Power-law Curve Research Articles

Scale breaks of suspended sediment rating in large rivers in Germany induced by organic matter

Abstract. Understanding the transport of suspended sediment and associated nutrients is of major relevance for sustainable sediment management aiming to achieve healthy river systems. Sediment rating curves are frequently used to analyze the suspended sediments and their potential sources and sinks. Here we use more than 750 000 measurements of suspended sediment concentrations (SSCs) and discharge (Q) collected at 62 gauging stations along 19 waterways in Germany based on the suspended sediment monitoring network of the German water and shipping authority, which started in the 1960s. Furthermore, we analyze more than 2000 measurements of the loss on ignition (LOI) of suspended matter at two stations along the rivers Moselle and Rhine to provide a proxy for the relative contributions of mineral load and organic matter. SSC and LOI are analyzed in terms of the power-law rating curve to identify discharge-dependent controls of suspended matter. Our results indicate that for most studied gauging stations, rating coefficients are not constant over the full discharge range, but there is a distinct break in the sediment rating curve, with specific SSC–Q domains above and below this break. The transition of the rating exponent likely results from increased supply of mineral suspended sediments from hillslope erosion at high flow and a shift of the organic matter sources from aquatic biomass-derived organic matter (i.e., high % LOI) at low flow, to mineral-associated organic matter with low % LOI eroded from hillslopes at higher flow. Based on these findings we developed a conceptual rating model for large (>10 000 km2) and low-turbidity (SSC < 1000 mg L−1) rivers separating the mineral and organic fraction of the suspended matter in German waterways. This model allows evaluating the sources of the mineral and organic fraction of the suspended matter and facilitates new insights into the first-order control of discharge on the quality and quantity of suspended sediments.

Enhancement of hydrophilicity, biocompatibility and biodegradability of poly(ε-caprolactone) electrospun nanofiber scaffolds using poly(ethylene glycol) and poly(L-lactide-co-ε-caprolactone-co-glycolide) as additives for soft tissue engineering

In this study, poly(ε-caprolactone) (PCL) has been blended with a more hydrophilic poly(ethylene glycol) (PEG) and with a biocompatible block-co-polymer: poly(L-lactide-co-ε-caprolactone-co-glycolide) (PLCG) in order to improve hydrophilicity, biocompatibility and biodegradability of PCL. PCL and the blend solutions were subjected to electrospinning to produce nanofiber scaffolds by the addition of only 1 wt% of PEG and PLCG either singly or in combination in PCL to retain the mechanical properties of the scaffolds. PCL-PEG-PLCG ternary and two binary (PCL-PEG and PCL-PLCG) blend nanofiber scaffolds have been prepared for comparison. The resulting nanofibers showed a smooth and flaw-free surface and the diameter of the nanofibers displayed a normal distribution. The PCL-PEG nanofiber scaffold showed improved hydrophilicity [water contact angle (WCA) ∼84°] over pristine PCL (WCA ∼127°); while PCL-PLCG and PCL-PEG-PLCG scaffolds exhibited absolute wetting by water, likely due to high porosity. In vitro biocompatibility studies using gingival mesenchymal stem cells (gMSCs) suggested that, both the PCL and the blend scaffolds were biocompatible supporting cell-viability and growth of gMSCs following their seeding on these scaffolds. Biodegradation studies in phosphate buffer solution showed that the addition of PEG and PLCG in PCL increased the weight loss of scaffolds with time, indicating higher extent of biodegradation in the blend scaffolds and the weight loss followed the power law curve with time.

Determination of Empirical Rainfall Thresholds for Shallow Landslides in Slovenia Using an Automatic Tool

Rainfall-triggered shallow landslides represent a major threat to people and infrastructure worldwide. Predicting the possibility of a landslide occurrence accurately means understanding the trigger mechanisms adequately. Rainfall is the main cause of slope failures in Slovenia, and rainfall thresholds are among the most-used tools to predict the possible occurrence of rainfall-triggered landslides. The recent validation of the prototype landslide early system in Slovenia highlighted the need to define new reliable rainfall thresholds. In this study, several empirical thresholds are determined using an automatic tool. The thresholds are represented by a power law curve that links the cumulated event rainfall (E, in mm) with the duration of the rainfall event (D, in h). By eliminating all subjective criteria thanks to the automated calculation, thresholds at diverse non-exceedance probabilities are defined and validated, and the uncertainties associated with their parameters are estimated. Additional thresholds are also calculated for two different environmental classifications. The first classification is based on mean annual rainfall (MAR) with the national territory divided into three classes. The area with the highest MAR has the highest thresholds, which indicates a likely adaptation of the landscape to higher amounts of rainfall. The second classification is based on four lithological units. Two-thirds of the considered landslides occur in the unit of any type of clastic sedimentary rocks, which proves an influence of the lithology on the occurrence of shallow landslides. Sedimentary rocks that are prone to weathering have the lowest thresholds, while magmatic and metamorphic rocks have the highest thresholds. Thresholds obtained for both classifications are far less reliable due to the low number of empirical points and can only be used as indicators of rainfall conditions for each of the classes. Finally, the new national thresholds for Slovenia are also compared with other regional, national, and global thresholds. The thresholds can be used to define probabilistic schemes aiming at the operative prediction of rainfall-induced shallow landslides in Slovenia, in the framework of the Slovenian prototype early warning system.

AT 2016dah and AT 2017fyp: the first classical novae discovered within a tidal stream

ABSTRACT AT 2016dah and AT 2017fyp are fairly typical Andromeda galaxy (M 31) classical novae. AT 2016dah is an almost text book example of a ‘very fast’ declining, yet uncommon, Fe ii‘b’ (broad-lined) nova, discovered during the rise to peak optical luminosity, and decaying with a smooth broken power-law light curve. AT 2017fyp is classed as a ‘fast’ nova, unusually for M 31, its early decline spectrum simultaneously shows properties of both Fe ii and He/N spectral types – a ‘hybrid’. Similarly, the light curve of AT 2017fyp has a broken power-law decline but exhibits an extended flat-topped maximum. Both novae were followed in the UV and X-ray by the Neil Gehrels Swift Observatory, but no X-ray source was detected for either nova. The pair were followed photometrically and spectroscopically into their nebular phases. The progenitor systems were not visible in archival optical data, implying that the mass donors are main-sequence stars. What makes AT 2016dah and AT 2017fyp particularly interesting is their position with respect to M 31. The pair are close on the sky but are located far from the centre of M 31, lying almost along the semiminor axis of their host. Radial velocity measurements and simulations of the M 31 nova population leads to the conclusion that both novae are members of the Andromeda Giant Stellar Stream (GSS). We find the probability of at least two M 31 novae appearing coincident with the GSS by chance is $\sim \!1{{\ \rm per\ cent}}$. Therefore, we claim that these novae arose from the GSS progenitor, not M 31 – the first confirmed novae discovered in a tidal steam.

Do Beach Profiles Under Nonbreaking Waves Minimize Energy Dissipation?

AbstractThe hypothesis that equilibrium beach profiles under nonbreaking waves minimize wave energy dissipation was considered by Larson et al. (1999 Coast. Eng. 36 59‐85). Larson et al. approached the hypothesis as a variational problem, assuming a priori that the solution (the extremal profile) followed a power law with a freely tunable exponent, which was varied so as to extremize the relevant functional. Here, we revisit this hypothesis and solve the associated variational problem approximately via analytical means, without a priori assumptions on the mathematical structure of the solution. We remark that for the solution to be realistic, the problem formulation must consider additional constraints; for example, the bed slope angle must not exceed the sediment's angle of repose. Incidentally, the solution we derive recovers the power law prescribed by Larson et al., which is in turn backed by a large body of empirical evidence. However, the exponent of the power in our solution is not an arbitrarily free parameter; it depends on the parametrization of the bed shear stress (the main mechanism by which nonbreaking waves dissipate energy), and predicted values of the exponent are supported by previous research. The power law curve derived here agrees well with empirical data from field and laboratory, suggesting that a principle of energy economy may indeed underpin the particular shape adopted by beach profiles under nonbreaking waves. This theoretical study aims at promoting and aiding further tests of this hypothesis.

Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies.

In this work, we analyze the growth of the cumulative number of confirmed infected cases by a novel coronavirus (COVID-19) until March 27, 2020, from countries of Asia, Europe, North America, and South America. Our results show that (i) power-law growth is observed in all countries; (ii) by using the distance correlation, the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the world; and (iii) soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies that allow the government to reach the flattening of the power-law curves. We found that besides the social distancing of individuals, of well known relevance, the strategy of identifying and isolating infected individuals in a large daily rate can help to flatten the power-laws. These are the essential strategies followed in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicates that the government containment measures can be applied with success around the whole world. These measures are scathing and to be applied as soon as possible.

Application of modified normalization method for J-R curve determination using clamped SENT specimens with varying in-plane and out-of-plane constraints

In the present work, the normalization (NM) method was used to obtain J integral resistance (J-R) curves based on clamped single edge notched tension (SENT) specimens. The SENT fracture toughness tests using API X80 pipeline steel were carried out for a series of crack depth to specimen width ratios (a/W) and thickness to specimen width ratios (B/W), corresponding to varying in-plane and out-of-plane constraint conditions. To validate the normalization method, the unloading compliance (UC) method was adopted to derive the J-R curves for those clamped SENT specimens. In particular, two NM methods (modified NM method and unmodified NM method) are discussed and compared, and the experimental results indicated that the J-R curves calculated by the modified NM method have a better accuracy. Then, to quantify the modified NM method, the J-R curves, power law curve fitting parameters and the tearing modulus obtained from two methods (UC method and modified NM method) are compared. The comparison shows that good agreements are achieved among those methods. Moreover, three-dimensional finite element method (FEM) with GTN constitutive model is also used to determine J-R curves based on clamped SENT specimens. It is demonstrated that the modified NM method is an effective alternative tool for determining J-R curves of X80 steel based on clamped SENT specimens with different a/W and B/W ratios.

Sample size determination for biomedical big data with limited labels

The era of big data has produced vast amounts of information that can be used to build machine learning models. In many cases, however, there is a point where adding more data only marginally increases model performance. This is especially important for scenarios of limited labeled data, as annotation can be expensive and time consuming. If the required sample size for accurate model performance can be determined early, then resources can be allocated appropriately to minimize time and cost. In this study, we explore sample size determination methods for four real-world biomedical datasets, spanning genomics, proteomics, electronic health records, and insurance claims data, all with millions of instances each and<2% class ratio. The methods used involve approximating a learning curve for a large amount of data using a small amount of data. We evaluate an existing method that fits an inverse power law model to a small learning curve and introduce a novel semi-supervised method that utilizes the large amount of unlabeled data for estimating a learning curve. We find that the inverse power law method is applicable to big data, while the semi-supervised method can be better at detecting convergence. To the best of our knowledge, this is the first study to apply an inverse power law curve fitting method to big data with limited labels and compare it to a semi-supervised approach.

True Stress-strain Curves for HSLA Steel Weldment – Iteration Procedure Based on DIC and FEM

True stress-strain curves of HSLA steel welded joint regions were estimated by using numerical simulation of strains measured by DIC and special iteration procedure to match the results. Strains were measured at certain level of loading in all regions of welded joint with different tensile properties, namely base metal (BM), weld metal (WM) and two subzones of Heat-Affected-Zone (fine grain, FGHAZ, and coarse grain – CGHAZ). By converting engineering stress (load divided by initial cross section area) into true stress, experimental true stress-true strain curves are obtained and used as initial iteration for the Finite Element Method (FEM) simulation, after being fitted by the power law relation for stress-strain curves. Obtained results are then compared with the experimental results to find the differences and make appropriate correction in power law curves and make as many iterations as needed before the differences become small enough. This procedure has been verified by an example of welded tensile panel.

Reconstructing the spectral shape of a stochastic gravitational wave background with LISA

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB) . We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB . For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other GW observatories.

Creep-Induced Screw Preload Loss of Carbon-Fiber Sheet Molding Compound at Elevated Temperature.

The application of chopped-fiber reinforced polymers in screwed connections at high temperatures raises the question of creep under long-term loading. While up to now thermoplastic materials have mainly been the focus of attention when it comes to creep, this paper shows that thermoset carbon-fiber SMCs (sheet mold compounds) can also be affected by this phenomenon. Screwed connections were investigated regarding their loss of preload force at 120 °C ambient temperature. Additionally, strain–time diagrams were recorded at different stress levels at 120 °C in a creep test setup of a universal testing machine by using optical strain tracking of SMC coupons. The transverse modulus under compression in thickness direction was determined in the same test setup. For data application within a FEA (finite element analysis) software power law curves according to Norton–Bailey creep law were fitted in the strain–time graphs. The applicability of the obtained creep law was crosschecked with a test carried out on the loss of preload force of a screwed connection. The developed simulative methodology offers the possibility to simulate various mounting situations of the bolted connection and to investigate measures against the loss of preload force easily. A promising possibility to limit the loss of preload force due to creep was simulatively evaluated.

Superoscillations: a scale physics perspective

Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the total power in the field that is local at regions of superoscillations. It is found that the probability for a superoscillation of a particular scale follows a quadratic power-law decay curve above the scale of the bounded support of the spectrum. The detectability is found to be even more severely suppressed, following a four-order power-law decay curve above the scale of the spectrum.

An improved model to predict liquid holdup in vertical gas wells

Accurate prediction of the pressure gradient is crucial for gas-production design and gas well optimization. The most important role in modeling the pressure gradient is generally to calculate the liquid holdup accurately. Currently, numerous mechanistic and empirical models have been developed and modified to deal with all kinds of flow conditions. Due to the chaotic feature in the churn flow, it is difficult for mechanistic models to model this flow pattern accurately. Simplified assumptions for this pattern may lead to large deviations. For empirical models, the range of experimental parameters limits their application. In this study, a variation of liquid holdup with superficial gas velocity is analyzed in order to simplify the liquid-holdup correlation and improve its accuracy. Based on the annular/churn-flow and bubble/slug-flow transition points, a new empirical model is established using a power-law curve. Since the superficial gas velocity and liquid holdup corresponding to the two transition points are obtained from analytical or semi-analytical models, the proposed model is not subject to the experimental ranges, unlike other empirical models. In addition, it avoids dealing with modeling churn flow. The new model has been validated against the laboratory and field data from published studies. For comparison, some widely used models are also evaluated. The result shows that the proposed model, which is capable of predicting the pressure gradient at different pipe sizes, liquid velocities, and gas velocities, has better performance compared with other models.

Enabling High Spectral Resolution of Liquid Mixtures in Porous Media by Antidiagonal Projections of Two-Dimensional 1H NMR COSY Spectra.

The noninvasive, in situ chemical identification of liquid mixtures confined in porous materials is experimentally challenging. NMR is chemically resolved and applicable to optically opaque systems but suffers from a significant loss in spectral resolution in the presence of the magnetic field inhomogeneities typical of porous media. In this work, we introduce a method of analysis of conventional two-dimensional (2D) 1H NMR correlation spectroscopy (COSY) spectra based on the extraction of 1D antidiagonal projections, which are free from line-broadening effects and can therefore be used for chemical species identification. Here, we show the application of the technique to the measurement of linear n-alkanes where the cross-to-diagonal peak ratios are shown to follow a power-law curve as a function of the chain length. This calibration enables quantifying mixtures of linear hydrocarbons confined in any porous material independently of temperature or inter-molecular dynamics. Thus, this is a promising tool for quantitative chemical reaction monitoring studies in heterogeneous systems under operando experimental conditions.

Synthesis and High Alkaline Chemical Stability of Polyionic Liquids with Methylpyrrolidinium, Methylpiperidinium, Methylazepanium, Methylazocanium, and Methylazonanium Cations.

Herein, we present the synthesis of five styrene-based poly(ionic liquids) (PILs) containing (covalently linked) saturated N-heterocyclic cations with various ring sizes (i.e., methylpyrrolidinium, methylpiperidinium, methylazepanium, methylazocanium, and methylazonanium). High alkaline chemical stability was confirmed by 1H NMR spectroscopy after 4 weeks in 40 mol equiv of KOH (1.0 M KOH in D2O) at 80 °C for PILs with 5-, 6-, 7-, and 8-membered ring cations; a requirement for polymer electrolyte separators in long-lasting alkaline fuel cells. Additionally, ion conductivity of PILs increased by 4 orders of magnitude with increasing water content, where a master percolation power law curve was observed, that is, similar conductivity versus water volume fraction for all PILs, regardless of cation size.

A comparison between S-N Logistic and Kohout-Věchet formulations applied to the fatigue data of old metallic bridges materials

A new formulation of a Logistic deterministic S-N curve is applied to fatigue data of metallic materials from ancient Portuguese riveted steel bridges. This formulation is based on a modified logistic relation that uses three parameters to fit the low-cycle- (LCF), finite-life- and high-cycle-fatigue (HCF) regions. This model is compared to the Kohout-Věchet fatigue model, which has a refined adjustment from very low-cycle fatigue (VLCF) to very high-cycle fatigue (VHCF). These models are also compared with other models, such as, Power law and fatigue-life curve from the ASTM E739 standard. The modelling performance of the S-N curves was made using the fatigue data considering the stress fatigue damage parameter for the materials from the Eiffel, Luiz I, Fao and Trezoi riveted steel bridges. Using a qualitative methodology of graphical adjustment analysis and another quantitative using the mean square error, it was possible to evaluate the performance of the mean S-N curve formulation. The results showed that the formulation of the S-N curve using the Logistic equation applied to the metallic materials from the old bridges obtained superior performance to the analysed models, both in the estimation of fatigue behaviour in the low-cycle fatigue (LCF) region and in the lowest mean square error.

Spatial Distribution of Tourism Activities: A Polya Urn Process Model of Rank-Size Distribution

The power law is considered one of the most enduring regularities in human geography. This article aims to develop an understanding of the circumstances that may result in the power law distribution in the geography of tourism activities. The finite Polya urn process is adopted as a device to model the preferential attachment process in the flow of tourists. The model generates a rank-size distribution of tourism regions along with intuitively appealing parameters. Empirically examined using two independent sets of Australian inbound and outbound tourism data, results show that the rank-size distribution emerging from the finite Polya urn process is a superior fit to the conventional power law curve. This rank-size distribution (termed the Polya urn process model of visitor distribution) is compatible with tourist behaviors such as habit persistence and word-of-mouth effects, and can be adopted by tourism modelers to predict and efficiently summarize the spatiality of tourism.

The effects of in-plane and out-of-plane constraints on J-R curves for X80 steel: A study using clamped SENT specimens

In the present paper, an experimental program was carried out to develop J-R curves using clamped single edge notched tension (SENT) specimens. A wide range of geometrical parameter variations is considered including different crack depth to plate width ratios (a/W) and plate thickness to width ratios (B/W). The material studied is the oil and gas pipeline steel API X80. Power law curve fitting parameters and tearing modulus are obtained for the J-R curves using the unloading compliance (UC) method for the clamped SENT specimens. Moreover, in-plane and out-of-plane constraint effects on J-R curves using clamped SENT specimens are studied, the second terms in the Williams’ series expansion are used to quantify the constraint effects. Specifically, it is demonstrated that the normalized T11 and the independent portion of T33, which equals T33-νT11, can be used to quantify the in-plane and out-of-plane constraint effects, respectively. Comparisons show that the constraint dependent J-R curves can reproduce well with all experimental data for clamped SENT specimens. Finally, the present approach is applied to predict the J-R curves of ductile crack extension for other specimens or real engineering structures with varying in-plane and out-of-plane low constraint conditions.

Abundance and size-frequency distribution of boulders in Linné crater's ejecta (Moon)

This paper presents the abundances and the size-frequency distributions (SFD) of the ejected boulders surrounding the Linnè crater, located on the Moon's Mare Serenitatis basin. By means of Lunar Reconnaissance Orbiter Camera high-resolution images we prepare a context geological map of the Linné crater as well as we identify ∼ 12000 boulders ≥4.4 m, with a maximum measured size of 30.8 m. The cumulative number of boulders per km2 is fitted with a power-law curve with index −4.03 + 0.09/-0.10. By studying the radial ejecta abundances, we find that the largest ones are located within the first 2 km from the crater's centre, while few tens of boulders with sizes <8 m are detectable above 5 km from the crater's rim. We find that the Linné proximal ejecta blanket is slightly asymmetrical, as indicated in the geological map too, showing a density increase in the NE-SW direction. This may be the result of an oblique impact emplacement of the original impactor, or it may be explained with a perpendicular impact in the Mare Serenitatis location, but on a surface with lunar basalts with different local mechanical properties. By exploiting our boulders size density as a function of the distance from the crater's centre, we derive a possible regolith thickness at the Linnè impact of ∼4.75 m, supporting similar values based on Earth-based radar and optical data in the Mare Serenitatis basin.

Bubble Lifecycle During Heterogeneous Nucleate Boiling

Heterogeneous nucleate boiling over a flat surface has been studied through complete numerical simulations. During the growth and departure of the vapor bubble, the interface is tracked following a coupled level-set and volume of fluid approach. A microlayer evaporation model similar to Sato and Niceno [“A depletable microlayer model for nucleate pool boiling,” J. Comput. Phys. 300, 20–52 (2015)] has been deployed in this investigation. A detailed study of the changes in microlayer structure as a result of different modes of boiling scenario has been performed. The departure diameter is found to increase with an increase in substrate superheat. The predicted departure diameter has been compared with the available experimental and analytical results. A power-law curve has been obtained for depicting the growth rate of bubble depending on the degree of superheat at the wall. The space–time averaged wall-heat flux at different values of superheat temperature of substrate is obtained. Bubble growth during subcooled boiling at a low and intermediate subcooled degree has been observed through direct numerical simulations. The variations in bubble dynamics after departure in saturated and subcooled liquid states have been compared.