Two-parameter Power Law Research Articles

CHARACTERIZATION OF CHLORIDE IONS DIFFUSION IN CONCRETE USING FRACTIONAL BROWNIAN MOTION RUN WITH POWER LAW CLOCK

In this paper, we propose a revised fractional Brownian motion run with a nonlinear clock (fBm-nlc) model and utilize it to illustrate the microscopic mechanism analysis of the fractal derivative diffusion model with variable coefficient (VC-FDM). The power-law mean squared displacement (MSD) links the fBm-nlc model and the VC-FDM via the two-parameter power law clock and the Hurst exponent is 0.5. The MSD is verified by using the experimental points of the chloride ions diffusion in concrete. When compared to the linear Brownian motion, the results show that the power law MSD of the fBm-nlc is much better in fitting the experimental points of chloride ions in concrete. The fBm-nlc clearly interprets the VC-FDM and provides a microscopic strategy in characterizing different types of non-Fickian diffusion processes with more different nonlinear functions.

Postlingually Deafened Adult Cochlear Implant Users With Prolonged Recovery From Neural Adaptation at the Level of the Auditory Nerve Tend to Have Poorer Speech Perception Performance.

This study investigated the effects of two temporal response properties of the auditory nerve (i.e., neural adaptation and recovery from neural adaptation) on speech perception performance in postlingually deafened adult cochlear implant (CI) users. Study participants included 18 postlingually deafened adults who were Cochlear Nucleus device users with a full electrode array insertion in the test ear(s). Neural adaptation and adaptation recovery of the auditory nerve (AN) were evaluated using electrophysiological measures of the electrically evoked compound action potential (eCAP). The amount of neural adaptation was quantified by the adaptation index within three time windows: 0 to 8.89 (window 1), 44.44 to 50.00 (window 2), and 94.44 to 100.00 ms (window 3). The speed of neural adaptation was estimated using a two-parameter power law function. To evaluate adaptation recovery of the AN, eCAPs to the last pulse of the 100-ms pulse train were recorded at masker-probe-intervals ranging from 1.054 to 256 ms in logarithmic steps. The amount of adaptation recovery was quantified by the adaptation recovery ratio. The time-constant of adaptation recovery was estimated using an exponential function with up to three components. Speech perception performance was evaluated by measuring consonant-nucleus-consonant (CNC) word scores presented in quiet and in speech-shaped noise at a signal-to-noise ratio (SNR) of +10 dB. One-tailed Pearson Product Moment correlation tests were used (1) to assess the associations among parameters of neural adaptation and adaptation recovery and (2) to evaluate the strength of association between these parameters and CNC word scores measured in quiet and in noise. The contributions of different parameters quantifying neural adaptation and adaptation recovery on speech perception scores were evaluated using multivariable linear regression analyses. The Pearson Product Moment correlation coefficient demonstrated a moderate, negative correlation between the speed of adaptation recovery and CNC word scores measured in quiet and in noise. The speed of adaptation recovery accounted for 14.1% of variability in CNC word scores measured in quiet and 16.7% of variability in CNC word scores measured in noise. The correlation strengths between CNC word scores and the adaptation index, the adaptation recovery ratio and the speed of neural adaptation ranged from negligible to weak. The speed of adaptation recovery plays a more important role than other features of neural adaptation and adaptation recovery of the AN in speech perception in postlingually deafened adult CI users. Patients with prolonged adaptation recovery tend to show poorer speech perception performance.

Post-cure and γ-irradiation effects on the elastoplastic behavior of structural epoxy adhesive bulk specimens

The present work studies the effects of γ-irradiation on 3M™ Scotch-Weld™ EC-2216 B/A Gray, a commercial two-part flexible epoxy adhesive. The study aims to determine its mechanical characteristics by tensile testing bulk adhesive specimens and quantify the effect of different γ-ray doses (generated from a 60Co source) on the mechanical behavior of the adhesive. The elastoplastic stress-strain curve of the adhesive has been described until failure, varying the absorbed dose up to 500 kGy.Furthermore, a behavior evolution of the adhesive after the cure has been observed and described. The mechanical stabilization occurs between 48 and 85 days after the nominal end of the cure. It has been found that young specimens show a behaviour well described with a two-parameter power law, while for the other specimens, the Ramberg-Osgood model is more appropriate since it can also modelize their initial linear trend. A crosslinking increment can be hypothesized during this period, which could justify the overall embrittlement and stiffening of the adhesive.The adhesive, on the whole, has good mechanical stability after irradiation in the inspected interval, showing a reduction of Young’s modulus. Tensile strength and elongation at break result being quite stable with the absorbed dose, though the statistics for those parameters is poor because of the relevant quantity of invalid fractures.Attenuated Total Reflection Fourier Transform Infrared spectroscopy (ATR-FTIR), Electron Paramagnetic Resonance (EPR) spectroscopy, and colorimetric analysis have also been performed to investigate the modifications induced by γ-irradiation.

Neural Adaptation of the Electrically Stimulated Auditory Nerve Is Not Affected by Advanced Age in Postlingually Deafened, Middle-aged, and Elderly Adult Cochlear Implant Users.

This study aimed to investigate the associations between advanced age and the amount and the speed of neural adaptation of the electrically stimulated auditory nerve (AN) in postlingually deafened adult cochlear implant (CI) users. Study participants included 26 postlingually deafened adult CI users, ranging in age between 28.7 and 84.0 years (mean: 63.8 years, SD: 14.4 years) at the time of testing. All study participants used a Cochlear Nucleus device with a full electrode array insertion in the test ear. The stimulus was a 100-ms pulse train with a pulse rate of 500, 900, 1800, or 2400 pulses per second (pps) per channel. The stimulus was presented at the maximum comfortable level measured at 2400 pps with a presentation rate of 2 Hz. Neural adaptation of the AN was evaluated using electrophysiological measures of the electrically evoked compound action potential (eCAP). The amount of neural adaptation was quantified by the adaptation index (AI) within three time windows: around 0 to 8 ms (window 1), 44 to 50 ms (window 2), and 94 to 100 ms (window 3). The speed of neural adaptation was quantified using a two-parameter power law estimation. In 23 participants, four electrodes across the electrode array were tested. In three participants, three electrodes were tested. Results measured at different electrode locations were averaged for each participant at each pulse rate to get an overall representation of neural adaptation properties of the AN across the cochlea. Linear-mixed models (LMMs) were used (1) to evaluate the effects of age at testing and pulse rate on the speed of neural adaptation and (2) to assess the effects of age at testing, pulse rate, and duration of stimulation (i.e., time window) on the amount of neural adaptation in these participants. There was substantial variability in both the amount and the speed of neural adaptation of the AN among study participants. The amount and the speed of neural adaptation increased at higher pulse rates. In addition, larger amounts of adaptation were observed for longer durations of stimulation. There was no significant effect of age on the speed or the amount of neural adaptation. The amount and the speed of neural adaptation of the AN are affected by both the pulse rate and the duration of stimulation, with higher pulse rates and longer durations of stimulation leading to faster and greater neural adaptation. Advanced age does not affect neural adaptation of the AN in postlingually deafened, middle-aged and elderly adult CI users.

Numerical analysis of the impact of cytoskeletal actin filament density alterations onto the diffusive vesicle-mediated cell transport.

The interior of a eukaryotic cell is a highly complex composite material which consists of water, structural scaffoldings, organelles, and various biomolecular solutes. All these components serve as obstacles that impede the motion of vesicles. Hence, it is hypothesized that any alteration of the cytoskeletal network may directly impact or even disrupt the vesicle transport. A disruption of the vesicle-mediated cell transport is thought to contribute to several severe diseases and disorders, such as diabetes, Parkinson's and Alzheimer's disease, emphasizing the clinical relevance. To address the outlined objective, a multiscale finite element model of the diffusive vesicle transport is proposed on the basis of the concept of homogenization, owed to the complexity of the cytoskeletal network. In order to study the microscopic effects of specific nanoscopic actin filament network alterations onto the vesicle transport, a parametrized three-dimensional geometrical model of the actin filament network was generated on the basis of experimentally observed filament densities and network geometries in an adenocarcinomic human alveolar basal epithelial cell. Numerical analyzes of the obtained effective diffusion properties within two-dimensional sampling domains of the whole cell model revealed that the computed homogenized diffusion coefficients can be predicted statistically accurate by a simple two-parameter power law as soon as the inaccessible area fraction, due to the obstacle geometries and the finite size of the vesicles, is known. This relationship, in turn, leads to a massive reduction in computation time and allows to study the impact of a variety of different cytoskeletal alterations onto the vesicle transport. Hence, the numerical simulations predicted a 35% increase in transport time due to a uniformly distributed four-fold increase of the total filament amount. On the other hand, a hypothetically reduced expression of filament cross-linking proteins led to sparser filament networks and, thus, a speed up of the vesicle transport.

Power law distribution characteristics of daily streamflow in the Yellow River Basin under a changing environment

Abstract Natural streamflow series usually exhibit a power law tail with a magnitude–frequency relationship; however, it is not known how the power law distribution of daily streamflow varies under the influence of climate change and human activities. Based on the annual streamflow series of Toudaoguai, Longmen, Sanmenxia, Huayuankou, Gaocun, and Lijin stations located in the Yellow River in China, the Mann–Kendall and Mann–Whitney–Pettitt methods were used to identify change-points. Thereafter, the power law distributions of the daily streamflow series before and after abrupt changes were studied based on the two-parameter power law distribution method. The results reveal that, firstly, under the influence of human activities, abrupt changes have taken place in the streamflow series of the Yellow River, mainly in the storage year of large reservoirs. Secondly, the daily streamflow series at four out of six stations obey a power law distribution, however, with short tails. The power law characteristics of the series before the abrupt change are essentially consistent with the entire streamflow series; however, these characteristics gradually disappear after abrupt changes. Thirdly, human activities are the main factors underlying the variations in the power law distribution of daily streamflow in different periods. This study provides a way for the study of streamflow changes in the Yellow River and may also offer a scientific basis for water resources development and ecological restoration.

Joint Bayesian analysis of large angular scale CMB temperature anomalies

Cosmic microwave background measurements show an agreement with the concordance cosmology model except for a few notable anomalies: Power Suppression, the lack of large scale power in the temperature data compared to what is expected in the concordance model, and Cosmic Hemispherical Asymmetry, a dipolar breakdown of statistical isotropy. An expansion of the CMB covariance in Bipolar Spherical Harmonics naturally parametrizes both these large-scale anomalies, allowing us to perform an exhaustive, fully Bayesian joint analysis of the power spectrum and violations of statistical isotropy up to the dipole level. Our analysis sheds light on the scale dependence of the Cosmic Hemispherical Asymmetry. Assuming a scale-dependent dipole modulation model with a two-parameter power law form, we explore the posterior pdf of amplitude A(l = 16) and the power law index α and find the maximum a posteriori values A*(l = 16) = 0.064 ± 0.022 and α* = −0.92 ± 0.22. The maximum a posteriori direction associated with the Cosmic Hemispherical Asymmetry is (l,b) = (247.8o, −19.6o) in Galactic coordinates, consistent with previous analyses. We evaluate the Bayes factor BSI−DM to compare the Cosmic Hemispherical Asymmetry model with the isotropic model. The data prefer but do not substantially favor the anisotropic model (BSI−DM=0.4). We consider several priors and find that this evidence ratio is robust to prior choice. The large-scale power suppression does not soften when jointly inferring both the isotropic power spectrum and the parameters of the asymmetric model, indicating no evidence that these anomalies are coupled.

Effect of discharge and upstream jam angle on the flow distribution beneath a simulated ice jam

The velocity field beneath simulated rough ice jams under various upstream jam angles and discharge were investigated using a particle image velocimetry system. Three discharges were examined at 2.3 L/s, 3.4 L/s, and 4.0 L/s and two upstream ice jam angles were tested at 4° and 6°. Increasing the discharge resulted in high turbulence production beneath the jam. The adverse pressure gradient exerted on the flow increased the levels of the Reynolds shear stress. The measured velocities beneath the jam were used to assess the performances of three traditional field measurement techniques as well as the validity of the two-parameter power law. The two-point measurement technique performed remarkably well with the least mean bias error of 2.0%. The error associated with the different techniques showed their inability to accurately predict the average velocity under high discharge. The two-parameter power law accurately predicted velocity profiles within the equilibrium section of the jam, but failed within the boundary layers when the flow was subjected to a pressure gradient.

Main sequence of star forming galaxies beyond the Herschel confusion limit

Context. Deep far-infrared (FIR) cosmological surveys are known to be affected by source confusion, causing issues when examining the main sequence (MS) of star forming galaxies. In the past this has typically been partially tackled by the use of stacking. However, stacking only provides the average properties of the objects in the stack. Aims. This work aims to trace the MS over 0.2 ≤ z < 6.0 using the latest de-blended Herschel photometry, which reaches ≈10 times deeper than the 5σ confusion limit in SPIRE. This provides more reliable star formation rates (SFRs), especially for the fainter galaxies, and hence a more reliable MS. Methods. We built a pipeline that uses the spectral energy distribution (SED) modelling and fitting tool CIGALE to generate flux density priors in the Herschel SPIRE bands. These priors were then fed into the de-blending tool XID+ to extract flux densities from the SPIRE maps. In the final step, multi-wavelength data were combined with the extracted SPIRE flux densities to constrain SEDs and provide stellar mass (M⋆) and SFRs. These M⋆ and SFRs were then used to populate the SFR-M⋆ plane over 0.2 ≤ z < 6.0. Results. No significant evidence of a high-mass turn-over was found; the best fit is thus a simple two-parameter power law of the form log(SFR) = α[log(M⋆) − 10.5] + β. The normalisation of the power law increases with redshift, rapidly at z ≲ 1.8, from 0.58 ± 0.09 at z ≈ 0.37 to 1.31 ± 0.08 at z ≈ 1.8. The slope is also found to increase with redshift, perhaps with an excess around 1.8 ≤ z < 2.9. Conclusions. The increasing slope indicates that galaxies become more self-similar as redshift increases. This implies that the specific SFR of high-mass galaxies increases with redshift, from 0.2 to 6.0, becoming closer to that of low-mass galaxies. The excess in the slope at 1.8 ≤ z < 2.9, if present, coincides with the peak of the cosmic star formation history.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: ε′f and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

On the theoretical velocity distribution and flow resistance in natural channels

The velocity distribution in natural channels is of considerable interest for streamflow measurements to obtain information on discharge and flow resistance. This study focuses on the comparison of theoretical velocity distributions based on 1) entropy theory, and 2) the two-parameter power law. The analysis identifies the correlation between the parameters of the distributions and defines their dependence on the geometric and hydraulic characteristics of the channel. Specifically, we investigate how the parameters are related to the flow resistance in terms of Manning roughness, shear velocity and water surface slope, and several formulae showing their relationships are proposed. Velocity measurements carried out in the past 20 years at Ponte Nuovo gauged section along the Tiber River, central Italy, are the basis for the analysis.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: εf′ and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

Creep Model of Natural Fiber Reinforced Polymer Composite

The flexural performance, 24 h creep-24 h recovery of the Populus alba wood fiber reinforced high-density polyethylene composites prepared by forming mat-compression molding method is investigated. Two-parameter power law model, Findley’s power law model and Burgers model are used to describe the 24 h creep curve of wood fiber reinforced polymer composite. Through model testing and parameter testing, and comparing the sum squared error of three models found that four elements Burgers model is successfully simulated with the creep resistance performances of resulted wood fiber reinforced polymer composites, and the two-parameter power law model is the worst. In summary, the four elements Burgers model is suitable for describing the creep performances of wood fiber reinforced polymer composites and predicting the safety and stability during application.

Modeling and analysis of the creep behavior of jute/green epoxy composites incorporated with chemically treated pulverized nano/micro jute fibers

This paper reports the creep behavior of alkali treated jute/green epoxy composites incorporated with various loadings (1, 5 and 10wt%) of chemically treated pulverized jute fibers (PJF) at different environment temperatures. Composites were prepared by hand layup method and compression molding technique. The creep and dynamic mechanical tests were performed in three-point bending mode by dynamic mechanical analyzer (DMA). The incorporation of PJF is found to significantly improve the creep resistance and strain rate of composites. Three creep models i.e. Burger’s model, Findley’s power law model and a simpler two-parameter power law model were used to model the creep behavior in this study. The time temperature superposition principle (TTSP) was applied to predict the long-term creep performance. The Findley’s power law model was found to be satisfactory in predicting the long-term creep behavior. Dynamic mechanical thermal analysis (DMTA) results revealed the increase in storage modulus, glass transition temperature and reduction in the tangent delta peak height of composites with higher loading of PJF.

Effect of methane leakage on the greenhouse gas footprint of electricity generation

For the purpose of generating electricity, what leakage rate renders the greenhouse gas (GHG) footprint of natural gas equivalent to that of coal? This paper answers this question using a simple model, which assumes that the comprehensive GHG footprint is the sum of the carbon dioxide-equivalent emissions resulting from (1) electricity generation and (2) natural gas leakage. The emissions resulting from electricity generation are taken from published life-cycle assessments (LCAs), whereas the emissions from natural gas leakage are estimated assuming that natural gas is 80 % methane, whose global warming potential (GWP) is calculated using equations provided by the Intergovernmental Panel on Climate Change (IPCC). Results, presented on a straightforward plot of GHG footprint versus time horizon, show that natural gas leakage of 2.0 % or 4.8 % eliminates half of natural gas’s GHG footprint advantage over coal at 20- or 100-year time horizons, respectively. Leakage of 3.9 % or 9.1 % completely eliminates the GHG footprint advantage at 20- and 100-year time horizons, respectively. A two-parameter power law approximation of the IPCC’s equation for GWP is utilized and gives equivalent results. Results indicate that leakage control is essential for natural gas to deliver a smaller GHG footprint than coal.

Power law Starobinsky model of inflation from no-scale SUGRA

We consider a power law 1M2Rβ correction to Einstein gravity as a model for inflation. The interesting feature of this form of generalization is that small deviations from the Starobinsky limit β=2 can change the value of tensor-to-scalar ratio from r∼O(10−3) to r∼O(0.1). We find that in order to get large tensor perturbation r≈0.1 as indicated by BKP measurements, we require the value of β≈1.83 thereby breaking global Weyl symmetry. We show that the general Rβ model can be obtained from a SUGRA construction by adding a power law (Φ+Φ¯)n term to the minimal no-scale SUGRA Kähler potential. We further show that this two-parameter power law generalization of the Starobinsky model is equivalent to generalized non-minimal curvature coupled models of the form ξϕaRb+λϕ4(1+γ) and thus the power law Starobinsky model is the most economical parametrization of such models.

THE NEAR-ULTRAVIOLET LUMINOSITY FUNCTION OF YOUNG, EARLY M-TYPE DWARF STARS

Planets orbiting within the close-in habitable zones of M dwarf stars will be exposed to elevated high-energy radiation driven by strong magneto-hydrodynamic dynamos during stellar youth. Near-ultraviolet (NUV) irradiation can erode and alter the chemistry of planetary atmospheres, and a quantitative description of the evolution of NUV emission from M dwarfs is needed when modeling these effects. We investigated the NUV luminosity evolution of early M-type dwarfs by cross-correlating the Lepine & Gaidos (2011) catalog of bright M dwarfs with the GALEX catalog of NUV (1771-2831A) sources. Of the 4805 sources with GALEX counterparts, 797 have NUV emission significantly (> 2.5 sigma) in excess of an empirical basal level. We inspected these candidate active stars using visible-wavelength spectra, high-resolution adaptive optics imaging, time-series photometry, and literature searches to identify cases where the elevated NUV emission is due to unresolved background sources or stellar companions; we estimated the overall occurrence of these "false positives" as ~16%. We constructed a NUV luminosity function that accounted for false positives, detection biases of the source catalogs, and GALEX upper limits. We found the NUV luminosity function to be inconsistent with predictions from a constant star-formation rate and simplified age-activity relation defined by a two-parameter power law.

Fully-Developed Circular-Pipe Flow of a Non-Newtonian Pseudoplastic Fluid

A fully-developed flow of a non-Newtonian pseudoplastic fluid through a circular pipe has been studied using a four-parameter model, as an example, for the shear-rate dependent apparent viscosity. The model used in this investigation is a modification of the two-parameter Ostwald-de Waele power law [1], which correctly represents the lower and upper regions of Newtonian behavior characteristic of pseudoplastic polymer melts and solutions. Since there has only one set complete experimental data available for the shear-rate dependent viscosity, we use them to show that a perfect match can be achieved between the modified power-law viscosity model and the experimental data. Such a perfect match is required for an accurate prediction of the flow behavior in internal flow problems.

The influence of inorganic salts on the rheological properties of 1,3-propanediyl bis(dodecyl dimethylammonium bromide) and sodium dodecylsulfonate aqueous mixed system

The rheological properties of isotropic 12-3-12/AS/H2O mixed systems in the absence and in the presence of salt have been investigated. The addition of AS into 12-3-12 aqueous solution or vice versa, or the addition of salt into isotropic 12-3-12/AS/H2O mixed systems, leads to changes in microstructure, phase behavior, shear viscosity η, and rheological behavior. In the process of gradually adding AS (or salt) to 12-3-12 aqueous solution, the microstructural transitions are as follows: coexistence of spherical micelles and rodlike micelles→somewhat elongation of rodlike micelles→coexistence of rodlike micelles and vesicles→vesicles; and the rheological behaviors change as follows: antithixotropic and shear thickening→complex thixotropic→shear thinning and thixotropic. η increases initially to a peak, then decreases, and finally the further addition of AS or salt results in aqueous two-phase separation. The origin and the small value (∼510mPas) of the η peak for isotropic 12-3-12/AS/H2O mixed system with excess 12-3-12 are linked with the above microstructural transitions. The η peak becomes lower with the addition of salt. The salt effect on the η peak is related to the matching of water affinities between the counterions and ionic head groups of surfactant. The isotropic 12-3-12/AS/H2O mixed systems with excess AS are Newtonian fluids or near Newtonian fluids with η≈0.75mPas under the shear rate of 1500s−1 due to the coexistence of spherical micelles and short rodlike micelles. The addition of salt changes these Newtonian or near Newtonian fluids to antithixotropic fluids, or complex thixotropic fluids, or thixotropic fluids, and leads to somewhat increase of η (usually less than 25mPas). Two-parameter power-law is used to model the above mentioned fluids. Most of the fluids excepting a few shear thinning fluids located near the phase boundary between isotropic single-phase region and adjacent aqueous two-phase region obey the power-law model.

Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination

We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low ℓ. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.