Exponential Patterns Research Articles

Kinetic analysis of the self-discharge of the NiOOH OER active phase in KOH electrolyte: insights from in-situ Raman and UV–Vis reflectance spectroscopies

NiOOH has been established as the active phase of NiO-based electrocatalysts in the alkaline Oxygen Evolution Reaction (OER). Here, we investigate the self-discharge behavior of NiOOH electrodes under open circuit potential (OCP) conditions in 1 M KOH electrolyte by monitoring phase changes via in-situ Raman and UV–Vis reflectance spectroscopies and performing kinetic analyses on the OCP and spectroscopic data. Our findings reveal a linear phase change from NiOOH to Ni(OH)2 over time, indicative of a 0th-order reduction reaction. Contrarily, the OCP evolution associated with this phase reduction displayed a combination of linear and exponential decay patterns as a result of various kinetics, including Faradaic processes and diffusion-controlled mechanisms, influencing the self-discharge potential over 1.25 V (vs RHE). An additional linear region at lower potentials (<1.25 V (vs RHE)) suggests that charge redistribution due to the phase change from α-Ni(OH)2 to β-Ni(OH)2 dominates the self-discharge, a behavior confirmed by in-situ UV–Vis reflectance spectroscopy. These findings highlight the effectiveness of combining in-situ Raman and UV–Vis spectroscopy with electrochemical data for real-time monitoring of electrochemical processes, here potential-dependent electrocatalyst phase changes, leading to a more detailed and accurate understanding of the dynamic behavior, phase change kinetics, and self-discharge behaviors of solid electrocatalysts that can guide the design of more efficient and durable energy storage and conversion materials.

Rogue waves of the Nizhnik-Novikov-Veselov equation via self-mapping transformation

This paper introduces a new two-dimensional self-mapping transformation applied to the Nizhnik-Novikov-Veselov equation, resulting in the generation of numerous rogue wave solutions. We discover that temporal-localized and spatiotemporal-localized two-dimensional rogue waves respectively. Notably, these rogue waves emerge from a zero background and subsequently exhibit both algebraic and exponential decay patterns. The proposed technique offers a potential tool for constructing rogue-like waves within (2+1)-dimensional nonlinear wave frameworks. The findings presented here serve as a robust mathematical foundation for advancing both theoretical understanding and practical applications of rogue waves.

Sigmoidal heart rate response pattern during exercise in patients with chronic heart failure.

Detailed heart rate (HR) response patterns during exercise in patients with heart failure (HF) and sinus rhythm remain uncertain. We screened consecutive patients with HF who underwent cardiopulmonary exercise tests at a large academic center from November 2013 to July 2023. HR response during exercise was statistically classified using logistic differential equation models. A total of 99 patients were included. Of them, 75 patients were assigned to "sigmoidal pattern" and the other 24 to "exponential pattern." Patients with the sigmoidal pattern were older and exhibited higher plasma B-type natriuretic peptide levels. Increases in HR and oxygen consumption (V̇o2)/kg up to the anaerobic threshold level were not different between both patterns. However, beyond the threshold, the sigmoidal pattern group showed no further increase in HR and significantly lower V̇o2/kg than their counterparts (interactions for P < 0.001). HR response during exercise in patients with heart failure and sinus rhythm was categorized into two unique groups: sigmoidal and exponential patterns. More detailed clarification of the sigmoidal pattern, potentially indicating sinus node dysfunction, should offer new clinical insights for chronotropic incompetence.NEW & NOTEWORTHY Heart rate response patterns can be classified into two groups among patients with chronic heart failure reaching maximal exertion: sigmoidal and exponential.

Ten-Year Clinical Outcomes of V4c Implantable Collamer Lens Implantation: Longitudinal Analysis of Visual Acuity, Endothelial Cell Density, and Vault Dynamics

This study aimed to evaluate the long-term clinical outcomes of V4c Implantable Collamer Lens (ICL) implantation for myopia correction over a 10-year period. Retrospective interventional case series METHODS: This retrospective interventional study involved 103 myopic eyes from 54 patients. Visual outcomes, including visual acuity and manifest refraction were assessed. Annual measurements of endothelial cell density (ECD), vault, anterior chamber depth, and intraocular pressure were analyzed using mixed-effects models. At the 10-year follow-up, the mean Logarithm of the Minimum Angle of Resolution (logMAR) uncorrected distance visual acuity and corrected distance visual acuity (CDVA) were -0.037 ± 0.052 and -0.041 ± 0.046, respectively. The mean efficacy and safety indices were 1.11 ± 0.13 and 1.12 ± 0.12. A loss of one line of CDVA occurred in 2% of cases, while 59% gained one or more lines. Postoperative manifest refraction spherical equivalent (MRSE) was within ±0.5 diopters (D) and ±1.0 D in 74% and 99% of cases, respectively, with a mean MRSE of -0.19 ± 0.41 D. Data for ECD and vault fit an exponential decay model, demonstrating a continuous yet gradually slowing decrease over time. Decay rates were 0.012 ± 0.001 per year for ECD and 0.056 ± 0.003 per year for the vault. Notably, ECD lower outliers had significantly lower preoperative ECD values. There were no instances of cataract formation, angle closure, glaucoma, or ICL removal throughout the study. The 10-year outcomes of V4c ICL implantation demonstrate effective and safe visual results. Both ECD and vault exhibit exponential decay patterns over the decade. Patients with lower preoperative ECD values require careful post-implantation monitoring.

Exploring the similarity relationships from the nondimensionalization of atmospheric turbulence

Nondimensionalization, a theoretical approach for establishing interconnections among parameters within a set of equations, has proven to be an effective tool for the analysis of atmospheric turbulence. By applying nondimensionalization to turbulence equations, a concise form of dimensionless turbulence functions can be obtained. This process also yields several dimensionless parameters, defined as combinations of characteristic scales. From the dimensionless tensor B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${B}$$\\end{document} and vector βθ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\varvec{\\beta}}}_{\ heta}$$\\end{document} introduced in this study, the characteristic length scale, zs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${z}^{s}$$\\end{document}, can be defined as an alternative of length scale in similarity theories. Using the data from observational station in Horqin Sandy Land, quantified verifications of similarity relationships are carried out. The dimensionless parameters derived from nondimensionalization is not only in accordance with traditional turbulence theories but also facilitate the derivation of relationships among other dimensionless parameters. This reveals new similarity relationships that supplement the Monin–Obukhov theory. Under conditions of flat terrain and steady motions, the new length scale gives rise to similarity relationships exhibiting “4/3” exponential and near-linear patterns, which are associated with turbulent transport. These results make it possible to obtain the turbulent fluxes directly from the statistics of meteorological elements, even in stable stratifications. Consequently, the method of nondimensionalization can be taken as a reference in parameterization schemes of turbulence and climate models, and is fruitful in prospect of further study on atmospheric turbulence.

Degradation of fenitrothion by a falling-film plasma reactor

The contamination of surface water with organophosphates is an environmental concern due to their acute toxicity to wildlife and humans. This study reports an evaluation of the efficacy of a falling-film plasma reactor (FFPR) for degrading fenitrothion, which is an organophosphate insecticide and a simulant for nerve agents. An FFPR setup was demonstrated to effectively degrade fenitrothion in aqueous solutions. The degradation kinetics of the aqueous fenitrothion was found to follow an exponential decaying function and to have a destruction removal efficiency (DRE) of up to 95% within 60 min. The effectiveness of the FFPR treatment was attributed to its ability to efficiently generate reactive oxygen species, particularly hydroxyl radicals, to oxidize fenitrothion and byproducts. Four transient intermediate products from the fenitrothion degradation reaction were detected and identified. Their concentrations were found to increase in the first ca.15 min of the reaction and then follow exponential decay patterns. Quantum chemical calculations revealed that hydroxyl radicals react with fenitrothion through three major pathways. The first pathway involves the attack of the hydroxyl radical at the phosphorus atom and the subsequent leaving of the 3-methyl-4-nitrophenol radical, leading to two major products observed in experiments. The second pathway involves the hydrogen abstraction by hydroxyl radicals at the methoxy groups on the phosphorus atom and converts the methoxy groups to hydroxyl groups, resulting in a major product in experiments. The third pathway involves the hydrogen abstraction by hydroxyl radicals at the methyl group on the nitrophenol ring and converts the methyl group to a carboxyl group, resulting in another major product detected in experiments.

Assessment of the dynamic growth and potassium solubilization capability of three novel bacteria

Abstract. Bangun IH, Ketaren BR, Munar A, Sembiring P, Nurhajijah, Abdi A, Sitorus RS. 2024. Assessment of the dynamic growth and potassium solubilization capability of three novel bacteria. Biodiversitas 25: 177-185. Clay minerals are essential components that play a crucial role in soil cation exchangeable capacity and optimal plant growth. These components, including potassium (K), have the ability to bind with mineral crystals in the soil. Several studies have shown that K-solubilizing bacteria can facilitate the solubility of potassium, leading to optimal availability. However, the use of bacteria as biofertilizers is still limited due to challenges related to survival and growth patterns. To address these challenges, it is important to monitor the growth of the microbes and enhance their selection process to achieve effective utilization. Therefore, this study aimed to determine the bacterial growth dynamics and potential of Burkholderia paludis IHB_01, Burkholderia cepacia IHB_02, and Paraburkholderia phymatum IHB_03 in enhancing soil cation availability on clay minerals. The results showed a common initial adaptation phase among the 3 bacterial strains, followed by distinct exponential growth patterns. Burkholderia cepacia IHB_02 had the longest exponential growth phase, showing efficient resource utilization and extended growth. The results of soil cation enhancement by these bacteria showed that there were no major changes in measured parameters, such as total K, CEC, pH, and organic carbon. Furthermore, the variation in K exchange, organic carbon, and Na exchange provided insights into their unique interactions in the soil. The non-significant impact on potassium-related parameters in this study could be attributed to the presence of antagonistic cation interactions.

GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software (https://github.com/gchowell/forecasting_growthmodels), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Circular economy-based integrated farming system for indigenous chicken: Fostering food security and sustainability

Addressing the global challenge of food security necessitates innovative and sustainable approaches capable of meeting the demands of a growing population while ensuring a sufficient and nutritious food supply. This study explores circular economy-based integrated farming systems for indigenous chicken, focusing on the principles of circular economy, TBL approach and sustainable agriculture to enhance the food security landscape. To comprehensively assess the status of the indigenous chicken sector, a detailed analysis of farm operations is conducted. Qualitative data collection and a system dynamics approach provided valuable insights into the intricate dynamics of the system. Leveraging simulation and modelling, interactions and behaviours within the sub-systems are unveiled, ultimately leading to the integration of forward and reverse value chain linkages. The Indigenous Chicken-based Integrated Farming System value chain, developed because of this study, offers a transformative model for sustainable food production. This model provides clear insights into the dynamics of indigenous chicken farming, highlighting the importance of circular economy principles. It also aids in understanding the impact of varying parameters, such as egg production and parent chicken population, on the system's behavior. Moreover, the research identifies exponential growth patterns in critical components, shedding light on the system's scalability potential. Additionally, it emphasizes the significance of integrating forward and reverse linkages in achieving sustainability and minimizing waste throughout the value chain.

Segmented superimposed model of near-bore reservoir pollution skin factor for low porosity and permeability sandstone horizontal gas wells

Drilling and completion processes can often result in reservoir contamination around the wellbore, leading to decreased oil and gas productivity and significant economic losses for the oil field. This issue is particularly complex in sandstone reservoirs with low porosity and permeability horizontal wells, wherein traditional models have limited accuracy and applicability due to numerous unknown parameters. To address this challenge, this study focuses on non-uniform pollution around horizontal wells and proposes a new approach to divide the horizontal well pollution area into N micro-element sections. By establishing a seepage differential equation and employing the similar flow substitution method, we construct models for the pollution skin coefficient of each micro-element section as well as the total pollution skin coefficient. Furthermore, we combine empirical equation models and an oscillation-decreasing function model to develop a pollution radius distribution model that encompasses linear, parabolic, exponential, and logarithmic patterns. Through these advancements, we can realize a comprehensive reservoir damage assessment method. It is verified that the calculation error of this model is very small, and the influence of skin effect and reservoir anisotropy and the radius distribution of various heterogeneous pollution zones are fully considered. These findings indirectly suggest the rationality and practicality of the model presented in this paper. By incorporating actual gas well data into this model, it has been determined through discussion and analysis that the exponential distribution of the pollution radius has the greatest impact on the pollution skin factor along the horizontal well, from the heel to the toe. Increasing the pollution radius and decreasing the pollution permeability both result in an increase in the skin factor of the micro-segment and the total pollution skin factor of the horizontal well. However, compared to the pollution permeability, the radius of the pollution zone has a relatively minor effect on the total pollution skin factor. The proposed technique aims to serve as a valuable tool in optimizing and designing stimulation measures aimed at boosting production and minimizing formation damage. Through evaluation and analysis to reduce risks, protect reservoirs and extend well life, reduce costs, and enhance technical capabilities and economic benefits.

Exploring intrinsic distribution of phytoplankton relative abundance and biomass in combination with continental-scale field investigation and microcosm experiment

Phytoplankton are primary producers in aquatic ecosystems and their diversity directly affects the community stability and primary productivity. However, the commonly used diversity indices (such as Shannon and Pielou indices) were originally derived from other fields rather than ecology and did not have a direct biological explanatory function. There is still a need to incorporate biological explanatory functions into diversity evaluation methods and theories to bridge the gap between phytoplankton biodiversity and biological characteristics. This study aimed to explicate the intrinsic distribution patterns of phytoplankton relative abundance and biomass. Our study demonstrated an exponential distribution pattern of phytoplankton relative abundance and biomass ranking through field investigations of 367 phytoplankton samples in China and microcosm experiments, respectively. Microcosm experiments illustrated that the linear distribution of the specific growth rate ranking resulted in an exponential distribution of the relative phytoplankton biomass ranking due to exponential growth patterns. Through mathematical deduction, it was found that the three indices a, k and N in the exponential distribution could be considered as the critical relative abundance of extinction, competition coefficient and the environmental taxa capacity, respectively. We found that a was positively correlated with Shannon index and Pielou index, k was negatively correlated with Shannon index, Pielou index and Chao1 index. In addition, N and Chao1 index were almost exactly the same. Our study obtained these indices based on the distribution pattern of phytoplankton, enabling a comprehensive analysis of the phytoplankton community and providing novel insights for further evaluating the health of aquatic ecosystems.

Association between intraprocedural drops in blood pressure and infarct growth rate patterns after acute large-vessel occlusions

BackgroundInfarct growth rate (IGR) differs among patients with acute ischemic stroke due to large vessel occlusion (LVO-AIS), and this variability has critical clinical repercussions. We explored IGR patterns and their...

Modelling recall-based competing risks data with k different models

In competing risks model, subjects are exposed to failure due to more than one cause. In this study, we develop a model for recall-based competing risks data when the causes associated with time to event are assumed to follow different distributions respectively. The chances of an individual recalling an event will be high if elapsed time between monitoring time and time to event is less. This information is utilized by taking non-recall probability as a function of this elapsed time. For point estimation, an expectation-maximization based algorithm is developed. For interval estimation, we construct the observed Fisher information matrix by using the missing information principle. The study is further extended to the Bayesian paradigm under suitable choices of prior distributions. The samples from full conditionals are drawn using a Gibbs sampling-based algorithm. To assess the performance of proposed estimators, an extensive simulation study is carried out for different proportions of non-recall and censored data with varying sample sizes under uniform and exponential monitoring patterns. Finally, the median duration of breastfeeding cessation for US women is estimated.

Monochromatic exponential triples: An ultrafilter proof

We present a short ultrafilter proof of the existence of monochromatic exponential triples { a , b , b a } \{a, b, b^a\} in any finite coloring of the natural numbers. We then generalize the construction and prove a new result on the existence of infinite monochromatic exponential patterns.

Comparison of damping models for kink oscillations of coronal loops

ABSTRACT Kink oscillations of solar coronal loops are of intense interest due to their potential for diagnosing plasma parameters in the corona. The accurate measurement of the kink oscillation damping time is crucial for precise seismological diagnostics, such as the transverse density profile, and for the determination of the damping mechanism. Previous studies of large-amplitude rapidly decaying kink oscillations have shown that both an exponential damping model and a generalized model (consisting of Gaussian and exponential damping patterns) fit observed damping profiles sufficiently well. However, it has recently been shown theoretically that the transition from the decaying regime to the decayless regime could be characterized by a superexponential damping model. In this work, we reanalyse a sample of decaying kink oscillation events, and utilize the Markov chain Monte Carlo Bayesian approach to compare the exponential, Gaussian–exponential, and superexponential damping models. It is found that in 7 out of 10 analysed oscillations, the preferential damping model is the superexponential one. In two events, the preferential damping is exponential, and in one it is Gaussian–exponential. This finding indicates the plausibility of the superexponential damping model. The possibility of a non-exponential damping pattern needs to be taken into account in the analysis of a larger number of events, especially in the estimation of the damping time and its associated empirical scalings with the oscillation period and amplitude, and in seismological inversions.

ACCd and PGPRs: increasing plant productivity for more sustainable agricultural practices

Our current world population is nearly 8 billion people, and it is expected to reach 10 billion by the year 2055 (Schultz, 2018). As the population continues to experience exponential growth patterns, we are faced with increasing concerns regarding food security. Indeed, as of 2020, millions of people are experiencing hunger or food insecurity, especially those in Africa, Latin America, the Caribbean, and Asia (FAO, 2021). A great deal of food insecurity is indirectly caused by climate change because product yield is not sufficient to reach increasing food demands (FAO, 2021). Climate change is causing warmer winters and unpredictable precipitation, resulting in poor growing conditions for crops (Wheaton &amp; Kulshreshtha, 2017; Qian et al., 2011). In order to achieve high quality and quantity product yield, crops require rich soil conditions generated by sufficient periods of rainfall. This article discusses the effects of climate change on agriculture, with emphasis on aminocyclopropane-1-carboxylic acid deaminase (ACCd), an enzyme that plays an important role in increasing drought and salinity tolerance in plants.

Mining Top-k Frequent Patterns in Large Geosocial Networks: A Mnie-Based Extension Approach

Frequent pattern mining (FPM) has played an important role in many graph domains, such as bioinformatics and social networks. In this paper, we focus on geo-social graphs, a kind of social network augmented by geographical information. However, in addition to the exponential time complexity of the problem, we face the challenge of efficient subgraph retrieval since we are interested in patterns in a specific region in such a network. For this reason, we formulate the top-k FPM problem in large geo-social networks. Specifically, we devise a novel framework for subgraph retrieval and FPM mining with a series of optimizations. First, we propose a neighboring-aware R-tree (NaR-Tree) index structure to alleviate the challenge of retrieving subgraphs from a large graph. NaR-Tree is a variant of R-tree in which each nonleaf tree node further maintains some edge statistics information for the rectangle related to it. Second, we define the concept of minimum image-based support of edges (MNIE). With the help of the NaR-Tree and MNIE-based pattern extension approach, a mining algorithm that addresses the problem of exponential candidate patterns is proposed. We also present a lazy retrieval strategy to reduce the frequency of subgraph retrieval. Finally, we adopt an edge sampling approach to further accelerate the mining process. Extensive experiments on real-world and synthesized datasets are conducted to demonstrate the effectiveness and efficiency of our solution.

Volumetric Growth and Growth Curve Analysis of Residual Intracranial Meningioma.

After meningioma surgery, approximately 1 in 3 patients will have residual tumor that requires ongoing imaging surveillance. The precise volumetric growth rates of these tumors are unknown. To identify the volumetric growth rates of residual meningioma, growth trajectory, and factors associated with progression. Patients with residual meningioma identified at a tertiary neurosurgery center between 2004 and 2020 were retrospectively reviewed. Tumor volume was measured using manual segmentation, after surgery and at every follow-up MRI scan. Growth rates were ascertained using a linear mixed-effects model and nonlinear regression analysis of growth trajectories. Progression was defined according to the Response Assessment in Neuro-Oncology (RANO) criteria (40% volume increase). There were 236 patients with residual meningioma. One hundred and thirty-two patients (56.0%) progressed according to the RANO criteria, with 86 patients being conservatively managed (65.2%) after progression. Thirteen patients (5.5%) developed clinical progression. Over a median follow-up of 5.3 years (interquartile range, 3.5-8.6 years), the absolute growth rate was 0.11 cm 3 per year and the relative growth rate 4.3% per year. Factors associated with residual meningioma progression in multivariable Cox regression analysis were skull base location (hazard ratio [HR] 1.60, 95% CI 1.02-2.50) and increasing Ki-67 index (HR 3.43, 95% CI 1.19-9.90). Most meningioma exhibited exponential and logistic growth patterns (median R 2 value 0.84, 95% CI 0.60-0.90). Absolute and relative growth rates of residual meningioma are low, but most meet the RANO criteria for progression. Location and Ki-67 index can be used to stratify adjuvant treatment and surveillance paradigms.

Forward and back diffusion of reactive contaminants through multi-layer low permeability sediments

Contaminants stored in the low permeability sediments will continue to threaten the adjacent shallow groundwater system after the aquifer is remediated. Understanding the storage and discharge behavior of contaminants in the aquitards is essential for the efficient remediation of contaminated sites, but most of the previous analytical studies focused on nonreactive solutes in a single homogenous aquitard. This study presents novel analytical solutions for the forward and back diffusion of contaminants through multi-layer low permeability sediments considering abiotic and biotic environmental degradation. Three representative source depletion patterns (i.e., instantaneous, linear, and exponential patterns) were selected to describe the dissolution of dense non-aqueous phase liquids (DNAPL) in the aquifer more realistically. At the forward diffusion stage, the mass storage of contaminants in the aquitards with the instantaneous pattern is the largest, nearly twice that with the exponential pattern. A simple equivalent homogeneous model is generally adopted in the risk assessment. However, relative to the proposed multi-layer model, it will significantly underestimate the onset of the back-diffusion of heterogeneous aquitards and overestimate the persistence of aquifer plumes. The previously-reported semi-infinite boundary assumption is also not applicable, with a maximum error of over 200% in the long-term prediction of back diffusion behavior of a thin aquitard. Moreover, when the degradation half-life is less than 16 years, less than 10% of the contaminants stored in the aquitards will diffuse into the overlying aquifer, suggesting that biostimulation or bioaugmentation can effectively mitigate back-diffusion risk. Overall, the proposed diffusion-reaction coupled model with multi-layer media is of great value and high demand in predicting the back-diffusion behavior of heterogeneous aquitards and guiding the soil bioremediation.

Long-Distance Pollen Dispersal in Urban Green Roof and Ground-Level Habitats

Long-distance pollen dispersal is critical for gene flow in plant populations, yet pollen dispersal patterns in urban habitats such as green roofs have not been extensively studied. Pollen dispersal patterns typically are assessed either by fitting non-linear models to the relationship between the degree of pollen dispersal and distance to the pollen source (i.e., curve fitting), or by fitting probability density functions (PDFs) to pollen dispersal probability histograms (i.e., PDF fitting). Studies using curve fitting typically report exponential decay patterns in pollen dispersal. However, PDF fitting typically produces more fat-tailed distributions, suggesting the exponential decay may not be the best fitting model. Because the two approaches may yield conflicting results, we used both approaches to examine pollen dispersal patterns in the wind-pollinated Amaranthus tuberculatus and the insect-pollinated Solanum lycopersicum at two green roof and two ground-level sites in the New York (NY, United States) metropolitan area. For the curve fitting analyses, the exponential decay and inverse power curves provided good fits to pollen dispersal patterns across both green roof and ground-level sites for both species. Similar patterns were observed with the PDF fitting analyses, where the exponential or inverse Gaussian were the top PDF at most sites for both species. While the curve fitting results are consistent with other studies, the results differ from most studies using PDF fitting, where long-distance pollen dispersal is more common than we observed. These results highlight the need for further research to compare curve and PDF fitting for predicting pollen dispersal patterns. And, critically, while long-distance pollen dispersal may be an important component of overall pollen dispersal for A. tuberculatus and S. lycopersicum in both urban green roof and ground-level sites, our results suggest it potentially may occur to a lesser extent compared with plants in less-urban areas.