Inverse Power Law Relationship Research Articles

Universality in the emergence of oscillatory instabilities in turbulent flows

Self-organization driven by feedback between subsystems is ubiquitous in turbulent fluid mechanical systems. This self-organization manifests as emergence of oscillatory instabilities and is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near –2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.

Anisotropic plastic deformation of single crystals of the MAX phase compound Ti3SiC2 investigated by micropillar compression

The anisotropic deformation behavior of single crystals of Ti3SiC2 has been investigated at room temperature as a function of loading axis orientation and specimen size by micropillar compression tests. Basal slip is found to be only the operative slip system at room temperature. The a/3[12¯10] basal dislocation responsible for basal slip dissociates into two partial dislocations of the Shockley-type and glides between Ti1 and Si atomic layers, as confirmed both experimentally and theoretically. The CRSS value for basal slip increases with the decrease in the specimen size, following an inverse power-law relationship with a very large power-law exponent of about 1.0, which is almost the upper limit of those reported for FCC metals. When the loading axis is parallel to the basal plane, kink band formation occurs only after the occurrence of basal-plane delamination and the subsequent activation of a-dislocations gliding on the basal plane. Kink bands consists of a/3[12¯10] basal edge dislocations of the same sign, each of which had glided between Ti1 and Si atomic layers. These results indicates that the kink formation can simply be interpreted by the classical dislocation-based kink-formation model.

Precision of different fatigue methods for predicting glass-ceramic failure

This study aimed to characterize the fatigue behavior using two fatigue methods, boundary and staircase, and to predict the probability of failure (Pf) of zirconia-reinforced lithium silicate glass-ceramic (ZLS). Bar-shaped specimens of ZLS (18 ×4 ×1.2 mm) were fabricated. Thirty specimens were subjected to a three-point flexural strength test using a universal testing machine with 0.5 mm/min crosshead speed, in 37 °C distilled water. Flexural strength data were analyzed with Weibull statistics. Eighty-six bars were subjected to cyclic fatigue using boundary and staircase methods. Fatigue tests were performed in a pneumatic cycling machine (2 Hz, 37 °C distilled water) for 10 ³ and 104 cycles. Fatigue data were analyzed using an inverse power law relationship and log normal-lifetime distribution. Fracture toughness (KIc) was determined using V-notched specimens (18 ×4 ×3 mm) and the short beam toughness method (n = 7). Vickers hardness (VH) was evaluated (4.9 N, 20 s). Fractographic and EDS analyses were also performed. ZLS showed a characteristic strength of 197 MPa, Weibull modulus of 4, VH of 6.67 GPa and KIc of 1.93 MPa m1/2. After 103 cycles, for both methods, there was a degradation of 78% of the initial strength. There was no significant degradation when the number of cycles increased from 103 to 104. Both methods resulted in similar Pf and precision at 40 MPa (~50% Pf). Yet, staircase shows good accuracy and precision in predicting the stress amplitude for a Pf near 50%; while boundary is also effective for Pf lower than 50%. The fatigue methods evaluated show similar accuracy and precision for predicting the Pf of a glass-ceramic when simulations were made in the range of stress levels and lifetimes used in the fatigue tests.

Micropillar compression deformation of single crystals of Mo5SiB2 with the tetragonal D8l structure

The deformation behavior of single crystals of Mo5SiB2 (so-called T2 phase) with the tetragonal D8l structure has been investigated by micropillar compression at room temperature as a function of crystal orientation and specimen size. The dissociation scheme and glide plane (actual atomic layers) of the identified dislocations have been investigated both experimentally through atomic-resolution scanning transmission electron microscopy imaging of their core structures and theoretically by first-principles calculations of the relevant generalized stacking fault energy curves. Although plastic flow is observed only above 1500 °C even for single crystals in the bulk form, plastic flow is observed at room temperature in a wide range of crystal orientation in the micropillar form, and three different slip systems, (001)<100>, {110}<11¯0> and {01¯1}<111>, are identified to be operative in Mo5SiB2 at room temperature. Although (001)<100> slip was predicted by calculation in the past, the other two slip systems are identified for the first time. The values of critical resolved shear stress (CRSS) for the three slip systems are extremely high all exceeding 2 GPa. The CRSS value for each slip system increases with the decrease in the specimen size, following the inverse power-law relationship with an exponent much smaller than those reported for FCC and BCC metals. The <100> dislocation on (001) and the <11¯0> dislocation on {110} are observed to dissociate into two collinear partials on their slip plane, while the 1/2<111> dislocation on {01¯1} does not make any apparent dissociation, all of which are consistently confirmed by experiment and theoretical calculation.

An experimental framework for simulating stress corrosion cracking in cable bolts

Stress corrosion cracking (SCC) of cable bolts in underground mines is a universal issue with limited cost effective solutions at present. Understanding the SCC mechanism of cable bolt failure is crucial in maintaining effective ground support and hence increasing the safety and productivity of underground mines. However, to date, no practical laboratory system has been developed to replicate the SCC mechanism which occurs in underground mines. In this study, based on the chemical properties of mine water, an acidified solution containing sulphide is synthesized. The solution is exposed to the wire strands from cable bolt in the laboratory to model service failure. It is shown that the applied stress intensity and time to failure have an inverse power law relationship in wires of cable bolts. Similar features are observed in both laboratory-failed specimens and the service-failed cable bolts under macroscopic and microscopic examinations, demonstrating the ability of the proposed framework to simulate failure of cable bolt subjected to SCC in the laboratory. Furthermore, the impact of stress intensity and hydrogen concentration on SCC are examined and a cohesive failure mechanism on the cable bolt SCC crack initiation, growth and catastrophic failure are presented. The proposed framework can be applied to the reinforcement materials for improved understanding of the SCC mechanism in underground mines and tunnels.

Statistical analysis of dispersal and deposition patterns of volcanic emissions from Mt. Sakurajima, Japan

With the eruption of Eyjafjallajökull (Iceland) in 2010, interest in the transport of volcanic ash after moderate to major eruptions has increased with regards to both the physical and the emergency hazard management aspects. However, there remain significant gaps in the understanding of the long-term behaviour of emissions from volcanoes with long periods of activity. Mt. Sakurajima (Japan) provides us with a rare opportunity to study such activity, due to its eruptive behaviour and dense observation network. In the 6-year period from 2009 to 2015, the volcano was erupting at an almost constant rate introducing approximately 500 kt of ash per month to the atmosphere. The long-term characteristics of the transport and deposition of ash and SO2 in the area surrounding the volcano are studied here using daily surface observations of suspended particulate matter (SPM) and SO2 and monthly ashfall values.Results reveal different dispersal patterns for SO2 and volcanic ash, suggesting volcanic emissions’ separation in the long-term. Peak SO2 concentrations at different locations on the volcano vary up to 2 orders of magnitude and decrease steeply with distance. Airborne volcanic ash increases SPM concentrations uniformly across the area surrounding the volcano, with distance from the vent having a secondary effect. During the period studied here, the influence of volcanic emissions was identifiable both in SO2 and SPM concentrations which were, at times, over the recommended exposure limits defined by the Japanese government, European Union and the World Health Organisation.Depositional patterns of volcanic ash exhibit elements of seasonality, consistent with previous studies. Climatological and topographic effects are suspected to impact the deposition of volcanic ash away from the vent: for sampling stations located close to complex topographical elements, sharp changes in the deposition patterns were observed, with ash deposits for neighbouring stations as close as 5 km differing as much as an order of magnitude. Despite these effects, deposition was sufficiently approximated by an inverse power law relationship, the fidelity of which depended on the distance from the vent: for proximal to intermediate areas (<20 km), errors decrease with longer accumulation periods (tested here for 1–72 months), while the opposite was seen for deposition in distal areas (>20 km).

Reducing energy dissipation and surface effect of diamond nanoelectromechanical resonators by annealing in oxygen ambient

The authors report on the marked improvement of the quality factor (Q-factor) of single crystal diamond (SCD) nanoelectromechanical system (NEMS) resonators through annealing in oxygen ambient. The SCD NEMS resonators were fabricated by ion implantation assisted technique. The resonance frequency followed well the inverse power law relationship with the length of the cantilevers despite of the annealing. It was observed that there was little modification in the resonance frequency and Q-factor at 430 °C, while an obvious red-shift in the resonance frequency occurred at 500 °C. Meanwhile, a marked improvement in the Q-factor from around 3500 to 7000 was observed at 500 °C. The frequency red shift is due to the etching of diamond with a rate of 0.4–0.5 nm/h at 500 °C. The analysis of the energy dissipation discloses that the surface effect dominates the energy loss mechanism for the SCD NEMS resonator. The improvement of the Q-factor is thus attributed to the reduction of the surface defects in SCD NEMS.

Role of paclitaxel on critical nucleation concentration of tubulin and its effects thereof

Paclitaxel is an anticancer drug that stabilizes microtubules by suppressing their dynamic instability. It binds to the lumen of the microtubules and enhances subunit interaction. In the present work, we show that the critical concentration of tubulins required to polymerize microtubules follows an inverse power law relation with the amount of paclitaxel added during polymerization. With an increase in paclitaxel concentration from 0.1 μM to 10 μM, the critical nucleation concentration decreases by 89%. We propose stabilization of microtubule nuclei in the presence of taxol for this observation. In addition, lowering in the critical nucleation concentration left fewer tubulins for growth, which resulted in shorter microtubules. Addition of 10 μM taxol resulted in reduced steady state length of microtubules by 37.5%. These observations are explained based on microtubule nuclei stabilization and subsequent depletion of tubulin pool. We also show mathematically, that taxol reduces the rate constant of shortening more prominently (by 100 folds), compared to the rate constant of elongation.

Modelling degradation with multiple accelerated processes

Multivariate degradation models are important tools for reliability assessment of highly reliable products. The multivariate aspect of the models depends on the device under study and the type of test applied to it. A device may exhibit different performance characteristics (PC) or one PC may be affected by multiple environmental conditions. If a device is affected by multiple environmental conditions, then it is possible to subject it to multiple accelerating variables in an accelerated degradation test in order to obtain reliability information. In this paper, two accelerating stress variables are considered, which characterize two degradation processes (DP) on a PC. In this way, two degradation models based on the life–stress Arrhenius relationship and the inverse power law relationship are provided. It is shown that the final distribution function characterizing the failure times for each DP can be used to estimate the reliability of a fuel sensor, the example under study in this paper. The interaction of the models with respect to the DPs is described via copula1 function, in order to model the dependency structure. A Bayesian approach is proposed to estimate the parameters of the final models and the best fit models are selected using information criteria.

Abundance and size distribution of permanent and temporary farm ponds in the southeastern Great Plains

Using aerial images from the US Department of Agriculture National Agriculture Imagery Program and the US Geological Survey National Hydrology Dataset, we estimated 577 654 farm ponds with surface areas from 0.005 to 1 ha in a 229 489 km2 region of the southeastern Great Plains (2.52 ponds/km2). Ponds with surface areas from 0.005 to 0.1 ha were the numerically dominant size class in the study region. The distribution of farm pond sizes followed an inverse power law relationship. We estimated 376 209 permanent ponds and 201 445 temporary ponds were in our study area. The ratio of temporary to permanent ponds within a pond size class was inversely related to pond surface area; 47% of ponds with surface areas of 0.005–0.1 ha were temporary, whereas only 13% of ponds with surface areas of 0.91–1 ha were temporary. Because permanent and temporary farm ponds are abundant and have different physicochemical properties and ecological communities, assessments of regional biogeochemical processes and biodiversity in the Great Plains must consider both types of ecosystems.

Viscosity and creep compliance of polyoxymethylene copolymers of various average molecular weights

The effect of average molecular weight (Mw ) of polyoxymethylene (POM) on melt viscosity and solid state creep compliance were investigated. Viscosity follows the power function of Mw. Creep compliance results indicate that time-temperature superposition applies to POM copolymers. Creep compliance in ashort time (0.25 s) is independent of Mw, but in a longer time (10 years) it follows an inverse power law relation with Mw, up to a critical value of Mw = 81 100, where creep compliance becomes independent of Mw. At intermediate time (17 min), similar to short one, no effect on susceptibility to creep compliance was observed. It was also stated that the activation energy is independent of Mw.

Bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry

The influence of system parameters such as the flame location, Peclet number and Damköhler number on the bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry is presented in this paper. In the bifurcation plot with flame location as the bifurcation parameter, subcritical Hopf bifurcation is found for lower values of flame location and supercritical Hopf bifurcation for higher values of flame location, for all the Damköhler numbers used in this study. The flame shapes are captured at eight different phases of a cycle of time series data of acoustic velocity at both the fold and Hopf points for bifurcation with flame location as the parameter. We find that the range of flame height variations at the Hopf point is more than the range of flame height variations obtained at the fold point. We also find that the flame oscillates in the same phase as pressure fluctuation but in a phase different from both velocity and heat release rate fluctuations in the region of hysteresis for bifurcation with flame location. The non-dimensional hysteresis width is plotted as a function of Damköhler number for variation of flame location in the subcritical region. An inverse power law relation is found between the non-dimensional hysteresis width and the Damköhler number. The bifurcation plot with Peclet number as parameter shows a subcritical Hopf bifurcation.

Impedance spectroscopy studies of moisture uptake in low-k dielectrics and its relation to reliability

Assessing the reliability of low dielectric constant materials is an important problem for the scalability of integrated circuits to reduced dimensions. Here we report results of a study of the influence of moisture incursion on dielectric relaxation and reliability in porous low-k (2.55) dielectric constant BEOL capacitors. We apply impedance spectroscopy to measure the dielectric loss tangent as a function of temperature and frequency. From the results, we identify two relaxation modes of water in the porous dielectric, exhibiting thermal activation energies of 0.32eV and 0.56eV. Study of the lifetime against time-dependent dielectric breakdown (TDDB) as a function of the dielectric loss tangent measured at AC voltages below 0.5V yields an inverse power-law relationship. The dielectric loss tangent thus has the potential to serve as a low-voltage test of the susceptibility to early failure and to provide a link between high voltage, accelerated TDDB testing and the underlying physical processes responsible for dielectric breakdown.

Three‐dimensional versus two‐dimensional bed form‐induced hyporheic exchange

AbstractThe hyporheic zone is often a critical component of river systems. Hyporheic exchange is generally forced by variation in riverbed topography such as due to bed forms. Most previous research on bed form‐driven hyporheic flow has focused on two‐dimensional (2‐D) dunes and ripples, while little has been done on their three‐dimensional (3‐D) counterparts. Here we compared hyporheic exchange and associated metrics for a previously studied pair of corresponding 2‐D and 3‐D bed forms. To accomplish this, a series of multiphysics computational fluid dynamics models were conducted both in 2‐D and 3‐D with similar open channel Reynolds numbers (Re). Results show that the pressure gradient along the sediment‐water interface is highly sensitive to the spatial structure of bed forms, which consequently determines hyporheic flow dynamics. Hyporheic flux is a function of Re for both 2‐D and 3‐D dunes via a power law; however, the equivalent 3‐D dunes have a higher flux since the 3‐D form induces more drag. The hyporheic zone depths and volumes are only slightly different with the 3‐D case having a larger volume. The mean fluid residence times for both cases are related to Re by an inverse power law relationship, with the 3‐D dune having smaller residence times at moderate to high Re. The effects of increasing flux on residence time in 3‐D dunes are partly modulated by a slightly increasing hyporheic volume. Our results suggest that a 2‐D idealization is a reasonable approximation for the more complex 3‐D situation if local details are unimportant but that development of predictive models for mean fluxes and residence times, which are critical for biogeochemical processes, based on 2‐D models may be insufficient.

Power-law and exponential rank distributions: A panoramic Gibbsian perspective

Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.

Modelling Three-dimensional Interfacial Flow with Sand Dunes

Hyporheic zone is considered as a dynamic hydrologic ecotone that critical for maintaining the health of river systems. The hyporheic flux occurs generally in response to variations in river bedforms. In this study, we first generated several typical bedforms. The turbulent flow over the 3D dunes and hyporheic flow in the sediment are simulated through a computational fluid dynamics (CFD) approach. Turbulent flow in the water column is simulated by solving the Reynolds-averaged Navier-Stokes (RANS) equations with the k-ω turbulence closure model, and a steady state groundwater flow model is applied for the underlying porous media. These two sets of equations are coupled through the pressure distribution at the sediment-water interface (SWI).Each case was subjected to different hydraulic conditions, i.e., increasing open channel Reynolds Numbers (Re). Results show that the pressure gradient along the SWI is highly controlled by the spatial structure of bedform, which consequently determines flow dynamics in the porous media. The interfacial flux is dominated by the pressure configuration over the SWI which is a function of Re via a power-law trend. The mean fluid residence time is related to Re by an inverse-power law relationship. This study has led to the basic understanding of hyporheic flow induced by more natural 3D dunes.

Influence of particle shape on slurry wear of white iron

Slurry particle shape is an important variable in determining equipment life in mineral processing operations, especially in the grinding circuit. Slurry particles here are generally coarse, sharp and at high concentrations. Little information is available to guide practitioners in measuring particle shape or understanding the impact of particle shape on the wear rate of the hard white irons that are commonly used in processing equipment.The first part of the current work has explored the differences between 2 methods of measuring particle shape – Circularity Factor (CF) a ratio of the perimeter to projected area of the particles and spike parameter (SPQ) which is an analytical method of fitting triangles to the prominent features of the particle outline. Calculating the CF and SPQ for a wide range of particle shapes (from angular to round) found a close linear correlation between the two. This was surprising given that the more complex SPQ methodology was developed to improve particle shape characterisation.The second part of the work used a large scale Coriolis tester to determine the effect of particles of different shape on the wear rate of white cast iron. To simulate the type of wear experienced in grinding circuits a range of different particle shapes with similar CF to those observed in field applications were tested. Coarse silicon carbide, alumina and silica sand particles were individually run through the Coriolis tester. By recirculating the particles in the rig, the shape became more rounded (with CF eventually spanning the range seen in field applications) without dramatically impacting particle size. An inverse power law relationship was found between the CF and the erosion rate for white iron. This correlation should be able to be used to determine the impact of changes in CF on equipment wear life.A third element of the work was a microscopic investigation of the worn sample surface from the Coriolis tester to identify changes in wear mechanisms with particle hardness and shape. In addition a comparison was made with worn slurry pump parts to ensure that the mechanisms of wear from the Coriolis test were representative of those seen in equipment in the field.

Energy dissipation in micron- and submicron-thick single crystal diamond mechanical resonators

The authors report the resonance frequency and the energy dissipation of single crystal diamond cantilevers with different dimensions, which were fabricated by ion implantation assisted technique. The resonance frequency well followed the inverse power law relationship with the length of the cantilevers and exhibited a high reproducibility with varying the dimensions. The energy dissipation decreased with increasing the cantilever length and saturated or reduced at a certain value. For the shorter cantilevers, clamping loss governed the energy dissipation. As the cantilever length increased to a certain value, defects relaxation or surface effect became dominant. The possible origins for these energy dissipations were discussed.

Diffusive fractionation of BTEX and chlorinated ethenes in aqueous solution: quantification of spatial isotope gradients.

Laboratory experiments were performed to investigate and quantify the extent of diffusive isotope fractionation of organic contaminants in aqueous solution. We selected petroleum hydrocarbons (toluene and ethylbenzene, in 1:2 mixtures of labeled (perdeuterated) and nonlabeled isotopologues) and chlorinated solvents (trichloroethene, TCE, and cis-dichloroethene, cis-DCE, at their natural isotopic abundance) as model compounds. The experimental approach using gel diffusion tubes allowed us to resolve concentration and isotopic gradients induced by isotopologue-specific diffusion and to determine aqueous diffusion coefficients in agreement with the values calculated using published empirical correlations. The experimental results were quantitatively evaluated with numerical simulations to determine the aqueous diffusion coefficients, D, and the exponent of the inverse power-law relation between D and the molecular mass of the isotopologues. The results show remarkable diffusive isotope fractionation for all the investigated organic compounds; however, the extent of fractionation was found to be smaller for the chlorinated ethenes and remarkably deviating from an inverse square root relationship between the isotopologues diffusion coefficients and their molecular mass. The outcomes of this study are relevant for the interpretation of isotopic signatures of organic contaminants in environmental systems and for the quantitative application of compound specific isotope analysis (CSIA) that needs to take into account the fractionation effects of both physical and transformation processes.

Morphometric dating of the fluvial landscape response to a tectonic perturbation

Despite constant progress in numerical and field studies of landscape evolution, time evolution is still poorly constrained in many uplifted areas where low denudation rates prevent the use of low temperature thermochronology, especially outside high relief mountainous areas. Here, I show that regional statistics of the landscape metric R involving hypsometric integrals at three nested levels of a catchment are able to isolate the time effect on landscape geometry during the latter's transient response to a tectonic perturbation. Analysis of 210 catchments from 9 regions of known uplift age worldwide shows that the regionally characteristic, R‐derivedSRindex is in inverse power law relation with the time elapsed since a base level lowering. Suggesting a response time of ∼5 My, this finding has important implications for quantifying the rate of landform evolution and determining whether a landscape has reached steady‐state form.