Kinetic research on heterogeneously catalysed processes: a questionnaire on the state-of-the-art in industry

On the initiative of the Working Party `Chemical Engineering in the Applications of Catalysis¿ of the European Federation of Chemical Engineering an assessment of the issues in the determination and application of kinetic data within the European industry was performed. The basis of the analysis consisted of a questionnaire put together by researchers from Dow, DSM, Shell and Eindhoven University of Technology. The 24 companies, which have responded to the questionnaire, can be classified into four groups: chemical, oil, engineering contractors and catalyst manufacturers. From the overall input it appears that there are three, equally important, utilisation areas for kinetic data: process development, process optimisation and catalyst development. There is a wide variety of kinetic data sources. Most of the respondents make use of test units which were primarily designed for development and optimisation. Avoiding transport limitation is, certainly in the case of short range projects or for complex feedstocks, not always taken care of. With respect to the modelling approaches, a common philosophy is `as simple as possible¿. Most of the respondents state that `in principle¿ one should strive for intrinsic kinetics, but the majority nevertheless does for various reasons not separate all transport phenomena from reaction kinetics. Kinetic models are mostly simple first or nth order or Langmuir-Hinshelwood type expressions. More complex kinetic models are scarcely used. Three areas were frequently identified to offer opportunities for improvement. Gathering of kinetic data is too costly and time consuming. There is no systematic approach at all for determination and application of kinetics in case of unstable catalytic performance. Furthermore, the software available for the regression of kinetic data to rate equations based on mechanistic schemes as well as software to model reactors are insufficiently user friendly. The majority of the respondents state that the problems indicated should be solved by cooperation, e.g., between companies, between industry and academia and between the catalysis and the chemical engineering community. A workshop on the above topics was held in December 1996 with 15 companies and 6 academics attending. More information can be obtained from the secretariat of the Working Party

Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk

Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method for Bayesian analysis of models with ill-behaved posterior distributions. In order to sample efficiently from such a distribution, a location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a Metropolis-Hastings algorithm is applied to sample directions and, conditionally on these, distances are generated by inverting the CDF. A sequential procedure is applied to update the location and scale. Tested on a set of canonical models that feature near non-identifiability, strong correlation, and bimodality, APS compares favourably with the standard Metropolis-Hastings sampler in terms of parsimony and robustness. APS is applied within a Bayesian analysis of a GARCH-mixture model which is used for the evaluation of the Value-at-Risk of the return of the Dow Jones stock index.Markov Chain Monte Carlo;simulation;polar coordinates;GARCH;ill-behaved posterior;value-at-risk

Spectral imbalance and the normalized dissipation rate of turbulence

The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is observed for the two types of turbulence. This difference is found at moderate Reynolds number, and it is shown that it persists at high Reynolds number, where the value of $C_\epsilon$ becomes independent of the Reynolds number, but is still not unique. This difference can be explained by the influence of the nonlinear cascade time that introduces a spectral disequilibrium for statistically nonstationary turbulence. Phenomenological analysis yields simple analytical models that satisfactorily reproduce the numerical results. These simple spectral models also reproduce and explain the increase of $C_\epsilon$ at low Reynolds number that is observed in the simulations

Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

Adaptive radial-based direction sampling; Some flexible and robust Monte Carlo integration methods

Adaptive radial-based direction sampling (ARDS) algorithms are specified for Bayesian analysis of models with nonelliptical, possibly, multimodal target distributions.A key step is a radial-based transformation to directions and distances. After the transformations a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to evaluate generated directions. Next, distances are generated from the exact target distribution by means of the numerical inverse transformation method. An adaptive procedure is applied to update the initial location and covariance matrix in order to sample directions in an efficient way. Tested on a set of canonical mixture models that feature multimodality, strong correlation, and skewness, the ARDS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. The empirical examples include a regression model with scale contamination and a mixture model for economic growth of the USA.Markov chain Monte Carlo;importance sampling;radial coordinates

Explaining Adaptive Radial-Based Direction Sampling

In this short paper we summarize the computational steps of Adaptive Radial-Based Direction Sampling (ARDS), which can be used for Bayesian analysis of ill behaved target densities. We consider one simulation experiment in order to illustrate the good performance of ARDS relative to the independence chain MH algorithm and importance sampling.importance sampling;Markov Chain Monte Carlo;radial coordinates