Power-law Scaling Relationship Research Articles

Gate tuning of anomalous Hall effect in ferromagnetic metal SrRuO3

The electric field effect on ferromagnetism offers a new dimension in the recent advancement of spintronics. We report on the gate control of transport properties in thin films of oxide-based ferromagnetic metal, SrRuO3. An electric double layer transistor configuration was utilized with an ionic liquid dielectric to apply a strong electric field on a SrRuO3 thin film of 5 monolayers in thickness. The application of gate voltage induced a clear electroresistance effect, despite a considerably-large initial carrier density of the order of 1022 cm−3. Furthermore, we found that the gate modulation of the anomalous Hall conductivity σxy, which was as large as ∼±40% at low temperatures, was about three times larger than that of the longitudinal conductivity σxx. The variation of σxy is characterized by the power-law scaling relation with σxx, which is widely observed in a bad metal regime of the charge transport.

An allometric scaling relationship in the brain of preterm infants.

Allometry has been used to demonstrate a power–law scaling relationship in the brain of premature born infants. Forty-nine preterm infants underwent neonatal MRI scans and neurodevelopmental testing at age 2. Measures of cortical surface area and total cerebral volume demonstrated a power–law scaling relationship (α = 1.27). No associations were identified between these measures and investigated clinical variables. Term equivalent cortical surface area and total cerebral volume measures and scaling exponents were not related to outcome. These findings confirm a previously reported allometric scaling relationship in the preterm brain, and suggest that scaling is not a sensitive indicator of aberrant cortical maturation.

River basin organization around the main stem: Scale invariance in tributary branching and the incremental area function

AbstractThe incremental increase in contributing area along a main stem river, called here the incremental area function (IAF), has direct relevance to the spatial heterogeneity of environmental fluxes (water, sediment, nutrients, etc.) entering the stream from hillslopes and side tributaries. It also dictates, to a large extent, possible ecohydrologic discontinuities or transitions resulting from large tributary contributions. Mathematically, the IAF directly reflects the topological and geometrical structure of the river network and maps the two‐dimensional landscape organization into a one‐dimensional function. In this paper, we use two approaches to investigate the spatial heterogeneity of the IAF. First, we implement a multithreshold decomposition on IAF to study the distribution of distances between tributaries as a function of the imposed threshold contributing area and verify the presence of a simple power law scaling relationship between the threshold and the average distance between tributaries. Second, we use a wavelet‐based multiscale approach and document the presence of statistical self‐affinity (multifractality) in the IAF with a high intermittency coefficient, reflecting the complex arrangement of extreme contributions of different size tributaries. We propose a multiplicative cascade model, parameterized in terms of basin‐specific properties, to statistically simulate the IAF along the main stem. Finally, we point out the relation between the IAF and the widely used width function of a basin and show how the latter can be constructed from the former via a convolution on the self‐similar structure of a tree.

Scaling behavior of hysteresis in multilayer MoS2 field effect transistors

Extrinsic hysteresis effects are often observed in MoS2 field effect devices due to adsorption of gas molecules on the surface of MoS2 channel. Scaling is a common method used in ferroics to quantitatively study the hysteresis. Here, the scaling behavior of hysteresis in multilayer MoS2 field effect transistors with a back-gated configuration was investigated. The power-law scaling relations were obtained for hysteresis area (⟨A⟩) and memory window (ΔV) with varying the region of back-gate voltage (Vbg,max). It is interesting to find that the transition voltage in the forward sweep (VFW) and in the backward sweep (VBW) shifted to the opposite directions of back-gate voltage (Vbg) with increasing Vbg,max. However, when decreasing Vbg,max, VFW shifted to positive and reversibly recovered, but VBW almost kept unchanged. The evolution of ⟨A⟩, ΔV, VFW, and VBW with Vbg,max were discussed by the electrons transferring process between the adsorbate and MoS2 channel.

Scaling Laws for the Distribution of Gold, Geothermal, and Gas Resources

Mass dimensions of natural resources have important implications for ore-forming processes and resource estimation and exploration. The mass dimension is established from a power law scaling relationship between numbers of resources and distance from an origin. The relation between the total quantity of resource and distance, measured by the mass-radius scaling exponent, may be even more useful. Lode gold deposits, geothermal wells and volcanoes, and conventional and unconventional gas wells are examined in this study. Mass dimensions and scaling exponents generally increase from the lode gold through geothermal wells to gas data sets, reflecting decreasing degrees of clustering. Mass dimensions are similar to or slightly less than the mass-radius scaling exponents, and could be used as estimates of the minimum scaling exponent in the common case that data are not available for the latter. All the resources in this study are formed by fluid fluxes in the crust, and, therefore, percolation theory is an appropriate unifying framework to understand their significance. The mass dimensions indicate that none of the percolation networks that formed the deposits reached the percolation threshold.

Scaling and transport analyses based on an international edge turbulence database

Microscopic turbulence properties in the edge of toroidally confined fusion plasmas are studied by comparative analysis of experimental data from seven devices, collected in an international edge turbulence database. The database contains Langmuir probe measurements of fluctuations in the floating potential and ion saturation current across the last closed flux surface. They are used to address statistical properties and particle transport. Universal features of plasma edge turbulence such as an increase in skewness across the scrape-off layer (SOL) as footprints of density blobs are recovered in all devices. Analysis of the correlation lengths and times reveals power law scaling relations with macroscopic drift-wave parameters, albeit weaker than would be expected for drift-wave turbulence. As a result, the turbulent diffusivity scales with the inverse of the magnetic field strength, which is closer to Bohm-like scaling than to gyro-Bohm scaling. Nearly identical scaling relations are determined in the confined plasma edge and the SOL, pointing to a strong connection between drift-wave turbulence in the edge and blobs in the SOL. The contributions of blobs and holes (negative density spikes) to the radial particle transport are analyzed qualitatively with a conditional averaging approach. Blobs are connected to outward transport in the SOL of all devices whereas holes exhibit no uniform propagation pattern.

Intramolecular relaxation of flexible dendrimers with excluded volume.

The mechanical and dielectric relaxation moduli of dendrimers with the excluded volume interactions are theoretically investigated within the framework of Rouse-Zimm theory. The excluded volume interactions in dendrimers are expressed in terms of the effective co-volume between nearest non-bonded monomers, modeled through the delta function pseudopotential. These short range interactions play a decisive role in determining the mechanical moduli of dendrimers. The characteristic feature of excluded volume effect in the mechanical moduli is typically revealed in the intermediate frequency regime, where dendrimers with varied strengths of excluded volume interactions display power-law scaling relations with frequency. The value of the power-law scaling exponents for the mechanical moduli exactly matches with the earlier results for dendrimers in good solvent conditions. The mechanical moduli are dominated by the smaller eigenvalues in the low frequency region corresponding to the collective modes with smaller relaxation rates, which increase with the corresponding increase of the excluded volume interactions. The local modes are practically independent of excluded volume. A cross-over between the loss and storage moduli is observed at the intermediate frequency regime. The position of this cross-over shifts towards the low frequency region with the decrease in the strength of the excluded volume, which resembles the behavior of dendrimers with the variation of temperature as reported in an earlier experimental work. The structure of dendrimers show a conspicuous change as a function of the effective co-volume between the nearest non-bonded monomers. The real part of dielectric relaxation moduli remains unchanged by varying excluded volume parameters, while its imaginary part varies with the change in strength of excluded volumes for the entire range of frequency except in the high frequency regime. A comparison with the model semiflexible dendrimers show that in such densely packed molecules the mechanical relaxation moduli are strongly affected by the short-ranged excluded volume interactions between the nearest non-bonded monomers.

Brownian dynamics simulations of nanosheet solutions under shear.

The flow-induced conformation dynamics of nanosheets are simulated using a Brownian Dynamics (BD) formulation applied to a bead-rod sheetlike molecular model. This is the first-ever use of BD to simulate flow-induced dynamics of two-dimensional structures. Using this framework, we simulate dilute suspensions of coarse-grained nanosheets and compute conformation dynamics for simple shear flow. The data show power law scaling relationships between nanosheet parameters (such as bending moduli and molecular weight) and the resulting intrinsic viscosity and conformation. For nonzero bending moduli, an effective dimension of 2.77 at equilibrium is calculated from the scaling relationship between radius of gyration and molecular weight. We also find that intrinsic viscosity varies with molecular weight with an exponent of 2.12 ± 0.23; this dependence is significantly larger than those found for linear polymers. Weak shear thinning is observed at high Weissenberg number (Wi). This simulation method provides a computational basis for developing manufacturing processes for nanosheet-derived materials by relating flow forces and nanosheet parameters to the resulting material morphology.

A model for multiproperty galaxy cluster statistics

The massive dark matter halos that host groups and clusters of galaxies have observable properties that appear to be log-normally distributed about power-law mean scaling relations in halo mass. Coupling this assumption with either quadratic or cubic approximations to the mass function in log space, we derive closed-form expressions for the space density of halos as a function of multiple observables as well as forms for the low-order moments of properties of observable-selected samples. Using a Tinker mass function in a {\Lambda}CDM cosmology, we show that the cubic analytic model reproduces results obtained from direct, numerical convolution at the 10 percent level or better over nearly the full range of observables covered by current observations and for redshifts extending to z = 1.5. The model provides an efficient framework for estimating effects arising from selection and covariance among observable properties in survey samples.

Scale criticality in estimating ecosystem carbon dynamics

Scaling is central to ecology and Earth system sciences. However, the importance of scale (i.e. resolution and extent) for understanding carbon dynamics across scales is poorly understood and quantified. We simulated carbon dynamics under a wide range of combinations of resolution (nine spatial resolutions of 250 m, 500 m, 1 km, 2 km, 5 km, 10 km, 20 km, 50 km, and 100 km) and extent (57 geospatial extents ranging from 108 to 1 247 034 km(2) ) in the southeastern United States to explore the existence of scale dependence of the simulated regional carbon balance. Results clearly show the existence of a critical threshold resolution for estimating carbon sequestration within a given extent and an error limit. Furthermore, an invariant power law scaling relationship was found between the critical resolution and the spatial extent as the critical resolution is proportional to A(n) (n is a constant, and A is the extent). Scale criticality and the power law relationship might be driven by the power law probability distributions of land surface and ecological quantities including disturbances at landscape to regional scales. The current overwhelming practices without considering scale criticality might have largely contributed to difficulties in balancing carbon budgets at regional and global scales.

Complex permittivity scaling of functionally graded composites

In this paper, we provide a fundamental understanding of dielectric loss behavior as a function of applied electric field and frequency in functionally graded composites with varying numbers of layers and compositions. A new power-law scaling relation in the form of was derived based upon the ferroelectric hysteresis. The magnitude of the imaginary component of the dielectric permittivity was estimated from the polarization–electric field hysteresis loop. The changes in exponents of the scaling relation were correlated with the mechanism controlling the dielectric loss and interfacial coupling in graded structures. Building upon the scaling analysis, we investigated the effect of E-field on the domain mobility (μ) for various functionally graded systems. These results were correlated with the experimental investigation on ferroelectric domains using transmission electron microscopy and piezoresponse force microscopy.

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte (PE) with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.

Thinning and Rupture of Liquid Films by Moving Slot Jets

We present systematic experiments of the rupture and dewetting of thin films of a nonvolatile polar liquid on partially wetting substrates due to a moving slot jet, which impinges at normal incidence. The relative motion was provided by a custom-built spin coater with a bidirectionally accessible axis of rotation that enabled us to measure film thickness profiles in situ as a function of substrate velocity using dual-wavelength interference microscopy. On partially wetting polymeric substrates, dry spots form in liquid films with a residual thickness well below 1 μm. We measured the density of dry spots as well as the density and size distribution of the residual droplets as a function of film thickness. In a certain parameter range, the droplet distributions exhibit pronounced anisotropy due to the effect of long-range shear stresses on the dewetting rim instability. We find robust power-law scaling relations over a large range of film thicknesses and a striking similarity to literature data obtained with ultrathin polymer melt layers on silicon substrates.

Micromorphic modelling of grain size effects in metal polycrystals

AbstractA long‐standing problem in the modelling of polycrystal behavior from the knowledge of the constitutive equations of single crystals is the incorporation of grain size effects. Standard ho‐mogenization procedures efficiently take into account grain to grain interaction primarily induced by strain incompatibilities at grain boundary and grain morphology effects. Continuum crystal plasticity models are available that satisfactorily describe dislocation forest hardening associated with multiplication and dynamic recovery of dislocation populations. One strong limitation of these techniques is that the local crystal plasticity constitutive parameters at the grain scale are assumed to be known. Conversely, these material parameters can be identified from the macroscopic polycrystal response by an inverse approach involving the homogenization model. But then the found crystal plasticity model will be valid only for the considered grain size and the model can hardly be used for prediction of polycrystal behavior for another grain state of the material. Generalized continuum approaches arise as the suitable mechanical framework for formulating enhanced crystal plasticity models that intrinsically include grain size dependent local material responses. They incorporate the dislocation density tensor as a consitutive variable. Recent developments have shown the limitations of existing strain gradient models in the case of a two–phase laminate microstructure under single or double slip [1]. They plead for a theory even more general than the strain gradient or Cosserat approach, namely the micromorphic model presented here. The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of a micromor‐phic theory of single crystals. A computational homogenization strategy is presented in order to simulate the global and local responses of two–dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to induce a size–dependent kinematic hardening component which is responsible for the observed strong size effects. The yield stress at a given averaged plastic deformation is shown to follow a power law scaling relation for grain sizes larger than a critical grain size. The field of plastic deformation is also strongly affected by grain size, micron–size grains leading to the formation of intense slip bands crossing several grains. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Metabolic scaling law for mouse fetal and placental weight

Human birth weight does not scale linearly with the weight of the placenta: placental mass (PM) is proportional to the fetal mass (FM) raised to the scaling exponent of 0.75 (PM ∼ FM0.75) [1,2]. The mouse is a common model for studying genetic and physiological backgrounds of placental development, function and pathologies. However, to date it has not been known how placental weight scales relative to embryo weight in mice.We analyzed E12.5 litters of CD1 wild-type mice, and found that the mouse placental weight demonstrates a power-law scaling relationship with fetal weight; the value of the scaling exponent is approximately 0.72.

Temperature scaling behavior of dynamic hysteresis for (K,Na)NbO3 lead-free ferroelectric films

The temperature scaling of the ferroelectric hysteresis was first investigated in (K,Na)NbO3 films grown on SrRuO3/SrTiO3 over a temperature range from 100 K to 340 K. The power-law temperature scaling relations were obtained for ⟨A⟩, Pr, and Ec in the two distinguished temperature regions, separated by T ∼ 245 K. It was observed that ⟨A⟩ and Pr had a similar temperature dependence, compared with Ec. With increasing T, ⟨A⟩ and Pr decreased in the first region, and increased in the second region. While Ec decreased in the whole temperature range, but with different decrease rate in the two temperature regions.

Novel considerations about the non-equilibrium regime of the tricritical point in a metamagnetic model: Localization and tricritical exponents

We have investigated the time-dependent regime of a two-dimensional metamagnetic model at its tricritical point via Monte Carlo simulations. First, we obtained the temperature and magnetic field corresponding to the tricritical point of the model by using a refinement process based on optimization of the coefficient of determination in the log–log fit of magnetization decay as a function of time. With these estimates in hand, we obtained the dynamic tricritical exponents θ and z and the static tricritical exponents ν and β by using the universal power-law scaling relations for the staggered magnetization and its moments at an early stage of the dynamic evolution. Our results at the tricritical point confirm that this model belongs to the two-dimensional Blume–Capel model universality class for both static and dynamic behaviors, and they also corroborate the conjecture of Janssen and Oerding for the dynamics of tricritical points.

Scaling of Miniature Piston-Engine Performance, Part 1: Overall Engine Performance

While considerable effort has been devoted in recent years to building miniature heat engines, relatively little attention has been paid to understanding how their performance changes with engine size. This paper presents scaling rules for the performance of miniature two-stroke piston engines that are candidates for battery replacements in miniature unmanned vehicles and man-portable electronic systems. In so doing, it quantifies the current state of the art in small engine performance and provides a means to estimate a minimum thermodynamically sensible length scale for a two-stroke engine. The scaling rules are derived from comprehensive dynamometer investigations of nine of the smallest commercially available internal combustion engines. Engine mass ranges from 15 to 500 g, displacement ranges from 0.16 to , power outputs range from 8 to 650 W, and overall efficiency ranges from 3 to 12%. Peak torque, power, and normalized power follow power law scaling relationships with engine displacement. Efficiency and brake mean effective pressure follow similar scalings until approximately , where they begin to drop precipitously. The data show that the minimum length scale of a thermodynamically viable piston engine based on present technology is approximately 5 mm (displacement ). A companion paper (Menon, S., and Cadou, C. P., “Scaling of Miniature Piston-Engine Performance, Part 2: Energy Losses,” Journal of Propulsion and Power, doi:10.2514/1.B34639) quantifies the losses that drive the scaling results.

Linear temperature scaling of ferroelectric hysteresis in Mn-doped Pb(Mn1/3Sb2/3)O3-Pb(Zr,Ti)O3 ceramic with internal bias field

The temperature scaling of dynamic hysteresis was investigated in Mn-doped Pb(Mn1/3Sb2/3)O3-Pb(Zr,Ti)O3 ceramic with internal bias field. A set of simple linear temperature scaling relations were established for hysteresis area 〈A〉, coercivity Ec, and internal bias field Ei, which are different from the power-law scaling relationships for the soft and hard PZT ceramics. The proposed scaling relation between 〈A〉 and T can be predicted by the temperature dependent response of Ec and vice versa. It is suggested that the thermal deaging which related to the redistribution of the preferentially oriented defect dipoles is responsible for these dynamic hysteresis behaviors.

Double-averaged rough-bed open-channel flow with high Glossosoma (Trichoptera: Glossosomatidae) abundance

Spatially averaged velocity distributions, turbulence characteristics, and stream bed roughness elevations were collected in two streams with rough-bed substrate. Variogram analysis of substrate roughness height yielded characteristic length scales of the stream bed over which bed elevations were correlated from 0.14 to 0.41 m. Temporally and spatially averaged (double-averaged) vertical velocity profiles followed a composite distribution consisting of a linear distribution below the roughness crest height and a power or wake law above the crest. Our double-averaged velocity data demonstrated the applicability of both the wake law and power law to open-channel flow for which a low ratio of flow depth to roughness height does not support the development of the universal logarithmic velocity law. A power-law scaling relationship among spatially averaged Glossosoma density, stream bed roughness characteristics, and double-averaged fluid flow conditions was developed. The density of Glossosoma scaled directly with substrate crest elevation, normalized spatial fluctuation of longitudinal velocity in the proximity of the bed, and inversely with the standard deviation of the crest elevation. The proposed dimensionless scaling relationship explains 84 % of the Glossosoma variability.