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At least 73 records · Page 4

Detecting differential protein abundance by combining peptide level P -values

The majority of methods for detecting differentially abundant proteins between samples in label-free LC-MS bottom-up proteomics experiments rely on statistically testing inferred protein abundances derived from peptide ionization intensities or averaging peptide level statistics. Here in this paper, we statistically test peptide ionization intensities directly and combine the resulting dependent P-values using the Empirical Brown's Method (EBM), avoiding error introduced through the estimation of protein abundances or summarizing test statistics. We show that on a spike-in proteomics dataset, a peptide level approach using EBM outperforms differential abundance detection using a protein level approach and several analysis workflows, including MSstats. Additionally, we demonstrate the effectiveness of this approach by detecting enriched proteins from an activity-based protein profiling dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Retrofit California: Better Buildings Program Overview

Energy efficiency retrofits (also called upgrades) are widely recognized as a critical component to achieving energy savings in the building sector to help lower greenhouse gas (GHG) emissions. To date, however, upgrades have accounted for only a small percentage of aggregate energy savings in building stock, both in California and nationally. Although the measures and technologies to retrofit a building to become energy efficient are readily deployed, establishing this model as a standard practice remains elusive. Retrofit California sought to develop and test new program models to increase participation in the energy upgrade market in California. The Program encompassed 24 pilot projects, conducted between 2010 and mid-2013 and funded through a $30 million American Recovery and Reinvestment Act (ARRA) grant from the U.S. Department of Energy’s (DOE) Better Buildings Neighborhood Program (BBNP). The broad scope of the Program can be seen in the involvement of the following regionally based Grant Partners: Los Angeles County (as prime grantee); Association of Bay Area Governments (ABAG), consisting of: StopWaste.org for Alameda County, Regional Climate Protection Authority (RCPA) for Sonoma County, SF Environment for the City and County of San Francisco, and City of San Jose; California Center for Sustainable Energy (CCSE) for the San Diego region; Sacramento Municipal Utilities District (SMUD). Within these jurisdictions, nine different types of pilots were tested with the common goal of identifying, informing, and educating the people most likely to undertake energy upgrades (both homeowners and contractors), and to provide them with incentives and resources to facilitate the process. Despite its limited duration, Retrofit California undoubtedly succeeded in increasing awareness and education among home and property owners, as well as contractors, realtors, and community leaders. However, program results indicate that a longer timeframe will be needed to transform the market and establish energy retrofits as the new paradigm. Innovations such as Flex Path, which came about because of barriers encountered during the Program, have already shown promise and are enabling increased participation. Together, the pilots represent an unprecedented effort to identify and address market barriers to energy efficiency upgrades and to provide lessons learned to shape future program planning and implementation. The statistics reflects the scope of the marketing and outreach campaigns, which tested a variety of approaches to increase understanding of the benefits of energy upgrades to drive participation in the Program. More traditional methods such as TV and radio advertisements were complimented by innovative community based social marketing campaigns that sought to leverage the trusted status of neighborhood organizations and leaders in order to motivate their constituents to undertake retrofits. The remainder of this report provides an overview of Retrofit California including brief summaries of the pilots’ main components and highlights, followed by the major findings or takeaway lessons from the approaches that were tested. Eleven of the pilots will be continued, with modifications, under the ratepayer-funded Regional Energy Networks. Involvement in the RENS by many of the Retrofit California partners will ensure that early lessons learned are carried forward to guide future programs for energy upgrades in California.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Impact of Climate Variabilities and Human Activities on Surface Water Extents in Reservoirs of Yongding River Basin, China, from 1985 to 2016 Based on Landsat Observations and Time Series Analysis

Yongding River is the largest river flowing through Beijing, the capital city of China. In recent years, Yongding River Basin (YDRB) has seen increasing human impacts on water resources, posing serious challenges in hydrological and ecological health. In this study, remote sensing techniques and statistical time series approaches for hydrological studies were combined to characterize the dynamics and driving factors of reservoir water extents in YDRB during 1985–2016. First, 107 Landsat 4, 5, 7 and 8 images were used to extract surface water extents in YDRB during 1985–2016 using a combination of water indices and Otsu threshold algorithm. Significant positive correlation was found between water extents and the annual inflow for the two biggest reservoirs, the downstream Guanting and upstream Cetian reservoirs, proving their representativeness of surface water availability in this basin. Then, statistical time series approaches including trend-free pre-whitening Mann-Kendall trend test, Pettit change-point test and double mass curve method, which are frequently used in hydrological studies, were adopted to quantify the trend of reservoir water extents dynamics and the relative contributions of climate variability and human activities. Results showed that the water extents in both reservoirs exhibited significant downward trend with change point occurring in 2001 and 2005 for Guanting and Cetian, respectively. About 74%~75% of the shrinkage during the post-change period can be attributed to human activities, among which GDP, population, electricity power production, raw coal production, steel and crude iron production, value of agriculture output, and urban area were the major human drivers. Hydrological connectivity between the upstream Cetian and downstream Guanting reservoirs declined during the post-change period. Since 2012, water extents in both reservoirs recovered as a result of various governmental water management policies including the South-to-North Water Diversion Project. The methodology introduced in this study can be used for analyzing the dynamics and driving mechanism of surface water resources, especially for un-gauged or poorly-gauged watersheds.

47 OTHER INSTRUMENTATION↗

Conservative Estimation of Tail Probabilities from Limited Sample Data

Several sparse-sample uncertainty quantification (UQ) methods are compared for conservative but not overly conservative estimation of small tail probabilities involving responses that lay beyond specified thresholds in the tails of probability distributions. Sixteen very differently shaped distributions (or probability density functions, PDFs) and tail probability magnitudes ranging from 10 -5 to 10 -1 are considered in order for the study to be relevant to a wide range of risk analysis and quantification of margins and uncertainty (QMU) problems. The emphasis of the study is on limited data regimes ranging from N = 2 to 20 samples, reflective of most experimental and some expensive computational situations. Relatively simple sparse-sample UQ methods tested for this regime involve statistical tolerance interval "Equivalent Normal and related "Ensemble of Normals" and "Superdistribution (SD) approaches. (The independently derived SD is effectively equivalent to the Bayesian posterior predictive distribution given the assumptions of the derivation.) The performance of the methods was generally improved for N ≥ 5 samples with a generalized Jackknife resampling technique, which determines a tail probability estimate by averaging estimates from smaller sub-samples. Several quantitative metrics for method conservatism and accuracy of tail probability estimation are used to assess and rank the methods' performance over many random trials for each test PDF and probability magnitude. A variant of Bootstrap resampling was also tried, but did not significantly improve tail probability estimates in most cases. Detailed results are presented from over 100-million tests over the above factors that provide useful granular information on which methods or combination of methods perform best in various areas of the factor space.

97 MATHEMATICS AND COMPUTING↗

Multi-Level Anomaly Detection on Time-Varying Graph Data

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.

anomaly detection↗

A multi-level anomaly detection algorithm for time-varying graph data with interactive visualization

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating node probabilities, and these related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. Furthermore, to illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.

97 MATHEMATICS AND COMPUTING↗

Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic

We derive new constraints on the 𝐸 𝐺 statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the 𝐸 𝐺 statistic can distinguish Λ⁢ CDM from alternative models of gravity. We find 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢1$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢9$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢4$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢3$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ⁢ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺⁡}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$⁡(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 to be scale independent, with probability to exceed >5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

High temperature thermoplastic elastomers synthesized by living anionic polymerization in hydrocarbon solvent at room temperature

We present the synthesis and characterization of a new class of high temperature thermoplastic elastomers composed of polybenzofulvene–polyisoprene–polybenzofulvene (FIF) triblock copolymers. All copolymers were prepared by living anionic polymerization in benzene at room temperature. Homopolymerization and effects of additives on the glass transition temperature (T g ) of polybenzofulvene (PBF) were also investigated. Among all triblock copolymers studied, FIF with 14 vol % of PBF exhibited a maximum stress of 14.3 ± 1.3 MPa and strain at break of 1390 ± 66% from tensile tests. The stress–strain curves of FIF-10 and 14 were analyzed by a statistical molecular approach using a nonaffine tube model to estimate the thermoplastic elastomer behavior. Dynamic mechanical analysis showed that the softening temperature of PBF in FIF was 145 °C, much higher than that of thermoplastic elastomers with polystyrene hard blocks. Microphase separation of FIF triblock copolymers was observed by small-angle X-ray scattering, even though long-range order was not achieved under the annealing conditions employed. Additionally, the microphase separation of the resulting triblock copolymers was examined by atomic force microscopy.

36 MATERIALS SCIENCE↗

Grid-based minimization at scale: Feldman-Cousins corrections for light sterile neutrino search

High Energy Physics (HEP) experiments generally employ sophisticated statistical methods to present results in searches of new physics. In the problem of searching for sterile neutrinos, likelihood ratio tests are applied to short-baseline neutrino oscillation experiments to construct confidence intervals for the parameters of interest. The test statistics of the form Δχ2 is often used to form the confidence intervals, however, this approach can lead to statistical inaccuracies due to the small signal rate in the region-of-interest. In this paper, we present a computational model for the computationally expensive Feldman-Cousins corrections to construct a statistically accurate confidence interval for neutrino oscillation analysis. The program performs a grid-based minimization over oscillation parameters and is written in C++. Our algorithms make use of vectorization through Eigen3, yielding a single-core speed-up of 350 compared to the original implementation, and achieve MPI data parallelism by employing DIY. We demonstrate the strong scaling of the application at High-Performance Computing (HPC) sites. We utilize HDF5 along with HighFive to write the results of the calculation to file.

Wospakrik, Marianette↗

TH-CD-207A-07: Prediction of High Dimensional State Subject to Respiratory Motion: A Manifold Learning Approach

Purpose: The development of high dimensional imaging systems (e.g. volumetric MRI, CBCT, photogrammetry systems) in image-guided radiotherapy provides important pathways to the ultimate goal of real-time volumetric/surface motion monitoring. This study aims to develop a prediction method for the high dimensional state subject to respiratory motion. Compared to conventional linear dimension reduction based approaches, our method utilizes manifold learning to construct a descriptive feature submanifold, where more efficient and accurate prediction can be performed. Methods: We developed a prediction framework for high-dimensional state subject to respiratory motion. The proposed method performs dimension reduction in a nonlinear setting to permit more descriptive features compared to its linear counterparts (e.g., classic PCA). Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where low-dimensional prediction is performed. A fixed-point iterative pre-image estimation method is applied subsequently to recover the predicted value in the original state space. We evaluated and compared the proposed method with PCA-based method on 200 level-set surfaces reconstructed from surface point clouds captured by the VisionRT system. The prediction accuracy was evaluated with respect to root-mean-squared-error (RMSE) for both 200ms and 600ms lookahead lengths. Results: The proposed method outperformed PCA-based approach with statistically higher prediction accuracy. In one-dimensional feature subspace, our method achieved mean prediction accuracy of 0.86mm and 0.89mm for 200ms and 600ms lookahead lengths respectively, compared to 0.95mm and 1.04mm from PCA-based method. The paired t-tests further demonstrated the statistical significance of the superiority of our method, with p-values of 6.33e-3 and 5.78e-5, respectively. Conclusion: The proposed approach benefits from the descriptiveness of a nonlinear manifold and the prediction reliability in such low dimensional manifold. The fixed-point iterative approach turns out to work well practically for the pre-image recovery. Our approach is particularly suitable to facilitate managing respiratory motion in image-guide radiotherapy. This work is supported in part by NIH grant R01 CA169102-02.

60 APPLIED LIFE SCIENCES↗

Correlation approach for quality assurance of additive manufactured parts based on optical metrology

Surface topography and surface finish are two significant factors for evaluating the quality of products in additive manufacturing (AM). AM parts are fabricated layer by layer, which is quite different from traditional formative or subtractive methods. Despite rapid progress in additive manufacturing and associated optical metrology for quality control and in-situ monitoring, limited research has been conducted to investigate the reliability of 3D surface measurement data. The surface topologies scanned by multiple optical systems demonstrated significant differences due to varying sampling mechanisms, resolutions, system noises, etc. The 3D datasets should be trustworthy in order to extract parameters for quality assurance or feedback control from 3D surface measurements. In this paper, we set up new standards to evaluate the reliability of 3D surface measurement data and analyze the variation in the topographical profile. In this study, two non-contact optical methods based on Focus Variation Microscopy (FVM) and Structured Light System (SLS) were adopted to measure the surface topography of the target components. The two optical metrology systems generated two entirely different point cloud datasets. Statistical methods were applied to test the difference between the data obtained from the two systems. By using a data analytics approach for comparison, it was found that the surface roughness estimated from the point cloud data sets of FVM and SLS has no significant difference, though the point cloud data sets were completely different. This paper provides standard validation approach to evaluate the plausibility of metrology data from in-situ real-time surface analysis for process planning of AM.

36 MATERIALS SCIENCE↗

Toward In Situ Synchrotron Mapping of Crystal Selection Processes during Crystal Growth

In this work, we present an automated and rapid method for non-destructive mapping of crystal grains in a rod-shaped sample. The approach was designed for application to in situ float-zone crystal growth experiments at an x-ray synchrotron source, but could be useful in other applications. The methods have been tested on a TiO 2 boule grown in an optical float zone furnace. The approach applies a statistical filter to polycrystalline diffraction patterns on 2D detectors to rapidly determine the degree of powder-quality 1of the signal. When larger crystals emerge in the growth, their position, size and shape can be tracked using an automated blob-tracking algorithm that follows individual Bragg peaks as a function of position in a grid-scan, even when multiple crystals are contributing spots to diffraction images. This method is found to be robust as the same crystal shape can be independently reconstructed using different sets of Bragg reflections. Image segmentation methods are then used to map out the polycrystalline grains. We also note that other information about crystal quality, such as mosaicity or strain state, may be inferred and mapped from the intensity variation of the Bragg peaks at different locations within the sample.

36 MATERIALS SCIENCE↗

Plackett-Burman experimental design to facilitate syntactic foam development

The use of an eight-experiment Plackett–Burman method can assess six experimental variables and eight responses in a polysiloxane-glass microsphere syntactic foam. The approach aims to decrease the time required to develop a tunable polymer composite by identifying a reduced set of variables and responses suitable for future predictive modeling. The statistical design assesses the main effects of mixing process parameters, polymer matrix composition, microsphere density and volume loading, and the blending of two grades of microspheres, using a dummy factor in statistical calculations. Responses cover rheological, physical, thermal, and mechanical properties. The cure accelerator content of the polymer matrix and the volume loading of the microspheres have the largest effects on foam properties. These factors are the most suitable for controlling the gel point of the curing foam, and the density of the cured foam. The mixing parameters introduce widespread variability and therefore should be fixed at effective levels during follow-up testing. Some responses may require greater contrast in microsphere-related factors. As a result, compared to other possible statistical approaches, the run economy of the Plackett–Burman method makes it a valuable tool for rapidly characterizing new foams.

36 MATERIALS SCIENCE↗

Statistical Tests for Convergence in Monte Carlo Criticality Calculations

This report describes methods for using statistical tests to automatically determine convergence of Monte Carlo (MC) iterations in criticality calculations. The methods described herein are intended to replace the traditional approach used for the past 60 years: make a trial run; determine convergence based on plots of k-effective and Shannon entropy vs cycle; adjust the input parameters for controlling the iterations; make a final run to obtain results and statistics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Short-wavelength-sensitive 2 (Sws2) visual photopigment models combined with atomistic molecular simulations to predict spectral peaks of absorbance

For many species, vision is one of the most important sensory modalities for mediating essential tasks that include navigation, predation and foraging, predator avoidance, and numerous social behaviors. The vertebrate visual process begins when photons of the light interact with rod and cone photoreceptors that are present in the neural retina. Vertebrate visual photopigments are housed within these photoreceptor cells and are sensitive to a wide range of wavelengths that peak within the light spectrum, the latter of which is a function of the type of chromophore used and how it interacts with specific amino acid residues found within the opsin protein sequence. Minor differences in the amino acid sequences of the opsins are known to lead to large differences in the spectral peak of absorbance (i.e. the λ max value). In our prior studies, we developed a new approach that combined homology modeling and molecular dynamics simulations to gather structural information associated with chromophore conformation, then used it to generate statistical models for the accurate prediction of λ max values for photopigments derived from Rh1 and Rh2 amino acid sequences. In the present study, we test our novel approach to predict the λ max of phylogenetically distant Sws2 cone opsins. To build a model that can predict the λ max using our approach presented in our prior studies, we selected a spectrally-diverse set of 11 teleost Sws2 photopigments for which both amino acid sequence information and experimentally measured λ max values are known. The final first-order regression model, consisting of three terms associated with chromophore conformation, was sufficient to predict the λ max of Sws2 photopigments with high accuracy. This study further highlights the breadth of our approach in reliably predicting λ max values of Sws2 cone photopigments, evolutionary-more distant from template bovine RH1, and provided mechanistic insights into the role of known spectral tuning sites.

59 BASIC BIOLOGICAL SCIENCES↗

Code Comparison Study Fosters Confidence in the Numerical Simulation of Enhanced Geothermal Systems

Numerical simulation has become a standard analytical tool for scientists and engineers to evaluate the potential and performance of enhanced geothermal systems. A variety of numerical simulators developed by industry, universities, and national laboratories are currently available and being applied to better understand enhanced geothermal systems at the field scale. To yield credible predictions and be of value to site operators, numerical simulators must be able to accurately represent the complex coupled processes induced by producing geothermal systems, such as fracture aperture changes due to thermal stimulation, fracture shear displacement with fluid injection, rate of thermal depletion of reservoir rocks, and permeability alteration with mineral precipitation or dissolution. A suite of numerical simulators was exercised on a series of test problems that considered coupled thermal, hydraulic, geomechanical, and geochemical (THMC) processes. Problems were selected and designed to isolate selected coupled processes, to be executed on workstation class computers, and have simple but illustrative metrics for result comparisons. This paper summarizes the initial suite of seven benchmark problems, describes the code comparison activities, provides example results for problems and documents the capabilities of currently available numerical simulation codes to represent coupled processes that occur during the production of geothermal resources. Code comparisons described in this paper use the ISO (International Organization for Standardization) standard ISO-13538 for proficiency testing of numerical simulators. This approach was adopted for a recent code comparison study within the radiation transfer-modeling field of atmospheric sciences, which was focused on canopy reflectance models. This standard specifies statistical methods for analyzing laboratory data from proficiency testing schemes to demonstrate that the measurement results do not exhibit evidence of an unacceptable level of bias.

benchmark problems↗

Periodicity significance testing with null-signal templates: reassessment of PTF’s SMBH binary candidates

Periodograms are widely employed for identifying periodicity in time series data, yet they often struggle to accurately quantify the statistical significance of detected periodic signals when the data complexity precludes reliable simulations. We develop a data-driven approach to address this challenge by introducing a null-signal template (NST). The NST is created by carefully randomizing the period of each cycle in the periodogram template, rendering it non-periodic. It has the same frequentist properties as a periodic signal template, and we show with simulations that the distribution of false positives is the same as with the original periodic template, regardless of the underlying data. Thus, performing a periodicity search with the NST acts as an effective simulation of the null (no-signal) hypothesis, without having to simulate the noise properties of the data. We apply the NST method to the supermassive black hole binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi et al. had previously proposed 33 high signal-to-noise candidates utilizing simulations to quantify their significance. Our approach reveals that these simulations do not capture the complexity of the real data. There are no statistically significant periodic signal detections above the non-periodic background. To improve the search sensitivity, we introduce a Gaussian quadrature based algorithm for the Bayes Factor with correlated noise as a test statistic. We show with simulations that this improves sensitivity to true signals by more than an order of magnitude. However, the Bayes Factor approach also results in no statistically significant detections in the PTF data.

79 ASTRONOMY AND ASTROPHYSICS↗

Droplet size distributions in turbulent clouds: experimental evaluation of theoretical distributions

Precipitation efficiency and optical properties of clouds, both central to determining Earth's weather and climate, depend on the size distribution of cloud particles. Here in this paper, theoretical expressions for cloud droplet size distribution shape are evaluated using measurements from controlled experiments in a convective-cloud chamber. The experiments are a unique opportunity to constrain theory because they are in steady-state and because the initial and boundary conditions are well characterized compared to typical atmospheric measurements. Three theoretical distributions obtained from a Langevin drift-diffusion approach to cloud formation via stochastic condensation are tested: (a) stochastic condensation with a constant removal time-scale; (b) stochastic condensation with a size-dependent removal time-scale; (c) droplet growth in a fixed supersaturation condition and with size-dependent removal. In addition, a similar Weibull distribution that can be obtained from the drift-diffusion approach, as well as from mechanism-independent probabilistic arguments (e.g., maximum entropy), is tested as a fourth hypothesis. Statistical techniques such as the χ2 test, sum of squared errors of prediction, and residual analysis are employed to judge relative success or failure of the theoretical distributions to describe the experimental data. An extensive set of cloud droplet size distributions are measured under different aerosol injection rates. Five different aerosol injection rates are run both for size-selected aerosol particles, and six aerosol injection rates are run for broad-distribution, polydisperse aerosol particles. In relative comparison, the most favourable comparison to the measurements is the expression for stochastic condensation with size-dependent droplet removal rate. However, even this optimal distribution breaks down for broad aerosol size distributions, primarily due to deviations from the measured large-droplet tail. Lastly, a possible explanation for the deviation is the Ostwald ripening effect coupled with deactivation/activation in polluted cloud conditions.

54 ENVIRONMENTAL SCIENCES↗