Hyperbolic type metrics and distortion of quasiconformal map pings

This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.

A simulation model of the optimal maintenance strategy: conceptual agent-based approach

In this Master’s thesis agent-based modeling has been used to analyze maintenance strategy related phenomena. The main research question that has been answered was: what does the agent-based model made for this study tell us about how different maintenance strategy decisions affect profitability of equipment owners and maintenance service providers? Thus, the main outcome of this study is an analysis of how profitability can be increased in industrial maintenance context. To answer that question, first, a literature review of maintenance strategy, agent-based modeling and maintenance modeling and optimization was conducted. This review provided the basis for making the agent-based model. Making the model followed a standard simulation modeling procedure. With the simulation results from the agent-based model the research question was answered. Specifically, the results of the modeling and this study are: (1) optimizing the point in which a machine is maintained increases profitability for the owner of the machine and also the maintainer with certain conditions; (2) time-based pricing of maintenance services leads to a zero-sum game between the parties; (3) value-based pricing of maintenance services leads to a win-win game between the parties, if the owners of the machines share a substantial amount of their value to the maintainers; and (4) error in machine condition measurement is a critical parameter to optimizing maintenance strategy, and there is real systemic value in having more accurate machine condition measurement systems.

Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

Optimal design of 3R manipulators by using classical techniques and simulated annealin

In this paper, the optimum design of 3R manipulators is formulated and solved by using an algebraic formulation of workspace boundary. A manipulator design can be approached as a problem of optimization, in which the objective functions are the size of the manipulator and workspace volume; and the constrains can be given as a prescribed workspace volume. The numerical solution of the optimization problem is investigated by using two different numerical techniques, namely, sequential quadratic programming and simulated annealing. Numerical examples illustrate a design procedure and show the efficiency of the proposed algorithms.

Improving the Supply Chain Performance Management System in a Finnish paper mill

This Master’s Thesis studies performance management system and its benefits, risks and costs. Objective of the thesis is to describe and evaluate currently used supply chain performance management system (SCPMS) in a Finnish paper mill and its interfaces with its business unit’s SCPMS. As a result, the host company has improvement road map for improving its SCPMS. Used SCPMS in the host company and its interfaces to business unit’s SCPMS are described based on interviews held in the host company and the business unit. Evaluation of the host company’s SCPMS is based on literature study. For improvement road map, three areas in need of improvements are chosen. The study shows the need of high level top management commitment in successful performance management system implementation and usage, especially when the system is deployed to lower levels in the organization.

Towards optimal fractionation of lignocellulosic biomass using switchable ionic liquids

En ny familj av reversibla (switchable) joniska vätskor (SIL) innehållande 1,8-diazobicyklo-[5.4.0]-undek-7-en (DBU), en molekyl innehållande en eller flera hydroxyl- grupper (t.ex. glycerol) och en sur gas (CO2, SO2) syntetiserades via en enkel procedur samt karakteriserades. [DBU][karbonat] eller [sulfonat] bildades ur en respektive icke-jonisk blandning av en molekylär, organisk polyol (eller ennan molekyl innehållande en OH-grupp) och en amidinbas under bubblandet av en sur gas. Därtill kunde den joniska vätskan omvandlas tillbaka till sina beståndsdelar med hjälp av att upphetta och/eller bubbla en inert gas såsom kväve genom vätskan. SIL- strukturerna kartlades med bl.a. NMR- och FTIR- spektroskopi. Omvandlingen från lågpolära (molekylära) vätskor till högpolära joniska vätskor (SIL) bekräftades även genom att observera förändringar i deras fysikaliska egenskaper, såsom viskositet och färg. Nedbrytningstemperaturerna hos SILs bestämdes med hjälp av termogravimetrisk analys (TGA) som antydde att nedbrytningstemperaturen hos de syntetiserade föreningarna log mellan 50 och 200oC. De nya joniska vätskorna uppvisade högre nedbrytningstemperaturer jämfört med i litteraturen tidigare förekommande exempel och kunde därför tillämpas på flera ändamål. Därtill, reversibla (switchable) joniska vätskor uppbyggda av bl.a. alkoholer, antingen hexanol eller butanol, och CO2 samt en amidin (DBU) användes vid upplösning och fraktionering av ved. Joniska vätskor syntetiserade ur glycerol och sura gaser tillsammans med amidiner användes även för fraktionering av andra lignocellulosor såsom färsk björk (Betula pendula). Björkflis utsattes för behandling, för en period på en till fem dagar vid 100oC och under atmosfäriskt tryck. Alla syntetiserade joniska vätskor visade sig vara relativt neutrala i avseende på upplösning och avlägsnandet av lignin. Slutligen, optimala fraktioneringprocessbetingelser för ved med reversibla joniska vätskor kartlades. Fraktionering av vedbiomassa med dessa joniska vätskor uppvisade sig att vara en selektiv och effektiv metod för extraktion av olika komponenter från lignocellulosa. Den olösta fraktionen hos en vedflis, närmast cellulosa, fibrillerades. -------------------------------------------------------------------------------------------------------------------- Tässä työssä kehitettiin perhe uuden tyyppisiä, reversiibeleitä (switchable) ioninesteitä ( SIL ) joka koostuvat orgaanisesta super-emäksestä kuten 1,8- diatsabisyklo [ 5.4.0] undek- 7-eeni (DBU ) ja yhden tai useampia hydroksyyliryhmiä sisältältävästä molekyylistä (esim. glyseroli) ja happamasta kaasusta (CO2 , SO2) yksinkertaisen menetelmän avulla. [DBU] [ karbonaatti] tai [sulfonaatti] syntetisoitiin kunkin lähtöaineen seoksista kuplittamalla seosta happamalla kaasulla jolloin eksoterminen reaktio tapahtui ja ioninen neste syntyi. Ioniset nesteet voitiin palauttaa takaisin lähtöaineseokseksi kuumentamalla ja/tai kuplittamalla neutraalia kaasua (esim. typpi) seoksen läpi. SIL rakenteet määritettiin ja niiden ominaisuudet kartoitettiin eri menetelmillä, mukaan lukien NMR- ja FTIR -spektroskopia. Ionisen, korkeapoläärisen nesteen syntyminen todennettiin myös viskositeettimittauksilla ja värinmuutoksilla käyttäen hyväksi polariteetti-indikaattoria (Nile red). Myös hajoamislämpötilat määritettiin termogravimetrisellä analyysillä (TGA) ja todettiin että syntetisoitujen yhdisteiden hajoamislämpötila oli välillä 50 ja 200oC . Näiden uusien reversiibeleiden ioninesteiden hajoamisämpötilat olivat korkeammat verrattuna kirjallisuudessa aikaisemmin mainittuihin esimerkkeihin joten niitä voidaan soveltaa useisiin tarkoituksiin. Myös ioninesteitä jotka sisälsivät primäärejä alkoholeja rakennusaineina syntetisoitiin ja hyödynnettiin puun fraktioinnissa. Männyn ja kuusen lisäksi tuoreita koivulastuja onnistuttiin fraktioimaan miedoissa olosuhteissa. Kaikkien syntetisoitujen ioninesteiden todettiin olevan suhteellisen neutraaleja ligniinin liuotuksen suhteen. Vielä, optimaaliset fraktiointiolosuhteet määritettiin ryhmälle reversiibeleitä ioninesteitä ja näiden uudenlaisten ioninesteiden todettiin olevan tehokkaita puun ja muiden lignoselluloosien eri fraktioiden liuotuksessa. Liukenematon osa puulastua joka oli lähinnä selluloosaa fibrilloitui.

Towards sustainable Iron- and steelmaking with economic optimization

The iron and steelmaking industry is among the major contributors to the anthropogenic emissions of carbon dioxide in the world. The rising levels of CO2 in the atmosphere and the global concern about the greenhouse effect and climate change have brought about considerable investigations on how to reduce the energy intensity and CO2 emissions of this industrial sector. In this thesis the problem is tackled by mathematical modeling and optimization using three different approaches. The possibility to use biomass in the integrated steel plant, particularly as an auxiliary reductant in the blast furnace, is investigated. By pre-processing the biomass its heating value and carbon content can be increased at the same time as the oxygen content is decreased. As the compression strength of the preprocessed biomass is lower than that of coke, it is not suitable for replacing a major part of the coke in the blast furnace burden. Therefore the biomass is assumed to be injected at the tuyere level of the blast furnace. Carbon capture and storage is, nowadays, mostly associated with power plants but it can also be used to reduce the CO2 emissions of an integrated steel plant. In the case of a blast furnace, the effect of CCS can be further increased by recycling the carbon dioxide stripped top gas back into the process. However, this affects the economy of the integrated steel plant, as the amount of top gases available, e.g., for power and heat production is decreased. High quality raw materials are a prerequisite for smooth blast furnace operation. High quality coal is especially needed to produce coke with sufficient properties to ensure proper gas permeability and smooth burden descent. Lower quality coals as well as natural gas, which some countries have in great volumes, can be utilized with various direct and smelting reduction processes. The DRI produced with a direct reduction process can be utilized as a feed material for blast furnace, basic oxygen furnace or electric arc furnace. The liquid hot metal from a smelting reduction process can in turn be used in basic oxygen furnace or electric arc furnace. The unit sizes and investment costs of an alternative ironmaking process are also lower than those of a blast furnace. In this study, the economy of an integrated steel plant is investigated by simulation and optimization. The studied system consists of linearly described unit processes from coke plant to steel making units, with a more detailed thermodynamical model of the blast furnace. The results from the blast furnace operation with biomass injection revealed the importance of proper pre-processing of the raw biomass as the composition of the biomass as well as the heating value and the yield are all affected by the pyrolysis temperature. As for recycling of CO2 stripped blast furnace top gas, substantial reductions in the emission rates are achieved if the stripped CO2 can be stored. However, the optimal recycling degree together with other operation conditions is heavily dependent on the cost structure of CO2 emissions and stripping/storage. The economical feasibility related to the use of DRI in the blast furnace depends on the price ratio between the DRI pellets and the BF pellets. The high amount of energy needed in the rotary hearth furnace to reduce the iron ore leads to increased CO2 emissions.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

An optically coupled power stimulus isolation unit with high voltage and fast rise time output

Recent technological developments have created new devices that could improve and simplify the construction of stimulus isolators. HEXFET transistors can switch large currents and hundreds of volts in nanoseconds. The newer opto-isolators can give a pulse rise time of a few nanoseconds, with output compatible with MOSFET devices, in which delays are reduced to nanoseconds. Integrated DC/DC converters are now available. Using these new resources we developed a new electrical stimulus isolator circuit with selectable constant-current and constant-voltage modes, which are precise and easy to construct. The circuit works like a regulated power supply in both modes with output switched to zero or to free mode through an opto-isolator device. The isolator analyses showed good practical performance. The output to ground resistance was 1011 ohms and capacitance 35 picofarads. The rise time and fall time were identical (5 µs) and constant. The selectable voltage or current output mode made it very convenient to use. The current mode, with higher output resistance values in low current ranges, permits intracellular stimulation even with tip resistances close to 100 megaohms. The high compliance of 200 V guarantees the value of the current stimulus. The very low output resistance in the voltage mode made the device highly suitable for extracellular stimulation with low impedance electrodes. Most importantly, these characteristics were achieved with a circuit that was easy to build and modify and assembled with components available in Brazil.

Advanced analysis and design methods for preparative chromatographic separation processes

Preparative liquid chromatography is one of the most selective separation techniques in the fine chemical, pharmaceutical, and food industries. Several process concepts have been developed and applied for improving the performance of classical batch chromatography. The most powerful approaches include various single-column recycling schemes, counter-current and cross-current multi-column setups, and hybrid processes where chromatography is coupled with other unit operations such as crystallization, chemical reactor, and/or solvent removal unit. To fully utilize the potential of stand-alone and integrated chromatographic processes, efficient methods for selecting the best process alternative as well as optimal operating conditions are needed. In this thesis, a unified method is developed for analysis and design of the following singlecolumn fixed bed processes and corresponding cross-current schemes: (1) batch chromatography, (2) batch chromatography with an integrated solvent removal unit, (3) mixed-recycle steady state recycling chromatography (SSR), and (4) mixed-recycle steady state recycling chromatography with solvent removal from fresh feed, recycle fraction, or column feed (SSR–SR). The method is based on the equilibrium theory of chromatography with an assumption of negligible mass transfer resistance and axial dispersion. The design criteria are given in general, dimensionless form that is formally analogous to that applied widely in the so called triangle theory of counter-current multi-column chromatography. Analytical design equations are derived for binary systems that follow competitive Langmuir adsorption isotherm model. For this purpose, the existing analytic solution of the ideal model of chromatography for binary Langmuir mixtures is completed by deriving missing explicit equations for the height and location of the pure first component shock in the case of a small feed pulse. It is thus shown that the entire chromatographic cycle at the column outlet can be expressed in closed-form. The developed design method allows predicting the feasible range of operating parameters that lead to desired product purities. It can be applied for the calculation of first estimates of optimal operating conditions, the analysis of process robustness, and the early-stage evaluation of different process alternatives. The design method is utilized to analyse the possibility to enhance the performance of conventional SSR chromatography by integrating it with a solvent removal unit. It is shown that the amount of fresh feed processed during a chromatographic cycle and thus the productivity of SSR process can be improved by removing solvent. The maximum solvent removal capacity depends on the location of the solvent removal unit and the physical solvent removal constraints, such as solubility, viscosity, and/or osmotic pressure limits. Usually, the most flexible option is to remove solvent from the column feed. Applicability of the equilibrium design for real, non-ideal separation problems is evaluated by means of numerical simulations. Due to assumption of infinite column efficiency, the developed design method is most applicable for high performance systems where thermodynamic effects are predominant, while significant deviations are observed under highly non-ideal conditions. The findings based on the equilibrium theory are applied to develop a shortcut approach for the design of chromatographic separation processes under strongly non-ideal conditions with significant dispersive effects. The method is based on a simple procedure applied to a single conventional chromatogram. Applicability of the approach for the design of batch and counter-current simulated moving bed processes is evaluated with case studies. It is shown that the shortcut approach works the better the higher the column efficiency and the lower the purity constraints are.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.