal analysis of T levels at three time points (i.e., T0: baseline, T1: trigger day, and T2: day after the trigger day) in three groups with different pregnancy outcomes (i.e., group 1: no pregnancy; group 2: clinical pregnancy but no live birth; and group 3: live birth) as repeated measurement data using linear mixed-effects models. We also plotted fitted curves depicting the relationship between T levels and a number of oocytes retrieved at different time points and identified the inflection points of the curves. In total, 3,012 patients were recruited. Groups 1 and 3 had improvements in T levels at the three time points. After refitting, the slope in group 3 was significantly higher than that in group 1 (P = 0.000). Curves that reflected the association between T levels and numbers of retrieved oocytes presented an upward trend before a certain inflection point, after which the curves had no obvious changes or fell with increasing T levels. The inflection points for T0, T1, and T2 were calculated as 0.45, 0.94, and 1.09, respectively. A faster upward trend in T levels might be associated with better pregnancy outcomes. Within a range lower than a T level inflection point, more oocytes and embryos could be obtained with increasing T levels.

scholarly journals Using Probability Distribution Functions to Correlate Breakthrough Curves of Water and air Contaminants

2021 ◽  
Author(s):  
Khim Hoong Chu
Keyword(s):  
Breakthrough Curve ◽  
Inflection Point ◽  
Initial Period ◽  
Normal Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Good Representation ◽  
Air Contaminants ◽  
Inflection Points ◽  
Log Normal

Abstract This paper reports the use of five probability cumulative distribution functions (normal, log-normal, logistic, Gompertz, and Weibull) to correlate published breakthrough data of water and air contaminants (ciprofloxacin, ammonium, hydrogen chloride, and hydrogen sulfide). Because the shape of the ciprofloxacin breakthrough curve is fairly symmetric, it is well correlated by all five functions (R2 > 0.99). They also provide a good representation of the overall shape of the ammonium breakthrough curve (R2 > 0.99). However, none can describe the leakage of ammonium during the initial period of column operation. The log-normal and Weibull functions give an excellent representation of the tailing HCl data while the normal, logistic, and Gompertz functions are quite poor. This difference in performance can be explained by the different characteristics of their inflection points. The log-normal and Weibull functions have a floating inflection point, which gives them flexibility in tracing the shape of the tailing data. The invariant inflection points of the normal, logistic, and Gompertz curves restrict their data fitting ability. Only the log-normal function can provide a reasonable fit to the H2S data with strong tailing. It is shown that the invariant inflection point of a probability function can be converted to a floating one. A version of the Gompertz function so modified provides a good quantitative correlation of the tailing data of H2S (R2 = 0.99).

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