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At least 307 records · Page 17

Data Science Meets Physical Organic Chemistry

At the heart of synthetic chemistry is the holy grail of predictable catalyst design. In particular, researchers involved in reaction development in asymmetric catalysis have pursued a variety of strategies toward this goal. This is driven by both the pragmatic need to achieve high selectivities and the inability to readily identify why a certain catalyst is effective for a given reaction. While empiricism and intuition have dominated the field of asymmetric catalysis since its inception, enantioselectivity offers a mechanistically rich platform to interrogate catalyst-structure response patterns that explain the performance of a particular catalyst or substrate. In the early stages of an asymmetric reaction development campaign, the overarching mechanism of the reaction, catalyst speciation, the turnover limiting step, and many other details are unknown or posited based on related reactions. Considering the unclear details leading to a successful reaction, initial enantioselectivity data are often used to intuitively guide the ultimate direction of optimization. However, if the conditions of the Curtin-Hammett principle are satisfied, then measured enantioselectivity can be directly connected to the ensemble of diastereomeric transition states (TSs) that lead to the enantiomeric products, and the associated free energy difference between competing TSs (ΔΔ G ‡ = - RT ln[( S )/( R )], where ( S ) and ( R ) represent the concentrations of the enantiomeric products). We, and others, speculated that this important piece of information can be leveraged to guide reaction optimization in a quantitative way. Although traditional linear free energy relationships (LFERs), such as Hammett plots, have been used to illuminate important mechanistic features, we sought to develop data science derived tools to expand the power of LFERs in order to describe complex reactions frequently encountered in modern asymmetric catalysis. Specifically, we investigated whether enantioselectivity data from a reaction can be quantitatively connected to the attributes of reaction components, such as catalyst and substrate structural features, to harness data for asymmetric catalyst design. In this context, we developed a workflow to relate computationally derived features of reaction components to enantioselectivity using data science tools. The mathematical representation of molecules can incorporate many aspects of a transformation, such as molecular features from substrate, product, catalyst, and proposed transition states. Statistical models relating these features to reaction outputs can be used for various tasks, such as performance prediction of untested molecules. Perhaps most importantly, statistical models can guide the generation of mechanistic hypotheses that are embedded within complex patterns of reaction responses. Overall, merging traditional physical organic experiments with statistical modeling techniques creates a feedback loop that enables both evaluation of multiple mechanistic hypotheses and future catalyst design. In this Account, we highlight the evolution and application of this approach in the context of a collaborative program based on chiral phosphoric acid catalysts (CPAs) in asymmetric catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling the dosimetry of organ-at-risk in head and neck IMRT planning: An intertechnique and interinstitutional study

Purpose: To build a statistical model to quantitatively correlate the anatomic features of structures and the corresponding dose-volume histogram (DVH) of head and neck (HN) Tomotherapy (Tomo) plans. To study if the model built upon one intensity modulated radiation therapy (IMRT) technique (such as conventional Linac) can be used to predict anticipated organs-at-risk (OAR) DVH of patients treated with a different IMRT technique (such as Tomo). To study if the model built upon the clinical experience of one institution can be used to aid IMRT planning for another institution. Methods: Forty-four Tomotherapy intensity modulate radiotherapy plans of HN cases (Tomo-IMRT) from Institution A were included in the study. A different patient group of 53 HN fixed gantry IMRT (FG-IMRT) plans was selected from Institution B. The analyzed OARs included the parotid, larynx, spinal cord, brainstem, and submandibular gland. Two major groups of anatomical features were considered: the volumetric information and the spatial information. The volume information includes the volume of target, OAR, and overlapped volume between target and OAR. The spatial information of OARs relative to PTVs was represented by the distance-to-target histogram (DTH). Important anatomical and dosimetric features were extracted from DTH and DVH by principal component analysis. Two regression models, one for Tomotherapy plan and one for IMRT plan, were built independently. The accuracy of intratreatment-modality model prediction was validated by a leave one out cross-validation method. The intertechnique and interinstitution validations were performed by using the FG-IMRT model to predict the OAR dosimetry of Tomo-IMRT plans. The dosimetry of OARs, under the same and different institutional preferences, was analyzed to examine the correlation between the model prediction and planning protocol. Results: Significant patient anatomical factors contributing to OAR dose sparing in HN Tomotherapy plans have been analyzed and identified. For all the OARs, the discrepancies of dose indices between the model predicted values and the actual plan values were within 2.1%. Similar results were obtained from the modeling of FG-IMRT plans. The parotid gland was spared in a comparable fashion during the treatment planning of two institutions. The model based on FG-IMRT plans was found to predict the median dose of the parotid of Tomotherapy plans quite well, with a mean error of 2.6%. Predictions from the FG-IMRT model suggested the median dose of the larynx, median dose of the brainstem and D2 of the brainstem could be reduced by 10.5%, 12.8%, and 20.4%, respectively, in the Tomo-IMRT plans. This was found to be correlated to the institutional differences in OAR constraint settings. Re-planning of six Tomotherapy patients confirmed the potential of optimization improvement predicted by the FG-IMRT model was correct. Conclusions: The authors established a mathematical model to correlate the anatomical features and dosimetric indexes of OARs of HN patients in Tomotherapy plans. The model can be used for the setup of patient-specific OAR dose sparing goals and quality control of planning results. The institutional clinical experience was incorporated into the model which allows the model from one institution to generate a reference plan for another institution, or another IMRT technique.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Development of a two-dimensional zonally averaged statistical-dynamical model. I - The parameterization of moist convection and its role in the general circulation

The moist convection parameterization used in the GISS 3-D GCM is adapted for use in a two-dimensional (2-D) zonally averaged statistical-dynamical model. Experiments with different versions of the parameterization show that its impact on the general circulation in the 2-D model does not parallel its impact in the 3-D model unless the effect of zonal variations is parameterized in the moist convection calculations. A parameterization of the variations in moist static energy is introduced in which the temperature variations are calculated from baroclinic stability theory, and the relative humidity is assumed to be constant. Inclusion of the zonal variations of moist static energy in the 2-D moist convection parameterization allows just a fraction of a latitude circle to be unstable and enhances the amount of deep convection. This leads to a 2-D simulation of the general circulation very similar to that in the 3-D model. The experiments show that the general circulation is sensitive to the parameterized amount of deep convection in the subsident branch of the Hadley cell. The more there is, the weaker are the Hadley cell circulations and the westerly jets. The experiments also confirm the effects of momentum mixing associated with moist convection found by earlier investigators and, in addition, show that the momentum mixing weakens the Ferrel cell. An experiment in which the moist convection was removed while the hydrological cycle was retained and the eddy forcing was held fixed shows that moist convection by itself stabilizes the tropics, reduces the Hadley circulation, and reduces the maximum speeds in the westerly jets.

Yao, Mao-Sung↗

Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties

Some nanoporous, crystalline materials possess dynamic constituents, for example, rotatable moieties. These moieties can undergo a conformation change in response to the adsorption of guest molecules, which qualitatively impacts adsorption behavior. Here, we pose and solve a statistical mechanical model of gas adsorption in a porous crystal whose cages share a common ligand that can adopt two distinct rotational conformations. Guest molecules incentivize the ligands to adopt a different rotational configuration than maintained in the empty host. Our model captures inflections, steps, and hysteresis that can arise in the adsorption isotherm as a signature of the rotating ligands. The insights disclosed by our simple model contribute a more intimate understanding of the response and consequence of rotating ligands integrated into porous materials to harness them for gas storage and separations, chemical sensing, drug delivery, catalysis, and nanoscale devices. Particularly, our model reveals design strategies to exploit these moving constituents and engineer improved adsorbents with intrinsic thermal management for pressure-swing adsorption processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Extinction Dynamics of the Foot-and-Mouth Disease Virus Carrier State Under Natural Conditions

Foot-and-mouth disease (FMD) is one of the most economically important livestock diseases worldwide. Following the clinical phase of FMD, a large proportion of ruminants remain persistently infected for extended periods. Although extinction of this carrier state occurs continuously at the animal and population levels, studies vary widely in their estimates of the duration of persistent infection. There is a need for robust statistical models to capture the dynamics of persistent infection for the sake of guiding FMD control and trade policies. The goal of the current study was to develop and assess statistical models to describe the extinction of FMD virus (FMDV) persistent infection using data from primary longitudinal studies of naturally infected cattle and Asian buffalo in Vietnam and India. Specifically, accelerated failure time (AFT) models and generalized linear mixed models (GLMM) were developed to predict the probability of persistent infection in seropositive animals and identified carriers at the individual animal level at sequential time points after outbreaks. The primary studies were analyzed by country and combined using an individual-participant data meta-analysis approach. The models estimated similar trends in the duration of persistent infection for the study/species groups included in the analyses, however the significance of the trends differed between the models. The overall probabilities of persistent infection were similar as predicted by the AFT and GLMM models: 6 months: 99% (AFT) /80% (GLMM), 12 months: 51% (AFT) /32% (GLMM), 18 months: 6% (AFT) /5% (GLMM), 24 months: 0.8% (AFT) /0.6% (GLMM). These models utilizing diverse and robust data sets predict higher probabilities of persistence than previously published, suggesting greater endurance of carriers subsequent to an outbreak. This study demonstrates the utility of statistical models to investigate the dynamics of persistent infection and the importance of large datasets, which can be achieved by combining data from several smaller studies in meta-analyses. Results of this study enhance current knowledge of the FMDV carrier state and may inform policy decisions regarding FMDV persistent infection.

59 BASIC BIOLOGICAL SCIENCES↗

UV stars and the interstellar medium - A statistical time-dependent model

A statistical time-dependent model for the effects on the interstellar gas of the ionizing radiation from UV stars is presented. The radiation from the stars is assumed to be emitted as monochromatic bursts at random times and locations. The thermal and ionization history of the gas is followed in a Monte Carlo simulation. Probability densities as well as mean values for the ionization fraction, temperature, and other observable quantities are derived. The fluctuations in observed quantities due to the stochastic nature of the model are estimated. Models of the interstellar medium perpendicular to the galactic plane are developed and compared with observations. The action of the UV stars can explain the bulk properties of the interstellar gas toward the galactic poles and is consistent with the Copernicus satellite observations toward lambda Scorpii.

Lyon, J.↗

Upper-Stratospheric Ozone Trends 1979-1998

Extensive analyses of ozone observations between 1978 and 1998 measured by Dobson Umkehr, Stratospheric Aerosol and Gas Experiment (SAGE) I and II, and Solar Backscattered Ultraviolet (SBUV) and (SBUV)/2 indicate continued significant ozone decline throughout the extratropical upper stratosphere from 30-45 km altitude. The maximum annual linear decline of -0.8 +/- 0.2 %/yr(2sigma) occurs at 40 km and is well described in terms of a linear decline modulated by the 11-year solar variation. The minimum decline of -0.110.1% yr-1(2o) occurs at 25 km in midlatitudes, with remarkable symmetry between the Northern and Southern Hemispheres at 40 km altitude. Midlatitude upper-stratospheric zonal trends exhibit significant seasonal variation (+/- 30% in the Northern Hemisphere, +/- 40% in the Southern Hemisphere) with the most negative trends of -1.2%/yr occurring in the winter. Significant seasonal trends of -0.7 to -0.9%/yr occur at 40 km in the tropics between April and September. Subjecting the statistical models used to calculate the ozone trends to intercomparison tests on a variety of common data sets yields results that indicate the standard deviation between trends estimated by 10 different statistical models is less than 0.1%/yr in the annual-mean trend for SAGE data and less than 0.2%/yr in the most demanding conditions (seasons with irregular, sparse data) [World Meteorological Organization (WMO), 1998]. These consistent trend results between statistical models together with extensive consistency between the independent measurement-system trend observations by Dobson Umkehr, SAGE I and II, and SBUV and SBUV/2 provide a high degree of confidence in the accuracy of the declining ozone amounts reported here. Additional details of ozone trend results from 1978 to 1996 (2 years shorter than reported here) along with lower-stratospheric and tropospheric ozone trends, extensive intercomparisons to assess relative instrument drifts, and retrieval algorithm details are given by WMO [1998].

Newchurch, M. J.↗

coh3

CoH3 (CoH ver.3) is an optical model, exciton pre-equilibrium, and Hauser-Feshbach statistical model code, which calculates nuclear reaction cross sections for medium to heavy targets in the keV to MeV energy region. This program is written in standard C++, divided into approximately 200 source and header files. CoH solves the Schroedinger equation for optical potentials defined in the code, and calculates differential elastic scattering, reaction, and total cross sections, for neutron, proton, deuteron, triton, 3He, and alpha-particle. Deformed optical potentials are solved with the coupled-channels method, in which the ground state rotational band members, or vibrational phonon states are coupled. The optical model gives particle transmission coefficients that are fed into the statistical model calculations. CoH includes the pre-equilibrium model (exciton model), the direct/semidirect capture model, and the multi-stage Hauser-Feshbach statistical decay with width fluctuation correction based on the Gaussian orthogonal ensemble. For weakly coupled levels, the DWBA (distorted wave Born approximation) method is used to calculate the direct inelastic scattering process to the excited states.

Kawano, Toshihiko↗

Simulations of diffusion-reaction equations with implications to turbulent combustion modeling

An enhanced diffusion-reaction reaction system (DRS) is proposed as a statistical model for the evolution of multiple scalars undergoing mixing and reaction in an isotropic turbulence field. The DRS model is close enough to the scalar equations in a reacting flow that other statistical models of turbulent mixing that decouple the velocity field from scalar mixing and reaction (e.g. mapping closure model, assumed-pdf models) cannot distinguish the model equations from the original equations. Numerical simulations of DRS are performed for three scalars evolving from non-premixed initial conditions. A simple one-step reversible reaction is considered. The data from the simulations are used (1) to study the effect of chemical conversion on the evolution of scalar statistics, and (2) to evaluate other models (mapping-closure model, assumed multivariate beta-pdf model).

Girimaji, Sharath S.↗

Moist Process Biases in Simulations of the Madden–Julian Oscillation Episodes Observed during the AMIE/DYNAMO Field Campaign

Two Madden–Julian oscillation (MJO) episodes observed during the 2011 Atmospheric Radiation Measurement Program MJO Investigation Experiment (AMIE)/DYNAMO field campaign are simulated using a regional model with various cumulus parameterizations, a regional cloud-permitting model, and a global variable-resolution model with a high-resolution region centered over the tropical Indian Ocean. Model biases in relationships relevant to existing instability theories of MJO are examined and their relative contributions to the overall model errors are quantified using a linear statistical model. The model simulations capture the observed approximately log-linear relationship between moisture saturation fraction and precipitation, but precipitation associated with the given saturation fraction is overestimated especially at low saturation fraction values. This bias is a major contributor to the excessive precipitation during the suppressed phase of MJO. After accounting for this bias using a linear statistical model, the spatial and temporal structures of the model-simulated MJO episodes are much improved, and what remains of the biases is strongly correlated with biases in saturation fraction. The excess precipitation bias during the suppressed phase of the MJO episodes is accompanied by excessive column-integrated radiative forcing and surface evaporation. A large portion of the bias in evaporation is related to biases in wind speed, which are correlated with those of precipitation. Furthermore, these findings suggest that the precipitation bias sustains itself at least partly by cloud radiative feedbacks and convection–surface wind interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of Grammar-Based and Statistical Language Models Trained on the Same Data

This paper presents a methodologically sound comparison of the performance of grammar-based (GLM) and statistical-based (SLM) recognizer architectures using data from the Clarissa procedure navigator domain. The Regulus open source packages make this possible with a method for constructing a grammar-based language model by training on a corpus. We construct grammar-based and statistical language models from the same corpus for comparison, and find that the grammar-based language models provide better performance in this domain. The best SLM version has a semantic error rate of 9.6%, while the best GLM version has an error rate of 6.0%. Part of this advantage is accounted for by the superior WER and Sentence Error Rate (SER) of the GLM (WER 7.42% versus 6.27%, and SER 12.41% versus 9.79%). The rest is most likely accounted for by the fact that the GLM architecture is able to use logical-form-based features, which permit tighter integration of recognition and semantic interpretation.

Hockey, Beth Ann↗

β -delayed neutron emissions from N > 50 gallium isotopes

β-delayed γ-neutron spectroscopy has been performed on the decay of A = 84 to 87 gallium isotopes at the RI-beam Factory at the RIKEN Nishina Center using a high-efficiency array of 3 He neutron counters (BRIKEN). β-2n-γ events were measured in the decays of all of the four isotopes for the first time, which is direct evidence for populating the excited states of two-neutron daughter nuclei. Detailed decay schemes with the γ branching ratios were obtained for these isotopes, and the neutron emission probabilities (P xn ) were updated from the previous study. Hauser-Feshbach statistical model calculations were performed to understand the experimental branching ratios. We found that the P 1n and P 2n values are sensitive to the nuclear level densities of 1n daughter nuclei and showed that the statistical model reproduced the P 2n /P 1n ratio better when experimental levels plus shell-model level densities fit by the Gilbert-Cameron formula were used as the level-density input. We also showed the neutron and γ branching ratios are sensitive to the ground-state spin of the parent nucleus. Our statistical model analysis suggested J ≤ 3 for the unknown ground-state spin of the odd-odd nucleus 86 Ga, from the I γ (4 + → 2 + )/I γ (2 + → 0 + ) ratio of 84 Ga and the P 2n /P 1n ratio. In conclusion, these results show the necessity of detailed understanding of the decay scheme, including data from neutron spectroscopy, in addition to γ measurements of the multineutron emitters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain

The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grün (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. Furthermore, the KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to be used in micromechanical constitutive models.

42 ENGINEERING↗

An evaluation of the variable-resolution CESM for modeling California's climate

In this paper, the recently developed variable-resolution option within the Community Earth System Model (VR-CESM) is assessed for long-term regional climate modeling of California at 0.25° (~ 28 km) and 0.125° (~ 14 km) horizontal resolutions. The mean climatology of near-surface temperature and precipitation is analyzed and contrasted with reanalysis, gridded observational data sets, and a traditional regional climate model (RCM)—the Weather Research and Forecasting (WRF) model. Statistical metrics for model evaluation and tests for differential significance have been extensively applied. VR-CESM tended to produce a warmer summer (by about 1–3°C) and overestimated overall winter precipitation (about 25%–35%) compared to reference data sets when sea surface temperatures were prescribed. Increasing resolution from 0.25° to 0.125° did not produce a statistically significant improvement in the model results. By comparison, the analogous WRF climatology (constrained laterally and at the sea surface by ERA-Interim reanalysis) was ~1–3°C colder than the reference data sets, underestimated precipitation by ~20%–30% at 27 km resolution, and overestimated precipitation by ~ 65–85% at 9 km. Overall, VR-CESM produced comparable statistical biases to WRF in key climatological quantities. Moreover, this assessment highlights the value of variable-resolution global climate models (VRGCMs) in capturing fine-scale atmospheric processes, projecting future regional climate, and addressing the computational expense of uniform-resolution global climate models.

54 ENVIRONMENTAL SCIENCES↗

In silico environmental chemical science: properties and processes from statistical and computational modelling

Quantitative structure–activity relationships (QSARs) have long been used in the environmental sciences. More recently, molecular modeling and chemoinformatic methods have become widespread. These methods have the potential to expand and accelerate advances in environmental chemistry because they complement observational and experimental data with “in silico” results and analysis. The opportunities and challenges that arise at the intersection between statistical and theoretical in silico methods are most apparent in the context of properties that determine the environmental fate and effects of chemical contaminants (degradation rate constants, partition coefficients, toxicities, etc.). The main example of this is the calibration of QSARs using descriptor variable data calculated from molecular modeling, which can make QSARs more useful for predicting property data that are unavailable, but also can make them more powerful tools for diagnosis of fate determining pathways and mechanisms. Emerging opportunities for “in silico environmental chemical science” are to move beyond the calculation of specific chemical properties using statistical models and toward more fully in silico models, prediction of transformation pathways and products, incorporation of environmental factors into model predictions, integration of databases and predictive models into more comprehensive and efficient tools for exposure assessment, and extending the applicability of all the above from chemicals to biologicals and materials.

54 ENVIRONMENTAL SCIENCES↗

First Direct Measurement Constraining the Ar 34 ( α , p ) K 37 Reaction Cross Section for Mixed Hydrogen and Helium Burning in Accreting Neutron Stars

The rate of the final step in the astrophysical αp process, the 34 Ar(α,p) 37 K reaction, suffers from large uncertainties due to a lack of experimental data, despite having a considerable impact on the observable light curves of x-ray bursts and the composition of the ashes of hydrogen and helium burning on accreting neutron stars. Here, we present the first direct measurement constraining the 34Ar(α,p)37K reaction cross section, using the Jet Experiments in Nuclear Structure and Astrophysics gas jet target. The combined cross section for the 34 Ar,Cl(α,p) 37 K,Ar reaction is found to agree well with Hauser-Feshbach predictions. The 34 Ar(α,2p) 36 Ar cross section, which can be exclusively attributed to the 34 Ar beam component, also agrees to within the typical uncertainties quoted for statistical models. This indicates the applicability of the statistical model for predicting astrophysical (α,p) reaction rates in this part of the αp process, in contrast to earlier findings from indirect reaction studies indicating orders-of-magnitude discrepancies. This removes a significant uncertainty in models of hydrogen and helium burning on accreting neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Searching for the Beginning of the Ozone Turnaround Using a 22-Year Merged Satellite Data Set

We have used the data from six satellite instruments that measure the total column amount of ozone to construct a consistent merged data set extending from late 1978 into 2000. The keys to constructing a merged data set are to minimize potential drift of individual instruments and to accurately establish instrument-to-instrument offsets. We have used the short-wavelength D-pair measurements (306nm-313nm) of the SBUV and SBUV/2 instruments near the equator to establish a relatively drift-free record for these instruments. We have then used their overlap with the Nimbus 7 and EP TOMS instruments to establish the relative calibration of the various instruments. We have evaluated the drift uncertainty in our merged ozone data (MOD) set by examining both the individual instrument drift uncertainty and the uncertainty in establishing the instrument- to-instrument differences. We conclude that the instrumental drift uncertainty over the 22-year data record is 0.9 %/decade (2-sigma). We have compared our MOD record with 37 ground stations that have a continuous record over that time period. We have a mean drift with respect to the stations of +0.3 %/decade which is within 1-sigma of our uncertainty estimate. Using the satellite record as a transfer standard, we can estimate the capability of the ground instruments to establish satellite calibration. Adding the statistical variability of the station drifts with respect to the satellite to an estimate of the overall drift uncertainty of the world standard instrument, we conclude that the stations should be able to be used to establish the drift of the satellite data record to within and uncertainty of 0.6 %/decade (2-sigma). Adding to this an uncertainty due to the-incomplete global coverage of the stations, we conclude that the station data should be able to establish the global trend with an uncertainty of about 0.7 %/decade, slightly better than for the satellite record. We conclude that merging the two records together gives only a slight improvement in the uncertainty. Keeping them separate gives the greater confidence of two independent measures of the ozone trend and potential recovery. We fit the trend in our MOD record through May of 1991 and then extrapolated forward to see if the data at the end of the record was above the statistical model as a measure of ozone recovery as was done in the last WMO/UNEP assessment report. Because our data set drifts with respect to the ground-stations through May of 1991, we calculated a smaller global trend (-1.1 %/decade) than in the WMO/UNEP report. Our data in 1998 and 1999 was, on average 2 DU above the extrapolated statistical model with a 2-sigma uncertainty of 6 DU. For the combined mid-latitudes of the northern and southern hemispheres, the data was 5 DU above the extrapolated statistical model with a 2-sigma uncertainty of 10 DU. These may be signs of recovery, but they are still statistically insignificant.

Stolarski, Richard S.↗

Fully versus constrained statistical fragmentation of carbon clusters and their heteronuclear derivatives

The Microcanonical Metropolis Monte Carlo (MMMC) method has been shown to describe reasonably well fragmentation of clusters composed of identical atomic species. However, this is not so clear in the case of heteronuclear clusters as some regions of phase space might be inaccessible due to the different mobility of the different atomic species, the existence of large isomerization barriers, or the quite different chemical nature of the possible intermediate species. In this paper, we introduce a constrained statistical model that extends the range of applicability of the MMMC method to such mixed clusters. The method is applied to describe fragmentation of isolated clusters with high, moderate, and no heteronuclear character, namely, C n H m , C n N, and C n clusters for which experimental fragmentation branching ratios are available in the literature. We show that the constrained statistical model describes fairly well fragmentation of CnHm clusters in contrast with the poor description provided by the fully statistical model. The latter model, however, works pretty well for both C n and C n N clusters, thus showing that the ultimate reason for this discrepancy is the inability of the MMMC method to selectively explore the whole phase space. This conclusion has driven us to predict the fragmentation patterns of the C 4 N cluster for which experiments are not yet available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗