A generalized 1D particle transport method for convection diffusion reaction model

This work is devoted to the development of numerical method to deal with convection diffusion dominated problem with reaction term, non - stiff chemical reaction and stiff chemical reaction. The technique is based on the unifying Eulerian - Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves created by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that, each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients (steep fronts) and discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that, the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consumer when compared with other classical technique e.g., method of lines. Apart from this advantage, the particle transport method can be used to simulate problems that involve movingsteep/smooth fronts such as separation of two or more elements in the system.

The bifurcational behaviour of the spatially distributed Rayleigh equation

At the present work the bifurcational behaviour of the solutions of Rayleigh equation and corresponding spatially distributed system is being analysed. The conditions of oscillatory and monotonic loss of stability are obtained. In the case of oscillatory loss of stability, the analysis of linear spectral problem is being performed. For nonlinear problem, recurrent formulas for the general term of the asymptotic approximation of the self-oscillations are found, the stability of the periodic mode is analysed. Lyapunov-Schmidt method is being used for asymptotic approximation. The correlation between periodic solutions of ODE and PDE is being investigated. The influence of the diffusion on the frequency of self-oscillations is being analysed. Several numerical experiments are being performed in order to support theoretical findings.

Particle transport method for convection-diffusion-reaction problems

Convective transport, both pure and combined with diffusion and reaction, can be observed in a wide range of physical and industrial applications, such as heat and mass transfer, crystal growth or biomechanics. The numerical approximation of this class of problemscan present substantial difficulties clue to regions of high gradients (steep fronts) of the solution, where generation of spurious oscillations or smearing should be precluded. This work is devoted to the development of an efficient numerical technique to deal with pure linear convection and convection-dominated problems in the frame-work of convection-diffusion-reaction systems. The particle transport method, developed in this study, is based on using rneshless numerical particles which carry out the solution along the characteristics defining the convective transport. The resolution of steep fronts of the solution is controlled by a special spacial adaptivity procedure. The serni-Lagrangian particle transport method uses an Eulerian fixed grid to represent the solution. In the case of convection-diffusion-reaction problems, the method is combined with diffusion and reaction solvers within an operator splitting approach. To transfer the solution from the particle set onto the grid, a fast monotone projection technique is designed. Our numerical results confirm that the method has a spacial accuracy of the second order and can be faster than typical grid-based methods of the same order; for pure linear convection problems the method demonstrates optimal linear complexity. The method works on structured and unstructured meshes, demonstrating a high-resolution property in the regions of steep fronts of the solution. Moreover, the particle transport method can be successfully used for the numerical simulation of the real-life problems in, for example, chemical engineering.

Reaction paper : what? why? how?

Abstract

Detection of bovine foetal DNA from amniotic fluid using the polymerase chain reaction

Selostus: Sikiön DNA:n tunnistaminen naudan sikiövedestä polymeraasiketjureaktion avulla

Universally primed polymerase chain reaction analysis of Fusarium avenaceum isolated from wheat and barley in Finland

Selostus: Vehnästä ja ohrasta eristettyjen F. avenaceum -punahomekantojen analysointi UP-PCR-menetelmällä

Valsystem i lilleputtar: pluralitet och diffusion

Abstract: Elections in lilliputs: plurality and diffusion

Diffusion av valsystem

Lectio praecursoria Åbo Akademi 1.2.2006

Wet Oxidation of Concentrated Wastewaters: Process Combination and Reaction Kinetic Modeling

The accumulation of aqueous pollutants is becoming a global problem. The search for suitable methods and/or combinations of water treatment processes is a task that can slow down and stop the process of water pollution. In this work, the method of wet oxidation was considered as an appropriate technique for the elimination of the impurities present in paper mill process waters. It has been shown that, when combined with traditional wastewater treatment processes, wet oxidation offers many advantages. The combination of coagulation and wet oxidation offers a new opportunity for the improvement of the quality of wastewater designated for discharge or recycling. First of all, the utilization of coagulated sludge via wet oxidation provides a conditioning process for the sludge, i.e. dewatering, which is rather difficult to carry out with untreated waste. Secondly, Fe2(SO4)3, which is employed earlier as a coagulant, transforms the conventional wet oxidation process into a catalytic one. The use of coagulation as the post-treatment for wet oxidation can offer the possibility of the brown hue that usually accompanies the partial oxidation to be reduced. As a result, the supernatant is less colored and also contains a rather low amount of Fe ions to beconsidered for recycling inside mills. The thickened part that consists of metal ions is then recycled back to the wet oxidation system. It was also observed that wet oxidation is favorable for the degradation of pitch substances (LWEs) and lignin that are present in the process waters of paper mills. Rather low operating temperatures are needed for wet oxidation in order to destruct LWEs. The oxidation in the alkaline media provides not only the faster elimination of pitch and lignin but also significantly improves the biodegradable characteristics of wastewater that contains lignin and pitch substances. During the course of the kinetic studies, a model, which can predict the enhancements of the biodegradability of wastewater, was elaborated. The model includes lumped concentrations suchas the chemical oxygen demand and biochemical oxygen demand and reflects a generalized reaction network of oxidative transformations. Later developments incorporated a new lump, the immediately available biochemical oxygen demand, which increased the fidelity of the predictions made by the model. Since changes in biodegradability occur simultaneously with the destruction of LWEs, an attempt was made to combine these two facts for modeling purposes.

Mobile Communications within the European Union: The Role of Location in the Evolution and Forecasting of the Diffusion Process

In the European Union, the importance of mobile communications was realized early on. The process of mobile communications becoming ubiquitous has taken time, as the innovation of mobile communications diffused into the society. The aim of this study is to find out how the evolution and spatial patterns of the diffusion of mobile communications within the European Union could be taken into account in forecasting the diffusion process. There is relatively lot of research of innovation diffusion on the individual (micro) andthe country (macro) level, if compared to the territorial level. Territorial orspatial diffusion refers either to the intra-country or inter-country diffusionof an innovation. In both settings, the dif- fusion of a technological innovation has gained scarce attention. This study adds knowledge of the diffusion between countries, focusing especially on the role of location in this process. The main findings of the study are the following: The penetration rates of the European Union member countries have become more even in the period of observation, from the year 1981 to 2000. The common digital GSM system seems to have hastened this process. As to the role of location in the diffusion process, neighboring countries have had similar diffusion processes. They can be grouped into three, the Nordic countries, the central and southern European countries, and the remote southern European countries. The neighborhood effect is also domi- nating in thegravity model which is used for modeling the adoption timing of the countries. The subsequent diffusion within a country, measured by the logistic model in Finland, is af- fected positively by its economic situation, and it seems to level off at some 92 %. Considering the launch of future mobile communications systemsusing a common standard should implicate an equal development between the countries. The launching time should be carefully selected as the diffusion is probably delayed in economic downturns. The location of a country, measured by distance, can be used in forecasting the adoption and diffusion. Fi- nally, the result of penetration rates becoming more even implies that in a relatively homoge- nous set of countries, such as the European Union member countries, the estimated final pene- tration of a single country can be used for approximating the penetration of the others. The estimated eventual penetration of Finland, some 92 %, should thus also be the eventual level for all the European Union countries and for the European Union as a whole.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Comprehensive Study of Crystal Growth from Solution

Crystal growth is an essential phase in crystallization kinetics. The rate of crystal growth provides significant information for the design and control of crystallization processes; nevertheless, obtaining accurate growth rate data is still challenging due to a number of factors that prevail in crystal growth. In industrial crystallization, crystals are generally grown from multi-componentand multi-particle solutions under complicated hydrodynamic conditions; thus, it is crucial to increase the general understanding of the growth kinetics in these systems. The aim of this work is to develop a model of the crystal growth rate from solution. An extensive literature review of crystal growth focuses on themodelling of growth kinetics and thermodynamics, and new measuring techniques that have been introduced in the field of crystallization. The growth of a singlecrystal is investigated in binary and ternary systems. The binary system consists of potassium dihydrogen phosphate (KDP, crystallizing solute) and water (solvent), and the ternary system includes KDP, water and an organic admixture. The studied admixtures, urea, ethanol and 1-propanol, are employed at relatively highconcentrations (of up to 5.0 molal). The influence of the admixtures on the solution thermodynamics is studied using the Pitzer activity coefficient model. Theprediction method of the ternary solubility in the studied systems is introduced and verified. The growth rate of the KDP (101) face in the studied systems aremeasured in the growth cell as a function of supersaturation, the admixture concentration, the solution velocity over a crystal and temperature. In addition, the surface morphology of the KDP (101) face is studied using ex situ atomic force microscopy (AFM). The crystal growth rate in the ternary systems is modelled on the basis of the two-step growth model that contains the Maxwell-Stefan (MS) equations and a surface-reaction model. This model is used together with measuredcrystal growth rate data to develop a new method for the evaluation of the model parameters. The validation of the model is justified with experiments. The crystal growth rate in an imperfectly mixed suspension crystallizer is investigatedusing computational fluid dynamics (CFD). A solid-liquid suspension flow that includes multi-sized particles is described by the multi-fluid model as well as by a standard k-epsilon turbulence model and an interface momentum transfer model. The local crystal growth rate is determined from calculated flow information in a diffusion-controlled crystal growth regime. The calculated results are evaluated experimentally.

Effect of competitive situation and price on diffusion of mobile communications

Työn päätavoitteena oli selvittää hinnan ja kilpailutilanteen vaikutusta matkaviestinnän diffuusioon. Työn empiirinen osuus tarkasteli matkapuhelinliittymien hinnan vaikutusta liittymien diffuusioon sekä sitä, miten alan kilpailu on vaikuttanut matkaviestinnän hintatasoon. Työssä analysoitiin myös matkaviestinnän kilpailutilannetta Suomen markkinoilla. Tutkimuksen empiirinen aineisto kerättiin toissijaisista lähteistä, esimerkiksi EMC-tietokannasta. Tutkimus oli luonteeltaan kvantitatiivinen.Empiirisessä osassa käytetyt mallit oli muodostettu aikaisempien tutkimuksien perusteella. Regressioanalyysiä käytettiin arvioitaessa hinnan vaikutusta diffuusionopeuteen ja mahdollisten omaksujien määrään. Regressioanalyysissä sovellettiin ei-lineaarista mallia.Tutkimustulokset osoittivat, että tasaisesti laskevilla matkapuhelinliittymien sekä matkapuhelimien hinnoilla ei ole merkittävää vaikutusta matkaviestinnän diffuusioon. Myöskään kilpailutilanne ei ole vaikuttanut paljon matkaviestinnän yleiseen hintatasoon. Työn tulosten perusteella voitiin antaa myös muutamia toimenpide-ehdotuksia jatkotutkimuksia varten.

Predicting diffusion of innovations with self-organisation and machine learning

The main subject of this master's thesis was predicting diffusion of innovations. The prediction was done in a special case: product has been available in some countries, and based on its diffusion in those countries the prediction is done for other countries. The prediction was based on finding similar countries with Self-Organizing Map~(SOM), using parameters of countries. Parameters included various economical and social key figures. SOM was optimised for different products using two different methods: (a) by adding diffusion information of products to the country parameters, and (b) by weighting the country parameters based on their importance for the diffusion of different products. A novel method using Differential Evolution (DE) was developed to solve the latter, highly non-linear optimisation problem. Results were fairly good. The prediction method seems to be on a solid theoretical foundation. The results based on country data were good. Instead, optimisation for different products did not generally offer clear benefit, but in some cases the improvement was clearly noticeable. The weights found for the parameters of the countries with the developed SOM optimisation method were interesting, and most of them could be explained by properties of the products.