Realistic Fluctuations Research Articles

Adapted Linear Forcing for Inlet Turbulent Fluctuations Generation and Application to a Conical Vortex Flow

A method based on linear forcing is developed to generate realistic turbulent fluctuations at the inlet of a computational domain. The method uses a precursor computation of convected forced isotropic turbulence and variables are extracted from a plane to be imposed at the inlet of the main simulation. In the precursor computation, the turbulent fluctuations are generated and sustained using a synthetic generator and a linear forcing which have been adapted in order to allow the specification of the intensity and length scale. The method is then applied to the analysis of a conical vortex in interaction with a wall subjected to external turbulence using Improved Delayed Detached Eddy Simulation. Good agreement with experimental data is achieved both concerning the decay of the turbulent fluctuations in the upstream region and concerning the sensitivity of the vortex to the Free Stream Turbulence.

Metrological Characterization of a Pain Detection System Based on Transfer Entropy of Facial Landmarks

Pain is an alert state of the human body that can be conveyed to the external world through different modalities. A possible communication channel for human pain is represented by facial expressions, whose role in social interactions has been well established. In this work, the link between pain and transfer entropy (TE), passing through facial expressions, is investigated. A new approach to the vision-based measurement (VBM) of pain is presented, which is based on TE among the time-series of facial landmarks positions. The system is composed of three main blocks: A VBM block for the automatic landmarking and the generation of the time-series from the video-sequences; a second block for the evaluation of TE; and finally a classification model based on machine learning algorithms for pain assessment. A public database of video sequences of patients experiencing pain in a controlled scenario was used for the characterization of the system in terms of accuracy and precision. Different uncertainty contributions related to realistic signals interruptions and fluctuations were modeled and propagated to provide a comprehensive evaluation of the proposed measurement system. The obtained results indicate that TE-based approaches can provide great benefits in automatic pain assessment, opening new perspectives for remote management of patients.

Effects of initial state fluctuations on the mean transverse momentum

We show that in ideal hydrodynamic simulations of heavy-ion collisions, initial state fluctuations result in an increase of the mean transverse momentum of outgoing hadrons, 〈pt〉. Specifically, 〈pt〉 is larger by a few percent if realistic fluctuations are implemented than with smooth initial conditions, the multiplicity and impact parameter being kept fixed. We show that result can be traced back to the fact that for a given total entropy, the initial energy contained in the fluid is larger if the density profile is bumpy. We discuss the implication of these results for the extraction of the equation of state of QCD from experimental data.

Testing water fluxes and storage from two hydrology configurations within the ORCHIDEE land surface model across US semi-arid sites

Abstract. Plant activity in semi-arid ecosystems is largely controlled by pulses of precipitation, making them particularly vulnerable to increased aridity that is expected with climate change. Simple bucket-model hydrology schemes in land surface models (LSMs) have had limited ability in accurately capturing semi-arid water stores and fluxes. Recent, more complex, LSM hydrology models have not been widely evaluated against semi-arid ecosystem in situ data. We hypothesize that the failure of older LSM versions to represent evapotranspiration, ET, in arid lands is because simple bucket models do not capture realistic fluctuations in upper-layer soil moisture. We therefore predict that including a discretized soil hydrology scheme based on a mechanistic description of moisture diffusion will result in an improvement in model ET when compared to data because the temporal variability of upper-layer soil moisture content better corresponds to that of precipitation inputs. To test this prediction, we compared ORCHIDEE LSM simulations from (1) a simple conceptual 2-layer bucket scheme with fixed hydraulic parameters and (2) an 11-layer discretized mechanistic scheme of moisture diffusion in unsaturated soil based on Richards equations, against daily and monthly soil moisture and ET observations, together with data-derived estimates of transpiration / evapotranspiration, T∕ET, ratios, from six semi-arid grass, shrub, and forest sites in the south-western USA. The 11-layer scheme also has modified calculations of surface runoff, water limitation, and resistance to bare soil evaporation, E, to be compatible with the more complex hydrology configuration. To diagnose remaining discrepancies in the 11-layer model, we tested two further configurations: (i) the addition of a term that captures bare soil evaporation resistance to dry soil; and (ii) reduced bare soil fractional vegetation cover. We found that the more mechanistic 11-layer model results in a better representation of the daily and monthly ET observations. We show that, as predicted, this is because of improved simulation of soil moisture in the upper layers of soil (top ∼ 10 cm). Some discrepancies between observed and modelled soil moisture and ET may allow us to prioritize future model development and the collection of additional data. Biases in winter and spring soil moisture at the forest sites could be explained by inaccurate soil moisture data during periods of soil freezing and/or underestimated snow forcing data. Although ET is generally well captured by the 11-layer model, modelled T∕ET ratios were generally lower than estimated values across all sites, particularly during the monsoon season. Adding a soil resistance term generally decreased simulated bare soil evaporation, E, and increased soil moisture content, thus increasing transpiration, T, and reducing the negative bias between modelled and estimated monsoon T∕ET ratios. This negative bias could also be accounted for at the low-elevation sites by decreasing the model bare soil fraction, thus increasing the amount of transpiring leaf area. However, adding the bare soil resistance term and decreasing the bare soil fraction both degraded the model fit to ET observations. Furthermore, remaining discrepancies in the timing of the transition from minimum T∕ET ratios during the hot, dry May–June period to high values at the start of the monsoon in July–August may also point towards incorrect modelling of leaf phenology and vegetation growth in response to monsoon rains. We conclude that a discretized soil hydrology scheme and associated developments improve estimates of ET by allowing the modelled upper-layer soil moisture to more closely match the pulse precipitation dynamics of these semi-arid ecosystems; however, the partitioning of T from E is not solved by this modification alone.

Free space continuous-variable quantum key distribution with practical links

The transmittance fluctuation resulting from free space optics will impart the continuous-variable quantum key distribution (CV-QKD). In this paper, we study the CV-QKD over free space by taking practical transmittance fluctuation into account. The transmittance is modeled following the Gaussian distribution, which reflects the most realistic fluctuation since all sources of perturbation are required to be incorporated together in practice. The comprehensive comparison between the practical model and existing models in secret key rate is drawn. The numerical results reveal that the existing model of uniform distribution underestimates the impact of air link for both slow and fast fading scenarios, and the practical secret key rate will suffer severer degradation. Further, as the variance of the Gaussian model decreases, the secret key rate degrades as well. Also, a comparison between heterodyne and homodyne detection schemes is made, and we found that the heterodyne detection outperforms the homodyne detection in the secret key rate for both the slow and fast fading air quantum channels.

Daily fluctuating temperatures decrease growth and reproduction rate of a lethal amphibian fungal pathogen in culture

BackgroundEmerging infectious diseases (EIDs) are contributing to species die-offs worldwide. We can better understand EIDs by using ecological approaches to study pathogen biology. For example, pathogens are exposed to variable temperatures across daily, seasonal, and annual scales. Exposure to temperature fluctuations may reduce pathogen growth and reproduction, which could affect pathogen virulence, transmission, and environmental persistence with implications for disease. We examined the effect of a variable thermal environment on reproductive life history traits of the fungal pathogen Batrachochytrium dendrobatidis (Bd). Bd causes chytridiomycosis, an emerging infectious disease of amphibians. As a pathogen of ectothermic hosts, Bd can be exposed to large temperature fluctuations in nature. To determine the effect of fluctuating temperatures on Bd growth and reproduction, we collected temperature data from breeding pools of the Yosemite toad (Anaxyrus canorus), a federally threatened species that is susceptible to chytridiomycosis. We cultured Bd under a daily fluctuating temperature regime that simulated Yosemite toad breeding pool temperatures and measured Bd growth, reproduction, fecundity, and viability.ResultsWe observed decreased Bd growth and reproduction in a diurnally fluctuating thermal environment as compared to cultures grown at constant temperatures within the optimal Bd thermal range. We also found that Bd exhibits temperature-induced trade-offs under constant low and constant high temperature conditions.ConclusionsOur results provide novel insights on variable responses of Bd to dynamic thermal conditions and highlight the importance of incorporating realistic temperature fluctuations into investigations of pathogen ecology and EIDs.

Photosynthetic Acclimation to Fluctuating Irradiance in Plants.

Unlike the short-term responses of photosynthesis to fluctuating irradiance, the long-term response (i.e., acclimation) at the chloroplast, leaf, and plant level has received less attention so far. The ability of plants to acclimate to irradiance fluctuations and the speed at which this acclimation occurs are potential limitations to plant growth under field conditions, and therefore this process deserves closer study. In the first section of this review, we look at the sources of natural irradiance fluctuations, their effects on short-term photosynthesis, and the interaction of these effects with circadian rhythms. This is followed by an overview of the mechanisms that are involved in acclimation to fluctuating (or changes of) irradiance. We highlight the chain of events leading to acclimation: retrograde signaling, systemic acquired acclimation (SAA), gene transcription, and changes in protein abundance. We also review how fluctuating irradiance is applied in experiments and highlight the fact that they are significantly slower than natural fluctuations in the field, although the technology to achieve realistic fluctuations exists. Finally, we review published data on the effects of growing plants under fluctuating irradiance on different plant traits, across studies, spatial scales, and species. We show that, when plants are grown under fluctuating irradiance, the chlorophyll a/b ratio and plant biomass decrease, specific leaf area increases, and photosynthetic capacity as well as root/shoot ratio are, on average, unaffected.

Critical charge and density coupling in ionic spherical models.

We investigate ionic criticality on the basis of a specially devised spherical model that accounts both for Coulomb and nonionic forces in binary systems. We show in detail here the consequences of the entanglement of density and charge correlation functions G_{NN} and G_{ZZ} on criticality and screening. We also show on this soluble model how, because of electroneutrality, the long-range Coulomb interactions do not change the universality class of criticality in the model driven primarily by sufficiently attractive nonionic interactions. Near criticality, G_{NN} and G_{ZZ} are fully decoupled in charge symmetric systems. However, in more realistic nonsymmetric models, charge and density fluctuations couple in leading order so that the charge and density correlation lengths diverge asymptotically in a similar way. Similarly, the Stillinger-Lovett sum rule, which characterizes a conducting fluid, is violated at criticality in nonsymmetric models when the critical-point density-decay exponent η vanishes. In addition, if quantum effects are accounted for semiclassically by incorporating algebraically decaying interactions, G_{ZZ} decays only as a power law in the whole phase space, contrary to the usually expected exponential Debye screening. We expect these results on this soluble toy model to be general and to reveal general mechanisms ruling ionic criticality.

Super-Multi-Junction Solar Cells—Device Configuration with the Potential for More Than 50% Annual Energy Conversion Efficiency (Non-Concentration)

The highest-efficiency solar cell in the efficiency race does not always give the best annual energy yield in real world solar conditions because the spectrum is always changing. The study of radiative coupling of concentrator solar cells implies that efficiency could increase by recycling the radiative recombination generated by the surplus current in the upper junction. Such a configuration is called a super-multi-junction cell. We expand the model in the concentrator solar cell to a non-concentrating installation. It is shown that this super-multi-junction cell configuration is robust and can keep maximum potential efficiency (50% in realistic spectrum fluctuation) for up to 10 junctions. The super-multi-junction cell is also robust in the bandgap engineering of each junction. Therefore, a future multi-junction may not be required for tuning the bandgap to match the standard solar spectrum, as well as relying upon artificial technologies such as epitaxial lift-off (ELO), wafer-bonding, mechanical-stacking, and reverse-growth, but merely uses upright and lattice-matching growth technologies. We present two challenging techniques; one is the optical cap layer that may be the directional photon coupling layer in the application of the photonics technologies, and another is the high-quality epitaxial growth with almost 100% radiative efficiency.

The effects of model climate bias on ENSO variability and ensemble prediction

New methods are presented for determining the role of coupled ocean-atmosphere model climate bias on the strength and variability of the El Nino-Southern Oscillation (ENSO) and on the seasonal ensemble prediction of El Nino and La Nina events. An intermediate complexity model with a global atmosphere coupled to a Pacific basin ocean is executed with parallelised algorithms to produce computationally efficient year-long forecasts of large ensembles of coupled flow fields, beginning every month between 1980 and 1999. Firstly, the model is provided with forcing functions that reproduce the average annual cycle of climatology of the atmosphere and ocean based on reanalysed observations. We also configure the model to generate realistic ENSO fluctuations. Next, an ensemble prediction scheme is employed which produces perturbations that amplify rapidly over a month. These perturbations are added to the analyses and give the initial conditions for the ensemble forecasts. The skill of the forecasts is presented and the dependency on the annual and ENSO cycles determined. Secondly, we replace the forcing functions in our model with functions that reproduce the averaged annual cycles of climatology of two state of the art, comprehensive Coupled General Circulation Models. The changes in skill of subsequent ensemble forecasts elucidate the roles of model bias in error growth and potential predictability.
 
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Consequences of temperature and temperature variability on swimming activity, group structure, and predation of endangered delta smelt

Abstract The effects of water temperature on individual and group movement behaviour in prey fish can affect ecological interactions such as competition and predation, but how variability in temperature influence fish behaviour is less understood. Of particular concern is how increased warming in tidally fluctuating estuaries may impact the native and endangered delta smelt (Hypomesus transpacificus, Osmeridae). To help address this issue, we tested the effects of increased water temperature (fluctuating [17–21°C] and warm [21°C] acclimated treatments) on juvenile delta smelt individual and group behaviour, response to chemical alarm and predator cues, as well as capacity to evade predation. In addition, predation of delta smelt was tested in the presence of a dominant invasive competitor, Mississippi silversides (Menidia beryllina, Atherinopsidae), as well as comparative predation mortality on Mississippi silversides when isolated. After 7 days of increased temperature treatments, delta smelt in the warm treatment increased swimming velocity, decreased turning angle, and altered group structure with larger inter‐individual distances compared to fish in the control (17°C) and fluctuating temperature treatments. Following conspecific and predator chemical alarm cues, delta smelt showed anti‐predator responses. Control and fluctuating treatment fish responded to conspecific cues with increased swimming speeds, decreased inter‐individual distances and near‐neighbour distances, and, after 15 min, fish recovered back to baseline behaviours. In contrast, fish in the warm treatment had not recovered after 15 min, and swimming speeds were maintained at roughly 25 cm/s, close to maximum capabilities. Fish in control and fluctuating treatments showed minimal responses to predator cues, whereas delta smelt exposed to warm conditions significantly increased swimming speeds and decreased turning angle. Predation of delta smelt by largemouth bass (Micropterus salmoides, Centrarchidae) was greatest under the warm treatment, correlating with altered behaviours of delta smelt; however, predation of Mississippi silversides was greater than delta smelt, independent of temperature. This study provides novel insight into the group behaviour of delta smelt, their response to predation, and how prolonged exposure to elevated temperature may induce negative individual and group behaviours causing alterations in predator–prey dynamics. This work highlights the importance of testing ecologically realistic temperature fluctuations in experiments as delta smelt had significantly altered responses to elevated temperature, dependent on variability of warming.

An experimental method to identify a component of wave orbital motion in propeller effective inflow velocity and its effects on load fluctuations of a ship main engine in waves

Improvements of estimation accuracy on propeller torque fluctuations in waves will contribute assessments on safe operation of a ship main engine as in adverse sea condition. The propeller torque and thrust in waves can be estimated by propeller effective inflow velocity in waves, using the propeller open-water characteristics. Fluctuation components in the mathematical model of the propeller effective inflow velocity in waves can be composed of two components, respectively caused by ship surge motion and wave orbital motion at propeller position. In this study, an experimental method by the model test to directly identify the characteristics of the component by the wave orbital motion is newly proposed. Furthermore, the free-running model test in regular waves, using a simulator of the marine diesel engine which manages the shaft speed of the motor on a ship model as behaving the actual diesel engine, is carried out to obtain realistic torque fluctuations for comparisons of the estimated results applying the proposed identification method. Through comparisons of estimated fluctuations with the measured results, the proposed approach for the component of the inflow velocity due to wave orbital motion is successfully validated.

Adaptive P&O MPPT algorithm based wind generation system using realistic wind fluctuations

In this study, an efficient and fast adaptive perturb and observe (AD-PO) maximum power point tracking (MPPT) algorithm based on the variable - speed wind energy conversion system (WECS) is proposed to eradicate drawbacks of conventional fixed step-size P&O (CPO) algorithms and to enhance the operation of variable step-size P&O (VS-PO). The AD-PO divides the power-speed (P-ω) curve into modular sectors that depend on the estimated wind speed. The step-size is varied adaptively in each sector by observing the distance between the theoretical maximum power point (MPP) and operating power point. The AD-PO enhances the speed convergence with low steady-state oscillations around the MPP. The system configuration involves a 1.5 MW five-phase permanent magnet synchronous generator (PMSG). A back-to-back converter (BTBC) with a dc-link capacitor is used to integrate the PMSG with the utility grid. Simulation results confirm the superiority of the AD-PO over the CPO and the VS-PO MPPT algorithms based on speed convergence and oscillation levels. The performance of the proposed control scheme is validated by real wind data (Boulder City, Colorado) using MATLAB/SIMULINK environment.

Responses of seaweeds that use CO2 as their sole inorganic carbon source to ocean acidification: differential effects of fluctuating pH but little benefit of CO2 enrichment

AbstractLaboratory studies that test the responses of coastal organisms to ocean acidification (OA) typically use constant pH regimes which do not reflect coastal systems, such as seaweed beds, where pH fluctuates on diel cycles. Seaweeds that use CO2 as their sole inorganic carbon source (non-carbon dioxide concentrating mechanism species) are predicted to benefit from OA as concentrations of dissolved CO2 increase, yet this prediction has rarely been tested, and no studies have tested the effect of pH fluctuations on non-CCM seaweeds. We conducted a laboratory experiment in which two ecologically dominant non-CCM red seaweeds (Callophyllis lambertii and Plocamium dilatatum) were exposed to four pH treatments: two static, pHT 8.0 and 7.7 and two fluctuating, pHT 8.0 ± 0.3 and 7.7 ± 0.3. Fluctuating pH reduced growth and net photosynthesis in C. lambertii, while P. dilatatum was unaffected. OA did not benefit P. dilatatum, while C. lambertii displayed elevated net photosynthetic rates. We provide evidence that carbon uptake strategy alone cannot be used as a predictor of seaweed responses to OA and highlight the importance of species-specific sensitivity to [H+]. We also emphasize the importance of including realistic pH fluctuations in experimental studies on coastal organisms.

Assessment of resistance to fatigue crack growth of natural gas line pipe steels carrying gas mixed with hydrogen

Hydrogen embrittlement of line pipe steels in the natural gas transmission and distribution network is investigated. The objective is to assess whether the existing network can be used to safely transport a mixture of hydrogen and natural gas. The surveyed literature indicates that the hydrogen-induced acceleration of fatigue crack growth induced by natural gas pressure fluctuations can be the most probable type of failure. We analyzed the fatigue crack growth in line pipe steels containing a long axial crack in the inner diameter (ID) surface by accounting for random cyclic loading due to random and realistic pressure fluctuations, crack closure, and accurate calculation of the stress intensity factor. Using the available experimental data for the crack growth rate vs. stress intensity factor range in the presence of hydrogen, we simulated crack growth over a period of 100 years. The results show that under typical pressure fluctuations in the natural gas network, cracks with depths less than 40% of the wall thickness will never reach depths equal to 75% of the wall thickness. This is a conservative estimate that results from i) the nature of the geometry of the initial flaw in the ID surface that we used in the analysis, ii) the fact that the existing experimental data for the effect of hydrogen on the Paris law are for pressures that are orders of magnitude larger than the partial pressures intended for the hydrogen gas in the mixture, and iii) the experimental data are for fatigue crack growth in pure hydrogen gas without impurities normally present in natural gas, such as oxygen or methane, that can inhibit hydrogen uptake.

Precise Simulation of Electromagnetic Calorimeter Showers Using a Wasserstein Generative Adversarial Network

Simulations of particle showers in calorimeters are computationally time-consuming, as they have to reproduce both energy depositions and their considerable fluctuations. A new approach to ultra-fast simulations are generative models where all calorimeter energy depositions are generated simultaneously. We use GEANT4 simulations of an electron beam impinging on a multi-layer electromagnetic calorimeter for adversarial training of a generator network and a critic network guided by the Wasserstein distance. The generator is constraint during the training such that the generated showers show the expected dependency on the initial energy and the impact position. It produces realistic calorimeter energy depositions, fluctuations and correlations which we demonstrate in distributions of typical calorimeter observables. In most aspects, we observe that generated calorimeter showers reach the level of showers as simulated with the GEANT4 program.

On the performance of a cointegration-based approach for novelty detection in realistic fatigue crack growth scenarios

Abstract Confounding influences, such as operational and environmental variations, represent a limitation to the implementation of Structural Health Monitoring (SHM) systems in real structures, potentially leading to damage misclassifications. In this framework, this study considers cointegration as a state of the art method for data normalisation in fatigue crack propagation scenarios, where monitoring is performed by a distributed network of strain sensors. Specifically, the work is aimed at demonstrating the effectiveness of cointegration on real engineering data in a new context, where the damage is continuously growing. Cointegration is applied at first in a controlled scenario consisting of a numerical strain simulation by means of a finite element model, modified in order to take realistic temperature fluctuations and sensor noise into account. Afterwards, detrending and anomaly detection performances are verified in two different experimental programmes on realistic aeronautical structures subjected to fatigue crack growth, including a full-scale fatigue test on a helicopter tail boom. Strain measurements are taken from a network of Fibre Bragg Grating (FBG) sensors, known to be extremely sensitive to temperature variations, hence delivering challenging scenarios for cointegration testing. Results are shown to be in good agreement with the experimental evidence, with the cointegration algorithm capable of detecting the onset of damage propagation within a 4 mm increment from a baseline condition.

Trapping in and Escape from Branched Structures of Neuronal Dendrites

We present a coarse-grained model for stochastic transport of noninteracting chemical signals inside neuronal dendrites and show how first-passage properties depend on the key structural factors affected by neurodegenerative disorders or aging: the extent of the tree, the topological bias induced by segmental decrease of dendrite diameter, and the trapping probabilities in biochemical cages and growth cones. We derive an exact expression for the distribution of first-passage times, which follows a universal exponential decay in the long-time limit. The asymptotic mean first-passage time exhibits a crossover from power-law to exponential scaling upon reducing the topological bias. We calibrate the coarse-grained model parameters and obtain the variation range of the mean first-passage time when the geometrical characteristics of the dendritic structure evolve during the course of aging or neurodegenerative disease progression (a few disorders for which clear trends for the pathological changes of dendritic structure have been reported in the literature are chosen and studied). We prove the validity of our analytical approach under realistic fluctuations of structural parameters by comparison to the results of Monte Carlo simulations. Moreover, by constructing local structural irregularities, we analyze the resulting influence on transport of chemical signals and formation of heterogeneous density patterns. Because neural functions rely on chemical signal transmission to a large extent, our results open the possibility of establishing a direct link between the disease progression and neural functions.

Parsing propagule pressure: Number, not size, of introductions drives colonization success in a novel environment.

Predicting whether individuals will colonize a novel habitat is of fundamental ecological interest and is crucial to conservation efforts. A consistently supported predictor of colonization success is the number of individuals introduced, also called propagule pressure. Propagule pressure increases with the number of introductions and the number of individuals per introduction (the size of the introduction), but it is unresolved which process is a stronger driver of colonization success. Furthermore, their relative importance may depend upon the environment, with multiple introductions potentially enhancing colonization of fluctuating environments. To evaluate the relative importance of the number and size of introductions and its dependence upon environmental variability, we paired demographic simulations with a microcosm experiment. Using Tribolium flour beetles as a model system, we introduced a fixed number of individuals into replicated novel habitats of stable or fluctuating quality, varying the number of introductions through time and size of each introduction. We evaluated establishment probability and the size of extant populations through seven generations. We found that establishment probability generally increased with more, smaller introductions, but was not affected by biologically realistic fluctuations in environmental quality. Population size was not significantly affected by environmental variability in the simulations, but populations in the microcosms grew larger in a stable environment, especially with more introduction events. In general, the microcosm experiment yielded higher establishment probability and larger populations than the demographic simulations. We suggest that genetic mechanisms likely underlie these differences and thus deserve more attention in efforts to parse propagule pressure. Our results highlight the importance of preventing further introductions of undesirable species to invaded sites and suggest conservation efforts should focus on increasing the number of introductions or reintroductions of desirable species rather than increasing the size of those introduction events into harsh environments.

In search of ideas: Technological innovation and executive pay inequality

We develop a general equilibrium model that delivers realistic fluctuations in pay inequality as a result of changes in the technology frontier. In our model, executives add value to the firm not only by participating in production decisions, as do other workers in the economy, but also by identifying new investment opportunities. Improvements in technology that are specific to new vintages of capital raise the return to managers’ skills for discovering new growth projects and, thus, increase the compensation of executives relative to workers and disparities in pay across executives. Our model implies that, controlling for firm size, compensation is higher in fast-growing firms and that pay inequality increases as investment opportunities in the economy improve. Both predictions are consistent with the data.