Power-law Regime Research Articles

Acoustic emission study on avalanche dynamics of ferroelectric switching in lead zirconate titanate ceramics

The avalanche dynamics of ferroelectric switching in lead zirconate titanate ceramics was investigated using acoustic emission. Two distinct power-law regimes for ferroelectric switching events were identified by an anomaly in the histogram of probability density, in contrast to the single power-law behavior observed in BaTiO3 single crystals. Such an anomaly is ascribed to the different minimum cut-offs of two power-law distributions. The critical energy exponents were determined to be 1.25 ± 0.10 for energies <103 aJ and 1.51 ± 0.14 for energies >103 aJ. The events in both regimes can be attributed to the depinning of domain walls from two distinct types of defects. The events in the lower energy regime are associated with domain wall junctions due to long-range electric and elastic interactions, whereas the latter is related to extrinsic defects, such as vacancies and dislocations. Moreover, for both regions, the rate of aftershocks follows the Omori power-law, indicating the same critical temporal correlations between the avalanches.

Rheology of emulsions with polymer solutions as the continuous phase

We investigate the effect of the addition of polymers on the flow properties of emulsions. Surfactant-stabilised 80 v% oil-in-water emulsions, exhibiting a yield stress, with either xanthan gum (a stiff, rodlike polymer) or polyethylene oxide (PEO, a flexible, elastic polymer) in the continuous phase (concentrations between 0.005 wt% and 0.5 wt%) are prepared and investigated using shear rheology and confocal microscopy. The flow properties of the emulsions are very robust, and only at high concentrations of polymer (≥ 0.2 wt%), significant changes in the flow properties are observed. In the case of xanthan gum, higher shear stresses are measured. For high concentrations the yield stress is masked by the high zero shear viscosity and shear thinning behaviour of the xanthan gum giving rise to an apparent second power law regime. In the case of PEO, an increase in the shear thinning exponent is observed, together with a decrease in the yield stress. The interaction of PEO with the surfactant SDS (sodium dodecyl sulfate) at higher PEO concentrations strongly affects the emulsion rheology, perhaps by reducing the friction coefficient between the oil droplets.

Experimental characterization of shear-enhanced dispersion in porous media

The shear flow generated by natural convection in porous media considerably influences the dispersion of contaminants in various geological formations. Previous studies have revealed that the dispersion coefficient depends on the Péclet number (Pe), shear rate, and complex pore structures. In this study, the dispersion behavior of a NaI tracer cloud was investigated under different shear rates ranging from 0.001 to 0.04 s−1 and Pe ranging from 10 to 200 using an innovative experimental apparatus via an X-ray technique. In contrast to uniform flow, a considerably enhanced dispersion was observed in shear flow along the longitudinal direction, and spreading in the longitudinal and transverse directions grew with time as ∼t3 and ∼t, respectively. In the power-law regime, the dispersion behaviors in the transverse and longitudinal directions were strengthened by shear action, with a larger dependence of the power law on the shear rates and Pe compared with that in the uniform flow. The strengthened dispersion promoted the formation of a hyper-mixing state, which was evaluated using the temporal evolution of the maximum concentration of the tracer plume, dilution index, and scalar dissipation rate. The results indicate that the dispersion behavior in a two-dimensional shear flow is quantitatively equivalent to that in a four-dimensional uniform-flow field. The findings of this study can provide a deeper understanding of the influence of shear flow on the hydrodynamic dispersion in porous media.

Multi-scale satellite observations of Arctic sea ice: new insight into the life cycle of the floe size distribution.

This study provides a new conceptional framework to understand the life cycle of the floe size distribution of Arctic sea ice and the associated processes. We derived the floe size distribution from selected multi-scale satellite imagery data acquired from different locations and times in the Arctic. Our study identifies three stages of the floe size evolution during summer – ‘fracturing’, ‘transition’ and ‘melt/wave fragmentation’. Fracturing defines the initial floe size distribution (N ∼ d−α, where d is floe size) formed from the spring breakup, characterized by the single power-law regime over d = 30–3000 m with α 2. The initial floe size distribution is then modified by various floe fragmentation processes during the transition period, which is characterized by ‘selective’ fragmentation of large floes (d > 200–300 m) with variable α = 2.5–3.5 depending on the degree of fragmentation. As ice melt intensifies, the melt fragmentation expands the single power-law regime into smaller floes (d = 70 m) with α = 2.4–3.8, while a significant reduction of small floes (d < 30–40 m) occurs due to lateral melt. The shape factor shows an overall progression from elongated floes into rounded floes. The effects of scaling and wave-fracture are also discussed.This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.

Erratum: “Viscoelastic response of the impact process on dense suspensions” [Phys. Fluids 33, 093110 (2021)

We numerically study impact processes on dense suspensions using the lattice Boltzmann method to elucidate the connection between the elastic rebound of an impactor and relations among the impact speed $u_0$, maximum force acting on the impactor $F_{\rm max}$, and elapsed time $t_{\rm max}$ to reach $F_{\rm max}$. We find that $t_{\rm max}$ emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of $F_{\rm max}$ from $u_0$ independent regime for low $u_0$ to a power law regime satisfying $F_{\rm max}\propto u_0^\alpha$ with $\alpha\approx 1.5$ for high $u_0$. Similarly, $t_{\rm max}$ satisfies $t_{\rm max}\propto u_0^{\beta}$ with $\beta\approx -0.5$ for high $u_0$. Both power-law relations for $F_{\rm max}$ and $t_{\rm max}$ versus $u_0$ for high $u_0$ are independent of the system size, but the rebound phenomenon strongly depends on the depth of the container for suspensions. Thus, we indicate that the rebound phenomenon is not directly related to the relations among $u_0$, $F_{\rm max}$ and $t_{\rm max}$. We propose a floating + force chain model, where the rebound process is caused by an elastic term that is proportional to the number of the connected force chains from the impactor to the bottom plate. On the other hand, there are no elastic contributions in the relations for $F_{\rm max}$ and $t_{\rm max}$ against $u_0$ because of the absence of percolated force chains in the early stage. This phenomenology predicts $F_{\rm max}\propto u_0^{3/2}$ and $t_{\rm max}\propto u_0^{-1/2}$ for high $u_0$ and also recovers the behavior of the impactor quantitatively even if there is the rebound process.

Observation of Spectral Structures in the Flux of Cosmic-Ray Protons from 50GeV to 60TeV with the Calorimetric Electron Telescope on the International Space Station.

A precise measurement of the cosmic-ray proton spectrum with the Calorimetric Electron Telescope (CALET) is presented in the energy interval from 50GeV to 60TeV, and the observation of a softening of the spectrum above 10TeV is reported. The analysis is based on the data collected during ∼6.2 years of smooth operations aboard the International Space Station and covers a broader energy range with respect to the previous proton flux measurement by CALET, with an increase of the available statistics by a factor of ∼2.2. Above a few hundred GeV we confirm our previous observation of a progressive spectral hardening with a higher significance (more than 20 sigma). In the multi-TeV region we observe a second spectral feature with a softening around 10TeV and a spectral index change from -2.6 to -2.9 consistently, within the errors, with the shape of the spectrum reported by DAMPE. We apply a simultaneous fit of the proton differential spectrum which well reproduces the gradual change of the spectral index encompassing the lower energy power-law regime and the two spectral features observed at higher energies.

Thermal-hydraulic-dynamic investigation of an inverted self-fluttering vortex generator

Static vortex generators initiate vortical structures; an active generator intensifies the vortices through local agitations. Flow-induced vibrations present a hybrid approach to enhance thermal mixing: the role of vortical redistribution. To further our series of study regarding the self-fluttering vortex generator, machine learning was utilized in this work to analyze a large set of experimental data which includes a broader range of design parameters in order to find a general rule of the onset of the large flapping motion and its effect on the overall thermal transport and frictional pressure loss characteristics. In addition, this paper presented the differences in thermal hydraulic efficiencies of a flapping vortex generator to an aggregation of traditional ones of the same configuration. Through machine-learning-aided analysis, we captured a striking behavior of the generator: the power-law regime spanning across different designs, bridging a shorter flow speed range each time. Such findings highlight the localization and specialization of such setups to certain flow conditions. We observe a saturation effect of the vortical redistribution process and the eventual convergence between pumping power and thermal performance. Among all interactions, we see a propensity toward lower-speed flows: higher efficiencies and better thermal transport– stands out as the characteristic of this flapping vortex generator.

Optimized hot working parameters of Fe2.5Ni2.5CrAl multi-principal element alloys

The hot compressive deformation behavior of Co-free Fe2.5Ni2.5CrAl multi-principal element alloys (MPEAs) was investigated in the temperature and strain rate ranges of 800–1100∘C and 0.001 s−1 and 1 s−1, respectively. Microstructural observations were carried out by optical microscopy (OM) and electron backscatter diffraction (EBSD). A constitutive model based flow-stress analysis was carried out, the activation energy (Q) was obtained as 315.9 kJ/mol at steady state. The strain rate sensitivity (m), the power dissipation (η), and instability parameter (ξ) were utilized to construct the processing maps. Power-law breakdown and unstable flow occurred at the high strain rates at which strain hardening was pronounced. The optimal condition for successful hot working was determined to be at strain rates in the range of 10−2–10−3 s−1 and a temperature range of 850 ~ 1020∘C. FEM simulations revealed the strain and stress distribution during hot deformation and predicted instabilities during hot forming. The main deformation mechanism was dislocation climb with a stress exponent n > 5. The Q value for plastic flow in the power-law creep regime was calculated considering the effect of lattice diffusion of atoms and was in accordance with the measured Q value. Thus, our study revealed the hot working characteristics and the optimum processing parameters for successful hot working of Fe2.5Ni2.5CrAl MPEAs.

Anisotropic correlations of plasticity on the yielding of metallic glasses.

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Dislocation substructures in pure aluminium after creep deformation as studied by electron backscatter diffraction.

In the present work, electron backscatter diffraction was used to determine the microscopic dislocation structures generated during creep (with tests interrupted at the steady state) in pure 99.8% aluminium. This material was investigated at two different stress levels, corresponding to the power-law and power-law breakdown regimes. The results show that the formation of subgrain cellular structures occurs independently of the crystallographic orientation. However, the density of these cellular structures strongly depends on the grain crystallographic orientation with respect to the tensile axis direction, with 〈111〉 grains exhibiting the highest densities at both stress levels. It is proposed that this behaviour is due to the influence of intergranular stresses, which is different in 〈111〉 and 〈001〉 grains.

Assessment of relative dispersion in the Gulf of Tonkin using numerical modeling and HF radar observations of surface currents

Particle pair statistics from synthetic drifter trajectories reconstructed from realistic, high-resolution numerical simulations (SYMPHONIE model) and HF radar velocity measurements are used to investigate the dispersion properties in the Gulf of Tonkin (GoT). This study takes an approach based on two-particles statistics providing the relative dispersion, relative diffusivity and Finite Size Lyapunov Exponent (FSLE) estimates. In the GoT, the relative dispersion follows the predictions from the theory of two-dimensional turbulence with two inertial subranges identified in the kinetic energy spectrum with the spectral slopes −5/3 and −3. The time evolution of dispersion shows an exponential growth during 5–8 days, followed by a power law regime during the next 6–20 days. Fixed-length indicators from the relative diffusivity and the FSLE reveal a local dispersion at large and intermediate scales (above Rossby radius of deformation) and non-local dispersion in sub-mesoscale range (below Rossby radius of deformation). The effect of river runoff on the local hydrodynamics and dispersion processes is assessed using the numerical model simulations without river discharge. The results show that in the model, the river plume, when present, highly impacts the Lagrangian statistics. High gradients of buoyancy reinforce the sub-mesoscale circulation in a large region along the Vietnamese coast and modify the scales and intensity of turbulent dispersion. However, a clear change of dispersion regime in the sub-mesoscale range is not identified, suggesting that the mesoscale circulation in the GoT largely governs particle spreading even at small scale.

Characterizing the sea-ice floe size distribution in the Canada Basin from high-resolution optical satellite imagery

Abstract. The sea-ice floe size distribution (FSD) characterizes the sea-ice response to atmospheric and oceanic forcing and is important for understanding and modeling the evolving ice pack in a warming Arctic. FSDs are evaluated from 78 floe-segmented high-resolution (1 m) optical satellite images capturing a range of settings and sea-ice states during spring through fall from 1999 to 2014 in the Canada Basin. For any given image, the structure of the FSD is found to be sensitive to a classification threshold value (i.e., to specify an image pixel as being either water or ice) used in image segmentation, and an approach to account for this sensitivity is presented. The FSDs are found to exhibit a single power-law regime between floe areas 50 m2 and 5 km2, characterized by exponents (slopes in log-log space) in the range −2.03 to −1.65. A distinct linear relationship between slopes and sea-ice concentrations is found, with steeper slopes (i.e., a larger proportion of smaller to larger floes) corresponding to lower sea-ice concentrations. Further, a seasonal variation in slopes is found for fixed sites in the Canada Basin that undergo a seasonal cycle in sea-ice concentration, while sites with extensive sea-ice cover year-round do not exhibit any seasonal change in FSD properties. Our results suggest that sea-ice concentration should be considered in any characterization of a time-varying FSD (for use in sea-ice models, for example).

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface.

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a nonuniversal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a power-law regime at short lengthscales. We determine the corresponding exponent ζ_{dis} and find compelling numerical evidence that, contrarily to available analytic predictions, one has ζ_{dis}<1. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equationand the Burgers turbulence.

Peak fraction of infected in epidemic spreading for multi-community networks

Abstract One of the most effective strategies to mitigate the global spreading of a pandemic (e.g. coronavirus disease 2019) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially playing the roles of bridge nodes and bridge links between countries as individual communities, dominate the epidemic spreading characteristics in the whole multi-community system. Among all epidemic characteristics, the peak fraction of infected, $I_{\max}$, is a decisive factor in evaluating an epidemic strategy given limited capacity of medical resources but is seldom considered in multi-community models. In this article, we study a general two-community system interconnected by a fraction $r$ of bridge nodes and its dynamic properties, especially $I_{\max}$, under the evolution of the susceptible-infected-recovered model. Comparing the characteristic time scales of different parts of the system allows us to analytically derive the asymptotic behaviour of $I_{\max}$ with $r$, as $r\rightarrow 0$, which follows different power-law relations in each regime of the phase diagram. We also detect crossovers when $I_{\max}$ changes from one power law to another, crossing different power-law regimes as driven by $r$. Our results enable a better prediction of the effectiveness of strategies acting on bridge nodes, denoted by the power-law exponent $\epsilon_I$ as in $I_{\max}\propto r^{1/\epsilon_I}$.

The Ca ii H and K Rotation–Activity Relation in 53 Mid-to-late-type M Dwarfs

In the canonical theory of stellar magnetic dynamo, the tachocline in partially convective stars serves to arrange small-scale fields, generated by stochastic movement of plasma into a coherent large-scale field. Mid-to-late-type M dwarfs, which are fully convective, show more magnetic activity than classical magnetic dynamo theory predicts. However, mid-to-late-type M dwarfs show tight correlations between rotation and magnetic activity, consistent with elements of classical dynamo theory. We use data from the Magellan Inamori Kyocera Echelle Spectrograph to detail the relation between Ca ii H and K flux and rotation period for these low-mass stars. We measure values for 53 spectroscopically identified M dwarfs selected from the MEarth survey; these stars span spectral classes from M5.0 to M3.5 and have rotation periods ranging from hours to months. We present the rotation–activity relationship as traced through these data. We find power-law and saturated regimes consistent to within 1σ of previously published results and observe a mass dependence in .

Crack closure of Ni-based superalloy 718 at high negative stress ratios

Fatigue crack growth damage mechanisms for nickel-based superalloys at high, negative stress ratios challenge classical crack tip shielding and closure concepts. Fatigue crack growth rate and crack closure for single-edge notch Ni-based superalloy 718 specimens at 100°C were evaluated for several stress ratios (0.5, 0.1, −1, and −2). Multiple methods were used to calculate the effective driving force for crack growth rates in region II (i.e., Paris or power law regime). The relationships between the effective driving forces, the experimentally-measured crack closure levels, and the fractographic evidence of damage mechanisms are discussed.

Diversity behavior in a community model with spatial heterogeneity

Habitat heterogeneity plays an essential role in the processes of generating diversity. Another critical factor is the resource distribution in a community. Here we investigate the diversity patterns by introducing a computational model with spatial structure. Spatial heterogeneity is introduced through the distribution of resources, which is made using a fractal landscape constructed using fractional Brownian motion. In this way, we can adjust the landscape roughness by varying the Hurst exponent. In our model, a species is characterized by a set of half-saturation constants, so each species uses each resource differently. We investigate the evolution of the species number over time. We observed that the species-area relationship has two power-law regimes. The diversity relation with the Hurst exponent depends on the mutation rate and distribution of half-saturation constants. Species diversity does not depend on spatial heterogeneity for high mutation rate. However, a positive relationship is verified for low mutation probability.

The Magnetic Field versus Density Relation in Star-forming Molecular Clouds

Abstract We study the magnetic field to density (B–ρ) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density ρ T between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for ρ T based on the interplay of the magnetic field, turbulence, and gravity. The break density ρ T scales with the strength of the initial Alfvén Mach number  A 0 for sub-Alfvénic (  A 0 &lt; 1 ) and trans-Alfvénic (  A 0 ∼ 1 ) clouds. We fit the variation of ρ T for model clouds as a function of  A 0 , set by different values of initial sonic Mach number  0 and the initial ratio of gas pressure to magnetic pressure β 0. This implies that ρ T, which denotes the transition in mass-to-flux ratio from the subcritical to the supercritical regime, is set by the initial turbulent compression of the molecular cloud.

Reaction kinetics of supplementary cementitious materials in reactivity tests

This work characterizes the reaction kinetics of supplementary cementitious materials (SCMs) with calcium hydroxide in the modified R3 test. The heat flow curves of 58 SCMs of varying reactivities were studied. Based on the heat flow curves, the SCMs were classified as more reactive, less reactive, and inert. Most of the heat flow curves in the modified R3 test exhibit, after the peak of heat flow, an initial slow decaying power-law regime that transitions into a longer and faster decaying power-law regime. The pre-exponent of the first regime depends on the initial SCM reactivity and correlates well with the 24-hour heat release in the modified R3 test, thus making it a useful metric for rapid classification of SCMs.

Inhomogeneous phase separation kinetics in liquid binary mixtures: Sensitivity to initial local composition †

The kinetics of phase separation subsequent to a finite temperature quench is assumed to be driven by diffusion on the altered free energy surface and is generally assumed to be slow. The situation can be different in phase separating liquid binary mixtures, especially for systems characterized by the large difference in mutual interactions between solute and solvent molecules. In such cases, the phase separation kinetics could be fast and may get completed within a short time (ns) scale. As a result, in these systems, one may observe diverse dynamical features arising out of local heterogeneity leading to the onset of phase separation through pattern formation, spinodal decomposition, nucleation, and growth. By using a coarse-grained analysis, we examine phase separation kinetics in each spatial grid and indeed observe important effects of initial heterogeneity on the subsequent evolution. Interestingly, we observe slower separation kinetics for those regions that correspond to the composition at the minimum of the high-temperature surface. The heterogeneous dynamics has been captured here through the non-linear susceptibility function, which shows a pattern similar to what is observed in the supercooled liquid. Each grid shows somewhat different dynamics in the three-stage (exponential, power-law, and logarithmic regime) phase separation dynamics. The late stage of phase separation kinetics is usually attributed to the coarsening of the phase-separated domains. However, in a liquid binary mixture, the late-stage power-law decay undergoes a further change. A new dynamical regime arises characterized by a logarithmic time dependence, which is due to the “smoothening” of the rough interface of already well-separated phases. This can also be described as opposite to the roughening transition described by Chui and Weeks [Phys. Rev. Lett. 40, 733 (1978)]. This reverse roughening transition can explain the logarithmic time dependence observed in the simulation.