THE FUNDAMENTAL SOLUTIONS OF DIFFERENTIAL OPERATOR WITH BLOCK - TRIANGULAR OPERATOR COEFFICIENTS

For the non-selfadjoint Sturm-Liouville equation with a block-triangular operator potential that increases at infinity, both increasing and decreasing at infinity operator solutions are found. The asymptotics of these solutions at infinity is defined

Analyzing risk and returns of Norwegian equity mutual funds

Masteroppgave i bedriftsøkonomi - Nord universitet, 201

Room temperature surface piezoelectricity in SrTiO3 ceramics via piezoresponse force microscopy

SrTiO3 ceramics are investigated by piezoresponse force microscopy. Piezoelectric contrast is observed on polished surfaces in both vertical and lateral regimes and depends on the grain orientation varying in both sign (polarization direction) and amplitude. The observed contrast is attested to the surface piezoelectricity due to flexoelectric effect (strain gradient-induced polarization) caused by the surface relaxation. The estimated flexoelectric coefficient is approximately one order of magnitude smaller as compared to those recently measured in SrTiO3 single crystals. The observed enhancement of piezoresponse signal at the grain boundaries is explained by the dipole moments associated with inhomogeneous distribution of oxygen vacancies

Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients

In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out. The Green’s function and the resolvent for a non-self-adjoint differential operator are constructed. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For a non-self-adjoint Sturm-Liouville operator with a triangular matrix potential growing at infinity, an example of operator having spectral singularities is constructed

Domain Dynamics in Piezoresponse Force Microscopy: Quantitative Deconvolution and Hysteresis Loop Fine Structure

Domain dynamics in the Piezoresponse Force Spectroscopy (PFS) experiment is studied using the combination of local hysteresis loop acquisition with simultaneous domain imaging. The analytical theory for PFS signal from domain of arbitrary cross-section is developed and used for the analysis of experimental data on Pb(Zr,Ti)O3 polycrystalline films. The results suggest formation of oblate domain at early stage of the domain nucleation and growth, consistent with efficient screening of depolarization field within the material. The fine structure of the hysteresis loop is shown to be related to the observed jumps in the domain geometry during domain wall propagation (nanoscale Barkhausen jumps), indicative of strong domain-defect interactions.Comment: 17 pages, 3 figures, 2 Appendices, to be submmited to Appl. Phys. Let

Simulação de dano e fractura em ensaios de flexão em 3 pontos em provetes laminados

Mestrado em Engenharia MecânicaPolímeros reforçados por fibras (PRF) tem sido utilizados durante muito tempo para aplicações estruturais, particularmente com laminados. No projeto de laminados é importante caracterizar o seu comportamento mecânico. O comportamento mecânico é caracterizado por uma rigidez inicial e pela fractura. A estratégia de modelação utilizada nesta dissertação permite não só prever o “first-ply-failure”, como também modelar a sequência de eventos a seguir, como a delaminação e a fractura final da estrutura. Para isso é utilizado um modelo para a interface e para as camadas, permitindo a interação entre eles. A rigidez inicial também é avaliada com diferentes ratios comprimento para espessura, permitindo também diferentes contribuições do cisalhamento transversal e de flexão. Nesta dissertação com o método dos elementos finitos (FEM) é investigado o comportamento estrutural de uma viga compósita sobe ensaios de flexão em três pontos. Para este fim o programa comercial Abaqus é utilizado, permitindo simulações numéricas com elementos continuum casca e elementos convencionais casca. Também são realizadas simulações numéricas de modo a preparar a resultados para uma futura experiência, para o qual o tamanho do provete é escolhido com recomendações do EN ISO 14125Fiber-reinforced polymers (FRP) have been used for a long time for structural applications, particularly with laminates. It is important to characterize the mechanical behavior of laminates for their design. This behavior is characterized by an initial stiffness and by failure. The modeling strategy used in this thesis allows to predict not only first-ply-failure (FPF), but also to model the sequence of events afterwards, such as delamination and the final failure of the structure. This is achieved by using a damage model for the ply and for the interface, allowing the interaction between them. The initial stiffness is also evaluated with different length to thickness ratios, allowing different contributions from transverse shear and bending. In this thesis, with the finite element method (FEM) the structural behavior of a laminate composite beam under a three point bending configuration is investigated. For this purpose the commercial FEM package Abaqus is used, allowing numerical simulations with continuum shell and conventional shell elements. Also simulations are conducted, in order to prepare a future experiment for which the specimen size was chosen with recommendations from EN ISO 14125

Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential

A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained