Non-Markovianity and Quantum Correlations in Qubit-Systems

In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Diskreettiaikainen liukuvan moodin säätö kiinteäoksidipolttokennon DC-tasonnostossa

Huoli ympäristön tilasta ja fossiilisten polttoaineiden hinnan nousu ovat vauhdittaneet tutkimusta uusien energialähteiden löytämiseksi. Polttokennot ovat yksi lupaavimmista tekniikoista etenkin hajautetun energiantuotannon, varavoimalaitosten sekä liikennevälineiden alueella. Polttokenno on tehonlähteenä kuitenkin hyvin epäideaalinen, ja se asettaa tehoelektroniikalle lukuisia erityisvaatimuksia. Polttokennon kytkeminen sähköverkkoon on tavallisesti toteutettu käyttämällä galvaanisesti erottavaa DC/DC hakkuria sekä vaihtosuuntaajaa sarjassa. Polttokennon kulumisen estämiseksi tehoelektroniikalta vaaditaan tarkkaa polttokennon lähtövirran hallintaa. Perinteisesti virran hallinta on toteutettu säätämällä hakkurin tulovirtaa PI (Proportional and Integral) tai PID (Proportional, Integral and Derivative) -säätimellä. Hakkurin epälineaarisuudesta johtuen tällainen ratkaisu ei välttämättä toimi kaukana linearisointipisteestä. Lisäksi perinteiset säätimet ovat herkkiä mallinnusvirheille. Tässä diplomityössä on esitetty polttokennon jännitettä nostavan hakkurin tilayhtälökeskiarvoistusmenetelmään perustuva malli, sekä malliin perustuva diskreettiaikainen integroiva liukuvan moodin säätö. Esitetty säätö on luonteeltaan epälineaarinen ja se soveltuu epälineaaristen ja heikosti tunnettujen järjestelmien säätämiseen.

Modeling of electrolyte sorption – from phase equilibria to dynamic separation systems

In this thesis, general approach is devised to model electrolyte sorption from aqueous solutions on solid materials. Electrolyte sorption is often considered as unwanted phenomenon in ion exchange and its potential as an independent separation method has not been fully explored. The solid sorbents studied here are porous and non-porous organic or inorganic materials with or without specific functional groups attached on the solid matrix. Accordingly, the sorption mechanisms include physical adsorption, chemisorption on the functional groups and partition restricted by electrostatic or steric factors. The model is tested in four Cases Studies dealing with chelating adsorption of transition metal mixtures, physical adsorption of metal and metalloid complexes from chloride solutions, size exclusion of electrolytes in nano-porous materials and electrolyte exclusion of electrolyte/non-electrolyte mixtures. The model parameters are estimated using experimental data from equilibrium and batch kinetic measurements, and they are used to simulate actual single-column fixed-bed separations. Phase equilibrium between the solution and solid phases is described using thermodynamic Gibbs-Donnan model and various adsorption models depending on the properties of the sorbent. The 3-dimensional thermodynamic approach is used for volume sorption in gel-type ion exchangers and in nano-porous adsorbents, and satisfactory correlation is obtained provided that both mixing and exclusion effects are adequately taken into account. 2-Dimensional surface adsorption models are successfully applied to physical adsorption of complex species and to chelating adsorption of transition metal salts. In the latter case, comparison is also made with complex formation models. Results of the mass transport studies show that uptake rates even in a competitive high-affinity system can be described by constant diffusion coefficients, when the adsorbent structure and the phase equilibrium conditions are adequately included in the model. Furthermore, a simplified solution based on the linear driving force approximation and the shrinking-core model is developed for very non-linear adsorption systems. In each Case Study, the actual separation is carried out batch-wise in fixed-beds and the experimental data are simulated/correlated using the parameters derived from equilibrium and kinetic data. Good agreement between the calculated and experimental break-through curves is usually obtained indicating that the proposed approach is useful in systems, which at first sight are very different. For example, the important improvement in copper separation from concentrated zinc sulfate solution at elevated temperatures can be correctly predicted by the model. In some cases, however, re-adjustment of model parameters is needed due to e.g. high solution viscosity.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

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.

Calibration and simulations of SIXS-P's response to energetic particles

The Solar Intensity X-ray and particle Spectrometer (SIXS) on board BepiColombo's Mercury Planetary Orbiter (MPO) will study solar energetic particles moving towards Mercury and solar X-rays on the dayside of Mercury. The SIXS instrument consists of two detector sub-systems; X-ray detector SIXS-X and particle detector SIXS-P. The SIXS-P subdetector will detect solar energetic electrons and protons in a broad energy range using a particle telescope approach with five outer Si detectors around a central CsI(Tl) scintillator. The measurements made by the SIXS instrument are necessary for other instruments on board the spacecraft. SIXS data will be used to study the Solar X-ray corona, solar flares, solar energetic particles, the Hermean magnetosphere, and solar eruptions. The SIXS-P detector was calibrated by comparing experimental measurement data from the instrument with Geant4 simulation data. Calibration curves were produced for the different side detectors and the core scintillator for electrons and protons, respectively. The side detector energy response was found to be linear for both electrons and protons. The core scintillator energy response to protons was found to be non-linear. The core scintillator calibration for electrons was omitted due to insufficient experimental data. The electron and proton acceptance of the SIXS-P detector was determined with Geant4 simulations. Electron and proton energy channels are clean in the main energy range of the instrument. At higher energies, protons and electrons produce non-ideal response in the energy channels. Due to the limited bandwidth of the spacecraft's telemetry, the particle measurements made by SIXS-P have to be pre-processed in the data processing unit of the SIXS instrument. A lookup table was created for the pre-processing of data with Geant4 simulations, and the ability of the lookup table to provide spectral information from a simulated electron event was analysed. The lookup table produces clean electron and proton channels and is able to separate protons and electrons. Based on a simulated solar energetic electron event, the incident electron spectrum cannot be determined from channel particle counts with a standard analysis method.

Suorityskyvyn mittaaminen johtamisen apuvälineenä prosessiorganisaatiossa.

Prosessiorganisaatiossa johtamisen ja prosessien tavoitteena on tyydyttää asiakkaan (sisäinen tai ulkoinen) tarpeet. Mittaamisen sitominen prosessin suorityskyvyn mittaamiseen antaa johdolle kuvan yrityksen toiminnasta. Suorityskykymittariston ja yksittäisten mittareiden avulla yritysjohto pystyy arvioimaan toiminnan tasoa, asettamaan tavoitteita sekä seuraamaan asettamiensa tavoitteiden toteutumista. Työn ensimmäisenä tavoitteena oli kartoittaa edellytyksiä sekä tukea Balanced Scorecardin mukaisen suorityskykymittariston tulevaisuuden implementointia. Mittaristo on tarkoitettu toimitusketjun prosessien tehokkuuden mittaamiseen. Työn toisena tavoitteena oli prosessipohjaisen ajattelutavan tukeminen suorituskykymittariston avulla. Implementoinnin edellytyksiä testattiin valitsemalla kaksi ensimmäisen tason avainmittaria pilottimittareiksi. Varaston suorityskykyä mittaavien pilottimittareiden avulla selvitettiin SC tuoteryhmän osalta toimitusketjun suorituskyky avainasiakkaiden ja tärkeiden markkina-alueiden osalta. Erona käytössä oleviin mittareihin on se, että uudet avainmittarit kattavat koko yrityksen toimitusketjun, kun tällä hetkellä käytössä olevat mittarit mittaavat toimitusketjun yksittäisiä osia. Uusien avaimittareiden lähtöarvot selvitettiin tietokantakyselyjen avulla. Tietokyselyt suoritettiin useissa yksittäisissä tietojärjejestelmissä, jonka jälkeen niiden tulokset koottiin yhteen tiedostoon ja analysoitiin PC sovellusten avulla. Mittauskohteet oli valittu yhdessä linjaorganisaation kanssa. Näin taattiin yhtiön johdon sitoutuminen mittariston kehittämiseen ja käyttöönottoon. Organisaatiossa yksittäisten prosessien (esim. mittaamisprosessi) vastuualueiden selventämiseen käytettiin koeluonteisesti vastuumatriisitekniikkaa. Prosessiorganisaatiossa johtamisen ja prosessien tavoitteena on tyydyttää asiakkaan (sisäinen tai ulkoinen) tarpeet. Mittaamisen sitominen prosessin suorityskyvyn mittaamiseen antaa johdolle kuvan yrityksen toiminnasta. Suorityskykymittariston ja yksittäisten mittareiden avulla yritysjohto pystyy arvioimaan toiminnan tasoa, asettamaan tavoitteita sekä seuraamaan asettamiensa tavoitteiden toteutumista. Työn ensimmäisenä tavoitteena oli kartoittaa edellytyksiä sekä tukea Balanced Scorecardin mukaisen suorityskykymittariston tulevaisuuden implementointia. Mittaristo on tarkoitettu toimitusketjun prosessien tehokkuuden mittaamiseen. Työn toisena tavoitteena oli prosessipohjaisen ajattelutavan tukeminen suorituskykymittariston avulla.Implementoinnin edellytyksiä testattiin valitsemalla kaksi ensimmäisen tason avainmittaria pilottimittareiksi. Varaston suorityskykyä mittaavien pilottimittareiden avulla selvitettiin SC tuoteryhmän osalta toimitusketjun suorituskyky avainasiakkaiden ja tärkeiden markkina-alueiden osalta. Erona käytössä oleviin mittareihin on se, että uudet avainmittarit kattavat koko yrityksen toimitusketjun, kun tällä hetkellä käytössä olevat mittarit mittaavat toimitusketjun yksittäisiä osia. Uusien avaimittareiden lähtöarvot selvitettiin tietokantakyselyjen avulla. Tietokyselyt suoritettiin useissa yksittäisissä tietojärjejestelmissä, jonka jälkeen niiden tulokset koottiin yhteen tiedostoon ja analysoitiin PC sovellusten avulla. Mittauskohteet oli valittu yhdessä linjaorganisaation kanssa. Näin taattiin yhtiön johdon sitoutuminen mittariston kehittämiseen ja käyttöönottoon. Organisaatiossa yksittäisten prosessien (esim. mittaamisprosessi) vastuualueiden selventämiseen käytettiin koeluonteisesti vastuumatriisitekniikkaa.

Small and Large Scale Dynamics in the Milky Way

This thesis contains dynamical analysis on four different scales: the Solar system, the Sun itself, the Solar neighbourhood, and the central region of the Milky Way galaxy. All of these topics have been handled through methods of potential theory and statistics. The central topic of the thesis is the orbits of stars in the Milky Way. An introduction into the general structure of the Milky Way is presented, with an emphasis on the evolution of the observed value for the scale-length of the Milky Way disc and the observations of two separate bars in the Milky Way. The basics of potential theory are also presented, as well as a developed potential model for the Milky Way. An implementation of the backwards restricted integration method is shown, rounding off the basic principles used in the dynamical studies of this thesis. The thesis looks at the orbit of the Sun, and its impact on the Oort cloud comets (Paper IV), showing that there is a clear link between these two dynamical systems. The statistical atypicalness of the orbit of the Sun is questioned (Paper I), concluding that there is some statistical typicalness to the orbit of the Sun, although it is not very significant. This does depend slightly on whether one includes a bar, or not, as a bar has a clear effect on the dynamical features seen in the Solar neighbourhood (Paper III). This method can be used to find the possible properties of a bar. Finally, we look at the effect of a bar on a statistical system in the Milky Way, seeing that there are not only interesting effects depending on the mass and size of the bar, but also how bars can capture disc stars (Paper II).

Computational Evaluation of Print Unevenness According to Human Vision

Print quality and the printability of paper are very important attributes when modern printing applications are considered. In prints containing images, high print quality is a basic requirement. Tone unevenness and non uniform glossiness of printed products are the most disturbing factors influencing overall print quality. These defects are caused by non ideal interactions of paper, ink and printing devices in high speed printing processes. Since print quality is a perceptive characteristic, the measurement of unevenness according to human vision is a significant problem. In this thesis, the mottling phenomenon is studied. Mottling is a printing defect characterized by a spotty, non uniform appearance in solid printed areas. Print mottle is usually the result of uneven ink lay down or non uniform ink absorption across the paper surface, especially visible in mid tone imagery or areas of uniform color, such as solids and continuous tone screen builds. By using existing knowledge on visual perception and known methods to quantify print tone variation, a new method for print unevenness evaluation is introduced. The method is compared to previous results in the field and is supported by psychometric experiments. Pilot studies are made to estimate the effect of optical paper characteristics prior to printing, on the unevenness of the printed area after printing. Instrumental methods for print unevenness evaluation have been compared and the results of the comparison indicate that the proposed method produces better results in terms of visual evaluation correspondence. The method has been successfully implemented as ail industrial application and is proved to be a reliable substitute to visual expertise.

Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.

Synthesis and characterization of nanoperforated metal oxide thin films

For advanced devices in the application fields of data storage, solar cell and biosensing, one of the major challenges to achieve high efficiency is the fabrication of nanopatterned metal oxide surfaces. Such surfaces often require both precise structure at the nanometer scale and controllable patterned structure at the macro scale. Nowadays, the dominating candidates to fabricate nanopatterned surfaces are the lithographic technique and block-copolymer masks, most of which are unfortunately costly and inefficient. An alternative bottom-up approach, which involves organic/inorganic self-assembly and dip-coating deposition, has been studied intensively in recent years and has proven to be an effective technique for the fabrication of nanoperforated metal oxide thin films. The overall objective of this work was to optimize the synthesis conditions of nanoperforated TiO2 (NP-TiO2) thin films, especially to be compatible with mixed metal oxide systems. Another goal was to develop fabrication and processing of NP-TiO2 thin films towards largescale production and seek new applications for solar cells and biosensing. Besides the traditional dip-coating and drop-casting methods, inkjet printing was used to prepare thin films of metal oxides, with the advantage of depositing the ink onto target areas, further enabling cost-effective fabrication of micro-patterned nanoperforated metal oxide thin films. The films were characterized by water contact angle determination, Atomic Force Microscopy, Scanning Electron Microscopy, X-ray Photoelectron Spectroscopy and Grazing Incidence XRay Diffraction. In this study, well-ordered zinc titanate nanoperforated thin films with different Zn/Ti ratios were produced successfully with zinc precursor content up to 50 mol%, and the dominating phase was Zn2Ti3O8. NP-TiO2 structures were also obtained by a cost-efficient means, namely inkjet printing, at both ambient temperature and 60 °C. To further explore new biosensing applications of nanoperforated oxide thin films, inkjet printing was used for the fabrication of both continuous and patterned polymeric films onto NP-TiO2 and perfluorinated phosphate functionalized NP-TiO2 substrates, respectively. The NP-TiO2 films can be also functionalized with a fluoroalkylsilane, resulting in hydrophobic surfaces on both titania and silica. The surface energy contrast in the nanoperforations can be tuned by irradiating the films with UV light, which provides ideal model systems for wettability studies.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.