Statistical Behavior Research Articles

Block approximations for probabilistic mixtures of elementary cellular automata

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied, making the study of their phase diagrams particularly interesting. The block approximation method, also known in this context as the local structure approach, is a powerful tool for studying the main features of these diagrams, improving upon Mean Field results. This work considers systems with multiple stationary states, aiming to understand how their interactions give rise to the structure of the phase diagram. Additionally, it shows how a simple algorithmic implementation of the block approximation allows for the effective study of the phase diagram even in the presence of several absorbing states.

Post-Hatching Development of Posture and Behavior in the Barn Owl (Tyto alba): From a General Behavioral Pattern of Vertebrates to the Typical Owl Behavior.

Hatching captive barn owl chicks underwent four developmental phases. In the first 10 days (phase 1), behavior consisted of lateral movements that gradually changed to forward progression and peaked a few days before and after eye-opening. This behavior resembled a general developmental pattern that characterizes other vertebrates. Chicks also underwent a postural change, from head bent underneath the ventrum to resting on the rear end of the trunk with the head lifted in the air. Then, once their eyes were opened, chicks became more stationary and preoccupied with visual exploration, manifested in lateral head movements and peering episodes (phase 2, until day 20). The latter behavior, which is also typical of mature owls when not on the wing, characterized the chicks' behavior after post-hatching day 20 (phase 3), when their flight and contour feathers grew, along with shedding the down plumage and standing tall. Development culminated in active flight, first observed by days 50-60 (phase 4). Altogether, during post-hatching development, barn owl chicks gradually shifted from egg posture to the adult upright body posture. At the same time, their behavior consisted of speciation from the general developmental pattern to the typical stationary barn owl behavior, and, finally, flight was incorporated.

Lattice polymers near a permeable interface

Abstract We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on one side or by the application of a force to manipulate the polymer. Different combinations of these three effects give slightly different statistical mechanical behaviours. The canonical lattice model of polymers is the self-avoiding walk which we mainly study with Monte Carlo simulation to calculate the phase diagram and critical phenomena. For comparison, a solvable directed walk version is also defined and the phase diagrams are compared for each case. We find broad agreement between the two models, and most minor differences can be understood as due to the different entropic contributions. In the limit where the bulk solvent on one side is overwhelmingly preferred we see how the localisation transition transforms to the adsorption transition; the permeable interface becomes effectively an impermeable surface.

Device-measured stationary behaviour and cardiovascular and orthostatic circulatory disease incidence.

Previous studies have indicated that standing may be beneficially associated with surrogate metabolic markers, whereas more time spent sitting has an adverse association. Studies assessing the dose-response associations of standing, sitting and composite stationary behaviour time with cardiovascular disease (CVD) and orthostatic circulatory disease are scarce and show an unclear picture. To examine associations of daily sitting, standing and stationary time with CVD and orthostatic circulatory disease incidence. We used accelerometer data from 83 013 adults (mean age ± standard deviation = 61.3 ± 7.8; female = 55.6%) from the UK Biobank to assess daily time spent sitting and standing. Major CVD was defined as coronary heart disease, heart failure and stroke. Orthostatic circulatory disease was defined as orthostatic hypotension, varicose vein, chronic venous insufficiency and venous ulcers. To estimate the dose-response hazard ratios (HR) we used Cox proportional hazards regression models and restricted cubic splines. The Fine-Gray subdistribution method was used to account for competing risks. During 6.9 (±0.9) years of follow-up, 6829 CVD and 2042 orthostatic circulatory disease events occurred. When stationary time exceeded 12 h/day, orthostatic circulatory disease risk was higher by an average HR (95% confidence interval) of 0.22 (0.16, 0.29) per hour. Every additional hour above 10 h/day of sitting was associated with a 0.26 (0.18, 0.36) higher risk. Standing more than 2 h/day was associated with an 0.11 (0.05, 0.18) higher risk for every additional 30 min/day. For major CVD, when stationary time exceeded 12 h/day, risk was higher by an average of 0.13 (0.10, 0.16) per hour. Sitting time was associated with a 0.15 (0.11, 0.19) higher risk per extra hour. Time spent standing was not associated with major CVD risk. Time spent standing was not associated with CVD risk but was associated with higher orthostatic circulatory disease risk. Time spent sitting above 10 h/day was associated with both higher orthostatic circulatory disease and major CVD risk. The deleterious associations of overall stationary time were primarily driven by sitting. Collectively, our findings indicate increasing standing time as a prescription may not lower major CVD risk and may lead to higher orthostatic circulatory disease risk.

China’s container freight prices on the global behavior of inflation rate after COVID-19

The main objective of this article is to analyze the relationship between increases in freight costs and inflation in the markets due to the increases reflected in the prices of the products in some economies in destination ports such as the United States, Europe, Japan, South Africa, the United Arab Emirates, New Zealand and South Korea. We use fractionally integrated methods and Granger causality test to calculate the correlation between these indicators. The results indicate that, after a significant drop in inflation in 2020, probably due to the confinement caused by the pandemic, the increases observed in inflation and freight costs are expected to be transitory given their stationary behavior. We also find a close correlation between both indicators in Europe, the United States and South Africa.

Particle response to oscillatory flows at finite Reynolds numbers

The response of spherical particles to oscillatory fluid flow forcing at finite Reynolds numbers exhibits significant deviations from classical analytical predictions due to nonlinear convective contributions. This study employs finite element simulations to explore the long-term (stationary) behavior of such particles across a wide range of conditions, including various external and particle Reynolds numbers, Strouhal numbers, and fluid-to-particle density ratios. Key contributions of this work include determining the range of validity of Tchen's equation of motion for infinitesimal and finite Reynolds numbers and correlating particle response for a wide range of density ratios and flow conditions at high frequency oscillations. This work introduces a modified form of the history drag term in a newly proposed Lagrangian equation of motion. The new equation incorporates a parameter-dependent fractional-order derivative tailored to accommodate nonlinearities due to convective effects. These novel correlations not only extend the operational range of existing model equations but also provide accurate estimates of particle response under a range of external flow conditions, as validated by comparison with numerical solutions of the Navier–Stokes flow around the particles.

Reporting and communication of sample size calculations in adaptive clinical trials: a review of trial protocols and grant applications

BackgroundAn adaptive design allows modifying the design based on accumulated data while maintaining trial validity and integrity. The final sample size may be unknown when designing an adaptive trial. It is therefore important to consider what sample size is used in the planning of the study and how that is communicated to add transparency to the understanding of the trial design and facilitate robust planning. In this paper, we reviewed trial protocols and grant applications on the sample size reporting for randomised adaptive trials.MethodWe searched protocols of randomised trials with comparative objectives on ClinicalTrials.gov (01/01/2010 to 31/12/2022). Contemporary eligible grant applications accessed from UK publicly funded researchers were also included. Suitable records of adaptive designs were reviewed, and key information was extracted and descriptively analysed.ResultsWe identified 439 records, and 265 trials were eligible. Of these, 164 (61.9%) and 101 (38.1%) were sponsored by industry and public sectors, respectively, with 169 (63.8%) of all trials using a group sequential design although trial adaptations used were diverse.The maximum and minimum sample sizes were the most reported or directly inferred (n = 199, 75.1%). The sample size assuming no adaptation would be triggered was usually set as the estimated target sample size in the protocol. However, of the 152 completed trials, 15 (9.9%) and 33 (21.7%) had their sample size increased or reduced triggered by trial adaptations, respectively.The sample size calculation process was generally well reported in most cases (n = 216, 81.5%); however, the justification for the sample size calculation parameters was missing in 116 (43.8%) trials. Less than half gave sufficient information on the study design operating characteristics (n = 119, 44.9%).ConclusionAlthough the reporting of sample sizes varied, the maximum and minimum sample sizes were usually reported. Most of the trials were planned for estimated enrolment assuming no adaptation would be triggered. This is despite the fact a third of reported trials changed their sample size. The sample size calculation was generally well reported, but the justification of sample size calculation parameters and the reporting of the statistical behaviour of the adaptive design could still be improved.

Living anionic copolymerization of 1,3-pentadiene isomers with alpha-methylstyrene in the presence of 2,2-di(2-tetrahydrofuryl)propane

The synthesis of statistical copolymers of alpha-methylstyrene (AMS) and 1,3-pentadiene (PD) isomers in the presence of 2,2-di(2-tetrahydrofuryl)propane (DTHFP) by living carbanionic polymerization was investigated in this paper. To the best of our knowledge, either AMS or PD monomer was rather difficult to homopolymerize in non-polar solvents without the help of polar additives even at high temperature due to its low ceiling temperature or relatively high electron cloud density of the conjugated CC double bond. However, the combination of RLi initiator and DTHFP regulator (0.1<DTHFP/Li < 0.5) allowed the rapid synthesis of the well-defined poly(AMS-stat-PD) with controlled molar masses (up to 32.5 kDa) and relatively narrow molecular weight distributions (1.10 < ĐMs < 1.52). Calculation of reactivity ratios by the Kelen–Tüdos method suggested that AMS copolymerized much more readily to with (Z)-1,3-pentadiene (ZP) than with (E)-1,3-pentadiene (EP) under the same conditions, whereas the EP/AMS copolymer exhibited much lower dispersity. 1H NMR results indicated that the polymer chain was found to be a mixture of 1,2-addition and 1,4-addition units, in the absence of 3,4-units. Kinetic experiments also showed that the apparent activation energy of EP/AMS copolymerization was slightly higher than that of the ZP/AMS case. To ensure complete conversion of the monomer, the feed ratio of AMS (fAMS) must be controlled to be within 0.3. In addition, the incorporation rate of AMS into the polymer chain increased with the increase in the feed ratio of AMS monomer. DSC curves showed that the Tg of the resulting copolymers increased gradually and could reach up to 25 °C (FAMS = 47). Based on the observation of the anionic statistical copolymerization behavior, an interpretation of the formation mechanism is presented here.

A novel stationary behaviour of nonlinear wave patterns for the (2 + 1)-dimensional 2-component coupled Maccari’s system

A novel stationary behaviour of nonlinear wave patterns for the (2 + 1)-dimensional 2-component coupled Maccari’s system

Diffusion across a concentration step: Strongly nonmonotonic evolution into thermodynamic equilibrium

Dynamical and statistical behaviour of the ionic particles in dissolved salts have long been known, but their hydration shells still raise unsettled questions. We engineered a “diffusion tunnel diode” that is structurally analogous to the well-known Esaki diode, but now concentration gradients serve as generalized voltages and the current means particle flow. In an equipartition sense, the hydrated ions enter a cavity as individual particles and later, upon increase of their concentration therein, they lose water molecules that henceforth are particles of their own. These temporarily attached water molecules thus are the tunnel current analogue. Unlike the original tunnel diode, our negative differential resistance has implications for the second law of thermodynamics, due to thermal effects of changes in the hydration shells.

Enhancement of the impacts 2050 model to enable a whole system sustainability assessment of rideshare

Emerging concepts, such as Mobility as a Service (MaaS), could evolve to provide sustainable mobility, especially in densely populated urban areas. However, recent studies highlight the challenge of evaluating how the complex interactions of user demographics, mode choice, vehicle automation, governance, and efficiency will impact the sustainability of future mobility. Given this challenge, this research identifies a whole system (STEEP - social, technical, economic, environmental, and political) framework as essential to assess the overall sustainability of emergent urban mobility systems such as rideshare. The need is a single tool that can rapidly explore the long-range sustainability impact of such alternative future mobility scenarios for a given city region. This paper documents enhancements made to Impacts 2050, a strategic-level model of urban mobility, to address this need, including updates to the statistical travel behavior model and the addition of rideshare including trip occupancy. Results obtained with the enhanced Impacts 2050 showed that, while rideshare use increased significantly for some scenarios, its overall mode share remained limited. In addition, though rideshare enabled users to shed car ownership, the overall percentage increase of “no car ownership” was low. An urban mobility sustainability scorecard based on STEEP and generated by output from the enhanced Impacts 2050 is presented.

Total Magnetic Field Perturbations at Martian Low Altitudes (≤500 km): MAVEN Observations in 2014–2023

AbstractMagnetic perturbations in the Martian ionosphere are often considered as representing plasma irregularities, but thorough statistical comparisons between the two independent phenomena have been rarely conducted. In this study, we investigate the statistical relationship between total magnetic field perturbations and those of O2+ density as observed by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft at altitudes below 500 km in 2014–2023. From the 1 Hz time series of magnetic field strength, perturbation intensity is estimated by subtracting a signal smoothed with a Savitzky‐Golay filter (window size ∼36 km). Statistically, the magnetic perturbations are stronger on the dayside than at night, in the local summer hemisphere than in winter, and away from crustal magnetic anomalies than nearby. Also, day‐to‐day variability of the magnetic perturbations exhibits a weak but significant correlation with that of solar wind electron density. The statistical behavior of total magnetic field perturbations is not the same as that of O2+ density perturbations: that is, the former is not a perfect proxy for the latter. The seemingly counter‐intuitive discrepancy can be explained by effects of inhomogeneous background magnetic field strength (participating in total pressure balance across plasma perturbations) and localized ionospheric currents at altitudes unreachable by MAVEN.

Tagged particle behavior in a harmonic chain of direction-reversing active Brownian particles

Abstract We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant k, rotation diffusion coefficient D R , and directional reversal rate γ. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time-scales, k − 1 , D R − 1 and γ −1, the strength of the spring constant k relative to D R and γ gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth t ν , where the value of the exponent ν depends on the specific regime. For a quenched initial orientation, the exponent ν crosses over from 3 to 1 / 2 , via intermediate values 5 / 2 or 1, depending on the specific coupling limits. However, for the annealed initial orientation, ν crosses over from 2 to 1 / 2 via an intermediate value 3 / 2 or 1 for the strong coupling limit and the weak coupling limit, respectively. An additional time-scale t N = N 2 / k emerges for a system with a finite number of oscillators N. We show that the behavior of the tagged particle variance across tN can be expressed in terms of a crossover scaling function, which we find exactly. Moreover, we study the velocity autocorrelation. Finally, we characterize the stationary state behavior of the separation between two consecutive particles by calculating the corresponding spatio-temporal correlation function.

Overview of Endovascular Treatment of Infra Renal Abdominal Aortic Aneurysms Over the Last 21 Years in Brazil

Introduction: Endovascular treatment of abdominal aortic aneurysms (EVAR) has emerged as an innovative therapeutic alternative with significant growth potential. Despite its advantages, factors such as costs, short- and long-term benefits and patient characteristics are still being analyzed and make it difficult to increase the number of these procedures when compared to the traditional open technique. Objectives: To describe the statistical behavior of endovascular treatment for AAA repair over the last 21 years in Brazil. Materials and Methods: Retrospective and descriptive study of data available in the DataSUS database, where variables relating to the number of hospitalizations, number of deaths, average length of stay and hospital and professional costs were analyzed. Results: Among the 1,618 hospitalizations for endovascular treatment of abdominal aortic aneurysms in Brazil between 2002 and 2023, 680 occurred in the South region, followed by the Southeast region with 674 hospitalizations. The mortality rate was 7.94% in this period and the number of deaths was 130. The highest number of deaths was recorded in the Southeast, while the highest mortality rates were in the North and Midwest, 66.67 and 47, respectively. Discussion: The results showed regional inequalities and the influence of socio-economic indices on access to healthcare in Brazil, so that the more economically developed regions showed better results in terms of hospitalizations and mortality. Conclusion: Although the study has limitations, it showed a growing trend in the use of EVAR in Brazil, with the South and Southeast regions having better results in terms of hospitalizations and mortality, while the North and Midwest regions had lower hospitalization rates and higher mortality rates, pointing to underreporting and limited access to advanced treatments.

Parameter identification of vibratory conveying systems including statistical part behavior

This work presents a complete workflow for the parameter identification of an MBS model representing a vibratory conveying system. First, the MBS model built within the multibody dynamics tool HOTINT is shown. Essential components, such as contact modeling and adaptive time step control, are explained in detail. The model includes a considerable amount of parameters that need to be identified. Altough, this model is fully deterministic, the complex contact dynamics can cause major effect on results by minor parameter variations. Thus, parameter variations usually show statistical variance, which is characteristic for real conveying processes too. For parameter identification it is important to detect parameters that significantly correlate with results. A method that allows to distinguish significant and non-significant parameters is presented. The application to the multibody system shows that stiffness, restitution and sliding friction of the contact model are the essential parameters. Next, the parameter identification is discussed with particular attention to multimodal distributions, that can occur in conveying systems. Furthermore, the integration of statistics into the deterministic simulation model is discussed. In order to demonstrate the applicability of the proposed methods, a parameter identification is performed based on measurement data of a single part on a real conveying system in the development site of STIWA Automation GmbH. Finally, the validity of the fully parametrized simulation model is shown by investigating geometric adjustments of the conveyor. In order to further verify the identified set of parameters, a conveying process with multiple parts is analyzed and compared in measurement and simulation.

Performance Evaluation of UOWC Systems from an Empirical Channel Model Approach for Air Bubble-Induced Scattering.

Underwater optical wireless communication (UOWC) systems provide the potential to establish secure high-data-rate communication links in underwater environments. The uniqueness of oceanic impairments, such as absorption, scattering, oceanic turbulence, and air bubbles demands accurate statistical channel models based on empirical measurements for the development of UOWC systems adapted to different types of water and link conditions. Recently, generalized Gamma and a mixture of two generalized Gamma probability density functions (PDF) were proposed to describe the statistical behavior of small and large air bubbles, respectively, when considering several levels of particle-induced scattering. In this paper, we derive novel closed-form analytic expressions to compute the bit error rate (BER) and outage performance using both proposed PDFs for various scattering conditions. Furthermore, simple asymptotic expressions are obtained to determine the diversity order of each scenario. Monte Carlo simulation results verify the obtained theoretical expressions. Our results also reveal that UOWC systems present lower BER and outage performance under more turbid water cases with respect to the tap water case due to the higher diversity order and despite the significant increases in pathloss at short link distances. Particle-induced scattering provides an inherent mechanism of turbid waters to mitigate air bubble-induced fluctuations and light blockages.

Long-term trends and probability distribution functions of air pollutant concentrations in the megacity of São Paulo

Air quality conditions in many urban areas have improved in the last decades as a consequence of air pollution control policies and regulations. Mitigation strategies have been successful in reducing the concentration of primary pollutants like inhalable particulate matter (PM10), but the control of secondary pollutants like tropospheric ozone (O3) is still challenging in megacities like the Metropolitan Area of São Paulo (MASP) in Brazil. To support the development of effective mitigation strategies, it is crucial to characterize the statistical behavior of air pollutant concentrations and its long-term evolution. Probability Density Functions (PDF) can be useful to model site-specific air quality conditions, providing estimates for the frequency of extreme pollution events and exceedance of air quality standards. The current study aims to characterize which PDF model better fits and characterizes the variability of PM10 and O3 concentrations in the MASP. For that, daily maximum moving average concentrations were analyzed between 2000 and 2023, characterizing the long-term trends and the frequency of exceedance of air quality standards. PM10 concentrations followed a lognormal PDF, with an expected value of 31 ± 15 µg.m-3. O3 followed a Gamma PDF, with an expected value of 68 ± 25 µg.m-3. A consistent long-term decrease was observed for PM10 (-1.04 ± 0.09 µg.m-3.yr-1), while O3 showed an increasing trend of 0.51 ± 0.04 µg.m-3.yr-1 in the summer. In recent years (2021-2023), the probability of exceedance of the World Health Organization guideline was 17.4 and 11.0%, respectively, for PM10 and O3. In 2020, a statistically significant increase in O3 expected values was observed, possibly associated with changes in the emission patterns of precursors due to the mobility restrictions imposed by the COVID-19 pandemic.

The Impact of “Negligible” Cross-Loadings in Investigations of Measurement Invariance with MGCFA and MGESEM

Measurement invariance (MI) is an essential part of validity evidence concerned with ensuring that tests function similarly across groups, contexts, and time. Most evaluations of MI involve multigroup confirmatory factor analyses (MGCFA) that assume simple structure. However, recent research has shown that constraining non-target indicators to zero when cross-loadings are present results in biased estimates of latent variable associations. Using Monte Carlo simulation, we investigate the behavior of fit statistics for identifying non-invariance when the target measurement model is the same for both groups, and the source of non-invariance is the presence and magnitude of non-zero cross-loadings in one group, but not in another. We consider differences between MGCFA and multigroup ESEM (MGESEM), and combined and separate group tests of configural invariance. Implications for applied researchers are provided.

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Investigating battery black mass leaching performance as a function of process parameters by combining leaching experiments and regression modeling

The current paper investigates the leaching phenomena of industrially produced Li-ion battery waste in hydrometallurgical recycling processes. Specifically, it studies the leaching reactions of NMC111-type (LiNi1/3Mn1/3Co1/3O2) black mass, as well as the statistical behavior of cathode material leaching yields under varying process conditions. The investigated process variables include reductive agent concentrations (Fe2+, Cu, H2O2) as well as process temperature, whereas S/L ratio (200 g/L) and initial acidity (2 M H2SO4) were kept constant. At lower temperatures (T = 30 °C), copper was found to act as the predominant reductant, enabled by the presence of sufficient solution iron concentrations (≥0.4 g/L Fe). Conversely, at higher temperatures (T ≥ 50 °C), the reductive capability of aluminum was substantially increased due to its decreased tendency for passivation. In contrast to copper, dissolved iron did not notably affect the reductive behavior of aluminum. The efficiency of metallic reductants initially present within the black mass was high, reaching cathode metal leaching yields above 90 % at 70 °C. A predictive leaching model for black mass leaching yields was built via regression analysis and can be used to indicate pregnant leach solution (PLS) composition – via leaching yields – after two hours of processing as a function of the investigated process variables. The model showed leaching temperature to be the most impactful parameter, while also indicating a higher reductive efficiency of copper when compared to equimolar additions of H2O2. As a case example, LFP (LiFePO4) cathode powder was also investigated as an alternative reductant/catalysis species (Fe2+) source in the system and was found to increase cathode metal leaching yields almost as much as FeSO4 while also resulting in a remarkable increase in Al dissolution in the process.