Monte Carlo simulations of molecular clusters in nucleation

A better understanding of the limiting step in a first order phase transition, the nucleation process, is of major importance to a variety of scientific fields ranging from atmospheric sciences to nanotechnology and even to cosmology. This is due to the fact that in most phase transitions the new phase is separated from the mother phase by a free energy barrier. This barrier is crossed in a process called nucleation. Nowadays it is considered that a significant fraction of all atmospheric particles is produced by vapor-to liquid nucleation. In atmospheric sciences, as well as in other scientific fields, the theoretical treatment of nucleation is mostly based on a theory known as the Classical Nucleation Theory. However, the Classical Nucleation Theory is known to have only a limited success in predicting the rate at which vapor-to-liquid nucleation takes place at given conditions. This thesis studies the unary homogeneous vapor-to-liquid nucleation from a statistical mechanics viewpoint. We apply Monte Carlo simulations of molecular clusters to calculate the free energy barrier separating the vapor and liquid phases and compare our results against the laboratory measurements and Classical Nucleation Theory predictions. According to our results, the work of adding a monomer to a cluster in equilibrium vapour is accurately described by the liquid drop model applied by the Classical Nucleation Theory, once the clusters are larger than some threshold size. The threshold cluster sizes contain only a few or some tens of molecules depending on the interaction potential and temperature. However, the error made in modeling the smallest of clusters as liquid drops results in an erroneous absolute value for the cluster work of formation throughout the size range, as predicted by the McGraw-Laaksonen scaling law. By calculating correction factors to Classical Nucleation Theory predictions for the nucleation barriers of argon and water, we show that the corrected predictions produce nucleation rates that are in good comparison with experiments. For the smallest clusters, the deviation between the simulation results and the liquid drop values are accurately modelled by the low order virial coefficients at modest temperatures and vapour densities, or in other words, in the validity range of the non-interacting cluster theory by Frenkel, Band and Bilj. Our results do not indicate a need for a size dependent replacement free energy correction. The results also indicate that Classical Nucleation Theory predicts the size of the critical cluster correctly. We also presents a new method for the calculation of the equilibrium vapour density, surface tension size dependence and planar surface tension directly from cluster simulations. We also show how the size dependence of the cluster surface tension in equimolar surface is a function of virial coefficients, a result confirmed by our cluster simulations.

Bootstrapping the Error Correction Model Cointegration Test

This paper is concerned with using the bootstrap to obtain improved critical values for the error correction model (ECM) cointegration test in dynamic models. In the paper we investigate the effects of dynamic specification on the size and power of the ECM cointegration test with bootstrap critical values. The results from a Monte Carlo study show that the size of the bootstrap ECM cointegration test is close to the nominal significance level. We find that overspecification of the lag length results in a loss of power. Underspecification of the lag length results in size distortion. The performance of the bootstrap ECM cointegration test deteriorates if the correct lag length is not used in the ECM. The bootstrap ECM cointegration test is therefore not robust to model misspecification.

The prehistory of Suomussalmi, eastern Finland; the first billion years as revealed by isotopes and the composition of granitoid suites

The four papers summarized in this thesis deal with the Archean and earliest Paleoproterozoic granitoid suites observed in the Suomussalmi district, eastern Finland. Geologically, the area belongs to the Kianta Complex of the Western Karelian Terrane in the Karelian Province of the Fennoscandian shield. The inherited zircons up to 3440 Ma old together with Sm Nd and Pb Pb data confirm the existence of previously anticipated Paleoarchean protocrust in Suomussalmi. The general timeline of granitoid magmatism is similar to that of the surrounding areas. TTG magmatism occurred in three distinct phases: ca 2.95 Ga, 2.83 2.78 Ga and 2.76 2.74 Ga. In Suomussalmi the TTGs sensu stricto (K2O/Na2O less than 0.5) belong to the low-HREE type and are interpreted as partial melts of garnet amphibolites, which did not significantly interact with mantle peridotites. Transitional TTGs (K2O/Na2O more than 0.5), present in Suomussalmi and absent from surrounding areas, display higher LILE concentrations, but otherwise closely resemble the TTGs sensu stricto and indicate that recycling of felsic crust commenced in Suomussalmi 200 Ma earlier than in surrounding areas. The youngest TTG phase was coeval with the intrusion of the Likamännikkö quartz alkali feldspar syenite (2741 ± 2 Ma) complex. The complex contains angular fragments of ultrabasic rock, which display considerable compositional heterogeneity and are interpreted as cumulates containing clinopyroxene (generally altered to actinolite), apatite, allanite, epidote, and albite. The quartz alkali feldspar syenite cannot be regarded as alkaline sensu stricto, despite clear alkaline affinities. Within Likamännikkö there are also calcite carbonatite patches, which display mantle-like O- and C-isotope values, as well as trace element characteristics consistent with a magmatic origin, and could thus be among the oldest known carbonatites in the world. Sanukitoid (2.73 2.71 Ga) and quartz diorite suites (2.70 Ga) overlap within error margins and display compositional similarities, but can be differentiated from each other on the basis of higher Ba, K2O and LREE contents of the sanukitoids. The Likamännikkö complex, sanukitoids and quartz diorites are interpreted as originating from the metasomatized mantle and mark the diversification of the granitoid clan after 200 Ma of evolution dominated by the TTG suite. Widespread migmatization and the intrusion of anatectic leucogranitoids as dykes and intrusions of varying size took place at 2.70 2.69 Ga, following collisional thickening of the crust. The leucogranitoids and leucosomes of migmatized TTGs are compositionally alike and characterized by high silica contents and a leucocratic appearance. Due to compositional overlap, definitive discrimination between leucogranitoids and transitional TTGs requires isotope datings and/or knowledge of field relationships. Leucogranitoids represent partial melts of the local TTGs, both the sensu stricto and transitional types, mostly derived under water fluxed conditions, with possible fluid sources being late sanukitoids and quartz diorites as well as dehydrating lower crust. The Paleoproterozoic 2.44 2.39 Ga A-type granitoids of the Kianta Complex emplaced in an extensional environment are linked to the coeval and more widespread mafic intrusions and dykes observed over most of the Archean nucleus of the Fennoscandian shield. The A-type intrusions in the Suomussalmi area are interpreted as partial melts of the Archean lower crust and display differences in composition and magnetite content, which indicate differences in the composition and oxidation state of the source.

Finite-State Spell-Checking with Weighted Language and Error Models

In this paper we present simple methods for construction and evaluation of finite-state spell-checking tools using an existing finite-state lexical automaton, freely available finite-state tools and Internet corpora acquired from projects such as Wikipedia. As an example, we use a freely available open-source implementation of Finnish morphology, made with traditional finite-state morphology tools, and demonstrate rapid building of Northern Sámi and English spell checkers from tools and resources available from the Internet.