Scaling Exponents Research Articles

Allocation of nitrogen and phosphorus in the leaves, stems, and roots of Artemisia: a case study in phylogenetic control.

The allocation of nitrogen (N) and phosphorus (P) among plant organs is an important strategy affecting growth and development as well as ecological processes in terrestrial ecosystems. However, due to lack of systematic investigation data, the allocation strategies of N and P in the three primary plant organs (e.g., leaves, stems and roots) are still unclear. A total of 912 individuals of 62 Artemisia species were examined across a broad environmental expanse in China, and the N and P concentrations of leaves, stems and roots were measured to explore the allocation strategies in different subgenera, ecosystem types, and local sites. Across all 62 species, the N vs. P scaling exponents for leaves, stems and roots were 0.67, 0.59 and 0.67, respectively. However, these numerical values differed among subgenera, ecosystem types, and local sites. Overall, the numerical values of N vs. P scaling exponents comply with a 2/3-power function for each Artemisia organ-type reflecting a phylogenetically conserved allocation strategy that has nevertheless diversified with respect to local environmental conditions. These results inform our understanding of N and P stoichiometric patterns and responses to abiotic factors in an ecologically broadly distributed angiosperm genus.

Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributions

The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, P(q)∼q−α with exponent α≈5.6, and a square lattice. We analyze the role of the disorder in the modified WPS model, considering the critical behavior of the contact process (CP). We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent ω=1/2, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.

Global self‐similarity of dense granular flow in silo: The role of silo width

AbstractThe influence of silo width on dense granular flow in a two‐dimensional silo is investigated through experiments and simulations. Though the flow rate remains stable for larger silo widths, a slight reduction in silo width results in a significant increase in flow rate for smaller silo widths. Both Beverloo's and Janda's formula accurately capture the relationship between the flow rate and outlet size. Flow characteristics in the regions near the outlet exhibit local self‐similarity, supporting Beverloo and Janda's principles. Moreover, global self‐similarity is analyzed, indicated by the transition in flow state from mass flow in regions far from the outlet to funnel flow near the outlet. The earlier occurrence of this transition favors to enhance the grain velocity and consequently increases the dense flow rate. An exponential scaling law is proposed to describe the dependencies of flow rate, grain velocity, and transition height on silo width.

Impact of fractal dimension and lateral correlation length on surface plasmon resonance activity in sputtered silver layers

Fractal and optical characteristics of self-affine surfaces of silver(Ag) thin films deposited through direct current (dc) magnetron sputtering as a function of thickness are investigated and explored here. The surface morphology of Ag thin films is characterized by field emission electron microscopy, and atomic force microscopy technique. The cube counting algorithm is used to extract the fractal dimension of Ag thin film. The surface roughness (interface width) shows monotonic increases with film thickness, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension exhibit linear variation with thickness. Our findings reveal distinctive scaling behaviors, with scaling exponents α, β, and 1/z indicating unique growth characteristics. The interface width w increases as a power law of thickness t, w(t)∝tβ, with β=0.39± 0.007, and the lateral correlation length ξ grows as ξt∝t1/z with 1/z=0.14± 0.002. The roughness exponent extracted from height-height correlation analysis is α=0.61–0.41. The self-affine nature of the Ag thin films is further confirmed by the autocorrelation function. X-ray photoelectron spectroscopy (XPS) is used to the confirm the growth of Ag thin film. Additionally, we have studied the role of fractal dimensions and lateral correlation length (ξ) on the surface plasmon resonance (SPR) of Ag thin film. Our results indicate a red-shifting behavior of SPR with increasing interface width (w), lateral correlation length (ξ), and fractal dimensions. This study suggests the significance of not only the roughness exponent and fractal dimension but also the local surface slope in SPR activity in Ag thin films.

Scaling Transition of Active Turbulence from Two to Three Dimensions.

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model wedevelop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organizedsystems.

Finite Size Effects in Antiferromagnetic Highly Strained BiFeO3 Multiferroic Films

AbstractEpitaxially strain‐engineered tetragonal (T)‐like BiFeO3 (BFO) is a multiferroic material with unique crystallographic and physical properties compared to its bulk rhombohedral parent. While the effect of this structural change on ferroelectric properties is understood, the influence on correlated antiferromagnetic (AFM) properties, especially with reduced film thickness, is less clear. Here, the AFM behavior of T‐like BFO films 9–58 nm thick on LaAlO3 (001) substrates fabricated by pulsed laser deposition was studied using conversion electron Mössbauer spectroscopy and X‐ray diffraction. The key findings include: i) Ultrathin T‐like BFO films (<10 nm) show a decoupling of magnetic and structural transitions, with the polar vector tilted 32 degrees from [001] in 9–13 nm films. ii) Films thinner than 13 nm exhibit no structural transition down to 150 K, with a Néel (TN) transition at ≈290 K, ≈35 K lower than thicker films. Interestingly, the TN scaling with thickness suggests realistic scaling exponents considering a critical correlation length for C‐type AFM order, rather than G‐type. The results show that finite size effects can tailor transition temperatures and modulate AFM wave modes in antiferromagnetic oxides, with implications for AFM spintronics for future information technologies.

Ecological succession shapes size–density scaling relationships of trees and soil invertebrates

Abstract The widely observed negative scaling relationship between organism size and abundance is predicted to have a universal −0.75 scaling exponent across all life forms. However, factors influencing frequently observed deviations from this exponent, such as ecosystem succession and organism traits, remain poorly understood. We explore the dependence of size–density scaling on ecosystem succession and organism traits by analysing size–density relationships in trees and soil invertebrates across 183 temperate forest plots comprising urban secondary forests, urban old‐growth forests and non‐urban natural forests. Exponents of scaling relationships in urban tree and invertebrate communities progressively steepened with increasing restored (planted) forest stand age as small organisms increased in abundance. In contrast, non‐urban tree scaling relationships flattened during succession with exponents veering away from −0.75, whereas urban tree and invertebrate communities converged towards this prediction in later successional stages. Our results shed light on how the body size structure of tree and soil invertebrate communities spanning multiple trophic levels shift over successional time as the relative abundances of large versus small‐bodied organisms increase. This study emphasises the fundamental influence of organismal traits and ecosystem succession on scaling relationships of organism body size and abundance. Read the free Plain Language Summary for this article on the Journal blog.

Effect of Dispersion Media Composition on the Structure and Rheology of the Short-Sidechain Perfluorosulfonic Acid Ionomer Dispersions

Perflourosulfonic acid (PFSA) ionomers are used in many applications including polymer-electrolyte membrane fuel cells and electrolysers owing to their many attractive properties such as excellent ion-conductivity, chemical resistance, mechanical properties, and thermal stability. In polymer-electrolyte membrane fuel cells and electrolysers, they are used as the membrane and as a component in the catalyst layers, to provide proton conductivity and serve as a binder for the catalyst particles, which are two key components of these devices. Understanding the structure and rheological properties of the ionomer dispersions is important for solution-processed fabrication of the membranes and the catalyst layers, and will enable better control their final structure/morphology, and improve the device performance. A water-alcohol solvent mixture is a common dispersion media for ionomer dispersions as well as the catalyst inks. While significant efforts exist on the structure of ionomer dispersions in water-alcohol solvent mixtures, their rheological properties, particularly the effect of solvent composition at non-dilute concentrations remain less explored. In this talk, the effect of water-alcohol (isopropanol) composition of the dispersion media on the rheological properties of ionomer dispersions will be presented. The results of small-angle x-ray scattering characterization of the ionomer dispersions will be also discussed. As a model ionomer, a short sidechain perfluorinated ionomer (PFSA), produced by 3M, was used. In dispersions with low ionomer concentrations, the zero-shear viscosity scaling with concentration was found to be similar for all alcohol fractions in the solvent mixture, following Fuoss’s law for polyelectrolytes. Whereas at higher concentrations, beyond the semi-dilute unentangled regime, their scaling was strongly dependent on alcohol fraction, where the scaling exponent increasing with increasing the alcohol fraction. Furthermore, the dispersions showed dramatic shear-thickening and strain-stiffening behaviors at higher alcohol fractions. The rheological observations suggest water-alcohol composition significantly alters the interactions between ionomer, and consequently their structure, and has strong implications in processing as well as on the morphology/structure of the membranes and the catalyst layers.

Two Methods Based on Integral Equation Approaches in Analyzing Polyelectrolyte Solutions: Macrophase Separation.

To understand the phase behaviors of polyelectrolyte solutions, we provide two analytical methods to formulate a molecular equation of state for a system of fully charged polyanions (PAs) and polycations (PCs) in a monomeric neutral component, based on integral equation theories. The mixture is treated in a primitive and restricted manner. The first method utilizes Blum's approach to charged hard spheres, incorporating the chain connectivity contribution by charged spheres via Stell's cavity function method. The second method employs Wertheim's multi-density Ornstein-Zernike treatment of charged hard spheres with Baxter's adhesive potential. The pressures derived from these methods are compared to available molecular dynamics simulations data for a solution of PAs and monomeric counterions as a limiting case. Two-phase equilibrium for the system is calculated using both methods to evaluate the relative strength of phase segregation that leads to complex coacervation. Additionally, the scaling exponents for a selected solution near its critical point are examined.

Temperature-dependent magnetic properties of bcc and fcc FeNi alloys: A machine learning assisted Monte-Carlo approach

The estimation of exchange integrals in metals and alloys from first-principle calculations yields Curie temperature (TC), which is not in agreement with the experiments. The microscopic exchange interactions of the bcc and fcc FeNi alloys are predicted by training large datasets of random magnetization curves simulated using the atomic scale Monte Carlo method with regression models to accurately reproduce the experimental TC. The estimation of Fe-rich bcc alloys reveals predominant Heisenberg-like Ruderman-Kittel-Kasuya-Yosida (RKKY) type oscillations in Fe–Fe interactions, similar to the behavior in bcc Fe. Furthermore, frustration in Fe–Fe and Fe–Ni/Ni–Fe couplings of fcc Invar alloy results in the reduction of TC. Additionally, the temperature dependence of cubic anisotropy is calculated using constrained Monte Carlo algorithm, and the validity of Callen-Callen 10th power law is demonstrated, which shows large deviations of scaling exponent L≪10 near permalloy composition attributing to dispersion of magnetic easy axis of Fe and Ni.

Anomalous diffusion of self-propelled particles

Abstract The transport equation of active motion is generalised to consider time-fractional dynamics to describe the anomalous diffusion of self-propelled particles. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the firsts moments, i.e. the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from 2α in the short-time regime to α in the long-time one, 0 < α < 1 being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active-motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher’s equation is recovered. The theoretical framework presented here can be applied as model of active motion that exhibits anomalous diffusion.

A comprehensive numerical study on heat transfer and friction characteristics of offset-strip fins

Offset-strip fins are among the most used geometries in compact heat exchangers. The geometric and flow parameters of the fins affect their heat transfer effectiveness and head losses. Hence, accurate predictive models are needed to guide the design process. However, most of the correlations available in the literature are valid only for a limited set of geometric configurations and flow regimes. This work discusses the derivation of multivariate response surfaces for the equivalent Darcy and Colburn factors in offset-strip fins. These surfaces feature clear applicability ranges and extend over wide Reynolds and Prandtl number ranges (50≤Re≤12000, 0.71≤Pr≤190). In addition, a novel empirical model for the Prandtl number scaling exponent is proposed. The analysis is carried out through a Design of Experiment approach, performed with computational techniques. Each numerical experiment is carried out by CFD analysis of a periodic fin geometry. The obtained response surfaces approximate CFD results with a mean deviation of ±8.4%. Moreover, application of the correlations to the analysis of complete heat exchangers issued mean and maximum deviations of ±7.8% and ±20%, respectively, thus highlighting the usefulness of the proposed models for the accurate modelling of offset-strip fins in heat transfer applications.

Solving Boltzmann optimization problems with deep learning

Decades of exponential scaling in high-performance computing (HPC) efficiency is coming to an end. Transistor-based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further miniaturization will be impossible. Future HPC efficiency gains will necessarily rely on new technologies and paradigms of computing. The Ising model shows particular promise as a future framework for highly energy-efficient computation. Ising systems are able to operate at energies approaching thermodynamic limits for energy consumption of computation. Ising systems can function as both logic and memory. Thus, they have the potential to significantly reduce energy costs inherent to CMOS computing by eliminating costly data movement. The challenge in creating Ising-based hardware is in optimizing useful circuits that produce correct results on fundamentally nondeterministic hardware. The contribution of this paper is a novel machine learning approach, a combination of deep neural networks and random forests, for efficiently solving optimization problems that minimize sources of error in the Ising model. In addition, we provide a process to express a Boltzmann probability optimization problem as a supervised machine learning problem.

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms.

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.

Leaf functional traits of Parrotia subaequalis from different environments in eastern China.

Functional traits are important in understanding how plants respond and adapt to their immediate environment. Parrotia subaequalis is a highly endangered arbor species found throughout eastern China, primarily inhabiting hillsides and valleys, yet, little is known about the variation in leaf traits across these environments. In the present study, we tested this by comparing leaf surface area, leaf weight, leaf length, leaf symmetry and leaf mass per unit area, as well as the relationship between leaf traits and environmental factors and the scaling relationship between leaf surface area versus leaf dry mass. We observed significant differences in leaf surface area, weight, and length among the population sites, and these variables were strongly affected by environmental factors, especially high mean annual temperatures in hillside habitats and high mean annual precipitation in valley habitats. The scaling exponents remained numerically variant among the 10 populations, with different slopes greater than 1.0, and the scaling exponents increased significantly with hillside habitats. These metrics correlated with soil thickness associated with different habitat types. The areal ratio (AR) values in all populations deviated from 1, indicating that the two lamina sides were asymmetrical. The standardized symmetry index (SI) values displayed significant variation, especially in leaves from hillside habitats with a high degree of asymmetry. Collectively, our findings demonstrated that leaf functional traits exhibit considerable variability in response to different environmental contexts and provide valuable reference data that could be useful for conserving this endangered species.

Global leaf sulfur stoichiometry and the relationships with nitrogen and phosphorus: phylogeny, growth form and environmental controls.

Sulfur (S) is an essential bioelement with vital roles in serving regulatory and catalytic functions and tightly coupled with N and P in plants. However, globally stoichiometric patterns of leaf S and its relationships to leaf N and P are less well studied. We compiled 31 939 records of leaf-based data for 2600 plant species across 6652 sites worldwide. All plant species were divided into different phylogenetic taxa and growth forms. Standard major axis analysis was employed to fit the bivariate element relationships. A phylogenetic linear mixed-effect model and a multiple-regression model were used to partition the variations of bioelements into phylogeny and environments, and then to estimate the importance of environmental variables. Global geometric mean leaf S, N and P concentrations were 1.44, 15.70 and 1.27 mg g-1, respectively, with significant differences among plant groups. Leaf S-N-P positively correlated with each other, ignoring plant groups. The scaling exponents of LN-LS, LP-LS and LN-LP were 0.64, 0.76 and 0.79, respectively, for all species, but differed among plant groups. Both phylogeny and environments regulated the bioelements. The variability, rather than mean temperature, controlled the bioelements. Phylogeny explained more for the concentrations of all the three bioelements than environments, of which S was the one most affected by phylogenetic taxa.

Associations of movement behaviours and dietary intake with arterial stiffness: results from the ORISCAV-LUX 2 cross-sectional study

ObjectiveAdopting a physically active lifestyle and maintaining a diet rich in antioxidants can reduce the risk of vascular diseases. Arterial stiffness is an early marker for cardiovascular diseases, indicating vascular...

Twinning, slip and size effect of phase-transforming ferroelectric nanopillars

Ferroelectric materials are widely used in energy applications due to their field-driven multiferroic properties. The stress-induced phase transformation plays an important role in the functionality over repeated and consecutive operation cycles, especially at the micro/nanoscales. Here we report a systematic in-situ uniaxial compression tests on cuboidal Barium titanate (BaTiO3) nanopillars with size varying from 100 nm to 3000 nm, by which we explore the stress-induced transformation and its interplay with plastic deformation. We confirm the superelasticity achieved in pillars by martensitic phase transformation from tetragonal to orthorhombic. There exists a critical size, 330 nm, for the yield stress. Above 330 nm, martensitic phase transformation aids slip along the plane with a low Schmid factor, in turn, the pseudo-compatible twins form within the shear band. The scaling exponent of size-dependent yield strength is found to be exactly 1. For nanopillars smaller than 330 nm, no twins form, only slips with large Schmid factors are activated, and size effect vanishes. All pillars with sizes from 100 nm to 300 nm achieve the theoretical yield limit around 9 GPa. Our experimental results uncover the interplay between twins and slips in BaTiO3 nanopillars, which pave the way for the optimization of microstructure design of ferroelectric materials for microelectronic applications at small scales.

Temporal turnover in species' ranks can explain variation in Taylor's slope for ecological timeseries.

The scaling exponent relating the mean and variance of the density of individual organisms in space (i.e., Taylor's slope: zspace) is well studied in ecology, but the analogous scaling exponent for temporal datasets (ztime) is underdeveloped. Previous theory suggests the narrow distribution of ztime (e.g., typically 1-2) could be due to interspecific competition. Here, using 1694 communities time series, we show that ztime can exceed 2, and reaffirm how this can affect our inference about the stabilizing effect of biodiversity. We also develop a new theory, based on temporal change in the ranks of species abundances, to help account for the observed ztime distribution. Specifically, we find that communities with minimal turnover in species' rank abundances are more likely to have higher ztime. Our analysis shows how species-level variability affects our inference about the stability of ecological communities.

Plasma performance and operational space with an RMP-ELM suppressed edge

The operational space and global performance of plasmas with edge-localized modes (ELMs) suppressed by resonant magnetic perturbations (RMPs) are surveyed by comparing AUG, DIII-D, EAST, and KSTAR stationary operating points. RMP-ELM suppression is achieved over a range of plasma currents, toroidal fields, and RMP toroidal mode numbers. Consistent operational windows in edge safety factor are found across devices, while windows in plasma shaping parameters are distinct. Accessed pedestal parameters reveal a quantitatively similar pedestal-top density limit for RMP-ELM suppression in all devices of just over 3×1019 m−3. This is surprising given the wide variance of many engineering parameters and edge collisionalities, and poses a challenge to extrapolation of the regime. Wide ranges in input power, confinement time, and stored energy are observed, with the achieved triple product found to scale like the product of current, field, and radius. Observed energy confinement scaling with engineering parameters for RMP-ELM suppressed plasmas are presented and compared with expectations from established H and L-mode scalings, including treatment of uncertainty analysis. Different scaling exponents for individual engineering parameters are found as compared to the established scalings. However, extrapolation to next-step tokamaks ITER and SPARC find overall consistency within uncertainties with the established scalings, finding no obvious performance penalty when extrapolating from the assembled multi-device RMP-ELM suppressed database. Overall this work identifies common physics for RMP-ELM suppression and highlights the need to pursue this no-ELM regime at higher magnetic field and different plasma physical size.