Constant Rate Of Change Research Articles

Structural performance evaluation of an aged structure using a modified plasticity model in inverse solution method

In this research, the trends of degradation of stiffness and compressive strength of mass concrete of the Dez concrete arch dam, over time have been evaluated using a new and robust method. In previous studies of the corresponding author, he was successful to estimate the degradation of the stiffness of dam’s concrete at the end of a selected time interval, i.e. the Year 2007 from the interval 1965–2007 using a novel thermal inverse analysis. But, he was interested in knowing the trend of this degradation over that time interval. In previous studies, the author used isotropic and transversely isotropic elastic material models for evaluating the stiffness degradation. By these material models, the reduction of the compressive strength of the mass concrete could not be determined. In this new attempt, to overcome the above-mentioned shortcomings, it was decided that the time interval is limited to a maximum of one year from 1965 to 2007. In addition, a more sophisticated material model for concrete of the dam, named as, concrete damaged plasticity model, from the ABAQUS standard material library, was employed to simulate the long-term concrete behaviour. By this material model, the reduction of the compressive strength of the dam’s concrete could be measured. Obtained results demonstrated that the reduction of stiffness and strength of dam’s concrete have not a constant rate of change and they have been accelerated considerably after passing approximately 20 years from the commissioning of the dam.

Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.

Projecting range-wide sun bear population trends using tree cover and camera-trap bycatch data.

Monitoring population trends of threatened species requires standardized techniques that can be applied over broad areas and repeated through time. Sun bears Helarctos malayanus are a forest dependent tropical bear found throughout most of Southeast Asia. Previous estimates of global population trends have relied on expert opinion and cannot be systematically replicated. We combined data from 1,463 camera traps within 31 field sites across sun bear range to model the relationship between photo catch rates of sun bears and tree cover. Sun bears were detected in all levels of tree cover above 20%, and the probability of presence was positively associated with the amount of tree cover within a 6-km2 buffer of the camera traps. We used the relationship between catch rates and tree cover across space to infer temporal trends in sun bear abundance in response to tree cover loss at country and global-scales. Our model-based projections based on this “space for time” substitution suggested that sun bear population declines associated with tree cover loss between 2000–2014 in mainland southeast Asia were ~9%, with declines highest in Cambodia and lowest in Myanmar. During the same period, sun bear populations in insular southeast Asia (Malaysia, Indonesia and Brunei) were projected to have declined at a much higher rate (22%). Cast forward over 30-years, from the year 2000, by assuming a constant rate of change in tree cover, we projected population declines in the insular region that surpassed 50%, meeting the IUCN criteria for endangered if sun bears were listed on the population level. Although this approach requires several assumptions, most notably that trends in abundance across space can be used to infer temporal trends, population projections using remotely sensed tree cover data may serve as a useful alternative (or supplement) to expert opinion. The advantages of this approach is that it is objective, data-driven, repeatable, and it requires that all assumptions be clearly stated.

Fast and slow change in neighbourhoods: characterization and consequences in Southern California

ABSTRACTDue to data limitations, most studies of neighbourhood change within regions assume that change over the years of a decade is relatively constant from year-to-year. We use data on home loan information to construct annual measures of key socio-demographic measures in neighbourhoods (census tracts) in the Southern California region from 2000 to 2010 to test this assumption. We use latent trajectory modelling to describe the extent to which neighbourhood change exhibits temporal nonlinearity, rather than a constant rate of change from year to year. There were four key findings: (1) we detected nonlinear temporal change across all socio-demographic dimensions, as a quadratic function better fit the data than a linear one in the latent trajectories; (2) neighbourhoods experiencing more nonlinear temporality also experienced larger overall changes in percent Asian, percent black, and residential stability during the decade; neighbourhoods experiencing an increase in Latinos or a decrease in whites experienced more temporal nonlinearity in this change; (3) the strongest predictor of racial/ethnic temporal nonlinearity was a larger presence of the group at the beginning of the decade; however, the racial and SES composition of the surrounding area, as well as how this was changing in the prior decade, also affected the degree of temporal nonlinearity for these measures in the current decade; (4) this temporal nonlinearity has consequences for neighbourhoods: greater temporal nonlinear change in percent black or Latino was associated with larger increases in violent and property crime during the decade, and the temporal pattern of residential turnover or changing average income impacted changes in crime. The usual assumption of constant year-to-year change when interpolating neighbourhood measures over intervening years may not be appropriate.

Direct numerical simulation of the flow around an aerofoil in ramp-up motion

A detailed analysis of the flow around a NACA0020 aerofoil at Rec = 2 × 104 undergoing a ramp up motion has been carried out by means of direct numerical simulations. During the manoeuvre, the angle of attack is linearly varied in time between 0° and 20° with a constant rate of change of α̇rad=0.12U∞/c. When the angle of incidence has reached the final value, the lift experiences a first overshoot and then suddenly decreases towards the static stall asymptotic value. The transient instantaneous flow is dominated by the generation and detachment of the dynamic stall vortex, a large scale structure formed by the merging of smaller scales vortices generated by an instability originating at the trailing edge. New insights on the vorticity dynamics leading to the lift overshoot, lift crisis, and the damped oscillatory cycle that gradually matches the steady condition are discussed using a number of post-processing techniques. These include a detailed analysis of the flow ensemble average statistics and coherent structures identification carried out using the Q-criterion and the finite-time Lyapunov exponent technique. The results are compared with the one obtained in a companion simulation considering a static stall condition at the final angle of incidence α = 20°.

Liquid chromatography coupled to quadrupole-time of flight tandem mass spectrometry based quantitative structure–retention relationships of amino acid analogues derivatized via n-propyl chloroformate mediated reaction

In the current study, quantitative structure-retention relationships (QSRR) were constructed based on data obtained by a LC–(ESI)-QTOF-MS/MS method for the determination of amino acid analogues, following their derivatization via chloroformate esters. Molecules were derivatized via n-propyl chloroformate/n-propanol mediated reaction. Derivatives were acquired through a liquid–liquid extraction procedure. Chromatographic separation is based on gradient elution using methanol/water mixtures from a 70/30% composition to an 85/15% final one, maintaining a constant rate of change. The group of examined molecules was diverse, including mainly α-amino acids, yet also β- and γ-amino acids, γ-amino acid analogues, decarboxylated and phosphorylated analogues and dipeptides. Projection to latent structures (PLS) method was selected for the formation of QSRRs, resulting in a total of three PLS models with high cross-validated coefficients of determination Q2Y. For this reason, molecular structures were previously described through the use of descriptors. Through stratified random sampling procedures, 57 compounds were split to a training set and a test set. Model creation was based on multiple criteria including principal component significance and eigenvalue, variable importance, form of residuals, etc. Validation was based on statistical metrics Rpred2, QextF22,QextF32 for the test set and Roy's metrics rm(Av)2 and rm(δ)2, assessing both predictive stability and internal validity. Based on aforementioned models, simplified equivalent were then created using a multi-linear regression (MLR) method. MLR models were also validated with the same metrics. The suggested models are considered useful for the estimation of retention times of amino acid analogues for a series of applications.

Evaluation of the Effect of Fuel Properties on the Fuel Spray and Jet Characteristics in a HGV DI Diesel Engine Operated by Used Cooking Oils

Fuel injection systems in modern diesel engines are designed and built to comply with very stringent environmental standards. They should also meet the highest level of fuel economy. Drivability, rapid response and easy and accurate control are a common demand. Changing the fuel characteristics could affect the performance of the fuel injection system. This study focuses on the evaluation of fuel spray characteristics of straight used cooking oil (SUCO) and its blends with petroleum diesel (PD) as a surrogate for pure PD. Used cooking oil blends have quite different physical properties from those of pure PD. Data for the lower heating value (LHV), density and viscosity were obtained from laboratory analysis. These data were merged with the physical and thermodynamic conditions of the diesel engine of interest to evaluate the dynamic behaviour of the fuel jet in 360° of crank rotation namely, the compression stroke, and the power stroke including the injection process. Engine operational conditions were calculated using a diesel dual thermodynamic cycle taking into account fuel injection adjustment at three different speeds, namely, idle speed, maximum torque speed and rated power speed. The results showed that fuel jet characteristics vary with SUCO content in the fuel blend. Two ranges of SUCO content in the blends were distinguished, 0 – 80% SUCO content and 80 – 100% SUCO content. Both showed a constant rate of change of jet characters per 10% increase in SUCO content in the fuel blend. Lower rates of change of fuel characters were observed at 0-80% SUCO content. The higher the temperature, the lower the rate of change of fuel jet characteristics.

Endogenous Savings Rate with Forward-Looking Households in a Recursive Dynamic CGE Model: Application to South Africa

In the vast majority of recursive dynamic CGE models, the savings rate is constant and exogenous. Intertemporal CGE models, by contrast, are solved simultaneously for all periods, and agents optimize intertemporally. But the theoretical consistency of intertemporal optimization is achieved only at the cost of more aggregated, less detailed models, due to computational limitations. In some applications, therefore, recursive dynamics should be preferred to intertemporal dynamics for practical reasons of computability. This paper presents a recursive dynamic CGE model in which households determine their savings rate from intertemporal optimization, by solving a simplified form of their intertemporal problem. This approach we call truncated rational expectations (TRE). In the TRE framework, households have rational expectations for the current period and the following one. Accordingly, the model is solved simultaneously for two periods at a time, the current period and the following one. Household (rational) expectations for period 1 are given by the model solution. For subsequent periods, household expectations are formed by extrapolating from and 1 solution values, assuming a constant rate of change. The TRE framework is implemented in a modified version of the Decaluwe et al. (2013) PEP-1-t model, and applied to South Africa, using a 2005 SAM by Davies and Thurlow (2011). Several simulations are run, with two variants of the 2005 SAM, the original one and a modified one with a high initial household savings rate. The results are compared with those of a static expectations model with intertemporal optimization, and of a fixed-savings rate model. The main difference is that in the first two models, the household savings rate is not constant, even in the BAU scenario. It is also responsive to changes in the rate of return on assets. On the other hand, an exogenous reduction in household wealth has very little effect.

Development of a frequency-separated knob with variable change rates by rotation speed

The principle of frequency separation is a design method to display different information or feedback in accordance with the frequency of interaction between users and systems. This principle can be usefully applied to the design of knobs. Particularly, their rotation speed can be a meaningful criterion for applying the principle. Hence a knob can be developed, which shows change rates varying depending on its rotation speed. Such a knob would be more efficient than conventional knobs with constant change rate. We developed a prototype of frequency-separated knobs that has different combinations of the number of rotation speed steps and the size of the variation of change rate. With this prototype, we conducted an experiment to examine whether a speed frequency-separated knob enhances users' task performance. The results showed that the newly designed knob was effective in enhancing task performance, and that task efficiency was the best when its change rate increases exponentially and its rotation speed has three steps. We conducted another experiment to investigate how a more rapid exponential increase of change rate and a more number of steps of rotation speed influence users' task performance. The results showed that merely increasing both the size of the variation of change rates and the number of speed steps did not result in better task performance. Although two experimental results cannot easily be generalized to other contexts, they still offer practical information useful for designing a speed frequency-separated knob in various consumer electronics and control panels of industrial systems.

Endogenous Savings Rate with Forward-Looking Households in a Recursive Dynamic CGE Model: Application to South Africa

In the vast majority of recursive dynamic CGE models, the savings rate is constant and exogenous. Intertemporal CGE models, by contrast, are solved simultaneously for all periods, and agents optimize intertemporally. But the theoretical consistency of intertemporal optimization is achieved only at the cost of more aggregated, less detailed models, due to computational limitations. In some applications, therefore, recursive dynamics should be preferred to intertemporal dynamics for practical reasons of computability. This paper presents a recursive dynamic CGE model in which households determine their savings rate from intertemporal optimization, by solving a simplified form of their intertemporal problem. This approach we call « truncated rational expectations » (TRE). In the TRE framework, households have rational expectations for the current period and the following one. Accordingly, the model is solved simultaneously for two periods at a time, the current period ? and the following one. Household (rational) expectations for period ? +1 are given by the model solution. For subsequent periods, household expectations are formed by extrapolating from ? and ? +1 solution values, assuming a constant rate of change. The TRE framework is implemented in a modified version of the Decaluwe et al. (2013) PEP-1-t model, and applied to South Africa, using a 2005 SAM by Davies and Thurlow (2011). Several simulations are run, with two variants of the 2005 SAM, the original one and a modified one with a high initial household savings rate. The results are compared with those of a static expectations model with intertemporal optimization, and of a fixed-savings rate model. The main difference is that in the first two models, the household savings rate is not constant, even in the BAU scenario. It is also responsive to changes in the rate of return on assets. On the other hand, an exogenous reduction in household wealth has very little effect.

D-stat culture for studying the metabolic shifts from oxidative metabolism to lipid accumulation and citric acid production in Yarrowia lipolytica

Lipid accumulation in oleaginous yeasts is triggered by nutrient imbalance in the culture medium between the carbon source in excess and the nitrogen source in limiting concentration. However Yarrowia lipolytica when cultivated on glucose as the sole carbon source, mainly produces citric acid upon nitrogen limitation over lipid accumulation (only 5–10% triacylglycerol). Therefore for developing bioprocess for the production of triacylglycerol from renewable carbon source as glucose it is of first importance to control this imbalance in order to avoid citric acid production during TAG accumulation.Using D-stat cultivation system, where the N/C was linearly decreased using a constant change rate we were able to identify the N/C ratio inducing TAG accumulation (0.085NmolCmol−1) and citric acid (0.021NmolCmol−1). We therefore demonstrated that it was possible to accumulate lipids without excretion citric acid as long as the N/C was within this indicated range. Moreover enzyme specific activities measurement during the D-stat indicated that ATP-citrate lyase, malic enzyme and acetyl-coA carboxylase were strongly induced at the onset of lipid accumulation and showed different patterns when citric acid was excreted.Our results give relevant information for future industrial bioprocess development concerning the production of lipids using renewable carbohydrate substrates as an alternative way to produce synthons for fuel or chemical industry. By controlling the N/C over the fermentation process on glucose Y. lipolytica can accumulate lipids without excreting citric acid.

Recertification revisited [Certification Corner

The July 2012 Certification Corner column explained the need for holders of the IEEE Wireless Communications Professional® (IEEE WCP) certification to recertify periodically in order to demonstrate that they are keeping their knowledge and skills up to date. Given the rapid and constant rate of change in the field of wireless communications, the Wireless Communication Engineering Technologies (WCET) program requires credential holders to recertify their competence at five-year intervals. That interval has now arrived for those who earned the IEEE WCP certification in the Fall of 2008.

The Concept of Slope: Comparing Teachers’ Concept Images and Instructional Content

In the field of mathematics education, understanding teachers’ content knowledge (Grossman, 1995; Hill, Sleep, Lewis, & Ball, 2007; Munby, Russell, & Martin, 2001) and studying the relationship between content knowledge and instructional decisions (Fennema & Franke, 1992; Raymond, 1997) are both crucial. Teachers need a robust understanding of key mathematical topics and connections to make informed choices about which instructional tasks will be assigned and how the content will be represented (Ball & Bass, 2000, Fennema & Franke, 1992). Ma (1999) described this profound understanding of fundamental mathematics as how accomplished teachers conceptualize key ideas in mathematics with a deep and flexible understanding so that they are able to represent those ideas in multiple ways and to recognize how those ideas fit into the preK-16 curriculum.Slope is a fundamental topic in the secondary mathematics curricula. Unit rate and proportional relationships introduced in sixth grade prepare students for interpreting equations such as y = 2x-3 as functions with particular, linear behavior in eighth grade (National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers [CSSO]), 2010; National Council of Teachers of Mathematics [NCTM], 2006). The focus on relationships with constant rate of change leads to distinctions between linear and non-linear functions (Yerushalmy, 1997) and the idea of average rate of change in high school (NGA Center for Best Practices & CCSSO, 2010). Ultimately, these ideas prepare students for instantaneous rates of change and the concept of a derivative in calculus. The diversity of conceptualizations and representations of slope across the secondary mathematics curriculum presents a challenge for secondary teachers. These teachers must work flexibly and fluently with various representations in many contexts in order for their students to build a coherent, connected conceptualization of slope. Since secondary mathematics teachers need a deep understanding of slope to mediate students’ conceptual development of this key topic, the study reported here investigates both how teachers think about and present slope.

Building a photovoltaic marketing model based on feed-in tariffs and system installed cost

The purpose of this research is to establish an analytic model that combines energy policy and the photovoltaic (PV) industry from the governmental perspective. We suggest that government decision-makers set a policy goal for the cumulated installed total quantity of grid-connected PV systems for a certain planning horizon. The objective of their mathematical programming is to minimize the system total average cost of feed-in tariffs (FITs) policy support and the learning investment per kilowatt (kW) PV system installed. In order to attain this goal, they must determine the appropriate FIT unit price and constant change rate that will stimulate residents of developing countries to install the PV systems rapidly. We also expect to achieve a learning effect through the accumulating experience in grid-connected PV systems that will reduce the system installed cost per kW each year. Our analysis reveals that the unit PV installed cost decreases with time and that the cost reduction is quite rapid when the change rate is large. To a certain extent, levering the magnitude of the change rate could affect the growth of the PV product life cycle. If governments in developing countries need to install a large quantity of PV systems at an early stage to reverse global warming or overcome the effects of climate change, then they must choose a higher change rate with a relatively larger initial FIT unit price to a FIT scheme.

Series Length Used during Trend Analysis Affects Sensitivity to Changes in Progression Rate in the Ocular Hypertension Treatment Study

Trend analysis techniques to detect glaucomatous progression typically assume a constant rate of change. This study uses data from the Ocular Hypertension Treatment Study to assess whether this assumption decreases sensitivity to changes in progression rate, by including earlier periods of stability. Series of visual fields (mean 24 per eye) completed at 6-month intervals from participants randomized initially to observation were split into subseries before and after the initiation of treatment (the "split-point"). The mean deviation rate of change (MDR) was derived using these entire subseries, and using only the window length (W) tests nearest the split-point, for different window lengths of W tests. A generalized estimating equation model was used to detect changes in MDR occurring at the split-point. Using shortened subseries with W = 7 tests, the MDR slowed by 0.142 dB/y upon initiation of treatment (P < 0.001), and the proportion of eyes showing "rapid deterioration" (MDR <-0.5 dB/y with P < 5%) decreased from 11.8% to 6.5% (P < 0.001). Using the entire sequence, no significant change in MDR was detected (P = 0.796), and there was no change in the proportion of eyes progressing (P = 0.084). Window lengths 6 ≤ W ≤ 9 produced similar benefits. Event analysis revealed a beneficial treatment effect in this dataset. This effect was not detected by linear trend analysis applied to entire series, but was detected when using shorter subseries of length between six and nine fields. Using linear trend analysis on the entire field sequence may not be optimal for detecting and monitoring progression. Nonlinear analyses may be needed for long series of fields. (ClinicalTrials.gov number, NCT00000125.).

The tau of flight control

AbstractWith this survey paper, the author proposes a new ‘tao’ – a new way of understanding – of how pilots do what they do. Research into the control of purposeful action in the natural world suggests that very rapid, efficient and ‘instinctive’ techniques have evolved based on the time to close on a goal, or close a gap, τ(t), and its derivatives. Purposeful actions involve the closure of one or more physical gaps, each with its own time to close, varying with time. Maintaining a constant rate of change of τ(t) with time (&lt; 1) during an approach will ensure a successful arresting when the gap is closed, but an animal’s strategy can be adapted to the circumstances to achieve either a hard stop (aggressive action with ṫ &gt; 0·5), or a soft stop (gentle action with ṫ &lt; 0·5). Synchronous coupling of two motions,x(t) andy(t), such that the times to close are coupled, τx=kτy, results in the motion gapsx(t) andy(t) being related through a power law,x=Cy1/k, and closing smoothly together; examples of such coupling in the form of pursuit tracking in the natural world abound. Research has also shown that gaps can be closed by following ‘intrinsic’ guides, or self-generated mental models of desired motion, that have particular forms; for example, constant deceleration or constant acceleration. The gathering evidence from research into animal behaviour in the natural-world forms a background for the exploration of flight control in the man-made world. The implications for control theory, flight control developments and flight handling qualities, are considered to be profound. τ-theory suggests that natural control has a particular non-linear, albeit very simple, time varying form and that pilots learn control strategy skills by developing mental models, or internalised schemata, in the form of what are described as ‘τ guides’. In this context the author presents his perspective on flight control, briefly reviewing τ-theory and providing examples from research conducted at The University of Liverpool during the period 1999-2011, including the work of several PhD students. Concepts for guidance algorithms suitable for augmented manual or autonomous control are discussed and the implications for handling qualities developments, particularly relating to flight in degraded visual conditions, are presented. Some outstanding questions pointing directions for future research are raised.

Modeling of the shrinkage kinetics of coffee berries during drying

The effects of drying conditions on the shrinkage of Coffea Arabica L., cultivar Catuaí Vermelho, were studied. An exponential model derived from the kinetic model was used to describe the shrinkage kinetics. In addition, an equation was proposed to describe the relationship between the superficial areas and weights of the coffee berries. Coffee berries were dried at temperatures (T) of 35, 45, 55 and 65ºC and at relative humidities (φ) of 25, 35, 45 and 55%, forming 16 different sets of conditions, with an initial moisture content for all conditions of 2.27 dry basis (d.b.), dried until 0.11 d.b. Changes in the product dimensions were measured continuously during drying. Surface area-to-volume ratio values increased with moisture content decrease. The model was suitable for representing the shrinkage kinetics, as well the empirical equation for predicting surface area. Temperature had a greater influence over the constant rate of change of the characteristic dimension (k values) than φ. Activation energies were also determined to have magnitudes of 39.31, 37.32, 36.28 and 36.22 kJ mol-1 for relative humidities of 25, 35, 45 and 55%, respectively.

Estimating average annual per cent change in trend analysis

Trends in incidence or mortality rates over a specified time interval are usually described by the conventional annual per cent change (cAPC), under the assumption of a constant rate of change. When this assumption does not hold over the entire time interval, the trend may be characterized using the annual per cent changes from segmented analysis (sAPCs). This approach assumes that the change in rates is constant over each time partition defined by the transition points, but varies among different time partitions. Different groups (e.g. racial subgroups), however, may have different transition points and thus different time partitions over which they have constant rates of change, making comparison of sAPCs problematic across groups over a common time interval of interest (e.g. the past 10 years). We propose a new measure, the average annual per cent change (AAPC), which uses sAPCs to summarize and compare trends for a specific time period. The advantage of the proposed AAPC is that it takes into account the trend transitions, whereas cAPC does not and can lead to erroneous conclusions. In addition, when the trend is constant over the entire time interval of interest, the AAPC has the advantage of reducing to both cAPC and sAPC. Moreover, because the estimated AAPC is based on the segmented analysis over the entire data series, any selected subinterval within a single time partition will yield the same AAPC estimate—that is it will be equal to the estimated sAPC for that time partition. The cAPC, however, is re-estimated using data only from that selected subinterval; thus, its estimate may be sensitive to the subinterval selected. The AAPC estimation has been incorporated into the segmented regression (free) software Joinpoint, which is used by many registries throughout the world for characterizing trends in cancer rates. Copyright © 2009 John Wiley & Sons, Ltd.

Acceleration Kinetics of PEG, PPG, and a Triblock Copolymer by SPS during Copper Electroplating

Three copper-plating suppressors are examined in three-additive baths: a polyethylene glycol (PEG), a polypropylene glycol (PPG), and a triblock copolymer of the two. Bis(3-sulfopropyl)-disulfide (SPS) is found to transition each to a state of nonsuppression, i.e., accelerate each, at a rate dependent on the suppressor molecule, the SPS concentration, and, to a lesser extent, the suppressor concentration. Using a planar microscale working electrode , the kinetic currents of the plating reactions are observed without the influence of ohmic resistance, revealing far higher current densities than previously reported. Potentiostatic and galvanostatic experiments of additive adsorption at short times, , are compared quantitatively using a surface-blocking model to transform the data to effective surface coverage, , vs time. A major difference is found in SPS acceleration between galvanostatic and potentiostatic experiments, with the rate of change in suppression being proportional to the current density. This results in a constant rate of change in under constant current but a self-reinforcing rate of change in at constant potential. A simple additive model is introduced to characterize the results.

A Primer in Longitudinal Data Analysis

Longitudinal data, comprising repeated measurements of the same individuals over time, arise frequently in cardiology and the biomedical sciences in general. For example, Frison and Pocock1 used repeated measurements of the liver enzyme creatine kinase in serum of cardiac patients to study changes in liver function over a 12-month study period. The main goal, indeed the raison d’etre , of a longitudinal study is characterization of changes in the response of interest over time. Ordinarily, changes in the response are also related to selected covariates. For example, Frison and Pocock1 compared changes in creatine kinase between patients randomized to active drug and placebo. The past 25 years have witnessed remarkable developments in statistical methods for the analysis of longitudinal data. Despite these important advances, researchers in the biomedical sciences have been somewhat slow to adopt these methods and often rely on statistical techniques that fail to adequately account for longitudinal study designs. The goal of the present report is to provide an overview of some recently developed methods for longitudinal analyses that are more appropriate, with a focus on 2 methods for continuous responses: the analysis of response profiles and linear mixed-effects models. The analysis of response profiles is better suited to settings with a relatively small number of repeated measurements, obtained on a common set of occasions, whereas linear mixed-effects models are suitable in more general settings. Before describing these methods, we review some of the defining features of longitudinal studies and highlight the main aspects of longitudinal data that complicate their analysis. ### Covariance Structure A common feature of repeated measurements on an individual is correlation; that is, knowledge of the value of the response on one occasion provides information about the likely value of the response on a future occasion. Another common feature of longitudinal data is heterogeneous …