Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Statistical Analysis and Numerics of Heat Exchanger Models

The identifiability of the parameters of a heat exchanger model without phase change was studied in this Master’s thesis using synthetically made data. A fast, two-step Markov chain Monte Carlo method (MCMC) was tested with a couple of case studies and a heat exchanger model. The two-step MCMC-method worked well and decreased the computation time compared to the traditional MCMC-method. The effect of measurement accuracy of certain control variables to the identifiability of parameters was also studied. The accuracy used did not seem to have a remarkable effect to the identifiability of parameters. The use of the posterior distribution of parameters in different heat exchanger geometries was studied. It would be computationally most efficient to use the same posterior distribution among different geometries in the optimisation of heat exchanger networks. According to the results, this was possible in the case when the frontal surface areas were the same among different geometries. In the other cases the same posterior distribution can be used for optimisation too, but that will give a wider predictive distribution as a result. For condensing surface heat exchangers the numerical stability of the simulation model was studied. As a result, a stable algorithm was developed.

TitGer: uma planilha eletrônica para simulação de titulação de mistura de compostos polipróticos

The aim of this paper is to present a simple way of treating the general equation for acid-base titrations based on the concept of degree of dissociation, and to propose a new spreadsheet approach for simulating the titration of mixtures of polyprotic compounds. The general expression, without any approximation, is calculated a simple iteration method, making number manipulation easy and painless. The user-friendly spreadsheet was developed by using MS-Excel and Visual-Basic-for-Excel. Several graphs are drawn for helping visualizing the titration behavior. A Monte Carlo function for error simulation was also implemented. Two examples for titration of alkalinity and McIlvaine buffer are presented.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

Ratiomuuttujat ja näennäinen korrelaatio

Eri tieteenalojen tutkijat ovat kiistelleet jo yli vuosisadan ajan ratiomuodossa olevien muuttujien käytön vaikutuksista korrelaatio- ja regressioanalyysien tuloksiin ja niiden oikeaan tulkintaan. Strategiatutkimuksen piirissä aiheeseen ei ole kuitenkaan kiinnitetty suuresti huomiota. Tämä on yllättävää, sillä ratiomuuttujat ovat hyvin yleisesti käytettyjä empiirisen strategiatutkimuksen piirissä. Tässä työssä luodaan katsaus ratiomuuttujien ympärillä käytyyn debattiin. Lisäksi selvitetään artikkelikatsauksen avulla niiden käytön yleisyyttä nykypäivän strategiatutkimuksessa. Työssä tutkitaan Monte Carlo –simulaatioiden avulla ratiomuuttujien ominaisuuksien vaikutuksia korrelaatio- ja regressioanalyysin tuloksiin erityisesti yhteisen nimittäjän tapauksissa.

Validação da metodologia da avaliação de incerteza em curvas de calibração melhor ajustadas por polinômios de segundo grau

The most widespread literature for the evaluation of uncertainty - GUM and Eurachem - does not describe explicitly how to deal with uncertainty of the concentration coming from non-linear calibration curves. This work had the objective of describing and validating a methodology, as recommended by the recent GUM Supplement approach, to evaluate the uncertainty through polynomial models of the second order. In the uncertainty determination of the concentration of benzatone (C) by chromatography, it is observed that the uncertainty of measurement between the methodology proposed and Monte Carlo Simulation, does not diverge by more than 0.0005 unit, thus validating the model proposed for one significant digit.

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Resolvendo a equação de Schrödinger utilizando procedimentos numéricos fundamentais

A combination of the variational principle, expectation value and Quantum Monte Carlo method is used to solve the Schrödinger equation for some simple systems. The results are accurate and the simplicity of this version of the Variational Quantum Monte Carlo method provides a powerful tool to teach alternative procedures and fundamental concepts in quantum chemistry courses. Some numerical procedures are described in order to control accuracy and computational efficiency. The method was applied to the ground state energies and a first attempt to obtain excited states is described.

PRACTICAL STOCHASTIC MODEL FOR CHEMICAL KINETICS

The Practical Stochastic Model is a simple and robust method to describe coupled chemical reactions. The connection between this stochastic method and a deterministic method was initially established to understand how the parameters and variables that describe the concentration in both methods were related. It was necessary to define two main concepts to make this connection: the filling of compartments or dilutions and the rate of reaction enhancement. The parameters, variables, and the time of the stochastic methods were scaled with the size of the compartment and were compared with a deterministic method. The deterministic approach was employed as an initial reference to achieve a consistent stochastic result. Finally, an independent robust stochastic method was obtained. This method could be compared with the Stochastic Simulation Algorithm developed by Gillespie, 1977. The Practical Stochastic Model produced absolute values that were essential to describe non-linear chemical reactions with a simple structure, and allowed for a correct description of the chemical kinetics.

Demographic Modelling of Human Population Growth

This work presents models and methods that have been used in producing forecasts of population growth. The work is intended to emphasize the reliability bounds of the model forecasts. Leslie model and various versions of logistic population models are presented. References to literature and several studies are given. A lot of relevant methodology has been developed in biological sciences. The Leslie modelling approach involves the use of current trends in mortality,fertility, migration and emigration. The model treats population divided in age groups and the model is given as a recursive system. Other group of models is based on straightforward extrapolation of census data. Trajectories of simple exponential growth function and logistic models are used to produce the forecast. The work presents the basics of Leslie type modelling and the logistic models, including multi- parameter logistic functions. The latter model is also analysed from model reliability point of view. Bayesian approach and MCMC method are used to create error bounds of the model predictions.

Reaktoreiden termisen tehon laskennan epävarmuuksien kartoitus

Diplomityössä selvitettiin Fortum Power and Heat Oy:n Loviisan VVER-440 painevesireaktorilaitosten termisen tehon laskentaan liittyviä epävarmuuksia. Laitoksen turvallisuusteknisissä käyttöehdoissa (TTKE) määrätään reaktorin suurimmaksi sallituksi lämpötehoksi 1500 MW. Tähän perustuen haluttiin selvittää nykyiseen RT1 laskentaan liittyvät epävarmuudet tarkastamalla nykyinen laskenta ja siinä käytetyt termohydrauliset laskentasovitteet. Työn alussa selostetaan lyhyesti Loviisan voimalaitoksen toimintaperiaate, jonka jälkeen esitellään laskentaan osallistuvat prosessimittaukset ja niihin liittyvät epävarmuustekijät. Mittauksille määritettiin epävarmuudet käyttäen hyödyksi komponenttivalmistajien tietoja sekä laitoksen kalibrointitodistuksia ja näiden lisäksi laskettiin standardin mukainen virhe virtauslaipoille. Edellä mainittujen virheiden perusteella voitiin laskea tehon epävarmuudet yksittäiselle höyrystimelle, josta edelleen varianssien summamenetelmällä saatiin reaktorin termiselle teholle 0,78 %:n epävarmuus 95 % luottamustasolla. Laskettua tehon epävarmuutta verrattiin Monte Carlo -menetelmällä suoritettuun tarkistuslaskentaan, jolla termisen tehon epävarmuudeksi saatiin 0,53 %, luottamustason ollessa 95 %. Työssä tarkasteltiin keskiarvotuksen vaikutusta mittausdataan. Näissä tarkasteluissa havaittiin pinnansäädöstä aiheutuva reaktoritehon huojunta, joka oli työn merkittävin havainto.

Kinetic modeling of mechanisms of industrially important organic reactions in gas and liquid phase

This dissertation is based on 5 articles which deal with reaction mechanisms of the following selected industrially important organic reactions: 1. dehydrocyclization of n-butylbenzene to produce naphthalene 2. dehydrocyclization of 1-(p-tolyl)-2-methylbutane (MB) to produce 2,6-dimethylnaphthalene 3. esterification of neopentyl glycol (NPG) with different carboxylic acids to produce monoesters 4. skeletal isomerization of 1-pentene to produce 2-methyl-1-butene and 2-methyl-2-butene The results of initial- and integral-rate experiments of n-butylbenzene dehydrocyclization over selfmade chromia/alumina catalyst were applied when investigating reaction 2. Reaction 2 was performed using commercial chromia/alumina of different acidity, platina on silica and vanadium/calcium/alumina as catalysts. On all catalysts used for the dehydrocyclization, major reactions were fragmentation of MB and 1-(p-tolyl)-2-methylbutenes (MBes), dehydrogenation of MB, double bond transfer, hydrogenation and 1,6-cyclization of MBes. Minor reactions were 1,5-cyclization of MBes and methyl group fragmentation of 1,6- cyclization products. Esterification reactions of NPG were performed using three different carboxylic acids: propionic, isobutyric and 2-ethylhexanoic acid. Commercial heterogeneous gellular (Dowex 50WX2), macroreticular (Amberlyst 15) type resins and homogeneous para-toluene sulfonic acid were used as catalysts. At first NPG reacted with carboxylic acids to form corresponding monoester and water. Then monoester esterified with carboxylic acid to form corresponding diester. In disproportionation reaction two monoester molecules formed NPG and corresponding diester. All these three reactions can attain equilibrium. Concerning esterification, water was removed from the reactor in order to prevent backward reaction. Skeletal isomerization experiments of 1-pentene were performed over HZSM-22 catalyst. Isomerization reactions of three different kind were detected: double bond, cis-trans and skeletal isomerization. Minor side reaction were dimerization and fragmentation. Monomolecular and bimolecular reaction mechanisms for skeletal isomerization explained experimental results almost equally well. Pseudohomogeneous kinetic parameters of reactions 1 and 2 were estimated by usual least squares fitting. Concerning reactions 3 and 4 kinetic parameters were estimated by the leastsquares method, but also the possible cross-correlation and identifiability of parameters were determined using Markov chain Monte Carlo (MCMC) method. Finally using MCMC method, the estimation of model parameters and predictions were performed according to the Bayesian paradigm. According to the fitting results suggested reaction mechanisms explained experimental results rather well. When the possible cross-correlation and identifiability of parameters (Reactions 3 and 4) were determined using MCMC method, the parameters identified well, and no pathological cross-correlation could be seen between any parameter pair.

Some defects in two-dimensional spin-1/2 Heisenberg antiferromagnets: a numerical study of magnetic effects

En del av de intressantaste fenomenen inom dagens materialfysik uppstår ur ett intrikat samspel mellan myriader av elektroner. Högtemperatursupraledare är det mest berömda exemplet. Varken klassiska teorier eller modeller där elektronerna är oberoende av varandra kan förklara de häpnadsväckande effekterna i de starkt korrelerade elektronsystemen. I vissa kopparoxider, till exempel La2CuO4, är det känt att valenselektronerna till följd av en stark ömsesidig växelverkan lokaliseras en och en till kopparatomerna i föreningens CuO2 plan. Laddningarnas inneboende magnetiska moment—spinnet—får då en avgörande roll för materialets elektriska och magnetiska egenskaper, vilka i exemplets fall kan beskrivas med Heisenbergmodellen som är den grundläggande teoretiska modellen för mikroskopisk magnetism. Men exakt varför föreningarna kan bli supraledande då de dopas med överskottsladdningar är än så länge en obesvarad fråga. Min avhandling undersöker orenheters inverkan på Heisenbergmodellens magnetiska egenskaper—ett problem av både experimentell och teoretisk relevans. En etablerad numerisk metod har använts—en kvantmekanisk Monte Carlo teknik—för att utföra omfattande datorsimuleringar av den matematiska modellen på två dedikerade Linux datorkluster. Arbetet hör till området beräkningsfysik. De teoretiska modellerna för starkt korrelerade elektronsystem, däribland Heisenbergmodellen, är ytterst invecklade matematiskt sett och de kan inte lösas exakt. Analytiska utredningar bygger för det mesta på antaganden och förenklingar vars inverkningar på slutresultatet är ofta oklara. I det avseende kan numeriska studier vara exakta, det vill säga de kan behandla modellerna som de är. Oftast behövs bägge tillvägagångssätten. Den röda tråden i arbetet har varit att numeriskt testa vissa högaktuella analytiska förutsägelser rörande effekterna av orenheter i Heisenbergmodellen. En del av dem har vi på basen av mycket noggranna data kunnat bekräfta. Men våra resultat har också påvisat felaktigheter i de analytiska prognoserna som sedermera delvis reviderats. En del av avhandlingens numeriska upptäckter har i sin tur stimulerat till helt nya teoretiska studier.

Hakkuutähteestä valmistetun pyrolyysiöljyn elinkaaren kasvihuonekaasupäästöt

Kasvihuonekaasupäästöjen vähentämiseksi ja uusiutuvan energian käytön lisäämiseksi EU:ssa on säädetty direktiivi uusiutuvan energian käytön edistämisestä(RES-direktiivi). Direktiivissä annetaan ohjeet biopolttoaineiden ja bionesteiden kasvihuonekaasuvaikutusten laskemiseen. Tämän työn tarkoituksena oli selvittää, täyttääkö hakkuutähteistä valmistettu pyrolyysiöljy RES-direktiivin asettamat määrälliset vaatimukset kasvihuonekaasujen päästövähennykselle silloin, kun pyrolyysiöljyllä korvataan raskasta polttoöljyä lämmöntuotannossa. Laskenta suorittiin direktiivin ohjeiden mukaan. Lisäksi työssä pohdittiin laskentamenetelmän soveltuvuutta pyrolyysiöljyn ilmastovaikutusten arviointiin yleisesti. Laskennassa huomioitiin raaka-aineen tuotannosta, jalostuksesta sekä kuljetuksesta ja jakelusta aiheutuvat kasvihuonekaasupäästöt. Päästöt laskettiin ensin oletusarvoilla, jonka jälkeen suoritettiin todennäköisyyspohjainen herkkyystarkastelu valituille parametreille. Herkkyystarkastelun tuloksista huomattiin, että päästövähennys riippuu pääasiassa kahdesta tekijästä: maaperän hiilitaseen muutoksesta aiheutuvista päästöistä ja pyrolyysiprosessin tarvitseman lämmön tuotantoon käytetyistä polttoaineista. Eniten tuloksiin vaikutti kuitenkin se, oletettiinko pyrolysaattori ja kattila tarkastelussa erillisiksi yksiköiksi (tapaus 1) vai kokonaisuudeksi (tapaus 2). Tulosten perusteella näyttää siltä, että pyrolyysiöljyn käyttö lämmöntuotannossa raskaan polttoöljyn sijasta johtaa päästövähennyksiin. Saatuja tuloksia ei kuitenkaan voida pitää ennusteina pyrolyysiöljyn todellisista ilmastovaikutuksista, koska elinkaariarviointiin liittyy monia epävarmuuksia. RES-direktiivin laskentaohjeet esimerkiksi järjestelmärajausten muodostamisesta ja päästöjen kohdentamisesta ovat epätarkat. Tästä syystä direktiiviä on mahdollista tulkita usealla eri tavalla, jolloin toisistaan poikkeavat tulokset voivat silti olla kaikki direktiivin mukaisesti laskettuja. Jotta liika tulkinnanvaraisuus ei aiheuttaisi ongelmia, olisi RES-direktiivin laskentaohjetta hyvä tarkentaa.