Power-law Regime Research Articles

Accounting for the effect of dislocation climb-mediated flow on the anisotropy and texture evolution of Mg alloy, AZ31B

The current study explores the role that dislocation climb has in mediating plasticity a Mg alloy at moderately elevated temperatures. Interrupted tensile tests were performed on samples of Mg alloy, AZ31B, sheet in the O temper condition over a range of strain rates (10-5 to 10-1 s-1) and temperatures (20–350 °C) along the rolling and transverse directions. Experimental measurements of the resulting strain anisotropy and texture evolution were used as constraints during a parametric study employing a new crystal plasticity model (VPSC-CLIMB), which explicitly accounts for the kinematics of dislocation climb. The results reveal that the climb of basal <a> dislocations is not only important for dislocation recovery, but also demonstrate that climb accommodates a significant fraction of the strain in conditions where a power-law creep-type constitutive response prevails. This work does not discredit the notion that non-basal slip of <a> and <c+a> dislocations is important over a wide range of temperatures and strain rates. However, it demonstrates that the activation of dislocation climb as the mechanistic change within the power law regime provides an explanation for a wide range of observations, including the simultaneous reduction in strain anisotropy, slowed texture evolution, and rapid increase in strain rate sensitivity. Finally, it is hypothesized that these conclusions may even apply to cases in which grain boundary sliding and/or dynamic recrystallization are observed.

Inheritances, social classes, and wealth distribution.

We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring. All other sources of wealth are neglected. We consider different societies characterized by a different offspring probability distribution. We find that, if the population remains constant, the society reaches a stationary wealth distribution. We show that inequality emerges every time the number of children per family is not always the same. For realistic offspring distributions from developed countries, the model predicts a Gini coefficient of G ≈ 0.3. If we divide the society into wealth classes and set the probability of getting married to depend on the distance between classes, the stationary wealth distribution crosses over from an exponential to a power-law regime as the number of wealth classes and the level of class distinction increase.

On the use of modified Boussinesq equation for studying double-layered hillslope recession characteristics

Recession flow analysis based on the Boussinesq equation has been widely used to estimate hydraulic parameters of hillslope aquifers. However, previous studies mainly focused on homogeneous hillslope aquifers and showed that the recession curves satisfy the power law, with two transition points and three power law regimes (b1, b2 and b3). Since the variation trends of b for homogeneous hillslopes are inconsistent and even opposite, it is necessary to investigate the law of recession curves of double-layered hillslope aquifers. In the current study, a modified Boussinesq equation applicable to double-layered hillslope aquifers was proposed. After validating against laboratory experiments and numerical simulations, this modified Boussinesq equation was used to examine the recession characteristics of double-layered hillslope aquifers. The results show that the recession curves of double-layered hillslope aquifers also follow three power law regimes. However, the variations of b values are more complex than those of homogeneous hillslopes. Specifically, while b monotonically changes with slope angle for homogeneous hillslopes, the variations of b are non-monotonic for double-layered hillslopes, depending on the soil configuration, e.g., the thickness of subsoil. These findings are of great significance for determining the hydraulic parameters of hillslopes.

Structure and conformational properties of ideal nanogel particles in athermal solutions.

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids.

Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses that in turn determines the stress drop statistics. As reported earlier, the most unstable sites are located in a flat "plateau" region that decreases with system size. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form of the residual stress distribution comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average residual stress of the weakest sites is located in an intermediate power-law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.

Viscoelastic response of impact process on dense suspensions

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 u0, maximum force acting on the impactor Fmax, and elapsed time tmax to reach Fmax. We find that tmax emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of Fmax from the u0 independent regime for low u0 to a power law regime satisfying Fmax∝u0α with α≈1.5 for high u0. Similarly, tmax satisfies tmax∝u0β with β≈−0.5 for high u0. Both power-law relations for Fmax and tmax vs u0 for high u0 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 u0, Fmax and tmax. 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 Fmax and tmax against u0 because of the absence of percolated force chains in the early stage. This phenomenology predicts Fmax∝u03/2 and tmax∝u0−1/2 for high u0 and also recovers the behavior of the impactor quantitatively even if there is the rebound process.

Modeling the Creep of Nickel

Abstract Many metals and alloys have a stress exponent for the creep rate that is considerably higher than the value of three that is typically predicted by creep recovery models. One example is pure Ni. Creep data from Norman and Duran that are analyzed in the paper give a stress exponent of about seven in the temperature range 0.3–0.55 of the melting point. It has recently been shown that the high creep exponent of Al and Cu in the power-law breakdown regime can be explained by the presence of strain-induced vacancies. By applying a creep recovery model that does not involve adjustable parameters, it is shown that strain-induced vacancies can also explain the high-stress exponent of pure nickel.

Impact of COVID-19 on older adults and role of long-term care facilities during early stages of epidemic in Italy

Older adults are the main victims of the novel COVID-19 coronavirus outbreak and elderly in Long Term Care Facilities (LTCFs) are severely hit in terms of mortality. This paper presents a quantitative study of the impact of COVID-19 outbreak in Italy during first stages of the epidemic, focusing on the effects on mortality increase among older adults over 80 and its correlation with LTCFs. The study of growth patterns shows a power-law scaling regime for the first stage of the pandemic with an uneven behaviour among different regions as well as for the overall mortality increase according to the different impact of COVID-19. However, COVID-19 incidence rate does not fully explain the differences of mortality impact in older adults among different regions. We define a quantitative correlation between mortality in older adults and the number of people in LTCFs confirming the tremendous impact of COVID-19 on LTCFs. In addition a correlation between LTCFs and undiagnosed cases as well as effects of health system dysfunction is also observed. Our results confirm that LTCFs did not play a protective role on older adults during the pandemic, but the higher the number of elderly people living in LTCFs the greater the increase of both general and COVID-19 related mortality. We also observed that the handling of the crises in LTCFs hampered an efficient tracing of COVID-19 spread and promoted the increase of deaths not directly attributed to SARS-CoV-2.

Distribution of Gaps and Adhesive Interaction Between Contacting Rough Surfaces

Understanding the distribution of interfacial separations between contacting rough surfaces is integral for providing quantitative estimates for adhesive forces between them. Assuming non-adhesive, frictionless contact of self-affine surfaces, we derive the distribution of separations between surfaces near the contact edge. The distribution exhibits a power-law divergence for small gaps, and we use numerical simulations with fine resolution to confirm the scaling. The characteristic length scale over which the power-law regime persists is given by the product of the rms surface slope and the mean diameter of contacting regions. We show that these results remain valid for weakly adhesive contacts and connect these observations to recent theories for adhesion between rough surfaces.

Thermal creep fracture of a Zr1%Nb cladding alloy in the α and (α+β) phase regions

The objective of the present study was to provide new relevant information on creep behaviour and fracture processes in a sponge-based modified Zr1%Nb cladding alloy (modified E110 alloy) in the α-Zr and (α+β)-Zr phase regions. To this end, constant load creep tests were carried out in argon at testing temperature intervals from 350°C to 950°C, and applied tensile stresses ranging from 5 MPa to 210 MPa, corresponding to the power-law breakdown creep regime and/or high testing temperatures, and thus to simulate disaster conditions. Creep tests were followed by metallographic and fractographic analyses of the specimens to explain the observed creep behaviour. It was found that in the power-law region (at 350°C) the values of the stress exponent n of the minimum creep rate ε˙m (n = ∂lnε˙m /∂lnσ)T, and the stress exponent m of the time to fracture tf (m = - ∂lntf /∂lnσ)T, were very high and near to each other, indicating a close relationship between creep deformation and fracture. Further support for the idea that creep deformation and fracture are interconnected can be observed by the validity of the empirical Monkman-Grant relationship. Creep tests in the α-Zr phase region revealed creep cavitation near to, and at, the fracture surface. The final fracture is a ductile dimple mode with the synergistic effect of creep cavitation. By contrast, the final fracture in the (α+β)-Zr phase region is caused by a local strain-induced instability of the matrix leading to a loss of an external section of specimen (necking). There is a marked difference between the values of the strain to fracture εf. In the α-Zr region, typical values of εf ~ 0.3-0.5 were found, whereas for the (α+β)-Zr region, the value εf increases with testing temperature up to 850°C. Following drop of εf at temperatures ≥ 900°C was explain by intensive oxidation of the alloy.

Critical behavior of the Ising model under strong shear: The conserved case

The non-equilibrium phase transitions of the two-dimensional magnetization-conserved Ising model under the action of an external shear field is investigated. This field, that simulates a convective velocity profile with shear rate γ̇, introduces anisotropic effects and forces the system to evolve into non equilibrium states. By employing the short-time dynamics (STD) methodology, it was possible to detect first- and second-order phase transitions, and in this last case the critical exponent were calculated. As a function of the absolute magnetization |M| the system exhibits phase transitions of different order. On the one hand, If |M|=0, the model undergoes a second-order phase transition. The estimated critical temperature Tc depends on γ̇ and two regimes can be distinguished: a power-law regime for low γ̇′s, and a saturation regime at larger values of it. For the investigated shear field interval, the estimated values of the anisotropic critical exponents suggest that the critical behavior is on a crossover between the Ising and mean-field critical behaviors, respectively. On the other hand if |M|>0, the model exhibits for each γ̇ first-order phase transitions, ending in a critical point at |M|=0.

A Perspective on the Scaling of Magnetosheath Turbulence and Effects of Bow Shock Properties

Abstract We analyze magnetic field data from two magnetosheath crossings, representative of a larger collection of similar cases in the database of the Cluster spacecraft. We apply a novel data analysis method to identify the power-law behavior of the structure functions and to find the validity range of the power-law scaling. We validate the technique with solar wind magnetic field data and a synthetic magnetic field signal. This approach grants a rigorous determination of the scale range for a linear fit of the structure function in the log–log representation, which most often is chosen arbitrarily. The fitting allows an estimation of the power spectral index from the scale variation of the second-order structure function exponent. Data recorded during the first Cluster magnetosheath crossing, called Event 1, indicate three different power-law scaling regimes (injection, inertial, and kinetic) separated by two spectral breaks, consistent with the scenario of fully developed turbulence. However, data from the second Cluster magnetosheath crossing, called Event 2, depict a different scenario with only two power-law scaling regimes determined from the fit. A spectral slope shallower than the Kolmogorovian solar wind power-law index is determined at magnetohydrodynamic scales, spanning more than three frequency decades, which is separated by a spectral break from the kinetic regime. An analysis of simultaneous solar wind data from the Advanced Composition Explorer suggests that the scale behavior of the magnetosheath fluctuations might be controlled by the structure of the bow shock; solar wind turbulent fluctuations are only partially destroyed while they are carried across the bow shock. Both events are recorded in a quasi-perpendicular magnetosheath.

High Temperature Creep Behaviour of Cast Nickel-Based Superalloys INC 713 LC, B1914 and MAR-M247

Cast nickel-based superalloys INC713 LC, B1914 and MAR-M247 are widely used for high temperature components in the aerospace, automotive and power industries due to their good castability, high level of strength properties at high temperature and hot corrosion resistance. The present study is focused on the mutual comparison of the creep properties of the above-mentioned superalloys, their creep and fracture behaviour and the identification of creep deformation mechanism(s). Standard constant load uniaxial creep tests were carried out up to the rupture at applied stress ranging from 150 to 700 MPa and temperatures of 800–1000 °C. The experimentally determined values of the stress exponent of the minimum creep rate, n, were rationalized by considering the existence of the threshold stress, σ0. The corrected values of the stress exponent correspond to the power-law creep regime and suggest dislocation climb and glide as dominating creep deformation mechanisms. Fractographic observations clearly indicate that the creep fracture is a brittle mostly mixed transgranular and intergranular mode, resulting in relatively low values of fracture strain. Determined main creep parameters show that the superalloy MAR-M247 exhibits the best creep properties, followed by B1914 and then the superalloy INC713 LC. However, that each of the investigated superalloys can be successfully used for high temperature components fulfils the required service loading conditions.

The luminosity functions and redshift evolution of satellites of low-mass galaxies in the COSMOS survey

ABSTRACT The satellite populations of the Milky Way, and Milky Way mass galaxies in the local Universe, have been extensively studied to constrain dark matter and galaxy evolution physics. Recently, there has been a shift to studying satellites of hosts with stellar masses between that of the Large Magellanic Cloud and the Milky Way, since they can provide further insight on hierarchical structure formation, environmental effects on satellites, and the nature of dark matter. Most work is focused on the Local Volume, and little is still known about low-mass host galaxies at higher redshift. To improve our understanding of the evolution of satellite populations of low-mass hosts, we study satellite galaxy populations as a function of host stellar mass 9.5 &amp;lt; log (M*/M⊙) &amp;lt; 10.5 and redshifts 0.1 &amp;lt; $z$ &amp;lt; 0.8 in the COSMOS survey, making this the first study of satellite systems of low-mass hosts across half the age of the universe. We find that the satellite populations of low-mass host galaxies, which we measure down to satellite masses equivalent to the Fornax dwarf spheroidal satellite of the Milky Way, remain mostly unchanged through time. We observe a weak dependence between host stellar mass and number of satellites per host, which suggests that the stellar masses of the hosts are in the power-law regime of the stellar mass to halo mass relation (M*–Mhalo) for low-mass galaxies. Finally, we test the constraining power of our measured cumulative luminosity function to calculate the low-mass end slope of the M*–Mhalo relation. These new satellite luminosity function measurements are consistent with Lamda cold dark matter predictions.

The transition from the power-law to the power-law breakdown regimes in thermal creep of Zr1%Nb cladding alloys

The transition from the power-law to the power-law breakdown regimes in thermal creep of Zr1%Nb cladding alloys

Creep Micromechanics in Meso-Length Scale Samples

This study focuses on the creep response of meso-length scale systems, whose smallest dimensions lie in the range of a few hundred micrometers to a few millimeters. Here, uniaxial creep experiments were performed on commercially pure Al polycrystals using samples having the smallest (or, characteristic sample) dimension of 500 μm to 7 mm in the “five”-power law regime. Compared to the interior, the near-surface region developed creep compliant dislocation substructures, marked by lower dislocation density and larger subgrain size. Furthermore, the extent of this surface-affected region (SAR) inversely varied with applied stress and was limited by the grain size. As SAR became comparable to the characteristic sample dimension (CSD), the creep response of the material was significantly affected by the “weaker” surface, thereby reducing the overall creep resistance. This also resulted in a decrease in stress exponent with a decrease in CSD. The differential creep resistance of the surface and the interior leads to load-shedding between the “weak” surface and the “strong” interior. A microstructure-sensitive iso-strain composite model quantifying this load-shedding effect was formulated to explain the observed creep response across various length scales. The critical insights into the creep micro-mechanics obtained in this study, therefore, seamlessly unify the power-law creep response at large and small length scales.

Double Power-Law in Leucosome Width Distribution: Implications for Recognizing Melt Movement in Migmatites

Leucosome sizes in migmatites has been shown to follow power-law distribution, which is indicative of self-organized criticality governing accumulation and transport of partial melts in anatexis. In our measurements of leucosome widths in the Olkiluoto migmatite in western Finland, we found double power-law distributions in addition to single power-law distributions. We divided the double power-law behaviors into those with positive and negative kinks separating the two power-law regimes. We propose that double power-law distributions in migmatites result from impediments on the bottom-up self-organized criticality that melt transport processes commonly display. These impediments can be caused by some leucosomes solidifying before others, in which case the leucosomes were effectively formed in two distinct events or phases. We also consider the emergence of double power-laws as a result of melt accumulation in and sudden melt removal from conduits of a specific size.

WITHDRAWN: Influence of processing routes on the creep deformation and damage evolution of Zr-2.5Nb alloy

Abstract Tensile creep behavior of the Zr-2.5Nb alloy tubes having outer diameters of 90 mm and 110 mm, processed by extrusion and forging, respectively has been studied in the temperature range of 350-450°C under the stress range of 82-319 MPa. The creep curves have shown that the minimum creep rate and time to rupture changes with the applied stress and temperature. The apparent activation energy of creep ( Q C ) values, have been determined by using the power law for 90 mm and 110 mm tube samples are found to be ∼ 231 kJ/mol and ∼ 264 kJ/mol respectively, which is significantly higher than that for lattice self-diffusion of Zr (113 kJ/mol). The microstructural examination of the creep-ruptured samples through transmission electron microscopy (TEM) has shown evidence for multiplication of dislocations, along with their interaction with the β-(Nb, Zr) precipitates in the α-Zr matrix, which is mainly contributed to origin of threshold stress during creep. By incorporating the threshold stress data in the modified power-law relation, the true activation energy of creep ( Q t ) values from the samples of 90 mm and 110 mm tubes are found as 118 kJ/mol and 132 kJ/mol, respectively, which are close to that for lattice self-diffusion in Zr. The obtained true stress exponent ( n t ) values of 3.6 and 4.9 and formation of dislocations sub-grains in the power-law regime of steady state creep, which suggests that the dislocation climb is the rate-controlling mechanism. Further, creep data of the alloy are validated by the Monkman-Grant and Modified Monkman-Grant relationship, and time to rupture effectively predicted using the Larson-Miller Parameter. The creep damage tolerance factors are in the range of 1.5-2.5 for the tubes suggest cavity growth mechanism. Additionally, the comparison of creep data with the Ashby-Dyson maps indicates early formation of cavities due to creep.

Effects of habitat fragmentation on biodiversity patterns of ecosystems with resource competition

The natural ecosystems provide services that are crucial for our survival as climate control, food and water security. A very persistent pattern is loss of biodiversity caused by human activities all over the world, mainly due to deforestation and agricultural expansion. One very important challenge for human societies is to find the equilibrium between economic growth and environmental sustainability. In this contribution we address the role developed by spatial heterogeneity due to resource distribution and fragmentation on the species diversity. We propose a spatial model in which species compete on a lattice that is divided in habitats containing different amount of resources. The landscape here is a fractal structure which changes gradually from highly fragmented to highly clumped. Fractal landscapes are constructed through the use of fractional Brownian motion and characterized by the Hurst exponent. We found from our simulation results that there is an optimum number of habitats in which the fragmentation level has no effect. As habitat number drift away from optimal value, fragmentation has a growing effect on biodiversity promotion, mostly for small values of the Hurst exponent H. We observed two power law regimes describing the species–area relationship, in which the exponent for small areas is always smaller than the one observed for large areas. We also observe for the majority of the cases we studied, that the value of species–area exponent in both regimes grows with the number of habitats and then drops when the number of habitats becomes large. The number of habitats revealed to be the most important variable to foster and control the biodiversity in all scenarios.

Influence of excluded volume interactions on the dynamics of dendrimer and star polymers in layered random flow

The influence of excluded volume interactions (EVIs) governs the dynamics of branched polymeric structures. Therefore, we developed a theory with the inclusion of ubiquitous EVIs on average square displacement (ASD) of the centre of mass in layered random flow (LRF). The mean-field approach is used to account for effective EVIs between non-bonded monomers of generalised Gaussian structures. The effect of polymer topology is analysed under the influence of $$\delta $$ - and power-law correlated LRF. Qualitatively, the theory predicts two anomalous power-law regimes: (i) the intermediate time subdiffusive behaviour with enhanced ASD, due to EVIs, shows the internal motion of the chain and (ii) the long-time superdiffusive behaviour with slightly suppressed ASD represents the overall diffusion of the polymer. The time dependence of ASD in the presence of EVIs reveals the anomalous long-time dynamics governed by a power-law, $$t^{2-\alpha /2}$$ . The model with EVIs predicts enhanced swelling of the polymeric structure and the stretching regime in the magnitude of the ASD. The influence of EVIs in star polymer causes enhanced delay in cross-over time which is further increased with increase in functionality. Dendrimer structure with EVI delays the cross-over time with spacer length. Finally, the increase in EVIs in all topologies causes the enhancement in ASD and delay in cross-over time from subdiffusive to superdiffusive regime.