Truncated Power Law Research Articles

Understanding the Size‐Dependent Photostability and Photoluminescence Intermittency of Blue‐Emitting Core/Graded Alloy/Shell “giant”‐Quantum Dots

AbstractRecently, giant quantum dots (g‐QDs) with a core/interface graded alloy shell/shell structure have shown promise in reducing photoluminescence (PL) intermittency and improving photostability. However, this approach has been mainly demonstrated with red and green emitting g‐QDs but the blue‐emitting graded alloy QDs has remained less explored. To tackle this challenge, a composition gradient method is employed to create three blue‐emitting CdZnS/CdxZn1–xS/ZnS core/interface graded alloy shell/shell (C/A/S) quantum dots (QDs) with different diameters. The sample with the largest diameter (gQD‐3) exhibits superior optical characteristics, with a photoluminescence quantum yield (PLQY) of approximately 62% and around 80% ON/radiative events at the single‐particle level. Conversely, the smallest diameter (gQD‐1) sample shows lower PLQY and only 30% radiative events with longer OFF/nonradiative events. Probability distribution analysis of PL trajectories, fitted with a truncated power law, reveals a significantly higher carrier de‐trapping rate in gQD‐3 compared to gQD‐1, attributed to its proximity to band edge trap states. Additionally, the largest diameter sample retains remarkable optical performance during 48 h of continuous UV irradiation in colloidal suspension and single‐particle levels. These findings show optimized core/shell structures, gradual alloy interfaces, and outer shell coatings can stabilize blue‐emitting quantum dots, advancing next‐gen optoelectronics.

Competition among recombination pathways in single FAPbBr3 nanocrystals.

Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence.

Power Law in Deep Neural Networks: Sparse Network Generation and Continual Learning With Preferential Attachment.

Training deep neural networks (DNNs) typically requires massive computational power. Existing DNNs exhibit low time and storage efficiency due to the high degree of redundancy. In contrast to most existing DNNs, biological and social networks with vast numbers of connections are highly efficient and exhibit scale-free properties indicative of the power law distribution, which can be originated by preferential attachment in growing networks. In this work, we ask whether the topology of the best performing DNNs shows the power law similar to biological and social networks and how to use the power law topology to construct well-performing and compact DNNs. We first find that the connectivities of sparse DNNs can be modeled by truncated power law distribution, which is one of the variations of the power law. The comparison of different DNNs reveals that the best performing networks correlated highly with the power law distribution. We further model the preferential attachment in DNNs evolution and find that continual learning in networks with growth in tasks correlates with the process of preferential attachment. These identified power law dynamics in DNNs can lead to the construction of highly accurate and compact DNNs based on preferential attachment. Inspired by the discovered findings, two novel applications have been proposed, including evolving optimal DNNs in sparse network generation and continual learning tasks with efficient network growth using power law dynamics. Experimental results indicate that the proposed applications can speed up training, save storage, and learn with fewer samples than other well-established baselines. Our demonstration of preferential attachment and power law in well-performing DNNs offers insight into designing and constructing more efficient deep learning.

Assessing internal displacement patterns in Ukraine during the beginning of the Russian invasion in 2022

Given the worldwide increase of forcibly displaced populations, particularly internally displaced persons (IDPs), it’s crucial to have an up-to-date and precise tracking framework for population movements. Here, we study how the spatial and temporal pattern of a large-scale internal population movement can be monitored using human mobility datasets by exploring the case of IDPs in Ukraine at the beginning of the Russian invasion of 2022. Specifically, this study examines the sizes and travel distances of internal displacements based on GPS human mobility data, using the combinations of mobility pattern estimation methods such as truncated power law fitting and visualizing the results for humanitarian operations. Our analysis reveals that, although the city of Kyiv started to lose its population around 5 weeks before the invasion, a significant drop happened in the second week of the invasion (4.3 times larger than the size of the population lost in 5 weeks before the invasion), and the population coming to the city increased again from the third week of the invasion, indicating that displaced people started to back to their homes. Meanwhile, adjacent southern areas of Kyiv and the areas close to the western borders experienced many migrants from the first week of the invasion and from the second to third weeks of the invasion, respectively. In addition, people from relatively higher-wealth areas tended to relocate their home locations far away from their original locations compared to those from other areas. For example, 19 % of people who originally lived in higher wealth areas in the North region, including the city of Kyiv, moved their home location more than 500 km, while only 9 % of those who originally lived in lower wealth areas in the North region moved their home location more than 500 km..

Fluid flow and solute transport simulations in tight geologic formations: Discrete fracture network and continuous time random walk analyses

Understanding the effect of fracture network heterogeneity on flow and transport in tight formations with low permeability values is of great importance in a wide variety of applications, such as groundwater pollution and storage as well as water production. Although numerous studies have investigated solute transport in fractured media, investigation about scale effects on flow and transport in low-permeability aquifers is limited. More specifically, we are not aware of any study that has addressed how the continuous time random walk (CTRW) model parameters vary with scale and fracture network properties. To this end, we performed a set of numerical simulations in sparse fracture networks of sizes L = 20, 35, and 50 m under two different volumetric fracture counts (p30 = 0.05 and 0.1) using the discrete fracture network approach. The fractures in the networks were elliptical in shape, and their radii followed a truncated power-law distribution with exponents α = 1.5, 2, and 2.5. We simulated fluid flow using the Reynolds equation, and solute transport was simulated using particle tracking. The solute transport behavior was quantified by fitting the solution of the CTRW transport equation to the arrival time distributions. Results showed that as the truncated power law exponent α increased, the permeability of the networks decreased. In all the fracture networks studied, we found non-Fickian solute transport behavior deduced from small values of β(0.69≤β≤1.25), the exponent in the truncated power-law arrival time distribution in the CTRW model. In our fracture networks, the aperture size spanned less than one order of magnitude meaning that the fracture permeability distribution was relatively narrow. Therefore, the observed non-Fickian behavior should be attributed to sparse fracture networks and low connectivity. We found that the effective permeability, keff, at p30 = 0.05 was more scale-dependent compared to that at p30 = 0.1 because the fracture networks with p30 = 0.05 were less connected and, thus, more heterogeneous. Our simulation also disclosed the scale dependence of the CTRW model parameters. We conducted multiple linear regression analysis to link the CTRW model parameters to the network size as well as the geometrical and topological properties of the network. Results of regression analysis showed that all the CTRW model parameters except the average solute velocity were significantly dependent on the system size L (p-value < 0.05). Further investigations using a broader range of fracture network properties, such as broader aperture size distributions, smaller and larger network sizes and volumetric fracture counts are still required.

Topological regularization of networks in temporal lobe epilepsy: a structural MRI study.

Patients with temporal lobe epilepsy (TLE) often exhibit neurocognitive disorders; however, we still know very little about the pathogenesis of cognitive impairment in patients with TLE. Therefore, our aim is to detect changes in the structural connectivity networks (SCN) of patients with TLE. Thirty-five patients with TLE were compared with 47 normal controls (NC) matched according to age, gender, handedness, and education level. All subjects underwent thin-slice T1WI scanning of the brain using a 3.0 T MRI. Then, a large-scale structural covariance network was constructed based on the gray matter volume extracted from the structural MRI. Graph theory was then used to determine the topological changes in the structural covariance network of TLE patients. Although small-world networks were retained, the structural covariance network of TLE patients exhibited topological irregularities in regular architecture as evidenced by an increase in the small world properties (p < 0.001), normalized clustering coefficient (p < 0.001), and a decrease in the transfer coefficient (p < 0.001) compared with the NC group. Locally, TLE patients showed a decrease in nodal betweenness and degree in the left lingual gyrus, right middle occipital gyrus and right thalamus compared with the NC group (p < 0.05, uncorrected). The degree of structural networks in both TLE (Temporal Lobe Epilepsy) and control groups was distributed exponentially in truncated power law. In addition, the stability of random faults in the structural covariance network of TLE patients was stronger (p = 0.01), but its fault tolerance was lower (p = 0.03). The objective of this study is to investigate the potential neurobiological mechanisms associated with temporal lobe epilepsy through graph theoretical analysis, and to examine the topological characteristics and robustness of gray matter structural networks at the network level.

4Ward: A relayering strategy for efficient training of arbitrarily complex directed acyclic graphs

Thanks to their ease of implementation, multilayer perceptrons (MLPs) have become ubiquitous in deep learning applications. The graph underlying an MLP is indeed multipartite, i.e. each layer of neurons only connects to neurons belonging to the adjacent layer. In contrast, in vivo brain connectomes at the level of individual synapses suggest that biological neuronal networks are characterized by scale-free degree distributions or exponentially truncated power law strength distributions, hinting at potentially novel avenues for the exploitation of evolution-derived neuronal networks. In this paper, we present “4Ward”, a method and Python library capable of generating flexible and efficient neural networks (NNs) from arbitrarily complex directed acyclic graphs. 4Ward is inspired by layering algorithms drawn from the graph drawing discipline to implement efficient forward passes, and provides significant time gains in computational experiments with various Erdős-Rényi graphs. 4Ward not only overcomes the sequential nature of the learning matrix method, by parallelizing the computation of activations, but also addresses the scalability issues encountered in the current state-of-the-art and provides the designer with freedom to customize weight initialization and activation functions. Our algorithm can be of aid for any investigator seeking to exploit complex topologies in a NN design framework at the microscale.

Uncertainty quantification for the squeeze flow of generalized Newtonian fluids

The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of uncertainty quantification (UQ) can be used to improve the predictive capabilities of rheological models in such flow scenarios. For this demonstration, we consider the squeeze flow of generalized Newtonian fluids. To systematically study uncertainties, we have developed a tailored squeeze flow setup, which we have used to perform experiments with glycerol and PVP solution. To mimic these experiments, we have developed a three-region truncated power law model, which can be evaluated semi-analytically. This fast-to-evaluate model enables us to consider uncertainty propagation and Bayesian inference using (Markov chain) Monte Carlo techniques. We demonstrate that with prior information obtained from dedicated experiments – most importantly rheological measurements – the truncated power law model can adequately predict the experimental results. We observe that when the squeeze flow experiments are incorporated in the analysis in the case of Bayesian inference, this leads to an update of the prior information on the rheological parameters, giving evidence of the need for recalibration in the considered complex flow scenario. In the process of Bayesian inference we also obtain information on quantities of interest that are not directly observable in the experimental data, such as the spatial distribution of the three flow regimes. In this way, besides improving the predictive capabilities of the model, the uncertainty quantification framework enhances the insight into complex flow scenarios.

Protocol and Software for Automated Detection of Lysosome Active "Runs" and "Flights" with Wavelet Transform Approach.

Lysosomes are highly dynamic degradation/recycling organelles that harbor sophisticated molecular sensors and signal transduction machinery through which theycontrol cell adaptation to environmental cues and nutrients. The movements of these signaling hubs comprise persistent, directional runs-active, ATP-dependent transport along the microtubule tracks-interspersed by short, passive movements and pauses imposed by cytoplasmic constraints. The trajectories of individual lysosomes are usually obtained by time-lapse imaging of the acidic organelles labeled with LysoTracker dyes or fluorescently-tagged lysosomal-associated membrane proteins LAMP1 and LAMP2. Subsequent particle tracking generates large data sets comprising thousands of lysosome trajectories and hundreds of thousands of data points. Analyzing such data sets requires unbiased, automated methods to handle large data sets while capturing the temporal heterogeneity of lysosome trajectory data. This chapter describes integrated and largely automated workflow from live cell imaging to lysosome trajectories to computing the parameters of lysosome dynamics. We describe an open-source code for implementing the continuous wavelet transform (CWT) to distinguish trajectory segments corresponding to active transport (i.e., "runs" and "flights") versus passive lysosome movements. Complementary cumulative distribution functions (CDFs) of the "runs/flights" are generated, and Akaike weight comparisons with several competing models (lognormal, power law, truncated power law, stretched exponential, exponential) are performed automatically. Such high-throughput analyses yield useful aggregate/ensemble metrics for lysosome active transport.

Sampling uncertainties of particle size distributions and derived fluxes

AbstractIn this study, we provide a method to quantify the uncertainty associated with sampling particle size distributions (PSD), using a global compilation of Underwater Vision Profiler observations (UVP, version 5). The UVP provides abundant in situ data of the marine PSD on global scales and has been used for a diversity of applications, but the uncertainty associated with its measurements has not been quantified, including how this uncertainty propagates into derived products of interest. We model UVP sampling uncertainty using Bayesian Poisson statistics and provide formulae for the uncertainty associated with a given sampling volume and observed particle count. We also model PSD observations using a truncated power law to better match the low concentration associated with rare large particles as seen by the UVP. We use the two shape parameters from this statistical model to describe changes in the PSD shape across latitude band, season, and depth. The UVP sampling uncertainty propagates into an uncertainty for modeled carbon flux exceeding 50%. The statistical model is used to extend the size interval used in a PSD‐derived carbon flux model, revealing a high sensitivity of the PSD‐derived flux model to the inclusion of small particles (80–128 μm). We provide avenues to address additional uncertainties associated with UVP‐derived carbon flux calculations.

Size distribution of the quasi-circular vegetation patches in the Yellow River Delta, China

Recent empirical studies have suggested that the patch-size distribution of vegetation can be fitted by a power law, truncated power law, or lognormal model to provide explanatory mechanisms for vegetation pattern formation in arid and semiarid regions. However, contradictory results have been reported. Therefore, additional empirical studies are necessary to test the patch-size distribution of vegetation over several regions before it can be considered as an indicator for assessing the discontinuous transition of ecosystems and understanding the mechanisms of vegetation pattern formation. Analogous to arid and semiarid regions of the world, vegetation patterns are characterized by a two-phase mosaic composed of dense vegetation patches interspersed with areas of bare soil, referred to as quasi-circular vegetation patches (QVPs), in the Yellow River Delta (YRD), China. However, research on the patch-size distribution of the QVPs reflecting vegetation patterns and ecosystem functioning is lacking. To fill this gap, for the first time, we examined the patch-size distribution of the QVPs using the fused IKONOS high-spatial-resolution image and evaluated the statistical distributions that better fit the patch size data of the QVPs in the YRD. We found that a power law, truncated power law, or lognormal distribution was not supported in the study area, whereas gamma distribution reasonably fits the size data of QVPs, implying that micro-depressions, combined with the water-limited and salinization environments had considerable effects on vegetation pattern formation. Our results provide helpful insights and suggest that further studies are needed to classify different types of QVPs. Additionally, more efficient approaches need to be used to fit the statistical distributions for elucidating the spatial vegetation patterns in the YRD.

Pacemaker translocations and power laws in 2D stem cell-derived cardiomyocyte cultures.

Power laws are of interest to several scientific disciplines because they can provide important information about the underlying dynamics (e.g. scale invariance and self-similarity) of a given system. Because power laws are of increasing interest to the cardiac sciences as potential indicators of cardiac dysfunction, it is essential that rigorous, standardized analytical methods are employed in the evaluation of power laws. This study compares the methods currently used in the fields of condensed matter physics, geoscience, neuroscience, and cardiology in order to provide a robust analytical framework for evaluating power laws in stem cell-derived cardiomyocyte cultures. One potential power law-obeying phenomenon observed in these cultures is pacemaker translocations, or the spatial and temporal instability of the pacemaker region, in a 2D cell culture. Power law analysis of translocation data was performed using increasingly rigorous methods in order to illustrate how differences in analytical robustness can result in misleading power law interpretations. Non-robust methods concluded that pacemaker translocations adhere to a power law while robust methods convincingly demonstrated that they obey a doubly truncated power law. The results of this study highlight the importance of employing comprehensive methods during power law analysis of cardiomyocyte cultures.

Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos.

Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.

基于无人机影像的阿拉善东南部荒漠灌丛植被空间格局研究

PDF HTML阅读 XML下载 导出引用 引用提醒 基于无人机影像的阿拉善东南部荒漠灌丛植被空间格局研究 DOI: 10.5846/stxb202109142585 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金项目（41771101）；中国科学院"一带一路"生态水文学团队项目（Y929731） Spatial pattern of shrub in southeast Alxa Desert based on high resolution unmanned aerial vehicle images Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:干旱区灌丛植被空间格局受多种物理和生态过程影响，能够指示生态系统的状态。研究通过量化灌丛斑块大小的空间分布来评估阿拉善高原东南部覆沙荒漠植被生态系统的状态，采用点格局分析法分析灌木种群的相互关系，以阐明不同灌木种在斑块格局形成中的作用，并结合土壤条件及下垫面粗糙度等指标验证评估的准确性，探讨灌丛空间格局差异的内在机理。结果表明，研究区样方2灌丛斑块大小符合截尾幂律分布，其他样方符合对数正态分布，前者的空间结构及生境条件均优于后者，说明植被空间格局可以准确表征生态系统状态。在局地尺度上灌木种内和种间呈现不同的相互关系，以竞争关系为主导是导致斑块破碎化的主要驱动机制。小灌木（如猫头刺）的种内互利关系有利于促进多样化斑块形态的形成，而大灌木（如沙冬青和蒙古扁桃）种间的互利作用则有利于形成异质性更强的复杂空间格局。基于灌丛斑块的空间格局评估生态系统状态，可为保护和恢复生态脆弱区受损植被提供重要的借鉴。 Abstract:The vegetation spatial pattern in drylands, which is dictated by various physical and ecological processes, could be interpreted as an indicator of the ecosystem state. According to the statistical analysis of shrub patch size distribution, we estimated the ecosystem state of desert vegetation in the southeast of the Alxa Plateau. The interactions among shrub populations were shown by point pattern analysis, to illustrate that different species might act as various ingredients in patchiness. Soil properties and roughness of underlying surface were surveyed to support the estimation. Ultimately, the internal mechanism of the differentiation of shrub spatial pattern was discussed. The results show that the truncated power law is the best fitting model for the patch sizes distribution in quadrat 2, while the lognormal distribution is the best for others. Assessment of ecosystem states is verified by the comparation of habitat conditions, which shows that quadrat 2 is better too. The interaction at small scales between shrubs varies with different species, competition dominated relationship is the main reason for the narrowing down of patch size distribution. The positive relationship within species of small patch size, such as Oxytropis aciphylla, is conducive to the formation of diversified patches, whereas species of large patch size with facilitation at small scales, such as Ammopiptanthus mongolicus and Prunus mongolica, give rise to a complex pattern. Sound management should consider to comprise assessment of ecosystem states through shrub spatial patterns, which will provide indications of conservation and restoration of vulnerable vegetation. 参考文献 相似文献 引证文献

Feedback mechanisms between precipitation and dissolution reactions across randomly heterogeneous conductivity fields

Abstract. Our study investigates interplays between dissolution, precipitation, and transport processes taking place across randomly heterogeneous conductivity domains and the ensuing spatial distribution of preferential pathways. We do so by relying on a collection of computational analyses of reactive transport performed in two-dimensional systems where the (natural) logarithm of conductivity is characterized by various degrees of spatial heterogeneity. Our results document that precipitation and dissolution jointly take place in the system, with the latter mainly occurring along preferential flow paths associated with the conductivity field and the former being observed at locations close to and clearly separated from these. High conductivity values associated with the preferential flow paths tend to further increase in time, giving rise to a self-sustained feedback between transport and reaction processes. The clear separation between regions where dissolution or precipitation takes place is imprinted onto the sample distributions of conductivity which tend to become visibly left skewed with time (with the appearance of a bimodal behavior at some times). The link between conductivity changes and reaction-driven processes promotes the emergence of non-Fickian effective transport features. The latter can be captured through a continuous-time random-walk model where solute travel times are approximated with a truncated power law probability distribution. The parameters of such a model shift towards values associated with increasingly high non-Fickian effective transport behavior as time progresses.

Experimental Research on the Thresholds of Scale-Dependent Dispersivity of Solute Transport

Abstract The conventional advection-dispersion equation (ADE) has been widely used to describe the solute transport in porous media. However, it cannot interpret the phenomena of the early arrival and long tailing in breakthrough curves (BTCs). In this study, we aim to experimentally investigate the behaviors of the solute transport in both homogeneous and heterogeneous porous media. The linear-asymptotic model (LAF solution) with scale-dependent dispersivity was used to fit the BTCs, which was compared with the results of the ADE model and the conventional truncated power-law (TPL) model. Results indicate that (1) the LAF model with linear scale-dependent dispersivity could better capture the evolution of BTCs than the ADE model; (2) dispersivity initially increases linearly with the travel distance and is stable at some limited value over a large distance, and a threshold value of the travel distance is provided to reflect the constant dispersivity; and (3) compared with the TPL model, both the LAF and ADE models can capture the behavior of solute transport as a whole. For fitting the early arrival, the LAF model is less than the TPL; however, the LAF model is more concise in mathematics and its application will be studied in the future.

The extended generalized radial flow model and effective conductivity for truncated power law variograms

Pumping tests are established for characterizing spatial average properties of aquifers. At the same time, they are promising tools to identify heterogeneity characteristics such as log-conductivity variance and correlation scales. We present the extended Generalized Radial Flow Model (eGRF) which combines the characterization of well flow in fractal geometry with an upscaled conductivity for pumping tests in heterogeneous media. We show that the eGRF is a generalization of previously solutions, such as that of Barker, Butler and Neuman. We derive effective conductivities for uniform and well flow conditions in heterogeneous log-normal media with a truncated power law correlation structure through the upscaling procedure Coarse Graining. The radial-dependent effective conductivity for well flow reflects the gradual change of heterogeneity impact on average pumping test drawdowns. We then combine upscaled conductivities with the eGRF model to determine the effective pumping test solution. We provide a proof of concept by comparing theoretical upscaling results with Monte Carlo well flow simulations in heterogeneous fractal fields. The eGRF and upscaling results are implemented and made freely available as python code for transport simulation as well as pumping test analysis.

Influence of Clay on Solute Transport in Saturated Homogeneous Mixed Media

In this study, four homogeneous porous media (HPM1-HPM4), consisting of distinct proportions of sand-sized and clay-sized solid beads, were prepared and used as single fracture infills. Flow and nonreactive solute transport experiments in HPM1-HPM4 under three flow rates were conducted, and the measured breakthrough curves (BTCs) were quantified using conventional advection-dispersion equation (ADE), mobile-immobile model (MIM), and continuous time random walk (CTRW) model with truncated power law transition time distribution. The measured BTCs showed stronger non-Fickian behaviour in HPM2-HPM4 (which had clay) than in HPM1 (which had no clay), implying that clay enhanced the non-Fickian transport. As the fraction of clay increased, the global error of ADE fits also increased, affirming the inefficiency of ADE in capturing the clay-induced non-Fickian behaviour. MIM and CTRW performed better in capturing the non-Fickian behaviour. Nonetheless, CTRW’s performance was robust. 12.5% and 25% of clay in HPM2 and HPM3, respectively, decreased the flowing fluid region and increased the solute exchange rate between the flowing and stagnant fluid regions in MIM. For CTRW, the power law exponent ( β CTRW ) values were 1.96, 1.75, and 1.63 in HPM1-HPM3, respectively, implying enhanced non-Fickian behaviour. However, for HPM4, whose clay fraction was 50%, the β CTRW value was 1.87, implying a deviation in the trend of non-Fickian enhancement with increasing clay fraction. This deviation indicated that non-Fickian behaviour enhancement depended on the fraction of clay present. Moreover, increasing flow rate enhanced the non-Fickian transport based on β CTRW .

Coin wear: A power law for small shocks

The study of coin wear is useful for numismatics and economics. We examine a 19th century gold coin with a SEM and show that weight loss is due to a large number of small shocks that follow a truncated power law. Under the compound Poisson process we propose, weight loss over time is nearly deterministic in the proportion of time actually spent in circulation.

Characteristics and controlling factors of alpine grassland vegetation patch patterns on the central Qinghai-Tibetan plateau

Vegetation patch patterns, which are used as indicators of state, functionality, and catastrophic changes in the arid ecosystem, have received much attention. However, little is known about the controlling factors and indicators that underlie vegetation patch patterns in the alpine grassland ecosystem. Here, we firstly studied characteristics of vegetation patch patterns with aerial photography by using an unmanned aerial vehicle and evaluated the vegetation patch-size distribution with power law (PL) and truncated power law (TPL) models on the central part of the Qinghai-Tibetan Plateau (QTP). We then investigated the effects of environmental factors and biotic disturbances on vegetation patch patterns. The results showed that (1) there were four typical vegetation patch patterns, i.e. spot, stripe, sheet, and uniform patterns; (2) soil water content and air temperature were major environmental factors affecting vegetation patch patterns; (3) biotic disturbance of plateau pika (Ochotona curzoniae) affected vegetation patch patterns by changing the number, area, and connectivity of vegetation patches; and (4) vegetation patch-size distribution parameters were significantly related to soil hydrothermal variables (P < 0.01). We concluded that the development of alpine vegetation patch patterns was controlled by soil hydrothermal conditions and plateau pika’s disturbance. We also proposed that γ (TPL-PL) (difference between absolute values of slopes of TPL and PL curve fits) could serve as an effective indicator for monitoring alpine grassland conditions, and preventing patchiness was a critical task for the alpine ecosystem management and restoration.