In this thesis, we prove the existence of large frequency periodic solutions for the nonlinear wave equations utt − uxx − v(x)u = u3 + [fnof]([Omega]t, x) (1) with Dirichlet boundary conditions. Here, [Omega] represents the frequency of the solution. The method we use to find the periodic solutions u([Omega]) for large [Omega] originates in the work of Craig and Wayne [10] where they constructed solutions for free vibrations, i.e., for [fnof] = 0. Here we construct smooth solutions for forced vibrations ([fnof] [not equal to] 0). Given an x-dependent analytic potential v(x) previous works on (1) either assume a smallness condition on [fnof] or yields a weak solution. The study of equations like (1) goes back at least to Rabinowitz in the sixties [25]. The main difficulty in finding periodic solutions of an equation like (1), is the appearance of small denominators in the linearized operator stemming from the left hand side. To overcome this difficulty, we used a Nash-Moser scheme introduced by Craig and Wayne in [10]. / text

The Earth's magnetic field is generated in its fluid outer core through dynamo action. In this process, convection and differential rotation of an electrically conducting fluid maintain the magnetic field against its ohmic decay. Using numerical models, we can investigate planetary dynamo processes and the importance of various core properties on the dynamo. In this thesis, I use numerical dynamo models in Earth-like geometry in order to understand the influence of inner core electrical conductivity and the choice of thermal and velocity boundary conditions on the resulting magnetic field. I demonstrate how an electrically conducting inner core can reduce the frequency of reversals and produce axial-dipolar dominated fields in our models. I also demonstrate that a strong planetary magnetic field intensity does not imply that the dynamo operates in the strong field regime as is usually presumed. Through a scaling law analysis, I find that irrespective of the choice of thermal or velocity boundary conditions, the available power determines the magnetic and velocity field characteristics like the field strength, polarity and morphology. Also, whether a dynamo model is in a dipolar, transitional or multipolar regime is dependent on the force balance in the model. I demonstrate that the Lorentz force is balanced by the Coriolis force in the dipolar dynamo regime models resulting in magnetostrophically balanced dynamos whereas the Lorentz force is balanced by the Inertial force (and not the Coriolis force) in the multipolar dynamo regime models resulting in a non-magnetostrophically balanced dynamo. The generation mechanism differs between the regimes and depends on the velocity boundary conditions. The zonal flows of the stress-free models are stronger than in the no-slip models, and bistability is more prominent when stress-free boundary conditions are used. A single scaling law may be feasible for all the models, but there does appear to be some variation for models with different thermal and velocity boundary conditions. The results presented in this thesis are not only applicable to the geodynamo, but will also aid in understanding the dynamos of other planets and exoplanets.

The Earth's magnetic field is generated in its fluid outer core through dynamo action. In this process, convection and differential rotation of an electrically conducting fluid maintain the magnetic field against its ohmic decay. Using numerical models, we can investigate planetary dynamo processes and the importance of various core properties on the dynamo. In this thesis, I use numerical dynamo models in Earth-like geometry in order to understand the influence of inner core electrical conductivity and the choice of thermal and velocity boundary conditions on the resulting magnetic field. I demonstrate how an electrically conducting inner core can reduce the frequency of reversals and produce axial-dipolar dominated fields in our models. I also demonstrate that a strong planetary magnetic field intensity does not imply that the dynamo operates in the strong field regime as is usually presumed. Through a scaling law analysis, I find that irrespective of the choice of thermal or velocity boundary conditions, the available power determines the magnetic and velocity field characteristics like the field strength, polarity and morphology. Also, whether a dynamo model is in a dipolar, transitional or multipolar regime is dependent on the force balance in the model. I demonstrate that the Lorentz force is balanced by the Coriolis force in the dipolar dynamo regime models resulting in magnetostrophically balanced dynamos whereas the Lorentz force is balanced by the Inertial force (and not the Coriolis force) in the multipolar dynamo regime models resulting in a non-magnetostrophically balanced dynamo. The generation mechanism differs between the regimes and depends on the velocity boundary conditions. The zonal flows of the stress-free models are stronger than in the no-slip models, and bistability is more prominent when stress-free boundary conditions are used. A single scaling law may be feasible for all the models, but there does appear to be some variation for models with different thermal and velocity boundary conditions. The results presented in this thesis are not only applicable to the geodynamo, but will also aid in understanding the dynamos of other planets and exoplanets.

In this report the analysis of microstrip electrodynamic structures on basis of high-temperature superconductors is carried out and a mathematical model of microstrip devices with lumped and distributed nonlinear properties is created. For this purpose nonlinear integral equations method and method of moments are used. In the issue of the work a SHF filter based on the equivalent circuit of elements with lumped parameters is also studied. It is ascertained that the received mathematical model allows to achieve more proper results of modeling on compensation of variation of current-density distribution nearby the edges of conductor break.

In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introduction the topicality of the problem is defined, the goals and tasks of the research are formulated, the scientific novelty of the dissertation, the methodology of research, the practical value and the significance of the results are presented. m-order differential problem and its Green's function are investigated in the first chapter. The relation between two Green's functions and the existence condition of Green's function are obtained. In the second chapter, the main definitions and results of the first chapter are formulated for the second-order differential equation with additional conditions. In the examples the application of the received results is analyzed for problems with nonlocal boundary conditions in detail. In the third chapter, the second-order difference equation with two additional conditions is considered. The expression of Green's function and its existence... [to full text] / Disertacijoje tiriami antros ir aukštesnės eilės diferencialinis ir diskretusis uždaviniai su įvairiomis, tame tarpe ir nelokaliosiomis, sąlygomis, kurios yra aprašytos tiesiškai nepriklausomais tiesiniais funkcionalais. Pateikiamos šių uždavinių Gryno funkcijų išraiškos ir jų egzistavimo sąlygos, jei žinoma homogeninės lygties fundamentalioji sistema. Gautas dviejų Gryno funkcijų sąryšis uždaviniams su ta pačia lygtimi, bet su papildomomis sąlygomis. Rezultatai pritaikomi uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Įvadiniame skyriuje aprašyta tiriamoji problema ir temos objektas, išanalizuotas temos aktualumas, išdėstyti darbo tikslai, uždaviniai, naudojama tyrimų metodika, mokslinis darbo naujumas ir gautų rezultatų reikšmė, pateikti ginamieji teiginiai ir darbo rezultatų aprobavimas. m-tosios eilės diferencialinis uždavinys ir jo Gryno funkcija nagrinėjami pirmajame skyriuje. Surastas uždavinio sprendinys, išreikštas per Gryno funkciją. Pateikta Gryno funkcijos egzistavimo sąlyga. Antrajame skyriuje pateikti pirmojo skyriaus pagrindiniai apibrėžimai ir rezultatai antros eilės diferencialinei lygčiai. Pavyzdžiuose išsamiai išanalizuotas gautų rezultatų pritaikymas uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Trečiajame skyriuje nagrinėjama antros eilės diskrečioji lygtis su dviem sąlygomis. Surastos diskrečiosios Gryno funkcijos išraiška ir jos egzistavimo sąlyga. Taip pat pateiktas dviejų Gryno funkcijų sąryšis, kuris leidžia surasti diskrečiosios... [toliau žr. visą tekstą]

Disertacijoje tiriami antros ir aukštesnės eilės diferencialinis ir diskretusis uždaviniai su įvairiomis, tame tarpe ir nelokaliosiomis, sąlygomis, kurios yra aprašytos tiesiškai nepriklausomais tiesiniais funkcionalais. Pateikiamos šių uždavinių Gryno funkcijų išraiškos ir jų egzistavimo sąlygos, jei žinoma homogeninės lygties fundamentalioji sistema. Gautas dviejų Gryno funkcijų sąryšis uždaviniams su ta pačia lygtimi, bet su papildomomis sąlygomis. Rezultatai pritaikomi uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Įvadiniame skyriuje aprašyta tiriamoji problema ir temos objektas, išanalizuotas temos aktualumas, išdėstyti darbo tikslai, uždaviniai, naudojama tyrimų metodika, mokslinis darbo naujumas ir gautų rezultatų reikšmė, pateikti ginamieji teiginiai ir darbo rezultatų aprobavimas. m-tosios eilės diferencialinis uždavinys ir jo Gryno funkcija nagrinėjami pirmajame skyriuje. Surastas uždavinio sprendinys, išreikštas per Gryno funkciją. Pateikta Gryno funkcijos egzistavimo sąlyga. Antrajame skyriuje pateikti pirmojo skyriaus pagrindiniai apibrėžimai ir rezultatai antros eilės diferencialinei lygčiai. Pavyzdžiuose išsamiai išanalizuotas gautų rezultatų pritaikymas uždaviniams su nelokaliosiomis kraštinėmis sąlygomis. Trečiajame skyriuje nagrinėjama antros eilės diskrečioji lygtis su dviem sąlygomis. Surastos diskrečiosios Gryno funkcijos išraiška ir jos egzistavimo sąlyga. Taip pat pateiktas dviejų Gryno funkcijų sąryšis, kuris leidžia surasti diskrečiosios... [toliau žr. visą tekstą] / In the dissertation, second-order and higher-order differential and discrete equations with additional conditions which are described by linearly independent linear functionals are investigated. The solutions to these problems, formulae and the existence conditions of Green's functions are presented, if the general solution of a homogeneous equation is known. The relation between two Green's functions of two nonhomogeneous problems for the same equation but with different additional conditions is obtained. These results are applied to problems with nonlocal boundary conditions. In the introduction the topicality of the problem is defined, the goals and tasks of the research are formulated, the scientific novelty of the dissertation, the methodology of research, the practical value and the significance of the results are presented. m-order differential problem and its Green's function are investigated in the first chapter. The relation between two Green's functions and the existence condition of Green's function are obtained. In the second chapter, the main definitions and results of the first chapter are formulated for the second-order differential equation with additional conditions. In the examples the application of the received results is analyzed for problems with nonlocal boundary conditions in detail. In the third chapter, the second-order difference equation with two additional conditions is considered. The expression of Green's function and its existence... [to full text]

Small punch test (SPT) has been widely used to evaluate in-service materials in nuclear fusion facilities. Early use of SPTs is largely based on empirical relations or curve fitting from experimental data, while recent applications of SPTs take advantage of finite element methods. In this study, an improved inverse finite element analysis procedure is proposed to obtain constitutive relations from load-displacement curves recorded in SPTs. In addition, a parametric study is performed to evaluate the effects of SPT parameters including friction coefficient, punch head diameter, sample thickness, specimen scale and boundary conditions. The proposed inverse finite element (FE) method improves the accuracy of existing inverse FE methods, and the current parametric study provides a basis for the standardization of SPT procedures in the future.

As wind industry is developing steadily oshore, the wind turbine spacing remainsa key element for maximizing revenues and reducing loading from turbineswake interaction. In the case of relatively close to shore oshore wind farms, orlarge arrays onshore, the turbulence intensity coming from dierent sectors canhave an eect on wake growth and decay. In an attempt to obtain wind featuresat site, some boundary conditions for micro-siting simulation are found, using acommercial RANS ow solver CFD software was used. The approach in this workcould be described more practical than theoretical and could be more useful fordevelopers than pure CFD specialists.By simulating with three dierent roughness length for open sea, with theappropriate and contextual assumptions, for the oshore Lillgrund wind farm,vertical proles and turbulence intensity were extracted from the WindSim softwareat the meteorological mast position and enabled measurement comparison.In a second attempt to compare the eect of the wind and turbulence prolespreviously obtained, a sector of interest is simulated with the actuator disc model.In general, the site conditions over the large-scale domain evaluated by thecommercial software are satisfactory after adjusting the roughness length for theopen sea. The turbulence intensity trend for various in ow angle is capturedby the simulations and computed wind proles are for the most part adequately.A comparison of spring and winter ltered measurements enable discussion uponsome sectors disagreement. As for the small-scale actuator disc model using thedeveloped site conditions, the result is over-estimated by the simulations, especiallyfor the second row downstream.

The use of MEMS-based inertial sensors for a relative positioning estimation system (RPES) was investigated. A number of data acquisition and processing techniques are developed and tested, to determine which one would provide the best performance of the proposed method. Because inertial-based sensors don’t rely on other references to calibrate their position and orientation, there is a steady accumulation of errors over time. The errors are caused by various sources of noise such as temperature and vibration, and the errors are significant. This work investigates various methods to increase the signalto- noise ratio, in order to develop the best possible RPES method. The main areas of this work are as follows: (i) The proposed RPES application imposes specific boundary conditions to the signal processing, to increase the accuracy. (ii) We propose that using redundant inertial rate sensors would give a better performance over a single rate sensor. (iii) We investigate three Kalman filter algorithms to accommodate different combinations of sensors: Parallel sensors arrangement, Series sensors arrangement, and compression arrangement. In implementing these three areas, the results show that there is much better improvement in the data in comparison to using regular averaging techniques. / Graduate

Three different aspects of the sinh-Gordon model are explored in this thesis. We begin, in chapter one, with a summary of the model and the necessary background. Chapter two studies the model with two boundary conditions. Two approaches are presented to investigate the reflection factors off the boundaries and the energy of the theory. In chapter three, perturbation theory is developed to study the theory with one general boundary condition. A contribution to the quantum reflection factor is obtained and compared with the result obtained for the special boundary condition. Chapters four and five investigate the supersymmetric extension of the model in the presence of a single boundary. Firstly, the classical limits of the supersymmetric reflection matrices are checked. The exact reflection factors are studied perturbatively up to the second order of the coupling constant. Secondly, the perturbation theory and the path integral formalism are employed in the supersymmetric model to study the quantum reflection factors. We conclude with a brief sixth chapter describing the outlook for further investigations.