Comparison of global and local sensitivity techniques for rate constants determined using complex reaction mechanisms

![Figure][1] J. Patrick Kampf Torrey Pines Institute for Molecular Studies, San Diego, California ![Figure][1] Alan M. Kleinfeld Torrey Pines Institute for Molecular Studies, San Diego, California akleinfeld{at}tpims.org The mechanism of free fatty acid (FFA)

Nuclear-decay data: The statement of uncertainties

At the annual general meeting of the International Committee for Radionuclide Metrology (ICRM) held last June at the Physikalisch-Technische Bundesanstalt, it was suggested that letters should be sent to the editors of journals that publish nucleardecay data, drawing attention to the need for specific statements of the uncertainties that are associated with such data. Authors frequently fail to state clearly the nature of their estimates of uncertainty, and not all editors insist on such clarity, so that evaluators of nuclear-decay data often f'md that it is necessary to consult with the individual authors to arrive at the weighting factors appropriate to their data. If uncertainties could be dearly characterized in the abstracts or in the text of papers reporthag values of nuclear parameters, there would be a corresponding shortening of the time required for the data to be evaluated and tabulated. There are many methods of stating estimates of conventional random and systematic uncertainties that are acceptable, provided that the methods used are described. Thus random error may be stated as: (i) the estimate of the standard deviation (or the square root of the variance), which is in the same units as the observed data and indicates the order of magnitude of the spread of the data: (ii) the standard error (or the estimated standard deviation of the mean of the distribution); and (ri) the estimated limits for the mean at stated levels of confidence (C1) (e.g. limits at the 99-percent CI define the range within which there is a 99:percent probability of ineluding the mean of a population). Provided that the author states the number of independent measurements made of the given parameter, or the number of degrees of freedom, these statements of random uncertainty are related uniquely to each other. The other component of the overall uncertainty is the estimate of possible systematic error. The significance, or meaning, of the estimate of systematic uncertainties should be dearly stated and also related to the method chosen to state the random uncertainties. Thus an estimate of maximum conceivable systematic uncertainties would logically be combined with a random uncertainty at a 99-percent confidence level. An appropriate fraction of the estimate of maximum conceivable systematic uncertainty would be chose to match smaller random confidence levels. The methods used to combine random and systematic uncertainties should also be stated by authors, and an explicit listing of all components of these uncertainties will allow an evaluator of nuclear data to unravel the statements of uncertainty and to choose

GEMSFITS: Code package for optimization of geochemical model parameters and inverse modeling

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goal-oriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used.

Sensitivity analysis of a model for the radical recombination region of hydrocarbon-air flames

The folding pathways of some proteins include the population of partially structured species en route to the native state. Identification and characterization of these folding intermediates are particularly difficult as they are often only transiently populated and play different mechanistic roles, being either on-pathway productive species or off-pathway kinetic traps. To define the role of folding intermediates, a quantitative analysis of the folding and unfolding rate constants over a wide range of denaturant concentration is often required. Such a task is further complicated by the reversible nature of the folding reaction, which implies the observed kinetics to be governed by a complex combination of different microscopic rate constants. Here, we tackled this problem by measuring directly the folding rate constant under highly denaturing conditions, namely by inducing the folding of a PDZ domain through a quasi-irreversible binding reaction with a specific peptide. In analogy with previous works based on hydrogen exchange experiments, we present evidence that the folding pathway of the PDZ domain involves the formation of an obligatory on-pathway intermediate. The results presented exemplify a novel type of kinetic test to detect an on-pathway folding intermediate.

Exothermic intramolecular triplet energy transfer (TET) rate constants in various flexible bichromophoric systems D-(CH2)n-O-A (D = benzoyl, 4-methylbenzoyl; A = 2-naphthyl, 4-, 3-, 2-biphenyl; n = 3−14) have been determined from steady-state quenching and quantum yield measurements. The magnitude of the rate constants in molecules where n = 3 is comparable to those in molecules with a rigid spacer between chromophores, so that a through-bond mechanism is presumed to remain important. A very gradual drop in TET rate constants as the connecting polymethylene chain becomes longer indicates that through-space interactions compete and apparently provide the only mechanism responsible for transfer when n ≥ 5. Rate constants in long molecules (n = 11−14) remain remarkably high (∼108 s-1)lower than in those with four-atom tethers by only 1 order of magnitude. This effect is explained on the basis of rapid conformational equilibria always keeping a sufficient fraction of the molecules coiled so that the two chromophores are close enough to interact within 10 ns, the time required for the competing γ-hydrogen abstraction used to monitor triplet lifetimes. Energy transfer accounts for 40−75% of triplet decay for the longer molecules. This high efficiency indicates that only a small fraction involves static quenching in ground-state conformers with the two ends within 4 Å. The majority must represent a combination of rate-determining bond rotations to such geometries and equilibrated conformations with their ends farther apart but still able to undergo energy transfer within 10 ns. Thus, the measured rate constants are, in fact, a weighted average of three different conformational mechanisms. The decrease in rate constant with tether length is not monotonic: a relative increase in rate for medium-chain-length molecules is explained by a larger number of favorable conformers and further, in biphenyl derivatives, by a rotation along the terminal O−C bond between the tether and the aromatic ring. As was expected, replacement of the polymethylene tether with poly(ethylene oxide) promotes better flexibility and thus higher transfer rates. Rate constants were found to be lower by a factor of ∼2 when biphenyl rather than naphthyl is the acceptor, in agreement with earlier bimolecular measurements. With the 4-methylbenzoyl group (π,π* lowest triplet) as donor instead of benzoyl (n,π* lowest triplet), a small (∼1.5×) but consistent rate increase occurred for all tether lengths.

Rate constants for the overall reactions of OH with n-pentane, n-heptane, and n-nonane were measured in shock tube experiments behind reflected shock waves. Narrow-linewidth laser absorption by OH at 306.7 nm was used in pseudo first-order experiments with temperatures between 869 to 1364 K. tert-Butyl hydroperoxide (TBHP) was used as the OH precursor. Experiments were also performed to study the kinetics of the TBHP decomposition and resulting product chemistry, and an accurate mechanism describing OH precursor chemistry effects was developed to model OH concentration time-history in the n-alkane + OH experiments. The experimental results for the n-alkane + OH rate constant measurements can be expressed as rate constants in Arrhenius form as k n-pentane + OH = 2.10 × 10-10 exp(-2038/T[K]) (869–1364 K), k n-heptane + OH = 2.43 × 10-10 exp(-1804/T[K]) (869–1364 K), k n-nonane + OH = 3.17 × 10-10 exp(-1801/T[K]) (884–1352 K), each in units of cm3 molecule-1 s-1. The present rate constants measured for OH with n-pentane and n-heptane show agreement within 20% with recent work by Sivaramakrishnan and Michael [J. Phys. Chem. A, 113 (2009) 5047]. The measurements of the rate constant for n-nonane + OH presented here represent the first in the literature to depict the temperature dependence of the rate constant above 800 K. The measurements of each n-alkane + OH rate constant studied were compared with two models in the literature used to estimate the rate constants of n-alkane + OH reactions. The Structure-Activity Relationship of Kwok and Atkinson [Atmos. Environ., 29 (1995) 1685] shows the best agreement with the current data for all three n-alkanes over the entire temperature range studied, demonstrating that this model is capable of predicting the overall rate constants for reactions of OH with n-pentane, n-heptane, and n-nonane for temperatures up to 1364 K.

It is often necessary in optical analysis software to trace millions of rays in order to determine flux transfer, color chromaticity, and the distributions of intensity, irradiance, or radiance onto one or more targets. The key question of "have I traced enough rays?" cannot be answered unless the statistical error in the final simulated result is below some measurement criteria; for instance, if you are to determine irradiance uniformity to less than 1%, having a 2% statistical error across the target will wash out what you are trying to analyze. Some optical analysis software packages do not provide error estimation methods, while others use error estimation algorithms having assumptions that are not valid for all cases. This paper describes how subdividing and recombining raytraces provides a robust method for estimating error. We will show that this error estimation technique can be used with most optical analysis packages and we will compare it with algorithms employed currently. Example systems will be analyzed and presented.

Kinetics of the co/no surface reactions by the direct observation of the adsorbed species

We report here the first measurements of rate constants involving cluster ions with more than five ligands. We have measured rate constants, or lower limits to rate constants, for the reactions of H+(H2O)n=2–11 with NH3, CH3CN, CH3OH, CH3COCH3, and C5H5N (pyridine). The experimental techniques needed to study these ions and neutrals at low temperatures are described. The reactions all proceed rapidly by proton transfer with varying degrees of ligand transfer. At low temperatures the rate constants are larger than the collision rate constant based on an ion–dipole potential. Reasons for this are examined. Thermal dissociation appears to control the size distribution of the primary ion clusters and to affect the observed product distribution.

A general method for estimating the precision of parameters resulting from the use of various experimental designs (rate of injection and rate of tomographic data collection) in emission tomography studies is proposed. The sensitivity matrix of the study model and an estimate of the statistical uncertainty of the tomographic data are used to compute the covariance matrix of the parameters. The determinant of this covariance matrix (proportional to the total volume of uncertainty of the model parameters) serves as a criterion to be minimized. The method is applied to a three-compartment, three-transfer rate constant for glucose metabolism using dynamic positron emission tomography, and a comparison of various current protocols is made with simulated data. The results show that higher rates of injection and higher rates of tomographic data collection at early times lead to smaller statistical uncertainties for the estimates of rate constants. However, for the range of rate constants encountered in practice, differences are insignificant when an initial scan duration less than 30 s is used, without regarding the injection duration.

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

Aiming to solve the track refined correlation problem of the group targets with systematic errors, based on the characteristics of the group tracks, an algorithm of track refined correlation with in group targets based on systematic error compensation is proposed with the error estimation technique and the track correlation technique. In this algorithm, the groups are identified with the tracks of the sensors based on the circulatory threshold model firstly. Secondly, the preparatory correlation groups with the nearest resolving state are searched or established based on group track state identification model. Thirdly, the final systematic errors are estimated with group track systematic error estimation model and error validation model. What is more, the error compensation is completed. Finally, group track refined correlation is done with the traditional track correlation algorithms. The analysis results of the simulation data show that the general performance of this algorithm, which can meet the engineering requirement of the track refined correlation of the group targets with systematic errors very well, is better than that of fuzzy track alignment-correlation algorithm based on target topological information, track alignment-correlation algorithm based on iterative closest track and modified weighted track correlation algorithm.