Scaling Exponents Research Articles

Exposure, body size, and zooplankton overland dispersal capacity

AbstractThe dormant life stages of freshwater zooplankton are generally resistant to environmental exposure, and this facilitates their overland dispersal. However, environmental exposure and overland dispersal are less well studied for the active life stages of freshwater zooplankton. To characterize empirically the longevity of active life stages out of water, survival time to air exposure was measured in the laboratory for seven cladoceran species using heartbeat cessation to signify survival time. Survival time increased with body dry weight with an allometric scaling exponent near 2/3 in both a single‐species model with Daphnia mendotae and a multispecies model with five bivalved species that included Bosmina longirostris, Acroperus harpae, Ceriodaphnia dubia, D. mendotae, and Daphnia magna. The 2/3 scaling exponent is consistent with Euclidean geometry and points to water loss across the surface of a spherical body as the cause. Survival time of a 6th species, Holopedium gibberum, was 618% longer than predictions based on the multispecies model, likely due to its gelatinous mantle. Survival time of a 7th species, Bythotrephes cederströmii, was 58–83% shorter than predictions based on the multispecies model, likely due to its lack of a bivalve carapace. The longest survival time of an individual was 225.4 min (H. gibberum). Results suggest that at landscape scales, body size could be a proxy for the geographic extent of overland dispersal capacity of the active life stage.

Thermodynamic constraints and exact scaling exponents of flocking matter

Thermodynamic constraints and exact scaling exponents of flocking matter

A Monte Carlo study on a 3-dimensional comb polymer translocation through a nanopore driven by an electric field

Abstract A lattice Monte Carlo simulation study of the translocation of comb polymers through a nanopore subjected to an electric field is presented. The translocation dynamics was extensively studied in terms of the applied electric field strength, the pore size, and the comb polymer topology. The variations of the most probable translocation time $\tau_p$ and the mean translocation time \mt\ as a function of the applied electric field strength show distinct features, the latter exhibiting a nonmonotonic dependence on the electric field. We were able to show the existence of a critical field strength $\delta \epsilon_c$ defined by the narrowest distribution of the translocation time, which is closely related to the size of the nanopore. In addition, we have found that the critical field strength also defines a transition point between two regimes of translocation: a smooth translocation for a field strength below $\delta \epsilon_c$ and a chaotic translocation for a field strength above $\delta \epsilon_c$. Moreover, for the smallest pore size ($r_p = 1$), monomers can only cross the nanopore in a single file, while for larger pores different modes of polymer translocation are identified. Finally, the dependence of the mean translocation time on the backbone length is governed by a power law relationship $\left < \tau \right > \sim {N_B}^{\alpha}$, where the scaling exponent $\alpha$ is found to be in the range of 1.3--1.7 for the set of side chain lengths and nanopore sizes investigated. As for the side chain length $N_S$, the mean translocation time is found to follow a linear dependence $\left < \tau \right > \sim {N_S}$.

Experimental study of convective heat transfer with a multi-scale roughness

The heat transfer in a turbulent Rayleigh-Bénard convection with a multi-scale roughness at the bottom is studied experimentally. Two different regimes for the heat transfer are found. The first regime has scaling exponent γI=0.4 and corresponds to the reduced values of the Nusselt number. The second regime with enhanced values of the Nusselt number has a scaling exponent γII=0.32, which is noticeably larger than in the case of smooth boundaries. Significant variation in the Prandtl number (from 6.4 to 62) does not change the scaling exponent value of the second regime but increases the values of Nusselt number. The scaling exponent for the relation Re∼Raα is insensitive to the change of the heat transfer regime and is close to 1/2 for all values of Ra. The characteristic ratio of the velocity pulsations to the mean velocity does not depend on the Rayleigh number and is characterized by close values (about 0.8). The local temperature measurements support the mechanism of the transition from the reduced Nusselt number regime to the enhanced one, which is based on the formation of flows between obstacles.

Dissipation at limited resolutions: power law and detection of hidden dissipative scales

Abstract Non-equilibrium systems, in particular, living organisms, are maintained by irreversible transformations of energy that drive diverse functions. Quantifying their irreversibility, as measured by energy dissipation, is essential for understanding the underlying mechanisms. However, existing techniques usually overlook experimental limitations, either by assuming full information or by employing a coarse-graining method that requires knowledge of the structure behind hidden degrees of freedom. Here, we study the inference of dissipation from finite-resolution measurements by employing a recently developed model-free estimator that considers both the sequence of coarse-grained transitions and the waiting time distributions: σ 2 = σ 2 ℓ + σ 2 t . The dominant term σ 2 ℓ originates from the sequence of observed transitions. We find that it scales with resolution following a power law. Comparing the scaling exponent with a previous estimator highlights the importance of accounting for flux correlations at lower resolutions. σ 2 t comes from asymmetries in waiting time distributions. It is non-monotonic in resolution, with its peak position revealing characteristic scales of the underlying dissipative process, consistent with observations in the actomyosin cortex of starfish oocytes. Alternatively, the characteristic scale can be detected in a crossover of the scaling of σ 2 ℓ . This provides a novel perspective for extracting otherwise hidden characteristic dissipative scales directly from dissipation measurements. We illustrate these results in biochemical models as well as complex networks. Overall, this study highlights the significance of resolution considerations in non-equilibrium systems, providing insight into the interplay between experimental resolution, entropy production and underlying complexity.

Exploring the intermittency of magnetohydrodynamic turbulence by synchrotron polarization radiation

Context. Magnetohydrodynamic (MHD) turbulence plays a critical role in many key astrophysical processes, such as star formation, acceleration of cosmic rays, and heat conduction. However, its properties are still poorly understood. Aims. In this work, we explore how to extract the intermittency of compressible MHD turbulence from synthetic and real observations. Methods. We used three statistical methods, namely the probability distribution function, kurtosis, and scaling exponent of the multi-order structure function, to reveal the intermittency of MHD turbulence. Results. Our numerical results demonstrate that: (1) the synchrotron polarization intensity statistics can be used to probe the intermittency of magnetic turbulence, by which we can distinguish different turbulence regimes; (2) the intermittency of MHD turbulence is dominated by the slow mode in the sub-Alfvénic turbulence regime; and (3) the Galactic interstellar medium (ISM) in the low latitude region corresponds to the sub-Alfvénic and supersonic turbulence regime. Conclusions.We have successfully measured the intermittency of the Galactic ISM from synthetic and realistic observations.

Tensor networks for p-spin models

We introduce a tensor network algorithm for the solution of p-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the “easy” phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the p-spin model through lossless compression, all without explicit knowledge of the problem’s structure.

Folding behaviors of two-dimensional flexible polymers.

Unlike one-dimensional polymers, the theoretical framework on the behaviors of two-dimensional (2D) polymers is far from completeness. In this study, we model single-layer flexible 2D polymers of different sizes and examine their scaling behaviors in solution, represented by Rg ∼ Lν, where Rg is the radius of gyration and L is the side length of a 2D polymer. We find that the scaling exponent ν is 0.96 for a good solvent and 0.64 for under poor solvent condition. Interestingly, we observe a previously unnoticed phenomenon: under intermediate solvent conditions, the 2D polymer folds to maintain a flat structure, and as L becomes larger, multiple folded structures emerge. We introduce a shape parameter Q to diagram the relationship of folded structures with the polymer size and solvent condition. Theoretically, we explain the folding transitions by the competition between bending and solvophobic free energies.

Multifractal Analysis for Evaluating the Representation of Clouds in Global Kilometer‐Scale Models

AbstractClouds are one of the largest sources of uncertainty in climate predictions. Global km‐scale models need to simulate clouds and precipitation accurately to predict future climates. To isolate issues in their representation of clouds, models need to be thoroughly evaluated with observations. Here, we introduce multifractal analysis as a method for evaluating km‐scale simulations. We apply it to outgoing longwave radiation fields to investigate structural differences between observed and simulated anvil clouds. We compute fractal parameters which compactly characterize the scaling behavior of clouds and can be compared across simulations and observations. We use this method to evaluate the nextGEMS ICON simulations via comparison with observations from the geostationary satellite GOES‐16. We find that multifractal scaling exponents in the ICON model are significantly lower than in observations. We conclude that too much variability is contained in the small scales leading to less organized convection and smaller, isolated anvils.

Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling

Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling

Some unique anatomical scaling relationships among genera in the grass subfamily Pooideae.

Members of the grass family Poaceae have adapted to a wide range of habitats and disturbance regimes globally. The cellular structure and arrangements of leaves can help explain how plants survive in different climates, but these traits are rarely measured in grasses. Most studies are focussed on individual species or distantly related species within Poaceae. While this focus can reveal broad adaptations, it is also likely to overlook subtle adaptations within more closely related groups (subfamilies, tribes). This study, therefore, investigated the scaling relationships between leaf size, vein length area (VLA) and vessel size in five genera within the subfamily Pooideae. The scaling exponent of the relationship between leaf area and VLA was -0.46 (±0.21), which is consistent with previous studies. In Poa and Elymus, however, minor vein number and leaf length were uncorrelated, whereas in Festuca these traits were positively correlated (slope = 0.82±0.8). These findings suggest there are broad-scale and fine-scale variations in leaf hydraulic traits among grasses. Future studies should consider both narrow and broad phylogenetic gradients.

CHANG-ES. XXXIII. A 20 kpc radio bubble in the halo of the star-forming galaxy NGC 4217

Cosmic rays may be dynamically very important in driving large-scale galactic winds. Edge-on galaxies give us an outsider's view of radio haloes, and of their extra-planar cosmic-ray electrons and magnetic fields. We present a new radio continuum imaging study of the nearby edge-on galaxy NGC\,4217. We examine the distribution of extra-planar cosmic rays and magnetic fields. We observed it with both the Jansky Very Large Array (JVLA) in the $S$ band (2--4\,GHz) and the LOw Frequency ARray (LOFAR) at 144\,MHz. We measured vertical intensity profiles and exponential scale heights. We re-imaged both the JVLA and LOFAR data at matched angular resolution in order to measure radio spectral indices between 144\,MHz and 3\,GHz. Confusing point-like sources were subtracted prior to imaging. We then fitted intensity profiles with cosmic-ray electron advection models, using an isothermal wind model that is driven by a combination of pressure from the hot gas and cosmic rays. We discover a large-scale radio halo on the north-western side of the galactic disc. The morphology is reminiscent of a bubble extending up to 20\,kpc from the disc. We find spectral ageing in the bubble, which allowed us to measure the advection speeds of the cosmic-ray electrons, which accelerate from 300 to $600\ $. Assuming energy equipartition between the cosmic rays and the magnetic field, we estimate the bubble may have been inflated by a modest 10\,<!PCT!> of the kinetic energy injected by supernovae over its dynamical timescale of 35\,Myr. While no active galactic nucleus (AGN) has been detected, such activity in the recent past cannot be ruled out. Non-thermal bubbles with sizes of tens of kiloparsecs may be a ubiquitous feature of star-forming galaxies, and if so this would demonstrate the influence of feedback. Determining possible contributions by AGN feedback will require deeper observations.

Scaling properties of (2+1) directed polymers in the low-temperature limit

Abstract In terms of the replica method, we consider the low-temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows us to compute the scaling exponent θ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that θ = 1 / 4 , which is slightly different to the zero-temperature numerical value that is close to 0.241.

Ligand presentation controls collective MSC response to matrix stress relaxation in hybrid PEG-HA hydrogels

Cell interactions with the extracellular matrix (ECM) influence intracellular signaling pathways related to proliferation, differentiation, and secretion, amongst other functions. Herein, bone-marrow derived mesenchymal stromal cells (MSCs) are encapsulated in a hydrazone crosslinked hyaluronic acid (HA) hydrogel, and the extent of stress relaxation is controlled by systemic introduction of irreversible triazole crosslinks. MSCs form elongated multicellular structures within hydrogels containing RGD peptide and formulated with elastic composition slightly higher than the hydrogel percolation threshold (12 % triazole, 88 % hydrazone). A scaling analysis is presented (<RgStructure2>12 ∼Nα) to quantify cell-material interactions within these structures with the scaling exponent (α) describing either elongated (0.66) or globular (0.33) structures. Cellular interactions with the material were controlled through peptides to present integrin binding ECM cues (RGD) or cadherin binding cell-cell cues (HAVDI) and MSCs were observed to form highly elongated structures in RGD containing hydrogels (α=0.56±0.05), whereases collapsed structures were observed within HAVDI containing hydrogels (α=0.39±0.04). Finally, cytokine secretion was investigated, and a global increase in secreted cytokines was observed for collapsed structures compared to elongated. Taken together, this study presents a novel method to characterize cellular interactions within a stress relaxing hydrogel where altered cluster morphology imparts changes to cluster secretory profiles.

Comparative Analysis of Linear and Nonlinear sEMG Methods for Detecting Muscle Fatigue During Dynamic Biceps Curls

Muscle fatigue, a key concern in sports science, rehabilitation, and occupational health, influences performance, injury risk, and provides insights into muscle functionality and endurance. Surface electromyography (sEMG) has emerged as a vital tool for non-invasively tracking muscle electrical activity and gauging health. As its application for muscle fatigue assessment grows, identifying the most accurate analytical methods is essential. Current sEMG analyses employ both linear and nonlinear metrics to measure fatigue onset and progression, yet research is ongoing to determine which method is most effective in the context of dynamic contractions. The study was aimed to evaluate the efficacy of established linear and nonlinear methods in measuring muscle fatigue caused by dynamic contractions through surface electromyography (sEMG) signals. A group of twelve healthy individuals completed biceps curls at a consistent pace of one repetition per four seconds, which constituted 75% of their 10-repetition maximum. Concurrently, sEMG signals were captured from the biceps brachii muscle at 1000 Hz. To assess the sEMG signals during the initial, middle, and final sets of 10 repetitions, three linear metrics—mean frequency, median frequency, and spectral moment ratio (SMR)—along with two nonlinear approaches, namely sample entropy and detrended fluctuation analysis (DFA), were utilized. The study's outcomes indicated notable shifts in the SMR values and the two DFA-derived scaling exponents across the exercise sets. These results indicated that SMR, sample entropy, and DFA are effective in gauging muscle fatigue, with sample entropy and DFA demonstrating heightened sensitivity to the fatigue levels when compared to the linear metrics.

Nondirect-Product Local Diabatic Representation with Smolyak Sparse Grids.

Modeling nonadiabatic conical intersection dynamics is critical for understanding a wide range of photophysical, photochemical, and biological phenomena. Here we develop a nonadiabatic conical intersection wave packet dynamic method in the local diabatic representation using Smolyak sparse grids. Employing sparse grids avoids the direct-product grids in configuration space and alleviates the exponential scaling of computation costs with the molecular size. Numerical demonstrations are first performed for a two-dimensional vibronic model of pyrazine, where the results using sparse grids are in excellent agreement with those using direct-product grids, with sparse grids being much faster. Moreover, we demonstrate that for a four-dimensional pyrazine model, where direct-product grids are computationally infeasible, sparse grids can provide almost exact results. The sparse grid local diabatic representation method is further applied to a realistic model system of phenol photodissociation with much more complex potential energy surfaces; the results using sparse grids still agree very well with the direct-product grids. Finally, by combining with electronic structure calculations, we apply our method to the Shin-Metiu model without quasi-diabatization. The sparse grid and direct-product grid results are in good agreement, with the sparse grid computational cost being half of the full grid.

Neural-network approach to running high-precision atomic computations

Modern applications of atomic physics, including the determination of frequency standards and the analysis of astrophysical spectra, require prediction of atomic properties with exquisite accuracy. For complex atomic systems, high-precision calculations are a major challenge due to the exponential scaling of the involved electronic configuration sets. This exacerbates the problem of required computational resources for these computations and makes indispensable the development of approaches to select the most important configurations out of otherwise intractably huge sets. We have developed a neural-network (NN) tool for running high-precision atomic configuration interaction (CI) computations with iterative selection of the most important configurations. Integrated with the established atomic codes, our approach results in computations with significantly reduced computational requirements in comparison with those without NN support. We showcase a number of NN-supported computations for the energy levels of Fe16+ and Ni12+ and demonstrate that our approach can be reliably used and automated for solving specific computational problems for a wide variety of systems. Published by the American Physical Society 2024

MEDOC: A fast, scalable and mathematically exact algorithm for the site-specific prediction of the protonation degree in large disordered proteins.

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched in positively and negatively charged residues. While it is often convenient to assume these residues follow their model-compound pK a values, recent work has shown that local charge effects (charge regulation) can upshift or downshift sidechain pK a values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N , scales as ∼2 N . This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed MEDOC (Multisite Extent of Deprotonation Originating from Context) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytic, Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q -canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pK a values across the entire DisProt database. Our results show differences in the distribution of predicted pK a values for different amino acids, in agreement with NMR-measured distributions in proteins.

Size-frequency distribution of submarine mass movements on the Palomares continental slope (W Mediterranean)

In this work, over 3620 km2 from the Palomares continental slope, which is located in the W. Mediterranean Sea, was analysed to quantify the impact of recent mass movements on this margin. A total of 936 landslides were identified, mapped and characterised by defining several morphometric variables that outline the accumulated impact of landslides equivalent to 918 km2 and 10.34 km3 of eroded sediment on the continental slope. The smallest event area was 0.0014 km2, whereas the largest event area was 32.48 km2. Smaller scars with a higher headwall gradient tend to dominate when the environment is steeper, and major mass movements are located on open slopes and structural highs. However, the slight or null correlations between variables indicate that a wide range of sizes may occur on any slope gradient and at any depth.The Palomares continental slope is intensively affected by mass movements. Compared with other passive margins (e.g., the U.S. Atlantic continental margin), landslides mobilised a limited amount of sediment, although it is comparable to other Mediterranean areas where small- to moderate-sized events are characteristic.The cumulative size distribution can be defined by a power-law function that describes events larger than 0.7 km2 with an exponent of α = 1.269. These results are consistent with those of other published inventories, including onshore cases. This result allows us to assume that the scale-invariant properties of the events are mapped. Scale-invariant properties can be explained by different models; self-organised criticality (SOC) is probably the most assumed by the scientific community, although alternative models may be nominated. Each model has important implications in terms of the landslide distribution and long-term landslide history of any slope. Alternative scenarios, such as submarine slopes, with more precise landslide inventories may contribute to new hazard assessment models that consider scaling exponents derived from size–frequency distributions.

Scale dependence of local shearing motion in decaying turbulence generated by multiple-jet interaction

Scale dependence of local shearing motion is investigated experimentally in decaying homogeneous isotropic turbulence generated through multiple-jet interaction. The turbulent Reynolds number, based on the Taylor microscale, is between approximately 900 and 400. Velocity fields, measured using particle image velocimetry, are analysed through the triple decomposition of a low-pass filtered velocity gradient tensor, which quantifies the intensities of shear and rigid-body rotation at a given scale. These motions manifest predominantly as layer and tubular vortical structures, respectively. The scale dependence of the moments of velocity increments, associated with shear and rigid-body rotation, exhibits power-law behaviours. The scaling exponents for shear are in quantitative alignment with the anomalous scaling of the velocity structure functions, suggesting that velocity increments are influenced predominantly by shearing motion. In contrast, the exponents for rigid-body rotation are markedly smaller than those predicted by Kolmogorov scaling, reflecting the high intermittency of rigid-body rotation. The mean flow structure associated with shear at intermediate scales is investigated with conditional averages around locally intense shear regions in the filtered velocity field. The averaged flow field exhibits a shear layer structure with aspect ratio approximately 4.5, surrounded by rotating motion. The analysis at different scales reveals the existence of self-similar structures of shearing motion across various scales. The mean velocity jump across the shear layer increases with the layer thickness. This relationship is well predicted by Kolmogorov's second similarity hypothesis, which is useful in predicting the mean characteristics of shear layers across a wide range of scales.