Distortion properties of quasiconformal maps

In this Licentiate thesis we investigate the absolute ratio δ, j, ˜j and hyperbolic ρ metrics and their relations with each other. Various growth estimates are given for quasiconformal mpas both in plane and space. Some Hölder constants were refined with respect δ, j ˜j metrics. Some new results regarding the Hölder continuity of quasiconformal and quasiregular mapping of unit ball with respect to Euclidean and hyperbolic metrics are given, which were obtained by many authors in 1980’s. Applications are given to the study of metric space, quasiconformal and quasiregular maps in the plane and as well as in the space.

Dispersion of Hybrid Electromagnetic-Spin Waves in the Slotline

The presented thesis is devoted to investigation of wave processes in hybrid ferrite / ferroelectric structures. Spin wave devices based on ferrite films have such disadvantages, as huge size of the magnetic systems, low tuning velocity, considerable power inputs for parameters control that limits possible device applications. The considered layered structures allow to overcome the disadvantages mentioned and to promote the development of novel class of tunable microwave devices. The proposed theoretical analysis is intended to construct a model of hybrid electromagnetic-spin waves. Based on the theoretical analysis the experimental investigations were carried out. The experimental resonance characteristics of ferrite / ferroelectric resonator were obtained and their tunability by means of magnetic and electric field was demonstrated.

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.

Modeling of residual stresses and distortion due to welding in fillet welds

Welding has a growing role in modern world manufacturing. Welding joints are extensively used from pipes to aerospace industries. Prediction of welding residual stresses and distortions is necessary for accurate evaluation of fillet welds in relation to design and safety conditions. Residual stresses may be beneficial or detrimental, depending whether they are tensile or compressive and the loading. They directly affect the fatigue life of the weld by impacting crack growth rate. Beside theoretical background of residual stresses this study calculates residual stresses and deformations due to localized heating by welding process and subsequent rapid cooling in fillet welds. Validated methods are required for this purpose due to complexity of process, localized heating, temperature dependence of material properties and heat source. In this research both empirical and simulation methods were used for the analysis of welded joints. Finite element simulation has become a popular tool of prediction of welding residual stresses and distortion. Three different cases with and without preload have been modeled during this study. Thermal heat load set is used by calculating heat flux from the given heat input energy. First the linear and then nonlinear material behavior model is modeled for calculation of residual stresses. Experimental work is done to calculate the stresses empirically. The results from both the methods are compared to check their reliability. Residual stresses can have a significant effect on fatigue performance of the welded joints made of high strength steel. Both initial residual stress state and subsequent residual stress relaxation need to be considered for accurate description of fatigue behavior. Tensile residual stresses are detrimental and will reduce the fatigue life and compressive residual stresses will increase it. The residual stresses follow the yield strength of base or filler material and the components made of high strength steel are typically thin, where the role of distortion is emphasizing.

Electrical status epilepticus during sleep. Continuous spikes and waves during sleep

ABSTRACT Maria Peltola Electrical status epilepticus during sleep – Continuous spikes and waves during sleep Department of Clinical Neurophysiology, University of Turku Department of Clinical Neurophysiology and Department of Pediatric Neurology, Children’s Hospital, Helsinki University Central Hospital Annales Universitatis Turkuensis, Medica-Odontologica, Turku, Finland, 2014 Background: Electrical status epilepticus during sleep (ESES) is an EEG phenomenon of frequent spikes and waves occurring in slow sleep. ESES relates to cognitive deterioration in heterogeneous childhood epilepsies. Validated methods to quantitate ESES are missing. The clinical syndrome, called epileptic encephalopathy with continuous spikes and waves during sleep (CSWS) is pharmacoresistant in half of the patients. Limited data exists on surgical treatment of CSWS. Aims and methods: The effects of surgical treatment were studied by investigating electroclinical outcomes in 13 operated patients (nine callosotomies, four resections) with pharmacoresistant CSWS and cognitive decline. Secondly, an objective paradigm was searched for assessing ESES by the semiautomatic quantification of spike index (SI) and measuring spike strength from EEG. Results: Postoperatively, cognitive deterioration was stopped in 12 (92%) patients. Three out of four patients became seizure-free after resective surgery. Callosotomy resulted in greater than 90% reduction of atypical absences in six out of eight patients. The preoperative propagation of ESES from one hemisphere to the other was associated with a good response. Semiautomatic quantification of SI was a robust method when the maximal interspike interval of three seconds was used to determine the “continuous” discharge in ten EEGs. SI of the first hour of sleep appeared representative of the whole night SI. Furthermore, the spikes’ root mean square was found to be a stable measure of spike strength when spatially integrated over multiple electrodes during steady NREM sleep. Conclusions: Patients with pharmacoresistant CSWS, based on structural etiology, may benefit from resective surgery or corpus callosotomy regarding both seizure outcome and cognitive prognosis. The semiautomated SI quantification, with proper userdefined settings and the new spatially integrated measure of spike strength, are robust and promising tools for quantifying ESES. Keywords: Electrical status epilepticus during sleep, ESES, continuous spikes and waves during sleep, CSWS, epilepsy surgery, spike index, spike strength, RMS TIIVISTELMÄ Maria Peltola Unenaikainen sähköinen status epilepticus Kliininen neurofysiologia, Turun yliopisto Kliininen neurofysiologia ja lastenneurologia, Lasten ja nuorten sairaala, Helsingin yliopistollinen keskussairaala Annales Universitatis Turkuensis, Medica-Odontologica, Turku, Suomi, 2014 Tausta: Sähköinen status epilepticus unessa (ESES) on aivosähkökäyrä (EEG)-ilmiö, jossa hidasaaltounen aikana esiintyy tiheä piikkihidasaaltopurkaus. ESES:n kvantifioimiseen ei ole olemassa validoituja menetelmiä. ESES on liitetty kognitiivisen tason laskuun ja tällöin puhutaan CSWS (continuous spikes and waves during sleep) - oireyhtymästä. CSWS ei vastaa lääkehoitoon puolella potilaista ja sen epilepsiakirurgisesta hoidosta on olemassa vain vähän tietoa. Tavoitteet ja menetelmät: Selvitimme retrospektiivisesti epilepsiakirurgian vaikusta elektrokliinisiin löydöksiin 13:lla lääkeresistenttiä CSWS-oireyhtymää sairastavalla lapsella, joilla oli rakenteellinen aivojen poikkeavuus. Toinen tavoite oli löytää objektiivinen puoliautomaattinen tapa mitata purkauksen määrää ja piikkien voimakkuutta EEG:stä. Tulokset: Kognitiivisen tason jatkuva heikentyminen loppui 12 (92 %) potilaalla leikkauksen jälkeen. Kolme neljästä resektiopotilaasta tuli kohtauksettomaksi. Kallosotomian jälkeen kuudella kahdeksasta potilaasta päivittäiset kohtaukset vähenivät yli 90 %:lla. Purkauksen leviäminen leikkausta edeltävästi vain yhdestä hemisfääristä toiseen liittyi hyvään leikkaushoitovasteeseen. Piikki-indeksi, jossa käytetään jatkuvan purkauksen määritelmänä maksimissaan kolmea sekuntia piikkien välillä, osoittautui luotettavaksi menetelmäksi ESES:n kvantifioimiseen. Useammasta elektrodista integroitu piikkien neliöllinen keskiarvo oli piikin voimakkuuden vakaa mitta häiriintymättömässä NREM-unessa. Päätelmät: Lääkehoidolle vastaamatonta CSWS:ää sairastavat potilaat, joilla on rakenteellinen aivopoikkeavuus ja yhdensuuntainen purkauksen leviämismalli, näyttävät kohtausten vähenemisen lisäksi hyötyvän epilepsiakirurgiasta kognitiivisesti. Puoliautomaattinen piikki-indeksin kvantifiointi sopivilla käyttäjäasetuksilla ja uusi spatiaalisesti integroitu piikin voimakkuuden mittari ovat stabiileja ja lupaavia ESES:n kvantitatiivisia mittareita. Avainsanat: Unenaikainen sähköinen status epilepticus, ESES, CSWS, epilepsiakirurgia, piikki-indeksi, piikin voimakkuus, neliöllinen keskiarvo

Distortion and internal warping torsion of a double symmetric hollow section

This thesis is made in cooperation with Laboratory of Steel Structures and the steel company SSAB. Maximization of the benefits of high-strength steel usually requires the usage of thin wall thicknesses. This means the failures related to buckling, distortion and warping stand out. One must be aware of these phenomena to design thin-walled structures stressed with forces such as torsional loading. It is also important to take into account small stress ranges when evaluating the accurate fatigue strength of structures. The objective of this thesis is to clarify the theory of the uniform and non-uniform torsion. This paper focuses on warping due to the non-uniform torsion in double symmetric box girder and structural hollow section. The arisen stress states are explained and researched using the finite element method. Another research target is the distortion in double symmetric box girder due to torsion, and the restraining effect of transverse diaphragms at the load end. Multiple transverse diaphragms are used to study more efficient restraining against warping and distortion than a common one end plate structure.

Spin-electromagnetic waves spectra in multiferroic heterostructures

This work devotes to the theoretical investigations of spin-electromagnetic waves (SEW) propagating in a thin-film multiferroic structures that were composed of a slot-line and structures with several ferrite films. In contrast to earlier works, the spin-electromagnetic waves in the investigated structures are originated from two different electrodynamics coupling. The first one is coupling of the electromagnetic wave localized mainly in the slot-line with the spin wave excited mostly in the ferrite film. The second one is coupling of two spin waves in the different ferrite films separated by a thin ferroelectric film. For theoretical analysis of SEWs propagation in such kind of structures theories of their eigen-wave spectra were developed. Spectra of SEW in the investigated structures were calculated and analyzed. The range of electric and magnetic tunability of dispersion characteristic were investigated. Spectra of SEW in the investigated multiferroic structures are used for investigation of transfer function of periodic structures.

Static waves in corporate space : characterizing oscillating trading patterns in New York stock exchange

Various researches in the field of econophysics has shown that fluid flow have analogous phenomena in financial market behavior, the typical parallelism being delivered between energy in fluids and information on markets. However, the geometry of the manifold on which market dynamics act out their dynamics (corporate space) is not yet known. In this thesis, utilizing a Seven year time series of prices of stocks used to compute S&P500 index on the New York Stock Exchange, we have created local chart to the corporate space with the goal of finding standing waves and other soliton like patterns in the behavior of stock price deviations from the S&P500 index. By first calculating the correlation matrix of normalized stock price deviations from the S&P500 index, we have performed a local singular value decomposition over a set of four different time windows as guides to the nature of patterns that may emerge. I turns out that in almost all cases, each singular vector is essentially determined by relatively small set of companies with big positive or negative weights on that singular vector. Over particular time windows, sometimes these weights are strongly correlated with at least one industrial sector and certain sectors are more prone to fast dynamics whereas others have longer standing waves.

Benefits of a low-cost one-phase current distortion detection device in appliance supply in low-voltage residential networks

In this bachelor’s thesis are examined the benefits of current distortion detection device application in customer premises low voltage networks. The purpose of this study was to find out if there are benefits for measuring current distortion in low-voltage residential networks. Concluding into who can benefit from measuring the power quality. The research focuses on benefits based on the standardization in Europe and United States of America. In this research, were also given examples of appliances in which current distortion detection device could be used. Along with possible illustration of user interface for the device. The research was conducted as an analysis of the benefits of current distortion detection device in residential low voltage networks. The research was based on literature review. The study was divided to three sections. The first explain the reasons for benefitting from usage of the device and the second portrays the low-cost device, which could detect one-phase current distortion, in theory. The last section discuss of the benefits of usage of current distortion detection device while focusing on the beneficiaries. Based on the result of this research, there are benefits from usage to the current distortion detection device. The main benefitting party of the current distortion detection device was found to be manufactures, as they are held responsible of limiting the current distortion on behalf of consumers. Manufactures could adjust equipment to respond better to the distortion by having access to on-going current distortion in network. The other benefitting party are system operators, who would better locate distortion issues in low-voltage residential network to start prevention of long-term problems caused by current distortion early on.