Power-law Form Research Articles

The Scattering and Absorption Coefficients of Atmospheric Soot in the Hygroscopicity of Urban Aerosols

Aerosols are microscopic solid or liquid particles suspended in the atmosphere that have an impact on the Earth's radiative balance. This paper modeled and investigates the effect of scattering and absorption coefficients along with their respective hygroscopicity of atmospheric soot using extracted data from Optical Properties of Aerosols and Clouds (OPAC) incorporated with Fortran at spectral range of 0.25 to 1.00 m for eight different relative humidities (RHs) (0, 50, 70, 80, 90, 95, 98 and 99%). The fine – mode and coarse – mode aerosol size distribution were also investigated. The particle number densities of soot were varied as 110,000 120,000 and 130,000 cm-3 while the water soluble and insoluble components were kept constant. The scattering coefficient decreases with RHs and also with wavelength in the form of power law at all RHs. The absorption coefficient increases with addition of soot, reflecting warming effect. In this study, it was observed that there is a pronounced hygroscopicity growth as from 95-99% RHs. The Ångström exponent decreases with increase in RHs for the case of scattering coefficient but varies for absorption coefficient; the curvature reveals the presence of both fine and coarse mode particles. The results of the turbidity coefficient (????) based on the scattering coefficient indicated that the atmosphere is relatively clear and hazy while the absorption coefficient indicated that the atmosphere is relatively clear at 0 – 99% relative humidity. The results in this study revealed that the coefficient of determination, ???? 2 > 96% for all the models (1 – 3).

Eccentricity dynamics of wide binaries – I. The effect of Galactic tides

ABSTRACT A major puzzle concerning the wide stellar binaries (semimajor axes a ≳ 103 au) in the Solar neighbourhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well approximated by P(e) ∝ eα with α ≈ 1.3. This DF evolves under the combined influence of (i) tidal torques from the Galactic disc and (ii) scattering by passing stars, molecular clouds, and substructure. Recently, it was demonstrated that Galactic tides alone cannot produce a superthermal eccentricity DF from an initially isotropic, non-superthermal one, under the restrictive assumptions that the eccentricity DF was initially of power-law form and then was rapidly phase-mixed toward a steady state by the tidal perturbation. In this paper, we first prove analytically that this conclusion is valid at all times, regardless of these assumptions. We then adopt a thin Galactic disc model and numerically integrate the equations of motion for several ensembles of tidally perturbed wide binaries to study the time evolution in detail. We find that even non-power-law DFs can be described by an effective power-law index αeff which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) power-law index αi is transformed by Galactic tides into another power law with index αf ≈ (1 + αi)/2 on a time-scale $\sim 4\, \mathrm{Gyr}\, (a/10^4\mathrm{AU})^{-3/2}$. In a companion paper, we investigate separately the effect of stellar scattering. As the GAIA data continues to improve, these results will place strong constraints on wide binary formation channels.

Traffic Flow as a Simple Fluid: Toward a Scaling Theory of Urban Congestion

The analogy between the theory of phase transitions in simple fluids and vehicular traffic flow has long been suspected, promising a new level of understanding of urban congestion by standing on one of the firmer foundations in physics. The obstacle has been the interpretation of the thermal energy of the particle system, which remains unknown. This paper proposes the flow of cars through the network as a viable interpretation, where the fundamental diagram of traffic flow would be analogous to the coexistence curve in gas-liquid phase transitions. Through the power-law form of the coexistence curve, it was possible to formalize that the resulting network traffic model belongs to the Kardar–Parisi–Zhang universality class. The scaling relationships arising in this universality class were found to be consistent with West’s scaling theory for cities. It was shown that congestion costs (delays + fuel consumption) scaled superlinearly with city populations, possibly, and worryingly, more so than predicted by West’s theory. Implications for sustainability and resiliency are discussed.

Bianchi type-III holographic dark energy cosmological model in [formula omitted] theory of gravitation

In this paper, we have studied the spatially homogeneous and anisotropic Bianchi type-III cosmological model in the presence of pressureless matter and Holographic dark energy within the framework of f(R,T) gravity. We have constructed a cosmological model with an appropriate choice of function f(T). Field equations are solved using the relation between the metric potentials A=Cn and using a simple power-law form of a metric potential C=tn. The main objective behind this paper is to explore some physically significant discussions on the evolution of the universe. It is observed that the Hubble parameter H, scalar expansion θ and shear scalar σ diverge at the initial epoch while they approach zero for a large value of time and the anisotropic parameter Am is constant. The negative value of the deceleration parameter indicates the present acceleration of the universe.

Statistical Uncertainty in the Frequency Dependence of the Intensity Scintillation Index (S4)

AbstractThe intensity scintillation index (S4) exhibits a linear frequency dependence derived from a power law phase screen model, with the exponent determined by the phase spectral index (p). However, it is well known that a departure from linearity occurs as S4 increases and saturates under strong scatter conditions. Additionally, statistical errors over a finite time window can also cause the scintillation statistic to deviate from the power law dependence on frequency. This paper presents a parametric analysis on the deviation in the S4 frequency dependence from the power law form. This investigation focuses on the contribution of statistical uncertainty in S4 calculations to the deviation in the frequency dependence according to the selected parameters: S4 and Fresnel frequency (fF). The deviation is determined by comparing p estimates calculated from the power law relationship of S4 at different L‐band frequencies with those inferred from a model‐fitting method using a multi‐frequency global navigation satellite system scintillation data set. The results show the well‐known departure from linearity as S4 increases, and reveal increasing deviations with decreasing fF. The spectral analysis indicates that the variability at the lowest frequencies of intensity spectra contributes to the statistical errors in S4 calculations due to the finite time window, particularly when scintillations are dominated by low‐frequency contributions at low fF. Simulation results of scintillation realizations show much lower deviations with a 30‐min compared to 1‐min window. This suggests a 1‐min window can be too short for reliable S4 calculations due to statistical uncertainty, especially at low fF.

Investigation on the influence of heterogeneous synergy in contagion processes on complex networks.

Synergistic contagion in a networked system occurs in various forms in nature and human society. While the influence of network's structural heterogeneity on synergistic contagion has been well studied, the impact of individual-based heterogeneity on synergistic contagion remains unclear. In this work, we introduce individual-based heterogeneity with a power-law form into the synergistic susceptible-infected-susceptible model by assuming the synergistic strength as a function of individuals' degree and investigate this synergistic contagion process on complex networks. By employing the heterogeneous mean-field (HMF) approximation, we analytically show that the heterogeneous synergy significantly changes the critical threshold of synergistic strength σc that is required for the occurrence of discontinuous phase transitions of contagion processes. Comparing to the synergy without individual-based heterogeneity, the value of σc decreases with degree-enhanced synergy and increases with degree-suppressed synergy, which agrees well with Monte Carlo prediction. Next, we compare our heterogeneous synergistic contagion model with the simplicial contagion model [Iacopini et al., Nat. Commun. 10, 2485 (2019)], in which high-order interactions are introduced to describe complex contagion. Similarity of these two models are shown both analytically and numerically, confirming the ability of our model to statistically describe the simplest high-order interaction within HMF approximation.

On heterogeneous diffusion processes and the formation of spatial-temporal nonlocality.

Heterogeneous diffusion processes defined as a solution to the overdamped Langevin equation with multiplicative noise, the amplitude of which has a power-law space-dependent form, are studied. Particular emphasis is on discrete analogs of these processes, for which, in particular, an asymptotic estimate of their variance behavior in time is obtained. In addition, a class of processes formed by deformation of the discrete analog of the fractional Brownian motion using the Cantor ladder and its inverse transformation is considered. It is found that such a class turns out to be close in structure to discrete analogs of heterogeneous processes. This class of processes allows us to illustrate geometrically the emergence of sub- and superdiffusion transport regimes. On the basis of discrete analogs of heterogeneous processes and memory flow phenomenology, we construct a class of random processes that allows us to model nonlocality in time and space taking into account spatial heterogeneity.

Preliminary results of the search for helium nuclei in solar energetic events measured in the PAMELA experiment

We presented the preliminary results of the search for helium nuclei in solar energetic events measured in the PAMELA experiment in the rigidity range from 0.1 to 1 GV from 2006 to 2014. We constructed selection criteria for helium nuclei and estimated their efficiency. The spectra are approximated using a simple power-law function and functional form based on Ellison-Ramaty, consisting of a power-law spectrum modulated by an exponential.

Quintessence like behavior of symmetric teleparallel dark energy: Linear and nonlinear model

In Einstein’s General Relativity (GR), the gravitational interactions are described by the spacetime curvature. Recently, other alternative geometric formulations and representations of GR have emerged in which the gravitational interactions are described by the so-called torsion or non-metricity. Here, we consider the recently proposed modified symmetric teleparallel theory of gravity or [Formula: see text] gravity, where [Formula: see text] represents the non-metricity scalar. In this paper, motivated by several papers in the literature, we assume the power-law form of the function [Formula: see text] as [Formula: see text] (where [Formula: see text], [Formula: see text], and [Formula: see text] are free model parameters) that contains two models: Linear ([Formula: see text]) and nonlinear ([Formula: see text]). Further, to add constraints to the field equations we assume the deceleration parameter form as a divergence-free parametrization. Then, we discuss the behavior of various cosmographic and cosmological parameters such as the jerk, snap, lerk, [Formula: see text] diagnostic, cosmic energy density, isotropic pressure, and equation of state (EoS) parameter with a check of the violation of the strong energy condition (SEC) to obtain the acceleration phase of the Universe. Hence, we conclude that our cosmological [Formula: see text] models behave like quintessence dark energy (DE).

Traversable wormholes in [formula omitted] gravity with vanishing speed of sound

In this manuscript, we explore the existence of traversable wormholes (WHs) in the framework of f(R,T) (R is the Ricci scalar and T is the trace of energy–momentum tensor (EMT)) gravity with non-exotic matter and hypothetical condition of stability inside the WH throat. To this end, we choose two different suitable shape functions and obtain the necessary condition for overall stability of fluid evolution threading WH throat. To close the dynamical system of equations, we consider the power-law form of the f(R,T) model and adopt the Padé approximants to characterize rational shape function b(r)r. We consider the lowest Padé order, i.e., P(0,1), and obtain the negligible fluid perturbations inside the WH throat, which implies stable solutions. We determine the suitable bounds on model parameters for the above discussion. Finally, we conclude that only small deviations from general relativity (GR) are permitted where one can find the WH solutions with vanishing sound speed hypothesis in f(R,T) theory.

Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3

ABSTRACT The mass, spin, and merger rate distribution of the binary black holes (BBHs) across cosmic redshifts provide a unique way to shed light on their formation channel. Along with the redshift dependence of the BBH merger rate, the mass distribution of BBHs can also exhibit redshift dependence due to different formation channels and dependence on the metallicity of the parent stars. We explore the redshift dependence of the BBH mass distribution jointly with the merger rate evolution from the third gravitational wave (GW) catalogue GWTC-3 of the LIGO–Virgo–KAGRA collaboration. We study possible connections between peak-like features in the mass spectrum of BBHs and processes related to supernovae physics and time delay distributions. We obtain a preference for short-time delays between star formation and BBH mergers. Using a power-law form for the time delay distribution ($(t^{\rm min}_d)^{d}$), we find d < −0.7 credible at 90 per cent interval. The mass distribution of the BBHs could be fitted with a power-law form with a redshift-dependent peak feature that can be linked to the pair instability supernovae (PISN) mass-scale MPISN(Z*) at a stellar metallicity Z*. For a fiducial value of the stellar metallicity Z* = 10−4, we find the $\rm M_{\rm PISN}(Z_*)=44.4^{+7.9}_{-6.3}$$\rm M_\odot$. This is in accordance with the theoretical prediction of the lower edge of the PISN mass-scale and differs from previous analyses. Although we find a strong dependence of the PISN value on metallicity, the model that we explored is not strongly favoured over those that do not account for metallicity as the Bayes factors are inconclusive. In the future with more data, evidence towards metallicity dependence of the PISN will have a significant impact on our understanding of stellar physics.

Statistical determination of stress threshold and survival analysis on IASCC initiation data of stainless steels in pressurized water reactor conditions

This paper presents the first attempt to perform a rigorous statistical analysis of the compiled IASCC initiation data of 304 and 316 stainless steels available in the existing literature. First, the stress threshold for IASCC initiation was determined statistically as a function of the neutron dose. The 95% lower bound or 2.5% cumulative failure probability line appeared to be a conservative stress threshold, although it could be adjusted according to the required conservatism. Survival analysis was conducted using the filtered data set for 316 stainless steel IASCC initiation times. A proportional hazards model revealed statistically significant covariates in order of greatest impact: stress level as a percentage of irradiated yield strength, neutron dose, and component. Unsurprisingly, the failure rate was found to increase with increasing stress level and neutron dose. It was also found that FTT materials had higher failure rates than BFB materials. The effects of these covariates on the failure rate were constant with time. An accelerated life model based on a Weibull distribution was then used to model the IASCC initiation time. Two different link functions were used for the model: the link function with a power-law form for the stress level and neutron dose fitted the observed data better than a log-linear type link function.

Cosmology of a Chaplygin Gas Model Under f(T) Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas (GCG) with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences, studied in terms of equation of state (EoS) parameter. In the non-interacting scenario, the EoS parameter behaves as quintessence in both forms of the scale factor. In the interacting scenario, the EoS parameter behaves as phantom and for the truncated form of the scale factor, it violates the constraints of the positive parameter α. The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T) modified gravity, where T is the torsion scalar in teleparallelism. The interaction term is directly proportional to the GCG density with positive coupling constant. In f(T) gravity, the EoS is behaving like phantom. The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations, i.e., the squared speed of sound is non-negative and an increasing function of cosmic time t. We have observed that our reconstructed f(T) model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis. Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

Scaling law of correlated diffusion of colloidal particles confined to a rugged surface

Using optical microscopy and multiparticle tracking techniques, we investigate the correlated diffusion of colloidal particles over a rugged surface. Our findings demonstrate that the correlated diffusion caused by the hydrodynamic interactions of particles confined to energy landscapes displays a distinctive power-law behavior. The local energy landscape on the rugged surface reduces the long-range hydrodynamic interactions between colloidal particles. The energy landscape influences the strength of hydrodynamic interactions, but not their power-law form. The responding factor of the colloidal particles over the energy landscape to hydrodynamics decays exponentially with the potential energy minimum. We propose a scaling method, with which the correlated diffusion of colloidal particles over various energy landscapes can be scaled onto a master curve. The master curve characterizes the response of the particles over the energy landscape to the hydrodynamics. The scale factors used for the master curve allow for the calculation of the energy landscape. The findings provide physical insights into the confinement hydrodynamics and would be helpful for designing material surfaces and controlling the motion of particles on rough surfaces.

Measuring the giant radio galaxy length distribution with the LoTSS

Context. Many massive galaxies launch jets from the accretion disk of their central black hole, but only ∼103 instances are known in which the associated outflows form giant radio galaxies (GRGs, or giants): luminous structures of megaparsec extent that consist of atomic nuclei, relativistic electrons, and magnetic fields. Large samples are imperative to understanding the enigmatic growth of giants, and recent systematic searches in homogeneous surveys constitute a promising development. For the first time, it is possible to perform meaningful precision statistics with GRG lengths, but a framework to do so is missing. Aims. We measured the intrinsic GRG length distribution by combining a novel statistical framework with a LOFAR Two-metre Sky Survey (LoTSS) sample of freshly discovered giants. In turn, this allowed us to answer an array of questions on giants. For example, we can now assess how rare a 5 Mpc giant is compared with one of 1 Mpc, and how much larger – given a projected length – the corresponding intrinsic length is expected to be. Notably, we can now also infer the GRG number density in the Local Universe. Methods. We assumed the intrinsic GRG length distribution to be Paretian (i.e. of power-law form) with tail index ξ, and predicted the observed distribution by modelling projection and selection effects. To infer ξ, we also systematically searched the LoTSS for hitherto unknown giants and compiled the largest catalogue of giants to date. Results. We show that if intrinsic GRG lengths are Pareto distributed with index ξ, then projected GRG lengths are also Pareto distributed with index ξ. Selection effects induce curvature in the observed projected GRG length distribution: angular length selection flattens it towards the lower end, while surface brightness selection steepens it towards the higher end. We explicitly derived a GRG’s posterior over intrinsic lengths given its projected length, laying bare the ξ dependence. We also discovered 2060 giants within LoTSS DR2 pipeline products; our sample more than doubles the known population. Spectacular discoveries include the largest, second-largest, and fourth-largest GRG known (lp = 5.1 Mpc, lp = 5.0 Mpc, and lp = 4.8 Mpc), the largest GRG known hosted by a spiral galaxy (lp = 2.5 Mpc), and the largest secure GRG known beyond redshift 1 (lp = 3.9 Mpc). We increase the number of known giants whose angular length exceeds that of the Moon from 10 to 23; among the discoveries is the angularly largest known radio galaxy in the Northern Sky, which is also the angularly largest known GRG (ϕ = 2°). Combining theory and data, we determined that intrinsic GRG lengths are well described by a Pareto distribution, and measured the index ξ = −3.5 ± 0.5. This implies that, given its projected length, a GRG’s intrinsic length is expected to be just 15% larger. Finally, we determined the comoving number density of giants in the Local Universe to be nGRG = 5 ± 2(100 Mpc)−3. Conclusions. We developed a practical mathematical framework that elucidates the statistics of giant radio galaxy lengths. Through a LoTSS search, we also discovered 2060 new giants. By combining both advances, we determined that intrinsic GRG lengths are well described by a Pareto distribution with index ξ = −3.5 ± 0.5, and that giants are truly rare in a cosmological sense: most clusters and filaments of the Cosmic Web are not currently home to a giant. Thus, our work yields new observational constraints for analytical models and simulations featuring radio galaxy growth.

Constraining the merger history of primordial-black-hole binaries from GWTC-3

Primordial black holes (PBHs) can be not only cold dark matter candidates but also progenitors of binary black holes observed by LIGO-Virgo-KAGRA (LVK) Collaboration. The PBH mass can be shifted to the heavy distribution if multi-merger processes occur. In this work, we constrain the merger history of PBH binaries using the gravitational wave events from the third Gravitational-Wave Transient Catalog (GWTC-3). Considering four commonly used PBH mass functions, namely the log-normal, power-law, broken power-law, and critical collapse forms, we find that the multi-merger processes make a subdominant contribution to the total merger rate. Therefore, the effect of merger history can be safely ignored when estimating the merger rate of PBH binaries. We also find that GWTC-3 is best fitted by the log-normal form among the four PBH mass functions and confirm that the stellar-mass PBHs cannot dominate cold dark matter.

Yukawa–Casimir Wormholes in f(Q) Gravity

Casimir energy is always suggested as a possible source to create a traversable wormhole. It is also used to demonstrate the existence of negative energy, which can be created in a lab. To generalize this idea, Yukawa modification of a Casimir source has been considered in Remo Garattini (Eur. Phys. J. C 81 no.9, 824, 2021). In this work, we explore the Yukawa–Casimir wormholes in symmetric teleparallel gravity. We have taken four different forms of f(Q) to obtain wormhole solutions powered by the original Casimir energy source and Yukawa modification of the Casimir energy source. In power law form f(Q)=αQ2+β and quadratic form f(Q)=αQ2+βQ+γ, where α,β,γ are constants and Q is non-metricity scalar, we analyze that wormhole throat is filled with non-exotic matter. We find self-sustained traversable wormholes in the Casimir source where null energy conditions are violated in all specific forms of f(Q), while after Yukawa modification, it is observed that violation of null energy conditions is restricted to some regions in the vicinity of the throat.

Singularity of lithosphere mass density over the mid-ocean ridges and implication on floor depth and heat flow

The relation of heat flow and floor depth across the mid-ocean ridges versus lithosphere age can be described by linear functions of square root of age according to plate thermal conductive Half Space Models (HSM). However, one of the long-standing problems of these classical models is the discrepancies between predicted and observed heat flow and floor depth for very young and very old lithosphere. There have been several recent attempts to overcome this problem: one model incorporates temperature- and pressure-dependent parameters and the second model includes an additional low-conductivity crustal layer or magma rich mantle layer (MRM). Alternatively, in the current paper, the ordinary density of lithosphere in the plate conductive models is substituted with a reduction of lithosphere density towards axis that features the irregularity and nonlinearity of plates across the mid-ocean ridges. A new model is formulated incorporating the new form of density for predicting both peak heat flow and floor depth. Simple solutions of power-law forms derived from the model can significantly improve the predicting results of heat flow and floor depth over the mid-ocean ridges. Several datasets in the literature were reutilized for model validation and comparison. These datasets include both earlier datasets used for original model calibration and the more recently compiled high-quality datasets with both sedimentary and crustal loading corrections. The results indicate that both the heat flow and the slope (first order-derivative) of sea floor approach infinity (undifferentiability or singularities) around the mid-ocean ridges. These singularities are partially due to the boundary condition as it has been already known in the literature and partially to the reduction of density of lithosphere as discovered for the first time in the current research.

Necessary Condition of Self-Organisation in Nonextensive Open Systems

In this paper, we focus on evolution from an equilibrium state in a power law form by means of q-exponentials to an arbitrary one. Introducing new q-Gibbsian equalities as the necessary condition of self-organization in nonextensive open systems, we theoretically show how to derive the connections between q-renormalized entropies (ΔS˜q) and q-relative entropies (KLq) in both Bregman and Csiszar forms after we clearly explain the connection between renormalized entropy by Klimantovich and relative entropy by Kullback-Leibler without using any predefined effective Hamiltonian. This function, in our treatment, spontaneously comes directly from the calculations. We also explain the difference between using ordinary and normalized q-expectations in mean energy calculations of the states. To verify the results numerically, we use a toy model of complexity, namely the logistic map defined as Xt+1=1-aXt2, where a∈[0,2] is the map parameter. We measure the level of self-organization using two distinct forms of the q-renormalized entropy through period doublings and chaotic band mergings of the map as the number of periods/chaotic-bands increase/decrease. We associate the behaviour of the q-renormalized entropies with the emergence/disappearance of complex structures in the phase space as the control parameter of the map changes. Similar to Shiner-Davison-Landsberg (SDL) complexity, we categorize the tendencies of the q-renormalized entropies for the evaluation of the map for the whole control parameter space. Moreover, we show that any evolution between two states possesses a unique q=q* value (not a range for q values) for which the q-Gibbsian equalities hold and the values are the same for the Bregmann and Csiszar forms. Interestingly, if the evolution is from a=0 to a=ac≃1.4011, this unique q* value is found to be q*≃0.2445, which is the same value of qsensitivity given in the literature.

Discordances in Cosmology and the Violation of Slow-Roll Inflationary Dynamics.

We identify examples of single field inflationary trajectories beyond the slow-roll regime that improve the fit to Planck 2018 data compared to a baseline Λ cold dark matter model with power law form of primordial spectrum and at the same time alleviate existing tensions between different datasets in the estimate of cosmological parameters such as H_{0} and S_{8}. A damped oscillation in the first Hubble flow function-or equivalently a feature in the potential-and the corresponding localized oscillations in the primordial power spectrum partially mimic the improvement in the fit of Planck data due to A_{L} or Ω_{K}. Compared to the baseline model, this model can lead simultaneously to a larger value of H_{0} and a smaller value of S_{8}, a trend that can be enhanced when the most recent SH0ES measurement for H_{0} is combined with Planck and BICEP-Keck 2018 data. Large scale structure data and more precise cosmic microwave background polarization measurements will further provide critical tests of this intermediate fast-roll phase.