Wave Equation

In this study, the analytical solutions of the Dirac equation have been presented for the Hulthén and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, Delta(r) = C = constant, and pseudospin symmetry, Sigma(r) = C = constant, for any spin-orbit quantum number kappa. The energy eigenvalues and corresponding spinor wave functions are

A fluid-structure-interaction problem comprising a membrane interacting with an aerodynamic flow is of interest for research focused on the behavior of flexible aerospace structures. However, there are no systematic studies available in literature considering this type of problem. The present work examines the numerical solution method and the typical solutions for a 1D vibrating membrane, i.e. a vibrating string, subject to an Euler flow. To assess the vibrating string behavior we present a non-dimensionalization of the fluid-structure-interaction equations, showing us 3 similarity parameters characterizing the interaction system. Furthermore we present a specific space-time finite-element discretization technique for the structure part based on the discontinuous Galerkin method. To relate the discontinuous elements we introduce Riemann solutions on the inter-element boundaries. Accordingly we rewrite the vibrating string equation into a system of first order wave equations. In the...

A simple non-quasi-static small-signal equivalent circuit model is derived for the ideal MOSFET wave equation under the gradual channel approximation. This equivalent circuit represents each Y-parameter by its DC small-signal value shunted by a (trans) capacitor in series with a charging (trans) resistor. A large-signal model for the intrinsic MOSFET is derived by first implementing this RC topology in the

The dispersive properties of finite element semidiscretizations of the two-dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five-point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direction.

Autor: Eric Brandão. Revisão Técnica: William D'Andrea Fonseca. "Este livro aborda os princípios para a modelagem e caracterização da propagação do som em ambientes, bem como os fundamentos para o desenvolvimento de projetos de recintos com uma qualidade acústica adequada. A obra apresenta conceitos básicos sobre o som e processamento de sinais, propagação sonora em ambientes (em baixas, médias e altas frequências), cálculo e medição de parâmetros objetivos, como tempo de reverberação, claridade, espacialidade e inteligibilidade da fala etc. Além disso, aborda a modelagem, a caracterização e o projeto de dispositivos utilizados no tratamento acústico de ambientes (absorvedores e difusores). O capítulo final trata de diretrizes para o projeto de vários tipos de ambientes, como estúdios, salas de concerto, teatros, salas de aula, cinemas etc. A obra é destinada a professores, alunos e profissionais que atuam no projeto acústico de ambientes, como os engenheiros acústicos, engenheiros civis, arquitetos, físicos e técnicos de áudio; também serve de base para pessoas que almejam um bom entendimento sobre o tema da acústica de salas. O livro conta com sólido desenvolvimento matemático e diversos exemplos e discussões, contribuindo para solidificar os conceitos apresentados." Preview/amostra em: https://www.blucher.com.br/livro/detalhes/acustica-de-salas-1163

Prospecting for oil and gas resources poses the problem of determining the geological structure of the earth's crust from indirect measurements. Seismic migration is an acoustic image reconstruction technique based on the inversion of the scalar wave equation. Extensive computation is necessary before reliable information can be extracted from large sets of recorded data. In this paper a collection of "industrial" migration techniques, each giving rise to a data parallel algorithm, is outlined. Computer simulations on synthetic seismic data illustrate the problem and the approach

It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ``shape-invariant'' potentials. This generalization allows one to calculate the energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.