Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Design of boundary-scan testing in CMOS image sensors for industrial applications: internship repor

Tests on printed circuit boards and integrated circuits are widely used in industry,resulting in reduced design time and cost of a project. The functional and connectivity tests in this type of circuits soon began to be a concern for the manufacturers, leading to research for solutions that would allow a reliable, quick, cheap and universal solution. Initially, using test schemes were based on a set of needles that was connected to inputs and outputs of the integrated circuit board (bed-of-nails), to which signals were applied, in order to verify whether the circuit was according to the specifications and could be assembled in the production line. With the development of projects, circuit miniaturization, improvement of the production processes, improvement of the materials used, as well as the increase in the number of circuits, it was necessary to search for another solution. Thus Boundary-Scan Testing was developed which operates on the border of integrated circuits and allows testing the connectivity of the input and the output ports of a circuit. The Boundary-Scan Testing method was converted into a standard, in 1990, by the IEEE organization, being known as the IEEE 1149.1 Standard. Since then a large number of manufacturers have adopted this standard in their products. This master thesis has, as main objective: the design of Boundary-Scan Testing in an image sensor in CMOS technology, analyzing the standard requirements, the process used in the prototype production, developing the design and layout of Boundary-Scan and analyzing obtained results after production. Chapter 1 presents briefly the evolution of testing procedures used in industry, developments and applications of image sensors and the motivation for the use of architecture Boundary-Scan Testing. Chapter 2 explores the fundamentals of Boundary-Scan Testing and image sensors, starting with the Boundary-Scan architecture defined in the Standard, where functional blocks are analyzed. This understanding is necessary to implement the design on an image sensor. It also explains the architecture of image sensors currently used, focusing on sensors with a large number of inputs and outputs.Chapter 3 describes the design of the Boundary-Scan implemented and starts to analyse the design and functions of the prototype, the used software, the designs and simulations of the functional blocks of the Boundary-Scan implemented. Chapter 4 presents the layout process used based on the design developed on chapter 3, describing the software used for this purpose, the planning of the layout location (floorplan) and its dimensions, the layout of individual blocks, checks in terms of layout rules, the comparison with the final design and finally the simulation. Chapter 5 describes how the functional tests were performed to verify the design compliancy with the specifications of Standard IEEE 1149.1. These tests were focused on the application of signals to input and output ports of the produced prototype. Chapter 6 presents the conclusions that were taken throughout the execution of the work.

Thermodynamics of a Peyrard-Bishop One-Dimensional Lattice with On-site Hump Potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is solved numerically, and the main features of the solutions are briefly discussed.

Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

Mechanism of phase formation in Pb(ZrxTi1-x)O3 synthesized by a partial oxalate method

The phase formation mechanism, as well as the morphotropic phase boundary, of lead zirconate titanate (PZT) processed by a partial oxalate method was investigated by simultaneous thermal analysis (TG-DTA) and by qualitative and quantitative X-ray diffraction (XRD). The results show that the ZrxTi1-xO2 (ZT) phase reacts with PbO forming the PZT phase without intermediate phases. XRD analysis showed the coexistence of rhombohedral and tetragonal phases for 0.47 ≤ x ≤ 0.55 with the phase boundary composition for x = 0.51. For low calcination temperatures, preferential formation of the PZT rhombohedral phase was observed. A model for phase formation of PZT by the partial oxalate method is proposed based on the existence of two interfaces of reaction (PbO-PZT and PZT-ZT) and diffusion of cations.

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed. © SISSA 2006.

A 2-D delaunay refinement algorithm using an initial prerefinement from the boundary mesh

An improvement to the quality bidimensional Delaunay mesh generation algorithm, which combines the mesh refinement algorithms strategy of Ruppert and Shewchuk is proposed in this research. The developed technique uses diametral lenses criterion, introduced by L. P. Chew, with the purpose of eliminating the extremely obtuse triangles in the boundary mesh. This method splits the boundary segment and obtains an initial prerefinement, and thus reducing the number of necessary iterations to generate a high quality sequential triangulation. Moreover, it decreases the intensity of the communication and synchronization between subdomains in parallel mesh refinement. © 2008 IEEE.

Solution of two-body bound state problems with confining potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark (Υ(bb̄), ψ(cc̄)), are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results. © 2010 American Institute of Physics.

Modelos de redes unidimensionais aplicados ao estudo termodinâmico do DNA

Pós-graduação em Biofísica Molecular - IBILCE

Desenvolvimento de um algoritmo computacional MoM 3D aplicado em nanoplasmônica

Este trabalho apresenta o desenvolvimento de um algoritmo computacional para análise do espalhamento eletromagnético de nanoestruturas plasmônicas isoladas. O Método dos Momentos tridimensional (MoM-3D) foi utilizado para resolver numericamente a equação integral do campo elétrico, e o modelo de Lorentz-Drude foi usado para representar a permissividade complexa das nanoestruturas metálicas. Baseado nesta modelagem matemática, um algoritmo computacional escrito em linguagem C foi desenvolvido. Como exemplo de aplicação e validação do código, dois problemas clássicos de espalhamento eletromagnético de nanopartículas metálicas foram analisados: nanoesfera e nanobarra, onde foram calculadas a resposta espectral e a distribuição do campo próximo. Os resultados obtidos foram comparados com resultados calculados por outros modelos e observou-se uma boa concordância e convergência entre eles.