Heikki Haario

An adaptive Metropolis algorithm

A proper choice of a proposal distribution for Markov chain Monte Carlo methods, for example for the Metropolis-Hastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis (AM) algorithm, where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the process, the AM algorithm is non-Markovian, but we establish here that it has the correct ergodic properties. We also include the results of our numerical tests, which indicate that the AM algorithm competes well with traditional Metropolis-Hastings algorithms, and demonstrate that the AM algorithm is easy to use in practical computation.

DRAM: Efficient adaptive MCMC

We propose to combine two quite powerful ideas that have recently appeared in the Markov chain Monte Carlo literature: adaptive Metropolis samplers and delayed rejection. The ergodicity of the resulting non-Markovian sampler is proved, and the efficiency of the combination is demonstrated with various examples. We present situations where the combination outperforms the original methods: adaptation clearly enhances efficiency of the delayed rejection algorithm in cases where good proposal distributions are not available. Similarly, delayed rejection provides a systematic remedy when the adaptation process has a slow start.

Componentwise adaptation for high dimensional MCMC

SummaryWe introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.

Effect of nutrient loading on bacterioplankton community composition in lake mesocosms.

Changes in bacterioplankton community composition were followed in mesocosms set up in the littoral of Lake Vesijärvi, southern Finland, over two summers. Increasing nitrogen and phosphorus concentrations in the mesocosms represented different trophic states, from mesotrophic to hypertrophic. In 1998, the mesocosms were in a turbid state with a high biomass of phytoplankton, whereas in 1999, macrophytes proliferated and a clear-water state prevailed. The bacterial communities in the mesocosms also developed differently, as shown by denaturing gradient gel electrophoresis profiling of partial 16S rRNA gene fragments and by nonmetric multidimensional scaling analysis. In 1998, nutrient treatments affected the diversity and clustering of bacterial communities strongly, but in 1999, the bacterial communities were less diversified and not clearly affected by treatments. Canonical correspondence analysis indicated that bacterioplankton communities in the mesocosms were influenced by environmental physicochemical variables linked to the increasing level of eutrophication. Nitrogen concentration correlated directly with the bacterioplankton composition. In addition, the high nutrient levels had indirect effects through changes in the biomass and composition of phyto- and zooplankton. Sequencing analysis showed that the dominant bacterial divisions remained the same, but the dominant phylotypes changed during the 2-year period. The occurrence of Verrucomicrobia correlated with more eutrophic conditions, whereas the occurrence of Actinobacteria correlated with less eutrophic conditions.

Microbial functional activity during composting of chlorophenol-contaminated sawmill soil

Microbial status during a successful full-scale bioremediation by composting chlorophenol-contaminated soil was studied in three different ways: conventional enumeration of microbes on selective and general media, microbial activity assessed by soil respiration, and community structure studied by the utilization pattern of a large range of substrates using Biolog® microtitre plates. Utilization of ammonium, nitrate and soluble P was also followed. Chlorophenols were well removed in all compost piles which were mixtures of contaminated soil and bark chips or straw compost. The best indicator of the actual chlorophenol degradation efficiency was the number of microbes growing on plates with 2 mM pentachlorophenol (PCP) as the sole carbon source. Nutrient analyses showed that ammonium was rapidly used, and nitrification took place in some of the compost piles. The data from Biolog® microtitre plates was analyzed using the toolbox of Matlab® mathematical software. The areas under the substrate utilization curve were integrated for each substrate used, and they were used for principal component analysis. We were able to see pile-specific substrate usage for piles containing straw compost, but not for pile containing bark chips. All these characteristic substrates were either amino acids or amines. The results suggested that fast-growing microbes responsible for utilization of easily available substrates, measured by respiratory activity and substrate utilization patterns in Biolog, originated mainly from the added bulking agents, straw compost and bark chips. The chlorophenol-degraders originating from contaminated soil seemed not directly to contribute to the Biolog utilization pattern, but probably had benefited from the enhanced general microbial activity in the composts by cometabolism or synergism.

Combining soft and hard modelling in chemical kinetic models

Abstract Spectral data are increasingly used for the identification of the `hard kinetic parameters. The conventional approach is to perform a separate `soft calibration between spectra and concentration units. The calibrated concentration values are then used for the fit of the parameters. In the present work we suggest an approach which is based on a simultaneous soft calibration of the spectral data and hard kinetic parameter estimation. We study how the kinetics may be identified without any pure component spectral data and with minimal separate calibration. Such knowledge is valuable in situations where the concentrations of some components cannot be analysed or where a separate calibration is especially difficult or time consuming.

DETERMINATION OF PARTICLE AND CRYSTAL SIZE DISTRIBUTION FROM TURBIDITY SPECTRUM OF TIO2 PIGMENTS BY MEANS OF T-MATRIX

Abstract A method has been developed for the determination of particle and crystal size distributions of rutile titanium dioxide pigments. This is based on a rigorous model for the turbidity (light extinction) spectra of rutile particles in dilute water suspension. The inversion of the rigorous model leads to an ill-posed problem and to a semi-rigorous method, in which the constraints of the solution have been determined empirically. The pigment particles are approximated as spheroids and a two-dimensional size distribution of particle width and ratio of length and width is calculated. Most of the particles are single crystals but a small amount is in aggregate form. A method to separate the distributions of aggregates and single crystals is proposed. The extinction cross section values for spheroids, needed in the model, are calculated by the T-matrix method. A comparison of the crystal size results with the values determined by transmission electron microscopy shows a very good accuracy for mean values of both the volume equivalent size and for the width, whereas the results for the means of the length/width ratio are much less accurate.

Stationary kinetics of essential reactions on automobile exhaust PtRh/Al2O3 catalyst

Abstract The essential oxidation and reduction reactions over ceria promoted Pt Rh/Al2O3 catalyst were studied in a laboratory testing system consisting of a metallic three-way catalyst. Oxidation of CO and propene as well as reduction of NO were examined under steady state conditions at 100–400°C and at atmospheric pressure. The concentrations of CO, CO2, total hydrocarbons, NO/NOx and O2 at the monolith outlet were measured for different gas feeds. The presence of water had a considerable effect on the kinetics. Water enhanced the oxidation reactions at low temperatures, while water-gas shift reaction and steam reforming took place at higher temperatures. Steady-state rate equations based on plausible surface reaction mechanisms for the oxidation of CO and propene as well as the reduction of NO with CO were derived for dry and wet conditions. The kinetic parameters included in the rate equations were estimated with nonlinear regression analysis. The experimental and the predicted concentrations were in good agreement, indicating that the kinetic models with their underlying mechanistic assumptions are able to predict the behaviour of the Pt Rh/Al2O3 catalyst.

Investigation of CO oxidation and NO reduction on three-way monolith catalysts with transient response techniques

The kinetics of CO oxidation and NO reduction reactions over alumina and alumina-ceria supported Pt, Rh and bimetallic Pt/Rh catalysts coated on metallic monoliths were investigated using the step response technique at atmospheric pressure and at temperatures 30–350°C. The feed step change experiments from an inert flow to a flow of a reagent (O2, CO, NO and H2) showed that the ceria promoted catalysts had higher adsorption capacities, higher reaction rates and promoting effects by preventing the inhibitory effects of reactants, than the alumina supported noble metal catalysts. The effect of ceria was explained with adsorbate spillover from the noble metal sites to ceria. The step change experiments CO/O2 and O2/CO also revealed the enhancing effect of ceria. The step change experiments NO/H2 and H2/NO gave nitrogen as a main reduction product and N2O as a by-product. Preadsorption of NO on the catalyst surface decreased the catalyst activity in the reduction of NO with H2. The CO oxidation transients were modeled with a mechanism which consistent of CO and O2 adsorption and a surface reaction step. The NO reduction experiments with H2 revealed the role of N2O as a surface intermediate in the formation of N2. The formation of NN bonding was assumed to take place prior to, partly prior to or totally following to the NO bond breakage. High NO coverage favors N2O formation. Pt was shown to be more efficient than Rh for NO reduction by H2.

Mass transfer in tubular reactors equipped with static mixers

Abstract Gas—liquid mass transfer was studied in horizontal tubular reactors equipped with static mixers. In such reactors, it often makes sense to leave empty spaces between mixer elements to avoid excessive pressure drops. Increasing the length of these spaces improves the reactor performance because of the reduced pressure drop but, on the other hand, worsens it because of the decreased mass transfer efficiency. Pressure drop and mass transfer efficiency can also be affected by liquid velocity. A detailed model, including a description of mass transfer and pressure drop, is presented. A novel approach was developed to evaluate the interfacial area in the transition zones between the flow patterns in the mixers and in the empty spaces. The parameters of the model were estimated from a large set of experimental results obtained by two different methods, a chemical and a physical one. Utilization of the model in reactor optimization is demonstrated.