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.

Manifestation of the pairing symmetry in the vortex core structure in iron-based superconductors

The superconducting gap is a basic character of a superconductor. While the cuprates and conventional phonon-mediated superconductors are characterized by distinct d- and s-wave pairing symmetries with nodal and nodeless gap distributions respectively, the superconducting gap distributions in iron-based superconductors are rather diversified. While nodeless gap distributions have been directly observed in Ba1–xKxFe2As2, BaFe2–xCoxAs2, LiFeAs, KxFe2–ySe2, and FeTe1–xSex, the signatures of a nodal superconducting gap have been reported in LaOFeP, LiFeP, FeSe, KFe2As2, BaFe2–xRuxAs2, and BaFe2(As1–xPx)2. Due to the multiplicity of the Fermi surface in these compounds s± and d pairing states can be both nodeless and nodal. A nontrivial orbital structure of the order parameter, in particular the presence of the gap nodes, leads to effects in which the disorder is much richer in dx2–y2-wave superconductors than in conventional materials. In contrast to the s-wave case, the Anderson theorem does not work, and nonmagnetic impurities exhibit a strong pair-breaking influence. In addition, a finite concentration of disorder produces a nonzero density of quasiparticle states at zero energy, which results in a considerable modification of the thermodynamic and transport properties at low temperatures. The influence of order parameter symmetry on the vortex core structure in iron-based pnictide and chalcogenide superconductors has been investigated in the framework of quasiclassical Eilenberger equations. The main results of the thesis are as follows. The vortex core characteristics, such as, cutoff parameter, ξh, and core size, ξ2, determined as the distance at which density of the vortex supercurrent reaches its maximum, are calculated in wide temperature, impurity scattering rate, and magnetic field ranges. The cutoff parameter, ξh(B; T; Г), determines the form factor of the flux-line lattice, which can be obtained in _SR, NMR, and SANS experiments. A comparison among the applied pairing symmetries is done. In contrast to s-wave systems, in dx2–y2-wave superconductors, ξh/ξc2 always increases with the scattering rate Г. Field dependence of the cutoff parameter affects strongly on the second moment of the magnetic field distributions, resulting in a significant difference with nonlocal London theory. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair-breaking impurity scattering (interband scattering for s±-wave and intraband impurity scattering for d-wave superconductors). Here, ξc2 is the Ginzburg-Landau coherence length determined from the upper critical field Bc2 = Φ0/2πξ2 c2, where Φ0 is a flux quantum. Two types of ξ2/ξc2 magnetic field dependences are obtained for s± superconductors. It has a minimum at low temperatures and small impurity scattering transforming in monotonously decreasing function at strong scattering and high temperatures. The second kind of this dependence has been also found for d-wave superconductors at intermediate and high temperatures. In contrast, impurity scattering results in decreasing of ξ2/ξc2(B/Bc2) dependence in s++ superconductors. A reasonable agreement between calculated ξh/ξc2 values and those obtained experimentally in nonstoichiometric BaFe2–xCoxAs2 (μSR) and stoichiometric LiFeAs (SANS) was found. The values of ξh/ξc2 are much less than one in case of the first compound and much more than one for the other compound. This is explained by different influence of two factors: the value of impurity scattering rate and pairing symmetry.

Modeling and Parameter Estimation of Double-Star Permanent Magnet Synchronous Machines

The power rating of wind turbines is constantly increasing; however, keeping the voltage rating at the low-voltage level results in high kilo-ampere currents. An alternative for increasing the power levels without raising the voltage level is provided by multiphase machines. Multiphase machines are used for instance in ship propulsion systems, aerospace applications, electric vehicles, and in other high-power applications including wind energy conversion systems. A machine model in an appropriate reference frame is required in order to design an efficient control for the electric drive. Modeling of multiphase machines poses a challenge because of the mutual couplings between the phases. Mutual couplings degrade the drive performance unless they are properly considered. In certain multiphase machines there is also a problem of high current harmonics, which are easily generated because of the small current path impedance of the harmonic components. However, multiphase machines provide special characteristics compared with the three-phase counterparts: Multiphase machines have a better fault tolerance, and are thus more robust. In addition, the controlled power can be divided among more inverter legs by increasing the number of phases. Moreover, the torque pulsation can be decreased and the harmonic frequency of the torque ripple increased by an appropriate multiphase configuration. By increasing the number of phases it is also possible to obtain more torque per RMS ampere for the same volume, and thus, increase the power density. In this doctoral thesis, a decoupled d–q model of double-star permanent-magnet (PM) synchronous machines is derived based on the inductance matrix diagonalization. The double-star machine is a special type of multiphase machines. Its armature consists of two three-phase winding sets, which are commonly displaced by 30 electrical degrees. In this study, the displacement angle between the sets is considered a parameter. The diagonalization of the inductance matrix results in a simplified model structure, in which the mutual couplings between the reference frames are eliminated. Moreover, the current harmonics are mapped into a reference frame, in which they can be easily controlled. The work also presents methods to determine the machine inductances by a finite-element analysis and by voltage-source inverters on-site. The derived model is validated by experimental results obtained with an example double-star interior PM (IPM) synchronous machine having the sets displaced by 30 electrical degrees. The derived transformation, and consequently, the decoupled d–q machine model, are shown to model the behavior of an actual machine with an acceptable accuracy. Thus, the proposed model is suitable to be used for the model-based control design of electric drives consisting of double-star IPM synchronous machines.

The use and misuse of the "impact factor" as a parameter for evaluation of scientific publication quality: a proposal to rationalize its application

We present a critical analysis of the generalized use of the "impact factor". By means of the Kruskal-Wallis test, it was shown that it is not possible to compare distinct disciplines using the impact factor without adjustments. After assigning the median journal the value of one (1.000), the impact factor value for each journal was calculated by the rule of three. The adjusted values were homogeneous, thus permitting comparison among distinct disciplines.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Intensification of hemicellulose hot-water extraction from spruce wood by parameter tuning

The growing population on earth along with diminishing fossil deposits and the climate change debate calls out for a better utilization of renewable, bio-based materials. In a biorefinery perspective, the renewable biomass is converted into many different products such as fuels, chemicals, and materials, quite similar to the petroleum refinery industry. Since forests cover about one third of the land surface on earth, ligno-cellulosic biomass is the most abundant renewable resource available. The natural first step in a biorefinery is separation and isolation of the different compounds the biomass is comprised of. The major components in wood are cellulose, hemicellulose, and lignin, all of which can be made into various end-products. Today, focus normally lies on utilizing only one component, e.g., the cellulose in the Kraft pulping process. It would be highly desirable to utilize all the different compounds, both from an economical and environmental point of view. The separation process should therefore be optimized. Hemicelluloses can partly be extracted with hot-water prior to pulping. Depending in the severity of the extraction, the hemicelluloses are degraded to various degrees. In order to be able to choose from a variety of different end-products, the hemicelluloses should be as intact as possible after the extraction. The main focus of this work has been on preserving the hemicellulose molar mass throughout the extraction at a high yield by actively controlling the extraction pH at the high temperatures used. Since it has not been possible to measure pH during an extraction due to the high temperatures, the extraction pH has remained a “black box”. Therefore, a high-temperature in-line pH measuring system was developed, validated, and tested for hot-water wood extractions. One crucial step in the measurements is calibration, therefore extensive efforts was put on developing a reliable calibration procedure. Initial extractions with wood showed that the actual extraction pH was ~0.35 pH units higher than previously believed. The measuring system was also equipped with a controller connected to a pump. With this addition it was possible to control the extraction to any desired pH set point. When the pH dropped below the set point, the controller started pumping in alkali and by that the desired set point was maintained very accurately. Analyses of the extracted hemicelluloses showed that less hemicelluloses were extracted at higher pH but with a higher molar-mass. Monomer formation could, at a certain pH level, be completely inhibited. Increasing the temperature, but maintaining a specific pH set point, would speed up the extraction without degrading the molar-mass of the hemicelluloses and thereby intensifying the extraction. The diffusion of the dissolved hemicelluloses from the wood particle is a major part of the extraction process. Therefore, a particle size study ranging from 0.5 mm wood particles to industrial size wood chips was conducted to investigate the internal mass transfer of the hemicelluloses. Unsurprisingly, it showed that hemicelluloses were extracted faster from smaller wood particles than larger although it did not seem to have a substantial effect on the average molar mass of the extracted hemicelluloses. However, smaller particle sizes require more energy to manufacture and thus increases the economic cost. Since bark comprises 10 – 15 % of a tree, it is important to also consider it in a biorefinery concept. Spruce inner and outer bark was hot-water extracted separately to investigate the possibility to isolate the bark hemicelluloses. It was showed that the bark hemicelluloses comprised mostly of pectic material and differed considerably from the wood hemicelluloses. The bark hemicelluloses, or pectins, could be extracted at lower temperatures than the wood hemicelluloses. A chemical characterization, done separately on inner and outer bark, showed that inner bark contained over 10 % stilbene glucosides that could be extracted already at 100 °C with aqueous acetone.

Dendritic thickness: a morphometric parameter to classify mouse retinal ganglion cells

To study the dendritic morphology of retinal ganglion cells in wild-type mice we intracellularly injected these cells with Lucifer yellow in an in vitro preparation of the retina. Subsequently, quantified values of dendritic thickness, number of branching points and level of stratification of 73 Lucifer yellow-filled ganglion cells were analyzed by statistical methods, resulting in a classification into 9 groups. The variables dendritic thickness, number of branching points per cell and level of stratification were independent of each other. Number of branching points and level of stratification were independent of eccentricity, whereas dendritic thickness was positively dependent (r = 0.37) on it. The frequency distribution of dendritic thickness tended to be multimodal, indicating the presence of at least two cell populations composed of neurons with dendritic diameters either smaller or larger than 1.8 µm ("thin" or "thick" dendrites, respectively). Three cells (4.5%) were bistratified, having thick dendrites, and the others (95.5%) were monostratified. Using k-means cluster analysis, monostratified cells with either thin or thick dendrites were further subdivided according to level of stratification and number of branching points: cells with thin dendrites were divided into 2 groups with outer stratification (0-40%) and 2 groups with inner (50-100%) stratification, whereas cells with thick dendrites were divided into one group with outer and 3 groups with inner stratification. We postulate, that one group of cells with thin dendrites resembles cat ß-cells, whereas one group of cells with thick dendrites includes cells that resemble cat a-cells.

A simple model for circadian timing by mammals

Circadian timing is structured in such a way as to receive information from the external and internal environments, and its function is the timing organization of the physiological and behavioral processes in a circadian pattern. In mammals, the circadian timing system consists of a group of structures, which includes the suprachiasmatic nucleus (SCN), the intergeniculate leaflet and the pineal gland. Neuron groups working as a biological pacemaker are found in the SCN, forming a biological master clock. We present here a simple model for the circadian timing system of mammals, which is able to reproduce two fundamental characteristics of biological rhythms: the endogenous generation of pulses and synchronization with the light-dark cycle. In this model, the biological pacemaker of the SCN was modeled as a set of 1000 homogeneously distributed coupled oscillators with long-range coupling forming a spherical lattice. The characteristics of the oscillator set were defined taking into account the Kuramoto's oscillator dynamics, but we used a new method for estimating the equilibrium order parameter. Simultaneous activities of the excitatory and inhibitory synapses on the elements of the circadian timing circuit at each instant were modeled by specific equations for synaptic events. All simulation programs were written in Fortran 77, compiled and run on PC DOS computers. Our model exhibited responses in agreement with physiological patterns. The values of output frequency of the oscillator system (maximal value of 3.9 Hz) were of the order of magnitude of the firing frequencies recorded in suprachiasmatic neurons of rodents in vivo and in vitro (from 1.8 to 5.4 Hz).

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.

Phonon spectra and thermal properties of some fcc metals using embedded-atom potentials /

By employing the embedded-atom potentials of Mei et ai.[l], we have calculated the dynamical matrices and phonon dispersion curves for six fee metals (Cu,Ag,Au,Ni,Pd and Pt). We have also investigated, within the quasiharmonic approximation, some other thermal properties of these metals which depend on the phonon density of states, such as the temperature dependence of lattice constant, coefficient of linear thermal expansion, isothermal and adiabatic bulk moduli, heat capacities at constant volume and constant pressure, Griineisen parameter and Debye temperature. The computed results are compared with the experimental findings wherever possible. The comparison shows a generally good agreement between the theoretical values and experimental data for all properties except the discrepancies of phonon frequencies and Debye temperature for Pd, Pt and Au. Further, we modify the parameters of this model for Pd and Pt and obtain the phonon dispersion curves which is in good agreement with experimental data.

An experimental investigation of dechanneling in copper single crystals

This investigation comprises a comparison of experimental and theoretical dechanneling of MeV protons in copper single crystals. Dechanneling results when an ion's transverse energy increases to the value where the ion can undergo small impact parameter collisions with individual atoms. Depth dependent dechanneling rates were determined as functions of lattice temperature, ion beam energy and crystal axis orientation. Ion beam energies were IMeV and 2MeV,temperatures ranged from 35 K to 280 K and the experiment was carried out along both the (lOa) and <110) axes. Experimental data took the form of aligned and random Rutherford backscattered energy spectra. Dechanneling rates were extracted from these spectra using a single scattering theory that took explicit account of the different stopping powers experienced by channeled and dechanneled ions and also included a correction factor to take into account multiple scattering effects along the ion's trajectory. The assumption of statistical equilibrium and small angle scattering of the channeled ions allows a description of dechanneling in terms of the solution of a diffusion like equation which contains a so called diffusion function. The diffusion function is shown to be related to the increase in average transverse energy. Theoretical treatments of increase in average transverse energy due to collisions of projectiles with channel electrons and thermal perturbations in the lattice potential are reviewed. Using the diffusion equation and the electron density in the channel centre as a fitting parameter dechanneling rates are extracted. Excellent agreement between theory and experiment has been demonstrated. Electron densities determined in the fitting procedure appear to be realistic. The surface parameters show themselves to be good indicators of the quality of the crystal.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.