On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Generation of decelerating Airy pulses

The explicit expression for spatial-temporal Airy pulse is derived from the Maxwell's equations in paraxial approximation. The trajectory of the pulse in the time-space coordinates is analysed. The existence of a bifurcation point that separates regions with qualitatively different features of the pulse propagation is demonstrated. At this point the velocity of the pulse becomes infinite and the orientation of it changes to the opposite. © 2011 IEEE.

Essays on investment, growth and income distribution

In this dissertation, I examine both theoretically and empirically the relationship between stock prices and income distribution using an endogenous growth model with social status impatience.^ The theoretical part looks into how status impatience and current economic status jointly determine time preference, savings, future economic status, stock prices, growth and wealth distribution in the steady state. This work builds on Burgstaller and Karayalcin (1996).^ More specifically, I look at (i) the effects of the distribution of status impatience levels on the distribution of steady state assets, incomes and consumption and (ii) the effects of changes in relative levels of status impatience on stock prices. Therefore, from (i) and (ii), I derive the correlation between stock prices, incomes and asset distribution. Also, the analysis of the stack market is undertaken in the presence of adjustment costs to investments.^ The empirical chapter looks at (i) the correlation between income inequality and long run economic growth on the one hand and (ii) the correlation between stock market prices and income inequality on the other. The role of stock prices and social status is examined to better understand the forces that enable a country to grow overtime and to determine why output per capita varies across countries. The data are from Summers and Heston (1988), Barro and Wolf (1989), Alesina and Rodrik (1994), Global financial Database (1997) and the World Bank. Data for social status are collected through a primary sample survey on the internet. Twenty-five developed and developing countries are included in the sample.^ The model developed in this study was specified as a system of simultaneous equations, in which per capita growth rate and income inequality were endogenous variables. Additionally, stock price index and social status measures were also incorporated. The results indicate that income inequality is inversely related to economic growth. In addition, increase in income inequality arising from higher stock prices constrains growth. Moreover, where social status is determined by income levels, it influences long run growth. Therefore, these results support findings of Persson and Tabellini (1994) and Alesina and Rodrik (1994). ^

Eulerian-Lagrangian two phase debris flow model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier-Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Eulerian-Lagrangian Two Phase Debris Flow Model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier–Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Um estudo sobre o ensino de evaporação no contexto ciência, tecnologia e sociedade

The scope of this Dissertation is propose the teaching of the evaporation based on the approach Science, Technology and Society (STS) because we believe that this type of approach is able to provide students with a more critical and conscious learning about science. Moreover, with this search, it´s possible to show for students the importance of role to play for them as citizens in decision making aimed to benefit all who are part of the community to which they belong. From this perspective, broached the theme evaporation in a region characterized by constant lack of water for consumption, the municipality of Santa Cruz/RN because, despite the creation of dams to regulate the flow of rivers and increase the availability of water during periods of scarcity, we know that these reservoirs have a large free liquid surface allowing high water loss by evaporation. Thus, evaporation affects the performance of reservoirs for water supply and irrigation, being a phenomenon of particular interest to study. To this end, a questionnaire in order to identify students' preconceptions on the subject was applied. Was then prepared and conducted a workshop geared toward students majoring in Physics Campus Santa Cruz, Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN). The completion of the workshop served as a space for discussion of the topic within the context of the municipality of Santa Cruz/RN. As a product, we suggest to physics teachers a guide with recommendations to be taken into account when they teach this subject

Inércia e Natureza da Ciência no Ensino de Física: uma sequência didática centrada no desenvolvimento histórico do conceito de inércia

During the last decades the area of science education has discussed issues related to the inclusion of the History and Philosophy of Science (HFS) in the practice of science teaching. Among the arguments put forward in favour of this approach, it is pointed out the possible enhancement of scientific content learning and the understanding of the nature of Science (NoS). In spite of such considerations, we still have a very small number of research papers reporting results of practical interventions that utilize the historical approach, moreover, there is a lack of teaching materials in this perspective. Our work has sought to contribute to this area with regard to two aspects: on the one hand, with the production of didactic material, by drawing up texts on the history of inertia for graduate students. On the other hand, we investigate whether the arguments mentioned above in relation to the didactic use of HFS sustain themselves, in a particular context. We developed and applied a didactic sequence, using the texts that we built, to teach the concept of inertia and discuss selected contents of NoS. The didactic sequence was applied in two graduate classes, one from a course of Geophysics (BSc.) and another from the Physics (teaching formation), both from the Federal University of Rio Grande do Norte (UFRN). An initial survey exposed that students, even having approached the concept of inertia in basic education, presented conceptions of common sense regarding the relationship between force and motion. The questionnaire also allowed us to identify the existence of elements of concepts considered inadequate as regards to NoS. At the end of our research, our data indicated a greater number of positive hits on the issues concerning the concept of inertia. Regarding the aspects of NoS, we were able to identify, in a few cases, a move towards a more appropriate understanding, however, certain distortions persisted, highlighting the limitations of the approach used

Física do meio ambiente como disciplina nas licenciaturas em física: proposta de uma unidade didática para ensinar efeito estufa e aquecimento global

In this dissertation we propose a Teaching Unit of Physics to teach content through environmental discussions of the greenhouse effect and global warming. This teaching unit is based on a problem-methodological intervention from the application of the method of the Arch of Charles Maguerez. The methodological foundations of the thesis are embedded in action research and this is structured in five chapters: the first chapter deals with the Physical Environment (FMA) as a subject in Degree Courses in Physics in Brazil, bringing the concern of how this discipline has been taught. We started the first chapter explaining the reasons behind the inclusion of the discipline of Physical Environment in a Physics Degree Courses. Then we did a search on the websites of Institutions of Higher Education, to know of the existence or not of this discipline on curricular. We then analyzed the menus to see what bibliographies are being adopted and what content of Physics are being worked, and how it has been done. The courses surveyed were those of Federal and Federal Institutes Universities. Thus ended the first chapter. Given the inseparability between studies in Physics Teaching and studies on competencies, skills and significant learning, wrote the second chapter. In this chapter we discuss the challenge of converting information into knowledge. Initially on initial teacher training, because even if this is not our focus, the study is a discipline on the upper reaches, therefore, offered to future teachers. Then we talked about the culture of knowledge, where we emphasize the use of a teaching approach that promotes meanings taught by content and make sense to the student. We finished the third chapter, making some considerations on skills and abilities, in order to identify what skills and competencies were developed and worked during and after the implementation of Curriculum Unit. The third chapter is the result of a literature review and study of the radioactive EarthSun interaction. The subjects researched approach from the generation of energy in the sun to topics stain solar coronal mass ejections, solar wind, black body radiation, Wien displacement law, Stefan-Boltzmann Law, greenhouse effect and global warming. This chapter deals with material support for the teacher of the aforementioned discipline. The fourth chapter talks about the arc method of Charles Maguerez; Here we explain the structure of each of the five steps of the Arc and how to use them in teaching. We also show another version of this method adapted by Bordenave. In the fifth and final chapter brought a description of how the method of Arc was used in physics classes of Environment, with students majoring in Physics IFRN Campus Santa Cruz. Here, in this chapter, a transcript of classes to show how was the application of a problem-based methodology in the teaching of content proposed for Physics Teaching Unit from the environmental discussion about the greenhouse effect and global warming phenomena

Uma análise da formação de professores de física do IFRN a partir da epistemologia de Ludwik Fleck

This study arises in the context of physics teacher training and aims, from the speech of the teacher trainer, identify possible pedagogical models and characterize thinking styles present in the course of licentiate in physics of IFRN using the epistemology of Ludwik Fleck. We classify our research as qualitative with an empirical nature, and for the analysis we chose the discursive textual analysis - DTA (MORAES, 2003). The locus of our research will be the licentiate in physics at the Federal Institute of Education, Science and Technology of Rio Grande do Norte - IFRN, Natal-Central Campus and the research subjects, a group of teacher trainers of this course. We interviewed ten teachers, being six from the group dedicated to physics and four from the group dedicated to didactics and pedagogy. From this design, we performed data acquisition consisted of: 1) semi-structured interview, 2) document analysis. On the data analysis, with the support of pedagogical trends that were observed in our study based on the perception of the similarities and differences between the ideas presented by teachers about: education and teaching; ideal teaching practice, teacher's role, learning conceptions, and according to the student and on the ideological thinking of these former teachers on the professional profile of graduates, we noted subsidies to identify evidences of the presence of three distinct thinking styles that interrelate with each other in a considerably intense way. The relevance of the study is presented in the understanding of thinking styles that participate in the dynamics of the course of teacher training in physics, and by consequence, elucidation of a problem pointed out a priori as motivating the research: the difficulty of communicative interaction on educational practices among teacher trainers. We bring Fleck's epistemology as a motivating possibility of dialogue and negotiation, setting thus an instrument of real change, towards the significance of teacher training in physics.

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

Identidade pessoal em Hume e em Kant

The issue of this dissertation is the problem of personal identity. More specifically, the objective of this work is to investigate and compare how Hume and Kant construct, within their own philosophical systems, their theories of personal identity (of the self), so that these theories can set the grounds for the construction of theoretical knowledge. Hume’s theory of personal identity is closely connected to his empirical model of investigation, according to which no metaphysical conclusion can be accepted. This implies a very specific limitation to the humean description of personal identity. Because he can’t find a safe empirical reference for the self, Hume is obliged to describe it as a mere fiction, which the imagination creates to try to give unity to the set of perceptions that composes the mind. Kant, on the other hand, constructs his theory of the self with the aim of explaining the possibility of the a priori knowledge in Mathematics and in Physics. Kant tries to find which attributes must necessarily belong to the self so that this self can be, at the same time, the a priori transcendental condition of a subjectivity in general and the equally a priori transcendental condition for the construction of objective knowledge. Moreover, Kant shows the impossibility of objectively knowing, as intuition, the self, and limits himself to the description of the self as a mere subjective consciousness of the synthetic capacities of the understanding. Several disparities, thus, can be perceived between the theories of personal identity of these two authors. Based on these differences, the present work also examines the possibility of making an interpretation of the humean theory of the self by using elements of the kantian philosophy. The purpose of this kind of interpretation is to propose a solution to the difficulties faced by Hume in the description of his theory of personal identity.

Sequência didática com temas motivadores no ensino de física

This study is based on the design and development of a Didactic sequence in Physics for the first year of high school in a public school, involving structured activities on Astronomy topics, Astronautics and Aeronautics. In addition, it produced a didactic-pedagogic Tutorial for teachers to develop teaching-learning processes in Physics through activities with handmade rockets. These activities have been based on teaching moments of questioning, systematization and contextualization. In this context the understanding and the deepening of concepts and scientific and physical phenomena are related to everyday knowledge, in accordance with the historical-cultural theory, with the Three Pedagogic Moments, dialogicity and Information and Communication Technologies as instruments of triggering actions and motivation, like movies and applications in teaching Astronomy, Physics and Mathematics. The research activities were conduced by adopting a qualitative approach and included reports, questionnaires, semi-structured interviews and other notes. The development of the Didactic Sequence enabled a differentiated teaching and learning process, including aspects such as conceptualization, contextualization, flexibility, interdisciplinary and theoreticalexperimental relationship.

Growth, Characterization, and Properties of Hybrid Graphene-Carbon Nanotube Films and Related Carbon Nanostructures

Graphene, first isolated in 2004 and the subject of the 2010 Nobel Prize in physics, has generated a tremendous amount of research interest in recent years due to its incredible mechanical and electrical properties. However, difficulties in large-scale production and low as-prepared surface area have hindered commercial applications. In this dissertation, a new material is described incorporating the superior electrical properties of graphene edge planes into the high surface area framework of carbon nanotube forests using a scalable and reproducible technology.

The objectives of this research were to investigate the growth parameters and mechanisms of a graphene-carbon nanotube hybrid nanomaterial termed “graphenated carbon nanotubes” (g-CNTs), examine the applicability of g-CNT materials for applications in electrochemical capacitors (supercapacitors) and cold-cathode field emission sources, and determine materials characteristics responsible for the superior performance of g-CNTs in these applications. The growth kinetics of multi-walled carbon nanotubes (MWNTs), grown by plasma-enhanced chemical vapor deposition (PECVD), was studied in order to understand the fundamental mechanisms governing the PECVD reaction process. Activation energies and diffusivities were determined for key reaction steps and a growth model was developed in response to these findings. Differences in the reaction kinetics between CNTs grown on single-crystal silicon and polysilicon were studied to aid in the incorporation of CNTs into microelectromechanical systems (MEMS) devices. To understand processing-property relationships for g-CNT materials, a Design of Experiments (DOE) analysis was performed for the purpose of determining the importance of various input parameters on the growth of g-CNTs, finding that varying temperature alone allows the resultant material to transition from CNTs to g-CNTs and finally carbon nanosheets (CNSs): vertically oriented sheets of few-layered graphene. In addition, a phenomenological model was developed for g-CNTs. By studying variations of graphene-CNT hybrid nanomaterials by Raman spectroscopy, a linear trend was discovered between their mean crystallite size and electrochemical capacitance. Finally, a new method for the calculation of nanomaterial surface area, more accurate than the standard BET technique, was created based on atomic layer deposition (ALD) of titanium oxide (TiO2).

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.