Three-parameter Correlation Research Articles

CO2 capture using choline chloride-based eutectic solvents. An experimental and theoretical investigation

Eutectic solvents (ESs) have attracted considerable attention as CO2 absorbents due to their tunable and unique properties. In this study, ESs based on choline chloride (ChCl) as hydrogen bond acceptor were combined with four different hydrogen bond donors (HBDs): urea, formamide, monoethanolamine and 1-aminopropan-2-ol, in different molar ratios. The impact of the primary amino group in HBD, with particular focus on the functional groups present in the vicinity, on the physicochemical and structural properties of the ESs was investigated. The CO2 capture in these ESs was measured. 13C NMR, FTIR and Raman analyses were performed to provide evidence of chemical and structural changes after CO2 capture. Quantum chemical methods were used to investigate the interaction mechanism between the ESs and CO2. The resulting ESs were characterised by measuring their basic physicochemical properties, including melting point, density and viscosity as a function of temperature. A three-parameter correlation equation was proposed to predict the solubility of CO2 in ChCl-based physical absorbents. It is shown that the use of the free volume parameter of ESs can help to identify alternative CO2 absorbents.

The Intrinsic Correlations between Prompt Emission and X-ray Flares of Gamma-Ray Bursts

X-ray flare (XRF) is a common phenomenon in the X-ray afterglow of gamma-ray bursts (GRBs). Although it is commonly believed that XRFs may share a common origin with prompt emission, i.e., the “internal” origin, the origin of XRFs is still unknown. In this work, we compile a GRB sample containing 31 GRBs with a single XRF, a well-measured spectrum, and a redshift, and investigate the intrinsic properties and correlations between prompt emission and the XRFs of these events. We find that the distributions of main physical parameters of prompt emission and XRFs are basically log-normal. The median value of the rise time is shorter than the decay time for all flares, with a ratio of about 1:2, which is similar to the fast rise and exponential decay structure of prompt emission pulses. We also find that the prompt emission energy (Eiso) and peak luminosity (Liso) have tight correlations with XRF energy (EX,iso) and peak luminosity (LX,p), Eiso∝EX,iso0.74 (LX,p0.62) and Liso∝EX,iso0.85 (LX,p0.68). However, the durations of prompt emissions are independent of the temporal properties of XRFs. Furthermore, we also analyze the three-parameter correlations between prompt emissions and XRFs, and find that there are tight correlations among the XRF peak time (Tp,z), LX,p, and Eiso/Liso, LX,p∝Tp,z−1.08Eiso0.84 and LX,p∝Tp,z−1.09Liso0.71. Interestingly, these results are very similar to the properties of an X-ray plateau in GRBs, which indicates that X-ray flares and plateaus may have the same physical origin, and strongly supports that the two emission components originate from the late-time activity of the central engine.

Radio Plateaus in Gamma-Ray Burst Afterglows and Their Application in Cosmology

The plateau phase in radio afterglows has been observed in very few gamma-ray bursts (GRBs), and in this paper, 27 radio light curves with plateau phases were acquired from the published literature. We obtain the related parameters of the radio plateau, such as temporal indexes during the plateau phase (α 1 and α 2), break time (T b,z), and the corresponding radio flux (F b). The two-parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity (L b,z) in the radio band is . Including the isotropic energy E γ,iso and peak energy E p,i, the three-parameter correlations for the radio plateaus are written as and , respectively. The correlations are less consistent with those of the X-ray and optical plateaus, implying that radio plateaus may have a different physical mechanism. The typical frequencies crossing the observational band may be a reasonable hypothesis that causes the breaks of the radio afterglows. We calibrate the GRB empirical luminosity correlations as a standard candle for constraining cosmological parameters and find that our samples can constrain the flat ΛCDM model well but are not sensitive to the nonflat ΛCDM model. By combining GRBs with other probes, such as supernovae and the CMB, the constraints on the cosmological parameters are Ωm = 0.297 ± 0.006 for the flat ΛCDM model and Ωm = 0.283 ± 0.008, ΩΛ = 0.711 ± 0.006 for the nonflat ΛCDM model.

Constraints on the Cosmological Parameters with Three-Parameter Correlation of Gamma-Ray Bursts

As one of the most energetic and brightest events, gamma-ray bursts (GRBs) can be treated as a promising probe of the high-redshift universe. Similar to type Ia supernovae, GRBs with the same physical origin could be treated as standard candles. We select GRB samples with the same physical origin, which are divided into two groups. The first group consists of 31 GRBs with a plateau phase feature of a constant luminosity followed by a decay index of about −2 in the X-ray afterglow light curves, and the second group has 50 GRBs with a shallow decay phase in the optical light curves. For the selected GRB samples, we confirm that there is a tight correlation between the plateau luminosity L 0, the end time of plateau t b , and the isotropic energy release E γ,iso. We also find that the L 0–t b − E γ,iso correlation is insensitive to the cosmological parameters and that no valid limitations on the cosmological parameters can be obtained using this correlation. We explore a new three-parameter correlation L 0, t b , and the spectral peak energy in the rest-frame E p,i (L 0–t b –E p,i ), and find that this correlation can be used as a standard candle to constrain the cosmological parameters. By employing the optical sample only, we find the constraints of for a flat ΛCDM model. For the non-flat ΛCDM model, the best-fitting results are , . For the combination of the X-ray and optical samples, we find for a flat ΛCDM model, and , for a non-flat ΛCDM model.

The Intrinsic Statistical Properties and Correlations of Short Gamma-Ray Bursts

The intrinsic statistical properties and correlations of short gamma-ray bursts (SGRBs) have not been fully determined, due to the limitations of observations. In this paper, we compile a more extensive sample of 82 SGRBs with measured redshifts and present a comprehensive study of their intrinsic characteristics. We obtain the median values of the intrinsic duration (T 90,z), peak energy (E p,z), isotropic energy (E iso), and peak luminosity (L iso) as 0.47 s, 466 keV, 8.21 ×1050 erg, and 3.22 × 1051 erg s−1, respectively. We update the spectrum–energy correlations, and report and , which further confirm the previous results that the E p,z–E iso correlations of SGRBs and long gamma-ray bursts (LGRBs) are different and that this correlation can be used to distinguish GRB types. We report for the first time that there is a tighter correlation between the isotropic energy of the prompt emission of SGRBs and the star formation rate of their host galaxies, which reads . Using the measured jet break time (t jet) of 11 SGRBs, we tentatively investigate the E iso–E p,z–t jet,z and L iso–E p,z–t jet,z correlations of SGRBs and find that three-parameter correlations of SGRBs also exist and are different from those of LGRBs. Based on the E iso–E p,z–t jet,z correlation, we estimate the t jet,z values of other SGRBs and calculate the opening angles of SGRBs. We find that the median value of the SGRB opening angle is 7.°5, which is larger than that of LGRBs.

Introducing a Linear Empirical Correlation for Predicting the Mass Heat Capacity of Biomaterials.

This study correlated biomass heat capacity (Cp) with the chemistry (sulfur and ash content), crystallinity index, and temperature of various samples. A five-parameter linear correlation predicted 576 biomass Cp samples from four different origins with the absolute average relative deviation (AARD%) of ~1.1%. The proportional reduction in error (REE) approved that ash and sulfur contents only enlarge the correlation and have little effect on the accuracy. Furthermore, the REE showed that the temperature effect on biomass heat capacity was stronger than on the crystallinity index. Consequently, a new three-parameter correlation utilizing crystallinity index and temperature was developed. This model was more straightforward than the five-parameter correlation and provided better predictions (AARD = 0.98%). The proposed three-parameter correlation predicted the heat capacity of four different biomass classes with residual errors between −0.02 to 0.02 J/g∙K. The literature related biomass Cp to temperature using quadratic and linear correlations, and ignored the effect of the chemistry of the samples. These quadratic and linear correlations predicted the biomass Cp of the available database with an AARD of 39.19% and 1.29%, respectively. Our proposed model was the first work incorporating sample chemistry in biomass Cp estimation.

Statistical Properties of X-ray Flares in Gamma-ray Bursts

X-ray flares are frequently detected in the X-ray afterglow light curves and are highly correlated with the prompt emission of gamma-ray bursts (GRBs). We compile a comprehensive sample of X-ray flares up to 2021 April, comprising 697 flares. We classify the total sample into four types: early flares (tp≤103 s), late flares (tp>103 s), long gamma-ray burst (LGRB) flares and short gamma-ray burst (SGRB) flares, and analyze the distributions and relationships of the flare parameters. It is found that the early flares have a higher frequency, shorter duration, and more asymmetrical structure. In addition, the distributions of the morphological parameters of the SGRB flares are similar to those of the LGRB flares. We also find that the durations and rising (decay) times of the early flares are positively correlated with the peak times, but the late flares follow the different dependent relations. There is a strong anti-correlation between the peak luminosities (LX,P) and the peak times of the flares, e.g., LX,p∝tp,z−1.45 for the LGRB flares, and LX,p∝tp,z−1.27 for the SGRB flares, respectively. Furthermore, the peak luminosity is highly dependent on the isotropic energy (EX,iso) for the early LGRB flares, the best fit is LX,p∝EX,iso1.06(r=0.89). We also find a tight three-parameter correlation, LX,p∝tp,z−1.03EX,iso0.92(r=0.96). All the late flares fall into the 3σ confidence region defined by the early flares. In terms of the point of kinematic arguments, both the SGRB and LGRB flares support a common scheme of internal origin. The SGRB flares have similar properties to the LGRB flares, suggesting that both of them share a similar physical mechanism from the late-time activity of central engine.

Predictive energetic tuning of C-Nucleophiles for the electrochemical capture of carbon dioxide

SummaryThis work maps the thermodynamics of electrochemically generated C-nucleophiles for reactive capture of CO2. We identify a linear relationship between the pKa, the reduction potential of a protonated nucleophile (Ered), and the nucleophile’s free energy of CO2 binding (). Through synergistic experiments and computations, this study establishes a three-parameter correlation described by the equation for a series of twelve imidazol(in)ium/N-heterocyclic carbene pairs with an R2 of 0.92. The correlation allows us to predict the of C-nucleophiles to CO2 using reduction potentials or pKas of imidazol(in)ium cations. The carbenes in this study were found to exhibit a wide range CO2 binding strengths, from strongly CO2 binding to nonspontaneous. This observation suggests that the of imidazol(in)ium-based carbenes is tunable to a desired strength by appropriate structural changes. This work sets the stage for systematic energetic tuning of electrochemically enabled reactive separations.

A Tight Three-parameter Correlation and Related Classification on Gamma-Ray Bursts

Abstract Gamma-ray bursts (GRBs) are widely believed to be from massive collapsars and/or compact binary mergers,which, accordingly, would generate long and short GRBs, respectively. The details on this classification scheme have been in constant debate given more and more observational data available to us. In this work, we apply a series of data mining methods to studying the potential classification information contained in the prompt emission of GRBs detected by the Fermi Gamma-ray Burst Monitor. A tight global correlation is found between fluence (f), peak flux (F), and prompt duration (T 90) which takes the form of log f = 0.75 log T 90 + 0.92 log F − 7.14 . Based on this correlation, we can define a new parameter L = 1.66 log T 90 + 0.84 log f − 0.46 log F + 3.24 by linear discriminant analysis that would distinguish between long and short GRBs with much less ambiguity than T 90. We also discussed the three subclasses scheme of GRB classification derived from clusters analysis based on a Gaussian mixture model, and suggest that, besides SGRBs, LGRBs may be divided into long-bright gamma-ray bursts (LBGRBs) and long-faint gamma-ray bursts (LFGRBs), LBGRBs have statistical higher f and F than LFGRBs; further statistical analysis found that LBGRBs also have higher number of GRB pulses than LFGRBs.

X-Ray Plateaus in Gamma-Ray Burst Afterglows and Their Application in Cosmology

Abstract For gamma-ray bursts (GRBs) with a plateau phase in the X-ray afterglow, a so-called L–T–E correlation that tightly connects the isotropic energy of the prompt GRB (E γ,iso) with the end time of the X-ray plateau (T a ) and the corresponding X-ray luminosity at the end time (L X) has been found. Here we show that there is a clear redshift evolution in the correlation. Furthermore, because the power-law indices of L X and E γ,iso in the correlation function are almost identical, the L–T–E correlation is insensitive to cosmological parameters and cannot be used as a satisfactory standard candle. On the other hand, based on a sample including 121 long GRBs, we establish a new three-parameter correlation that connects L X, T a , and the spectral peak energy E p, i.e., the L–T–E p correlation. This correlation strongly supports the so-called Combo-relation established by Izzo et al. After correcting for the redshift evolution, we show that the de-evolved L–T–E p correlation can be used as a standard candle. By using this correlation alone, we are able to constrain the cosmological parameters as Ω m = 0.389 − 0.141 + 0.202 (1σ) for the flat ΛCDM model, or Ω m = 0.369 − 0.191 + 0.217 and w = − 0.966 − 0.678 + 0.513 (1σ) for the flat wCDM model. Combining with other cosmological probes, more accurate constraints on the cosmology models are presented.

Hydraulic characteristics of liquid–gas ejector pump with a coherent liquid jet

The gas suction rate of a conventional liquid–gas ejector pump was measured on a modular pilot plant unit utilizing convergent nozzles and a water–air system. Hydraulic characteristics were measured for various water flow rates, suction and discharge pressures, and ejector geometries, covering a wide range of configurations and operating conditions. The device configurations, providing the most stable and reproducible results, were identified. The air flow rates measured with these configurations were correlated by a simple, three-parameter correlation with a relative standard deviation (RSD) of 11%. The performance and behavior of the ejector in less stable configurations are discussed and the recommendations for the design of optimally operating units are provided. Finally, the correlation is tested against available literature data. The ejectors with comparable geometry agree well with the proposed correlation (within 20% RSD). The reasonable agreement with the discussed differences is found for other literature data. This comparison results in the validation of the proposed correlation to provide a safe prediction of minimal gas entrainment in units of various geometries, orientation and operating conditions.

Statistical Study of Gamma-Ray Bursts with Jet Break Features in Multiwavelength Afterglow Emissions

Abstract It is generally supposed that a transition from the normal decay phase (decay slope ∼−1) to a steeper phase (decay slope ∼−2) could be suggested as a jet break. The jet opening angle θ jet is then calculated from the jet break time of the afterglow light curve. This allows the derivation of the collimation-corrected energy E jet of those gamma-ray bursts (GRBs). We extensively searched for the GRBs with jet break features from multiwavelength afterglow light curves, and 138 GRBs with significant breaks were collected. The jet break times of those GRBs mainly range from 1000 to 106 s, and the distribution of the collimation-corrected energy E jet peaks at ∼1050 erg. We also confirmed the E γ,iso−E p,i, E jet−E p,i and E γ,iso−θ jet relations, and found E γ,iso−T j,z−E p,i relation remains tight with more multiwavelength data. This tight E γ,iso−T j,z−E p,i relation is also conformed by different groups of our selected GRBs in the paper. In addition, another two new and tighter correlations among E jet−T j,z−E p,i are well confirmed for different circumburst mediums in this paper. We suggest that those tight three-parameter correlations are more physical, and could be widely applied to constrain the cosmological parameters.

Three-parameter correlation for the temperature dependent thermal conductivity of saturated liquids

We here report a three-parameter correlation for the temperature T dependent thermal conductivity λ of different kinds of saturated liquids including n-alkanes, refrigerants and others such as argon and nitrogen. The correlation is proven to be more accurate than other known correlations. Compared with the REFPROP data in NIST, the proposed correlation reproduces the corresponding data with the average absolute deviation (AAD) less than 1.20% for all the liquids considered. At the same time, it well holds in a wider temperature range which begins from the triple point temperature and ends at about 0.98 times the critical temperature, at which the thermal conductivity experimentally takes a minimal value for the liquids we study. Engineers and researchers can use the proposed correlation to directly estimate/calculate the thermal conductivity of the liquids considered here with high accuracy. Thermal conductivity related industrial and engineering equipment designs and chemical process designs will benefit from it greatly.

Three-parameter correlation for the surface tension of saturated liquids

In this paper, we study the multiple-parameter correlations for the surface tension of saturated liquids. The proposed three-parameter correlation requires only the critical temperature as inputs and is tested by using the NIST REFPROP data for 72 saturated liquids including refrigerants, alkanes and some other simple liquids such as argon, carbon dioxide, etc. It is found that this correlation well stands in the whole temperature range from the triple point to the critical point with high accuracy for 71 liquids with average absolute deviations (AADs) less than 5% and for 66 liquids with AADs less than 1%. These results are clearly better than the ones of other available correlations. This correlation can be directly used to estimate the value of the surface tension of the corresponding liquids at any temperature point from the triple point to the critical point. The accuracy of the predictions would clearly have economic benefits since it would allow improvement of process operating conditions, the development of new processes, the reduction of oversizing in the design of new equipment and even reduction of energy requirements.

Statistical Study of Gamma-Ray Bursts with a Plateau Phase in the X-Ray Afterglow

Abstract A plateau phase in the X-ray afterglow is observed in a significant fraction of gamma-ray bursts (GRBs). Previously, a correlation among three key parameters concerning the plateau phase is found to exist, i.e., the end time of the plateau phase in the GRB rest frame (T a ), the corresponding X-ray luminosity at the end time (L X) and the isotropic energy of the prompt GRB (E γ,iso). In this study, we systematically search through all the Swift GRBs with a plateau phase that occurred between 2005 May and 2018 August. We collect 174 GRBs, with redshifts available for all of them. For the whole sample, the correlation between L X, T a , and E γ,iso is confirmed, with the best-fit relation being . Such an updated three-parameter correlation still supports that the central leftover after GRBs is probably a millisecond magnetar. Note that short GRBs with durations less than 2 s in our sample also follow the same correlation, which hints that the merger production of two neutron stars could be a high-mass magnetar but not necessarily a black hole. Moreover, GRBs with an “internal” plateau (i.e., with a following decay index being generally smaller than −3) also obey this correlation. It further strengthens the idea that the internal plateau is due to the delayed collapse of a high-mass neutron star into a black hole. The updated three-parameter correlation indicates that GRBs with a plateau phase may act as a standard candle for cosmology study.

Reliability Estimation of Aero-engine Based on Mixed Weibull Distribution Model

Aero-engine is a complex mechanical electronic system, based on analysis of reliability of mechanical electronic system, Weibull distribution model has an irreplaceable role. Till now, only two-parameter Weibull distribution model and three-parameter Weibull distribution are widely used. Due to diversity of engine failure modes, there is a big error with single Weibull distribution model. By contrast, a variety of engine failure modes can be taken into account with mixed Weibull distribution model, so it is a good statistical analysis model. Except the concept of dynamic weight coefficient, in order to make reliability estimation result more accurately, three-parameter correlation coefficient optimization method is applied to enhance Weibull distribution model, thus precision of mixed distribution reliability model is improved greatly. All of these are advantageous to popularize Weibull distribution model in engineering applications.

A FUNDAMENTAL PLANE FOR LONG GAMMA-RAY BURSTS WITH X-RAY PLATEAUS

ABSTRACT A class of long gamma-ray bursts (GRBs) presenting light curves with an extended plateau phase in their X-ray afterglows obeys a correlation between the rest-frame end-time of the plateau, T a , and its corresponding X-ray luminosity, L a , (Dainotti et al). In this work we perform an analysis of a total sample of 176 Swift GRBs with known redshifts, exhibiting afterglow plateaus. By adding a third parameter that is the peak luminosity in the prompt emission, L peak, we discover the existence of a new three-parameter correlation. The scatter of data about this plane becomes smaller when a class-specific GRB sample is defined. This sample of 122 GRBs is selected from the total sample by excluding GRBs with associated supernovae (SNe), X-ray flashes and short GRBs with extended emission. With this sample the three-parameter correlation identifies a GRB “fundamental plane.” Moreover, we further limit our analysis to GRBs with light curves with good data coverage and almost flat plateaus, 40 GRBs forming our “gold sample.” The intrinsic scatter, , for the three-parameter correlation for this last sub-class is more than two times smaller than the value for the one, making this the tightest three-parameter correlation that involves the afterglow plateau phase. Finally, we also show that a slightly less tight correlation is present between L peak and a proxy for the total energy emitted during the plateau phase, , confirming the existence of an energy scaling between the prompt and afterglow phases.

Update on the GRB universal scaling EX,iso–Eγ,iso–Epk with 10 years of Swift data

From a comprehensive statistical analysis of $Swift$ X-ray light-curves of gamma-ray bursts (GRBs) collected from December 2004 to the end of 2010, we found a three-parameter correlation between the isotropic energy emitted in the rest frame 1-10$^4$ keV energy band during the prompt emission (E$_{\rm{\gamma,iso}}$), the rest frame peak of the prompt emission energy spectrum (E$_{\rm{pk}}$), and the X-ray energy emitted in the rest frame 0.3-30 keV observed energy band (E$_{\rm{X,iso}}$), computed excluding the contribution of the flares. In this paper, we update this correlation with the data collected until June 2014, expanding the sample size with $\sim$35% more objects, where the number of short GRBs doubled. With this larger sample we confirm the existence of a universal correlation that connects the prompt and afterglow properties of long and short GRBs. We show that this correlation does not depend on the X-ray light-curve morphology and that further analysis is necessary to firmly exclude possible biases derived by redshift measurements. In addition we discuss about the behavior of the peculiar objects as ultra-long GRBs and we propose the existence of an intermediate group between long and short GRBs. Interestingly, two GRBs with uncertain classification fall into this category. Finally, we discuss the physics underlying this correlation, in the contest of the efficiency of conversion of the prompt $\gamma$-ray emission energy into the kinetic energy of the afterglow, the photosferic model, and the cannonball model.

A universal scaling for short and long gamma-ray bursts: EX,iso - Eγ,iso - Epk

The comprehensive statistical analysis of Swift X-ray light-curves, collecting data from six years of operation, revealed the existence of a universal scaling among the isotropic energy emitted in the rest frame 10-10^4 keV energy band during the prompt emission (E_{gamma,iso}), the peak of the prompt emission energy spectrum (E_{pk}), and the X-ray energy emitted in the 0.3-10 keV observed energy band (E_{X,iso}). In this paper we show that this three-parameter correlation is robust and does not depend on our definition of E_{X,iso}. It is shared by long, short, and low-energetic GRBs, differently from the well-known E_{gamma,iso}-E_{pk} correlation. We speculate that the ultimate physical property that regulates the GRB properties is the outflow Lorentz factor.

New three-parameter correlation for gamma-ray bursts with a plateau phase in the afterglow

Gamma ray bursts (GRBs) have great advantages for their huge burst energies, luminosities and high redshifts in probing the Universe. A few interesting luminosity correlations of GRBs have been used to test cosmology models. Especially, for a subsample of long GRBs with known redshifts and a plateau phase in the afterglow, a correlation between the end time of the plateau phase (in the GRB rest frame) and the corresponding X-ray luminosity has been found. In this paper, we re-analyze the subsample and found that a significantly tighter correlation exists when we add a third parameter, i.e. the isotropic $\gamma$-ray energy release, into the consideration. Additionally, both long and intermediate duration GRBs are consistent with the same three-parameter correlation equation. It is argued that the new three-parameter correlation is consistent with the hypothesis that the subsample of GRBs with a plateau phase in the afterglow be associated with the birth of rapidly rotating magnetars, and that the plateau be due to the continuous energy-injection from the magnetar. It is suggested that the newly born millisecond magnetars associated with GRBs might provide a good standard candle in the Universe.